MACROECONOMICS
© J.D. Han*
King’s University College
At the University of Western Ontario
Acknowledgement
"Of course, no reasonable man ought to insist that the facts are exactly as I have
described them. But that either this or something like it is a true account ...... This, I
think, is both a reasonable contention and a belief worth risking, for risk is a noble
one......" (Plato, Phaedo, II 4 d.)
I wish to acknowledge that this lecture note owes greatly to the macroeconomics I have learned
from Professor Jack Carr at the University of Toronto.
When I was leaving for my first teaching post at Carleton University in Ottawa, Professor Carr was
so kind as to give his handwritten lecture notes. Professor Carr took macroeconomics from
Professor Milton Friedman at the University of Chicago, and his notes contained many class
examples taken by Professor Friedman.
I simply typed his manuscript and started teaching based on the manuscript. Just like I had done so
in Professor Carr’s macroeconomics class, the students in my class positively responded to the
simplicity of exposition, the depth of theories, and the relevance of examples. It encouraged me to
expand the manuscript into a book length.
There are two reasons why I have decided to pursue a publication of my manuscript into a textbook
format: First, most textbooks are too voluminous and too verbose with irrelevant examples and
explanations. Second, they are expensive. The two issues are probably intertwined, and the
second reason, which is an economic one, seems to dictate the first: There is a certain threshold
price for a textbook in today’s marketing system, and a fair volume may be necessary to justify the
price. A major problem, with which most instructors are faced, is that due to external constraint of
time and voluntary choice to skip verbosity they end up using only a part of the textbooks.
Students get disgruntled, feeling that a partial use of the textbook does not justify the price they
pay. This book has come from our conviction that we can slim-down macroeconomics textbooks
for both a better understanding of essential models, and a better satisfaction of our customer
students.
I have been extremely fortunate to have talented and hard-working teaching and research assistants
over the last 10 years. Robert Faissal, Lui Leo, Lisa Mo, Leo Wang, Karen Xuan, Herbert Zhang,
Bochao Fan, and Kevin Chen have all worked on this manuscript at one point of time. They all
have taken my macroeconomics course based on this book, and many of them have become a
colleague economist. The copyright of this book is protected. No part of this material shall be
reproduced without the author’s consent.
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Chapter I. Introduction
Chapter I. Introduction
1. Key Issues in Macroeconomics: What are our interests and goals in Macroeconomics?
Economics is devoted to the betterment of human material welfare. The material welfare is
measured best, at the practical level, by the per capita national income, which is equal to the GDP
divided by the size of population.
In terms of per capita national income, the optimal situations can be described as follows: (1) The
per capita national income should be high at the maximum potential level at any point in time; (2)
the per capita national income should grow rapidly with minimum inflation, and (3) the national
income should be stable over time.
We may also want a lowest possible rate of inflation and a stable price level as well.
(1) Maximum Potential Income: Full Employment - Short-term Goal
It is ideal if the actual national income approaches its maximum potential. How would we know
whether or not the maximum potential is being realized now? One obvious indicator is the rate of
unemployment. There is a one-to-one relationship between the unemployment rate and the level
of national income: The higher the rate of unemployment, the lower the level of the national
income.
The maximum potential national income can be called the ‘Full Employment National Income’ (Yf
for its notation). The full employment national income or Yf does not correspond to the zero rate
of unemployment, but to a certain positive figure of unemployment rates. That positive figure of
unemployment rate is only ‘Natural’ and the best that we can achieve in terms of employment.
Thus it is also called ‘Natural Rate of Unemployment’. In other words, the Full Employment
means a positive figure of the Natural Rate of Unemployment or NRU in a short form (its notation
is UN).
How do we know when the actual national income is below the maximum potential level? One
sign is the existence of unemployment of production factors above and beyond the ‘natural level’.
When capital and labour available are `under-employed', the aggregate income created from the
employment of the factor does fall short of the maximum potential income, that is, the Full
Employment (National) Income or the Natural Rate (of Unemployment National) Income.
Under-employment indicates the situation where the actual rate of unemployment (U) exceeds the
natural rate of unemployment (UN): U>UN. The difference between the two unemployment rates
is called `Cyclical Unemployment', which points to under-employment. The natural rate of
unemployment is some positive rate of unemployment perfectly compatible with full employment,
and consists of frictional and structural employment.
Questions arise as to a) the cause of, b) the duration of and c) the remedy for the
under-employment situation where the actual national income is smaller than the full employment
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Chapter I. Introduction
income: What prevents an economy from enjoying the maximum potential income? How long
would the undesirable situation of the under-employment last? In other words, is the
under-employment transient meaning `will be gone', or of equilibrium, meaning `being stuck'?
What can be done about the under-employment?
(2) Strong Economic Growth with Minimum Inflation - Long-term Ideal
The performance of per capita national income over time determines the future path of an economy
in the long-run. In Canada, the national income evaluated at the current market prices or the
market prices of each year grew at an average 10% annum during the ten year period of
1976-1986, 7% of which could be attributed to the simple increases in the prices and the rest to the
actual growth of the amount of goods and services. In other words, the rate of the growth of
national income in real terms is 3% per annum. This is a strong growth in the light of the size of
the Canadian economy and its advanced stage of economic growth.
(3) Stabilization of National Income - Medium-term Ideal
We would like to have a stable national income over time, having the least fluctuations and
deviations from the Long-run Growth Trend. These ups and downs of the national income over
time are called, in their entirety, ‘business cycles’. Minimizing business cycles, if possible, is
welfare-increasing.
When the government is trying to stabilize the national income, it may use fiscal and monetary
policies. The policies are called ‘income stabilization policies’ or ‘activist policies’. Whether the
government can eliminate/reduce the amplitude and the duration of business cycles or not is an
open question. Keynesians do believe that it is possible, and Classical economists think otherwise.
(4) Stable Price Level: A Low Inflation
Inflation is not just a nuisance. It leads to misallocation of resources, diverting valuable resources
from their best uses. This may not decrease the accounting value of national income. However, it
certainly decreases economic welfares.
The costs of inflation are represented with Menu Cost, and Shoe-Leather Cost, for instance.
However, innocuous they may sound, they may seriously harm efficient allocation of resources.
Surprice inflation has an additional cost for the society: it helps employers at the expense of
employees, and debtors at the expense of creditors.
(5) Trade Off Between Two Goals: Income versus Inflation.
Some economists argue that the above the goal of high income cannot be obtained by a low
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Chapter I. Introduction
inflation: The two goals cannot be achieved at the same time, and there is an inevitable trade-off
between the two.
The level of national income is inversely related to unemployment rates. Therefore, the above
argument means that a low unemployment rate (meaning a high level of national income) can only
be achieved with a relatively high rate of inflation. As we will see later, this is the idea behind
Phillips Curve.
Inflation
Unemployment
Other economists do not agree with this. They argue that depending on the inflation expectations, a
low rate of inflation and a low rate of unemployment can be achieved at the same time. This will
be reviewed in terms of “Expectations Augmented Phillips Curve”.
2. Divided House of Macroeconomics Thoughts
In contrast to microeconomics (Price Theory) where there is a general consensus, the
macroeconomics has many irreconcilable divisions within its house: There are multiple schools of
macroeconomic thoughts, which have quite different, and competing frames of references.
Sometimes they are completely opposite. They tend to disagree on what the most important issues
are, let alone what the solutions should be. We are going to review the Keynesian School, the
Classical School, the Neo-Classical Synthesis, the New Classical School or the Rational
Expectations Theory Model, and the New Keynesian School.
For instance, as to the key issues raised above, each school of macroeconomics thought has
different views. Suppose that an economy is not achieving its maximum potential national
income, or that the actual rate of unemployment is higher than the natural rate of unemployment.
(1) The Keynesian School of Macroeconomics Thoughts
The Keynesian school of macroeconomics was initiated by John Maynard Keynes through his
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Chapter I. Introduction
publication of The General Theory of Employment, Interest, and Money in 1936.According to the
Keynesian school, it is the lack of the economy’s aggregate demand that prevents the economy
from achieving the maximum potential national income. The ‘cyclical’ component of
unemployment rates will not easily go away: Some equilibrating or ‘anchoring’ forces hold the
economy down at a level of under-employment. The remedy should be an injection of demand.
Given the bleak prospect of business, which presumably has caused the current recession, it is
unlikely that any private economic agents, such as households or firms, will bring an additional
demand for the economy: They are all concerned with, and thus constrained by the financial
bottom line.
It should be the government that has to bring more demand to the economy. In fact, according to
the Keynesian view, the government is able to do so, as it is not constrained by the budget
constraint: The government is the only economic agent that can spend more than earn for a
prolonged period of times due to its prerogative or sovereign privileges of printing paper monies
and issuing bonds.
How about an increase in the aggregate supply? It would not resolve the recession: The recession
was caused by ‘too little demand amid too much supply’. An increase in supply will be just added
to inventories, which will put more downward pressures on production processes at the corporate
level.
Can we reduce the unemployment with wage cuts? In fact, all the economists in the 1930swere
believed that wage cuts were classical. They believed that workers could not get a job or were
unemployed when they demanded too high wages. Thus, they thought that the only solution to the
Great Depression was a wage cut: If wages are cut, and thus the cost of hiring workers is reduced,
in the very short run there occur incentives for employers to hire more workers.
However, Keynes disagreed. The above solution is unsustainable. If wage rates are cut, some may
get new jobs. More outputs may be produced. However, there will be a reduction in the wages of
the previously employed labor forces. The total aggregate wage bills may decrease. If so, there
will be less consumption, and thus the newly produced outputs will not be sold. The production
should scale down, and the national income falls.
Keynesian Arithmetics: Why wage cuts worsen a recession?
A major component of the aggregate demand is consumption: AE = C (+ I + G + X-M).
The consumption of the workers’ households depend on the component of their income,
which is the total wage bills: C = f(Y), and Y = W (+ R + Int. + Profits).The total wage bill
for the economy = nominal wage rates (Wage rate) x number of employed workers (#):
When Wage rates go down and # goes up, the product of the two may go up or down,
depending on the relative magnitude of a changes in W and a change in #. If  Wage rate (a
decrease in the wage rate) exceeds  #, then the total wage bill rises. Thus the consumption
goes up and so does the aggregate demand.If  Wage rate (an increase in the wage rate)
falls short of  #, then the total wage bill falls. Thus the consumption goes down and so
does the aggregate demand.
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Chapter I. Introduction
(2) The Classical School of Macroeconomic Thoughts
On the other hand, according to the economists of the Classical school, as long as there is a
well-functioning labor market system without undesirable impediments, a prolonged recession is
impossible while certain degrees of short-run fluctuations might be inevitable.
Under-employment of a production factor (such as labor) situation comes from the temporary
failure of the alignment of supply and demand of the factor (labor) market. Most commonly,
unemployment occurs when some workers are demanding too high a wage rate and thus are not
hired by any willing employers. In the absence of any stubborn stupidity of individuals (such as
money illusion) and any structural rigidity of the economic system (such as unions), in the
long-run as the workers `come to their senses' out of hardship and lower their wage rate to a
reasonable level, the unemployment will vanish. Therefore, as long as the functioning of market
forces is not hindered, eventually (in the long-run) the national income gravitates to the level
corresponding to the full level of employment. The full employment (national) income is the very
equilibrium income at least in the long-run.
Money Illusion
How many workers are going to work for how many hours (a week) depends on the
workers’ motivation. The motivation in turn depends on the reward for work that workers
perceive to receive. Note that it does not have to be the actual reward, but the ‘perception
of rewards’. If workers somehow do not feel rewarded enough for their work efforts, they
would not supply labor forces and would rather go for leisure or unemployment.
The rewards for a worker should be measured by ‘how much commodities or outputs can
he purchase with the money wage’: In other words, the labor supply should be an
increasing function of real wages.
However, some workers may have some hang-up on a particular value of nominal values
for their wages. While they really should pay attention to real wages or real values of their
wages, they are erroneously sticking to a certain nominal or money value of wages. This
is called ‘money illusion’. The word ‘money’ is the opposite of ‘real (value)’.
In the Keynesian school of macroeconomics, money illusion is an important element in the
derivation of its aggregate supply curve.
In the classical school of macroeconomics, ultimately in the long-run, money illusion does
not exist.
The short-run fluctuations or business cycles are inevitable. In fact, recessions give a good lesson
to undisciplined workers and correct them. They are the periods of consolidation and adjustment
for the better. What we can do best to the economy in the short-run is to inform the worker correct
and to remove any structural rigidity because both hinder the smooth functioning of the market
forces.
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Chapter I. Introduction
Is there any way of increasing the full employment income in the classical model? Yes, in the
long-run, there is. The level of full employment income is constrained by the amount of production
factors. Even the national income might be at the full employment level, but the actual value is
small because the level of the full employment income is low. For instance, suppose that there is a
large population yet a small amount of capital in an economy. The scarcity of capital imposes a
bottleneck in the production: The low capital-labor ratio means a scarcely equipped worker having
a low productivity of labor. The national income is stuck low at the ‘low’ full employment of the
existing capital and labor. It is not too difficult to imagine an economy where workers are fully
employed, tinkering all day long with poor equipment, for a pittance. The situation is a kind of
‘low level equilibrium.’
According to the classical school of macroeconomics, the level of the full employment income can
be raised with a breakthrough in the availability of production factors. If the amount of capital
increases or there occurs an innovation of capital-saving technology, the workers’ productivity
will rise to bring larger wages. The level of the full employment national income will rise.
3) Differences between Classical and Keynesian Schools
This disagreement between the two schools is highly politicized in the realm of policy issues.
They do have fundamentally different views on the role of government in the economy: Except for
some monetarists (to whom the author belong), it is generally accepted that a government's
expansionary monetary or fiscal policy will increase aggregate demand. However, the rightward
shift of the aggregate demand curve may bring different impacts on the price level and the national
income depending on the shape and configuration of the aggregate supply curve.
In other words, Keynesian and Classical schools do operate on different assumptions of the
aggregate supply conditions. In the Keynesian School, there is a positive economic role for
government: Expansionary fiscal and monetary policies which shift the aggregate demand to the
right will bring about and increase in real national income without any increase in the price level.
In the Classical school in its alliance with fiscal and monetary conservatives, it is argued that the
lasting impact of the increased AD due to an expansionary monetary or fiscal policy is only
inflationary.
This difference in political implications comes from the different assumptions of the supply
conditions. Keynesians assume that the Aggregate Supply curve is horizontal or relatively flat.
What does the horizontal supply curve mean? It means that the (aggregate) supply (of all the
goods and services) increases greatly in response to a very small stimulus of an increase in the
price level. In other words, the aggregate supply is infinitely elastic with respect to the change in
the price level.
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Chapter I. Introduction
Recall that in microeconomics the price elasticity of supply measures the increase of supply in
response to a unit price rise.
For a given increase in price, the responsive increase in supply is relatively small in Case I: the
supply is inelastic with respect to price. For the same increase in price, the resultant increase in
supply is relatively large in Case II: the supply is elastic with respect to price. The first case is
close to the assumption of the Classical school and, the latter to the Keynesian aggregate supply
curve.
Why is the aggregate supply assumed to be elastic in the case of the Keynesian school? The
Keynesian economics came out during the Great Depression when there was a lot of unemployed
workers and idle capacities. In the face of a rising price of output, entrepreneurs could easily
increase production and supply of output without substantially raising the costs of hiring
production factors. This means that the supply could be so easily expanded, and was very
responsive and elastic with respect to a rise in output prices: the supply curve was in fact almost
horizontal.
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Chapter I. Introduction
With this configuration of the supply and demand curves, only the shift of the aggregate Demand
curve will bring about an increase in the equilibrium national income. Put differently, when a
government is engaged in expansionary monetary policy (by increasing money supply [MS])
or/and fiscal policy (by increasing government expenditures [G] or cutting taxes [T]), the
resultant increase in the aggregate demand shifts the aggregate demand curve. It will bring about
only benevolent impacts on the economy: the national income rises while the price level remains
unchanged. The rigidity of the general price level is the cornerstone of the Keynesian theory.
The Classical school consists of many branches, but they all basically assume a vertical aggregate
supply curve for the economy. For instance, the Monetarists belong to a branch of classical school
largely attributed to Milton Friedman. They argue that there are two kinds of the aggregate supply
curve. The long-run Aggregate Supply curve is vertical while the short-run Aggregate Supply
curve may be positively sloped. In the long-run, as all production factors are more or less fully
utilized in the economy in its own way. An increase in the price of outputs does not lead to any
increase in production. The aggregate supply curve is vertical at the full employment level. The
vertical AS curve implies that it is impossible to increase the equilibrium national income only by
increasing the AD.
With the given configuration of the aggregate supply and demand curves, expansionary monetary
policy (increasing money supply [MS]) or/and fiscal policy (increasing government expenditures
[G] or cutting taxes [T]) increases aggregate demand [AD] and shifts the AD curve. It will
bring about only a rise in the price level.
P
P0*
P
E0 E1
Y*
Y*
2
1
AS
AD'
AD
Y
AS
P1*
E1
P0*
E0
Y* = Yf
AD'
AD
Y
In this situation, only a (rightward) shift of the aggregate supply curve can bring about an increase
in the equilibrium national income. In this case, the equilibrium national income is also the full
employment income. It may be timely to be reminded of what the major production factors are:
capital, labor, and technology. Therefore, only an increase in the stock of capital, an increase in
labour force, and technological innovations can lead to an increase in national income. If the
government is going to increase the national income, it has to focus on the breakthrough in the
supply side. Its economics focuses on the Supply Side. It has to be the “Supply Side of
Economics”.
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Chapter I. Introduction
4) Neo-Classical Synthesis
The Neo-Classical School is a synthesis of the Keynesian and Classical ideas. It adopts the
Keynesian aggregate supply (horizontal) curve for the short-run and the Classical aggregate
supply (vertical) curve for the long-run. Thus the Neo-classical AS curve has upward sloping and
vertical segments. Therefore, an increase in the AD leads to an increase in the national income in
the first range, a simultaneous increase in the national income and the price level in the second
range, and an increase in the price level in the last range.
5) New Classical School of Macroeconomics: “Rational Expectations Theory”
As we might have noted, there is no obvious presentation of the short-run fluctuations of income in
the classical model. The New Classical Macroeconomics or Rational Expectations Theory is the
most recent offspring of the Classical school. It has come up with exposition of short-term
fluctuations in terms of expectations failures. In short, it states that only unanticipated changes in
the Aggregate Demand (AD) leads to short-run fluctuations of the national income.
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Chapter I. Introduction
The theory adds Expectations Augmented Aggregate Supply Curve (EAS hereafter) to the
classical model. This EAS curve moves around as the public's expectations as to the price level
which in turn depends on the aggregate demand:
When shifts of the AD are anticipated/expected (to bring about changes in the price level), the EAS
shifts up simultaneously to nullify any impact on the equilibrium national income. The path of
motion is given along the vertical AS curve in the first panel below. For instance, as long as it is
fully expected, any government policy which results in an increase in the AD will not have any
impacts on real variables such as real wages, level of employment, and real national income: When
a rise in the price level is expected, the workers and entrepreneurs will revise their expectations
about the price level and rewrite the wage contract to reflect the increase in the money wages.
Proportional increases in the price level and the money wages lead to the constancy of real wages
and all other real economic variables.
This is called the “Policy Invariance Theorem” or “Policy Ineffectiveness Theorem”: Any
anticipated (monetary) policy does not have any impacts on real variables such as real national
income. This is the major criticism of so-called “Activist Monetary Policy”, which advocates the
use of monetary policy to stabilize the national income. The Policy Invariance Theorem suggests
that as long as they are fully announced, monetary policies do not achieve the intended goal.
Only unanticipated shifts of the AD curve will not be accompanied with shifts of the AS curve.
Wrong expectations can happen in the short-run: over-expected, under-expected or unanticipated
events may occur. In this case, the AD shifts without the offsetting shifts of the short-run AS curve.
This leads to temporary deviations of national income from the full employment level. However,
in the long-run when expectations catch up with the reality, -unless another unexpected events
involving the AD happen- in any case the EAS will eventually shift by the same amount and in the
same direction of the AD curve to nullify the short-term deviation. The path of motion is given as
1 to 2, and to 3 in the second panel below.
Anticipated Changes in AD:
No changes in Y
*
Unanticipated Changes in AD:
Changes in Y* in the Short-run;
In the Long-run Y* = Yf
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Chapter I. Introduction
6) New Keynesian School of Macroeconomics
The New Keynesian school tries to explain fluctuations of national income in terms of structural
rigidifies such as long-term non-indexed labor contracts. Most wage contracts cover a multiple
number of periods and do not have the clause of escalating the money wages along with inflation.
In this model the wage contracts are signed on the basis of ex-ante expectations as to the future
price level. Once the contracts are signed, nothing can be done about the wage in response to
changes in the AD situations and the price level. Unexpected changes in the price level result in
changes in real wages, employment, and real national income.
7) A Pendulum of the History of Macroeconomic Thoughts
The above investigation suggests that the Keynesian school focuses on the demand; and that the
Classical school focuses on the supply.
Let’s put these macroeconomic theories in historical perspectives: The historical progression of
economics theories mirrors changes in an actual economy, with a time-lag. The most pressing
economic concern of the time called for a new frame of reference which suggests a new solution
for the problem. Each theory, to a large extent, is the child of times. And as the times change, the
theories change.
In the pre-industrial age, the greatest economic concern was the bottleneck in production, or the
shortage of the supply of goods and services. It was best epitomized in the famous `Malthusian
Apocalypse': the growth of production (of food) would never catch up with the increasing demand
(for food) propelled by a growing population. Therefore, excess demand or general famine
seemed inevitable. Naturally, the focus of economics was on how to make a breakthrough in
production or supply. For instance, Adam Smith extolled the benefit of the division of labour,
specialization, and scales of economy in production.
The bottleneck on the supply side was removed by the Industrial Revolution which accelerated
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Chapter I. Introduction
innovation and technology in production. The demand also grew: the territorial expansion of
imperial powers brought markets that created an increased demand for production. In the early
twentieth century, however, market expansion reached its limit. There occurred signs of general
glut, or of supply exceeding demand.
On October 24, 1929 the precipitous crash of the New York Stock Market triggered the Great
Depression. Unsold goods piled up. Physical capital, equipment and human capital was the
problem. The second part of the problem is called `unemployment'. Unemployment was the key
social issue. It was regarded by the classical school as a necessary adjustment period of `cooling
down' after a century of dashing expansion and growth on the supply side. However, Keynes
regarded the depression as a rising from the lack of purchasing power, or effective demand. As
there were idle capacities, the supply curve was not a problem: the production could increase very
easily with just a small stimulus. The larger the demand, the higher the equilibrium national
income level becomes. For instance, in order to increase in national income, consumption and
spending should be encouraged. Thrift, which leads to a smaller consumption and thus a smaller
demand, should be discouraged as a vice. This contrasts with the fact that thrift is a virtue and a
way of achieving prosperity at the level of individuals. What is true of individuals is not
necessarily true of the society as a whole. Keynes pointed out the fallacy of composition in
savings or thrift, and called it the `Paradox of Thrift.'
In addition, in order to ensure the stability of income, Keynes came up with the so called
`Aggregate Demand Management Policy'; He argued that the investment demand is the major
source of fluctuations of the equilibrium national income and thus too volatile to be trusted with
the private sector. So semi-autonomous institutions not based on profit principle should be created
to be in charge of the aggregate demand management.
The Keynesian economics was transplanted in the experimental farm of the American New-Deal
policy. It became a sort of hybrid by being merged with some classical economics into so-called
`Neoclassical Synthesis'. Behind this marriage was the social atmosphere of the time: the original
policy recommendations by Keynes were modified to be acceptable by the Americans. For
instance, the `Aggregate Demand Management Policy' by a semi-autonomous institution was too
suggestive, of a planned economy or a George Orwellian authoritarian society, for the Americans
to swallow. So the new eclectic policy recommendation was made that government should
intervene in an economy only when there is overheating or over cooling of economic activity, or in
other words, when there occurs a deviation of the economy from the long-run trend. That is called
`Counter-cyclical Policy' or `(Income) Stabilization Policy'. Subsequently, it gained a wide
acceptance particularly in the post-war United States and the world.
Up until the 1970s, on the basis of the Keynesian principle the government was freely engaged in
the `fine-tuning' of the economy. The end result was increased spending which led to the
development of an inflationary trend. The policies designed to counter inflation then smothered
the private production sector.
The resultant combination of high inflation and high unemployment, or stagflation, could not be
resolved within the Keynesian frame of reference.
Here came the Monetarists represented by Milton Friedman who reemphasized the basic tenet of
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Chapter I. Introduction
the classical school: “There is no such a thing as a free lunch.” The aggregate demand
management policy ultimately cannot increase the national income in the long-run. The real
national income cannot be increased at no real cost through gimmick policies: Increases in
production factors, such as capital stock (K), labour inputs (L), and better Technology (T) should
shift the AS curve in order to have a lager equilibrium national income. Capital stock can increase
only when the citizens save by practising thrift and the increased savings are channelled into a
larger amount of investment. ‘Toil and labour’ is required to increase the labour input. ‘Ingenuity’
should be encouraged to facilitate technological innovations. The government has no direct control
over these variables of the supply side.
He goes one step further to suggest that government policies can possibly do more harm than good.
The time-lag of policies severely limits the economic role of government. For instance, there
should be a ‘rule’ as opposed to discretion in money supply, so that the government cannot
arbitrarily resort to the increase in the money supply to finance its deficit.
New Classical economics or the rational expectations theory emerged in the 1970s. They shared
policy views with the Monetarists. The market consists of rationally forecasting and behaving
individual economic agents, and works best if being left alone. The basic tenet is the ‘Policy
Ineffectiveness Theorem’ that anticipated government policies are ineffective without any impact
on real macroeconomic variables such as real national income or investment: anticipating
economic agents.
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Chapter II. National Income Accounting
Chapter II. National Income Accounting
Now this is the time for some tedious, yet important, number crunching.
Our macroeconomic goals have been expressed in terms of national income.
How to calculate the national income?
What determines the level of national income as we have?
1. The Theoretical Part of the National Income Accounting System
1) Supply Sides of National Income
(1) Income Approach
There are two aspects of national income: How it is created, and how it is disposed of.
i) Creation of National Income
The National Income with its notation of Y is the sum of the incomes of all the
households/individuals. The categories of income are a) labor income such as wages and salaries
(W), b) investment income such as rents (R) and interest payment (Int.), c) profits (P) claimed by
entrepreneurs. They are the payments for the production factors (Factor Payment) engaged in
production, which are not explicitly shown but implied in the above table:
National Income or Y = W + R + Int. + P = Factor Payments
........(1)
The source of the Factor Payments/Costs and Profit is the Value-Added, which is equal to Total
Revenues minus Material Costs. At the aggregate level, VA is the sum of the net increase in values
over material inputs in all industries:
Value Added = Total Revenues – Material Costs
........(2)
Total Revenues from the sales of final goods are equal to Total Production Costs plus Profit: TR =
TC + P.
The Total Production Costs can be broken down roughly into the Costs of Materials (MC) and the
Costs of hired Factors(FC: Factor Payment minus Profit):
TR = MC + FC + P = MC + Factor Payment
........(3).
Therefore, from (1) and (3.b), we get
Y = W + R + Int. + P = VA = Factor Payments.
Note that not all incomes at a personal level are to be included in the national income. The only
personal income, which is the factor payment or the reward for participation of production process,
is qualified to be included in the national income. For instance, pension income has no counterpart
of production, and is not to be included in the national income.
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Chapter II. National Income Accounting
National Income versus Personal Income
The National Income is not simply a sum of incomes of all individual residents of the economy.
Personal income consists of two parts; one is earned income, and the other is given or
transferred from others' earned income. The first is a part of national income, and the second
not. For instance, out of the Gross National Income (= W + R + I + P), some portion will not
come to individuals: Depreciation does not go for consumption by individuals. Part of
Corporate Profits will remain undistributed in the firms to become UDCP (Undistributed
Corporate Profits). Corporate Profits taxes (CPT) will go to government. In addition, there are
some personal income items which are not earned -so they are not part of National Income, but
are simply given to individuals: Transfer payment (TR) and Interest payment on bonds (IB).
(Aggregate) PI = GDI - D - UDCP - CPT + TR + IB.
Personal Disposable Income is after-tax income for individuals:
PDI = PI - Direct Taxes.
The PDI is not equal to the National Income, but plays an important role in the determination of
ii)consumption:
Disposal of National
Income
PDI is the
major determinant of households' consumption decisions.
With income, first you pay taxes, and then you spend on goods and services. The latter is
Consumption Expenditures. Then, any left over will be saved: Savings.
Y=C+S+T
(2) Output Approach
Another way of measuring the national income is getting the total value of the goods and services
produced as the result of the above production process.
Frequently, we use GDP or GNP to measure this aspect of national income.
The GNP or Gross National Product is defined as
(a) the total market value
(b) of final (excluding intermediate) goods and services
(c) produced (not only sold but also added to inventory)
(d) by the citizens of an economy
(e) for a year (within a current year).
The GDP or Gross Domestic Product is defined as the total market value of final goods and
services produced in a country for a year.
First, let’s explain why only final goods and services are included :
For the above economy, in calculating the GNP, we count only $ 25, not $ 55. Here the principle is
to count the value of every good but once. The problem of double-accounting is counting the value
Macroeconomics
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Chapter II. National Income Accounting
of some outputs twice or more. The values of the material inputs or intermediate goods should not
be counted separately once the values of final goods which use them as ingredients are counted.
When we take account of final goods, we are taking the value of intermediate goods, which make
up the final goods, into account. Counting the value of intermediate goods separately in addition
to final goods leads to double counting.
 Double Counting in the National Income Accounting System:
Problem of double counting is the most serious with government sector. According to the
Output approach, the value of final goods and services produced by the government should be
included.
Since there are no markets where government goods and services are bought (or evaluated), the
value of goods and services produced by government or `public goods' are evaluated at their
production costs. Subsequently, the value on the basis of cost is included in the national
income.
Whenever government makes expenditures to produce some goods and services, the national
income accounting system simply assumes that there occurs an increase in national income by
the amount of government expenditures; all government expenditure is assumed to be on final
goods. The very problem blurs the distinction between final and intermediate goods in the
government sector.
Second, what does it mean by “by the citizens of an economy”:
If all the goods and services produced by the citizens or the nationals are summed up, the result is
Gross National Product.
If all the goods and services are produced by the residents, national or non-national, the result is
Gross Domestic Product.
 GDP
versus GNP
The difference is created by the foreign and overseas investment.
Some countries have many citizens as well as their capital (money) working overseas. In this
case, GNP is larger than GDP. Japan and Holland are good examples. Kuwait is another
example where a lot of her citizens doing business and residing in foreign countries.
The countries, which take a lot of foreign investment, should have GDP larger than GNP; not
all of what is produced in the countries is necessarily produced by the national. Canada belongs
to this group.
The difference between GDP and GNP is the net factor payments to foreign residents, who
have contributed production factors, such as capital, labor, and management skills to the
domestic production.
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Chapter II. National Income Accounting
Third, the only goods and services produced within the current year are included:
Last, but not least, what if there are no market prices? Certain goods and services do no go through
the market and thus they do not carry any prices.
The goods and services produced by the government or public goods should be included in the
National Product. There arises a question of how to come up with the market value of public
goods? How to include the value of the Gibbon's park service on Sunday? How about an hour of
lecture delivered by a professor? How about national defence by the military forces?
There is no market or market price for any of these public goods. So the National Income Account
calculates the value on a cost basis: The operating costs for the park service are its value. The total
costs incurred in creating an hour of a university lecture are the value of the educational session
that enters the national income accounting. Therefore the value of public goods is equal to their
cost of production.
In this method, we are measuring the National Product(NP) or the Aggregate Output (YS) while
Method I focuses on the National Income (NI or Y as a shorter abbreviation). It is found that in
this simple economy, without government or foreign sector, the National Income, obtained in
Method I, is equal to the National Product in Method II at all times:
National Income = National Product;
Domestic Income = Domestic Product;
Aggregate Income = Aggregate Product, or
Y = YS at all times.
If a $ 1,000 billion or $1 trillion of national income is created in the economy, then aggregate
outputs of the same amount must be produced newly in all industry in a year.
 In sum, the supply side of the national income is
W + R + Int. + P = Y = C + S + T
(Creation)
(Disposal)
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Can
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Chapter II. National Income Accounting
you express Y = YS graphically?
Put Y on the horizontal axis;
Put YS on the vertical axis;
Draw the line with an angle of 45 degrees – Remember a 45 degree line has the slope
equal to one.
YS
YS = Y
450
Y
Macroeconomics
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Chapter II Appendix
2) Demand Side = Expenditure Approach
Method III: Expenditure Approach)
We have so far focused on the supply side in the circular flow of goods and services in an
economy. The value of supply of final goods and services is equal to their value of demand.
In a general economic model, who demands goods and services?
Consumers, firms, government, and foreigners.
The value of demand for an entire economy or is the sum of expenditure or Aggregate
Expenditures (AE) on all the domestically or nationally produced goods and services. They consist
of the following demands: First the expenditures by the consumers is called ‘Consumption
Expenditure’ with the notation of C; the demand by the firms is called ‘Investment’ with the
notation of I; the demand by the government is called ‘Government Expenditures’ with the
notation of G; and the demand by the foreigners is called “Exports’ with the notation of X.
The sum of these expenditures is the Aggregate Expenditures: AE = C + I + G + X.
Two important points should be made:
Why C + I + G + X – M?
First, for the accounting simplicity, in reality the statistical data of C, I and G include the
components of foreign goods and services. For instance, you must know how much the total
amount of your annual consumption is. However, can you break the total amount into the
expenditures on the domestically produced goods –made in Canada- and the foreign made goods?
Probably, we cannot do that at the individual level. So, C, reported or collected, must contain the
expenditures on the domestic as well as the foreign (made) goods and services.
As the Aggregate Expenditures are on the domestically made or the nationally made goods and
services, the foreign components should be subtracted. Although we do not know our individual
expenditures on foreign goods and services, the total expenditures on the foreign goods and
services, which are made by all the civilian households, firms and government agencies, can be
captured by the customs office in its aggregate data of Imports (with the notation of M).
Therefore the aggregate expenditures on the purely domestically produced goods and services are
equal to C + I + G + X – M.
The difference between the Ex-ante and Ex-post Aggregate Expenditures
Second, there are the ex-ante aggregate expenditures and the ex-post aggregate expenditures.
There are two different kinds of demands or expenditures depending on whether or not the
expenditure or demand is planned ahead of time.
The difference between the ex-ante and the ex-aggregate expenditures is Inventories. Inventories
are goods which are not demanded now and thus carried over the next period. In a sense, as the
firms would not throw these inventories away, the inventories are regarded as ‘being demanded by
the firms themselves’. Obviously, this part of demand or expenditures was not planned at all by
the firms, but in fact is made after the unfolding of the unfortunate result of planned expenditures
Macroeconomics
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Chapter II Appendix
falling short of supply. In this sense, it is ex-post (after the event) demand. This part of
expenditures on inventories by the firms is regarded as ‘ part of Investment for the future sales’,
and thus is to be included in I.
In sum, ex-ante I + Inventories = ex-post I, or
AE ex-ante = C + planned I only + G + X – M: only sold part of aggregate products is included.
AE ex-post = C + planned I + unplanned I or Inventories + G + X: all part of aggregate product is
included.

What about the Depreciation of Capital?
Investment is the sum of net investment and depreciation (allowance). Depreciation is capital
consumption or wears and tears of capital stock. Allowances are needed to maintain the constant
level of production capacities. Capital Consumption Allowances and depreciations are different
names for the same thing:
Net Investment = Gross Investment - Depreciation
This depreciation makes difference between the Net and Gross concepts of National Income or
Product:
Net National Product = Gross National Product - Depreciation;
NDP (Net Domestic Product) = GDP (Gross Domestic Product) – Depreciation
 Elusive concept of Deprecation and Capital
In reality, however, we do not see any international comparison of national income done with
NDP (Net Domestic Product), NNP(Net National Product) or any Net concept of national
income or product.
The reason for this lies in the difficulties in measuring the wears and tears of capital. More
fundamentally, the main problem is defining capital in the first place; what is capital? It
involves a fair amount of ambiguity to draw a line between durable and non-durable goods.
Usually, all goods that have a life longer than certain duration will be treated on a capital basis,
their wears and tears are regarded as capital consumption. On the other hand, the goods that
have a life span shorter than this duration will be treated on an inventory basis and their using
up is treated as a cost of production. The dividing line is intrinsically arbitrary.
Each country could have different tax regulations concerning the allowances for capital
consumption. The `magic number' happens to be 3 years in Canada now. This amount of
depreciation (capital consumption) depends crucially on the above rule of defining what
constitutes capital. The Net Domestic Product is an economically more meaningful concept
than GDP, but because of the difficulty in measuring depreciation GDP is used.
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Chapter II Appendix
These Net concepts of national income or national product may measure the total amount of
outputs available for consumption and investment above the maintenance of the present economic
level. Thus they give us an idea of what is available for consumption. Deprecation Allowances of
the National Income should not be consumed away. Therefore, if we are interested in a national
income as a measure of the standard of living or, we must look at the Net concept of National
Income or Product.
3) Equilibrium National Income: Circular Flow of National Income
It is established that Y YS = AE ex-post in reality at all times. The equalities are of identity: they
are trivially equal to each other at all time, i.e., at the equilibrium as well as at the disequilibrium.
However, Y = YS = AE ex-ante only at the equilibrium.
Of course, Y = YS = AE ex-post.
And at the disequilibrium, (Y = YS)  AE ex-ante.
Still Y = YS = AE ex-post.
Let’s have some numerical examples which illustrate the difference between the ex-ante and the
ex-post Aggregate Expenditures:
Suppose that there is only one demander, and there is one supplier in the economy. They meet each
other only once a year on the market day.
Prior to the market day, the demander will come up with how much he would like to purchase on
the market day. The amount, say $100 billion, is the planned or ex-ante demand or expenditure.
On the other hand, the supplier guesses how much the demander will purchase, and produces
outputs. Suppose that the total amount of the outputs is $120 billions.
On the market day, the supplier and the demander reveal each other’s figure at the market.
Obviously, it turns out that the demand falls short of the supply by $ 20 billions. There will be $ 20
billion worth of products left over at the end of the day. They are not going to be left on the
market. They will be taken back by the supplier for future sales. Who demands these inventories?
The producer. Under what category? Investment on inventories, but they are unplanned or ex-post
(after the market day) demand.
YS = Y = 120, and ex-ante AE = 100.
Thus,YS > AE ex-ante.
This is a disequilibrium.
How much will be the production level for the next year, assuming that the AE level will remain
constant? The producer will produce only $ 80 billions so that the supply will be equal to the
Macroeconomics
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Chapter II Appendix
demand at $ 100 billions. That is how much income is going to be created: for the next year, Y =
YS = $ 80 billions. You note that Y will decrease as S > D or YS > AE.
In this case, the total ex-post demand is the sum of the ex-ante demand of $100 billions, which has
been planned, and the unplanned demand or inventory accumulation of $ 20 billions. Thus, the
total ex-post AE = 100 + 20 = 120, which is equal to the supply. The unplanned AE will always fill
the gap between the ex-ante AE (Demand) and the supply.
Now we are not going into specific mathematical equations for the aggregate expenditures. We
will cover them in the next section. However, in general what kind of AE curve are we looking for
the equilibrium?
Recall that the supply side of national income gives the curve Y = YS which is a 45 degree line.
The equilibrium means the intersection of Supply and Demand curve. The demand side curve or
AE curve should be sloped less than at 45 degrees, and should have some positive vertical
intercept.
S
D = AE
What kind of individual components of expenditures would lead to this Aggregate Expenditure
curve? We will examine them in the next section.
Let's sum up:
-National Income: W + R + Int. + P = Y = C + S+ T
-Aggregate Output or National Product: YS = Pmarket x Qfinal
-Supply Side: Y = YS at all times.
-Demand Side: ex-ante AE = C + I
+ G + X –M
ex-post AE = C + I + Inventories + G + X – M
-Equilibrium: Y = ex-ante AE in equilibrium.
C + S + T = C + I + G + X –M
S+T+M=I+G+X
↓
Leakage
↓
Injection
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Chapter II Appendix
This equality can be well illustrated with the following Circular Flow Chart:
Note: The following Leakages (S and T) and Injections (I + G) should be explicitly written on the
above corresponding arrows:
For Financial Intermediaries = Banks, the leakage is S(saving) to the right of the above graph,
and the injection is I(investment funds provided by banks) to the left of the above graph.
For Government: In this case, the leakage is T(tax) to the right of the above graph, and
the injection is G(government expenditures) to the left of the above graph.
4) Applications of the Equilibrium Condition for National Income
(1) Principle
Ex-ante (meaning that we exclude Inventories from the Aggregate Expenditures)
As we can see in the above chart, the injection combined together (I + G + X) is not necessarily
equal to the leakage put together (S + T + M). The investment here is the planned one. Only when
they are equal to each other, there is an equilibrium, where the current level of flow of the national
income persists.
When the injection is larger than the leakage (I + G + X > S + T + M), the flow levels up and the
national income rises.
Ex-post (meaning that we include Inventories in the Aggregate Expenditures)
I + Inv + G +X = S + T + M at all times, at both equilibrium and disequilibrium. The total
investment is the planned investment I plus the unplanned investment, i.e., inventory
accumulation.
Macroeconomics
24
Chapter II Appendix
(2) What we do actually see is the ex-post aggregate expenditure.
The statistical book of the National Income Accounting reports Investment as the sum of the
planned I and inventory accumulation: The investment reported in the NIA is the ex-post
aggregate expenditure. Thus, the Y=YS = ex-post AE: The three aspects of the national income
are equal to each other.
Thus, in the statistical book, the supply is equal to the demand. However, the demand is the ex-post
one. Thus, the equality of the supply and the demand does not mean that the economy is at the
equilibrium and the national income will persist at the present level.
(2) Applications:
i) “Twin Deficits”
The condition for the equilibrium national income is ex-ante I + G + X = S + T + M.
In economics, we assume that the economy gravitates to this equilibrium condition: related
economic variables do change in the way to bring about the equilibrium.
We can re-arrange the equilibrium condition for national income as
I - S + G - T = M –X.
I – S is the investment in excess of savings; G- T is government expenditures in excess of tax
revenues, or in a word, government budget deficit; and M-X is exports in excess of imports and
thus international trade deficit.
If the part of I-S is held constant, an increase in the other left-hand side variable, G-T or
government budget deficit, leads to an increase in the right-hand side variable, M-X or
international trade deficit. One cause of international trade deficits is government budget deficit.
In many cases, we observe the two deficits rising at the same time. Thus, government budget
deficit and international trade deficit are just like “Twins”. They are called “Twin Deficits”.
ii) “Trade deficit is an indicator of a good prospect of the economy”
We can look at another cause of international trade deficit:
In the above equation of the equilibrium condition for national income, if G-T is held constant, an
increase in M-X or international trade deficit goes hand-in-hand with an increase in the term I-S or
investment in excess of savings.
When investment exceeds savings, domestic savings falls short of the total investment. The
difference comes from the foreign country. In other words, the difference between investment and
savings is the foreign investment. If a country has a bad prospect, no foreigner would bring any
Macroeconomics
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Chapter II Appendix
investment to the country. The strong investment from foreign countries is an indicator of a good
prospect of the economy.
At this time, we can reflect on the U.S. trade deficits. Many argue that the U.S. trade deficits are
caused mainly by some countries’ unfair trade practices: The Japanese government might be
blocking the imports of the U.S. goods. However, the above applications of the equilibrium
condition for national income provide us with quite different perspectives: First, the U.S. trade
deficit may be caused by the government budget deficit. In fact, it can be supported with historical
data. Second, the U.S. trade deficit may be also caused by the strong investment demand, which
goes beyond the savings by the American people and thus is supplemented by the foreigners
bringing investment funds to the U.S. This is something to welcome.
2. Technical Part of the National Income Account (Review from the first year economics
class)
1) How to measure the National Income and the Price Level?
(1) Nominal versus Real National Income
We have obtained the National Income by evaluating the aggregate output of the current period,
say year t, at the current market prices. Let's call it the Nominal National Income (its notation is
Yt):
Yt =  Pt Qt
.........(1)
The nominal GDP was $190 billion in 1976 and $672 billion in 1989. Not all of what appears to be
the growth of GDP is the indication of a raised standard of living. Why? Because part of the
increase in the GDP is simply the result of an increase in the price level or inflation. Only the
increase in the real quantity of goods and services or the aggregate output helps raise the standard
of living. The change in the GDP consists of an increase in the price level and the growth of
aggregate output.
How can we measure a change in the aggregate output alone, separately from the changes in the
price level? We can do it by controlling the price level or by using the same price level for the two
time points. First of all, we choose a certain time-point(year) for a benchmark, and call it the base
period(year). There are two time points: the base period and the current period. In the base year
the price level is P0, and the aggregate output Q0 includes various final goods and services. In the
current period the price level is Pt and the aggregate output Qt.
The National Income of the base period is
y0 =  P0 Q0
........ (2)
Note: There is no difference between the Nominal and Real National Income for the base period as P 0= Pt for the base
period.
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Chapter II Appendix
The aggregate output of the current period Qt evaluated at base period's prices give the Real
National Income (its notation is yt):
yt =  P0 Qt
....... (3)
The ratio of the real national income of the current period (3) to that of the base year (2) gives an
indicator of the increase in the real national income. As the price level is being held constant here,
the index measures how much the aggregate output has increased between the base and current
year. It is called the Real National Income Index:
 PQ
income index =
PQ
t
0
real
0
0
t
t
0
0
P h Q h + P s Q s ....
 100 = 0 0
 100
0
0
+
.....
Q
Q
Ph h Ps s
(2) General Price Level
How can we measure a change in the price level itself? We have to control or fix the aggregate
output this time. We can get the ratio of the current period's price level Pt to the base period's price
level P0. There are two different indexes depending on how to assign weights to individual prices.
The first is to get the ratio of the price levels with fixed weights of the base period's output basket
Q0. In this case, we also confine the outputs in this bundle to consumer goods. In Canada, the
basket includes about 490 items of consumer goods. This price index is called the Consumer Price
Index:
 PQ
consumer price index =
PQ
t
0
0
0
0
0
t
t
P h q h + P s q s ....
 100 = 0 0
 100
0
0
P h q h + P s q s .....
Alternatively, we can get the price index by getting the ratio of Pt to P0 with fixed weights of the
current period's aggregate output Qt. The resultant price index is called the GDP Deflator:
 P Q  100 = P Q + P
GDP deflator =
P Q +P
PQ
t
t
t
t
h
0
t
t
0
h
0
h
t
t
h
s
s
Q s ....
 100
t
Q s .....
Note that the GDP deflator of the current period is equal to the ratio of the nominal to the real
national income: (1)/(3). Therefore, if the price level P represents the price index, then the
Nominal National Income is the Price Level times the Real National Income:
P = Y / y, or Y = P y.
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Chapter II Appendix
(3) Numerical Examples
Refer to questions in Review Questions #1.
2) Various National Income Accounting System Equations (Review from Eco 100 or Eco 20).
GDP = GDI + IT = (W + I + R + P + D) + IT,
where IT denotes indirect taxes; GDP denotes Gross Domestic Product; and GDI denotes
Gross Domestic Income.
NDP = GDP – D,
where D denotes depreciation or capital consumption; and NDP denotes Net Domestic
Product.
NNI = NNP – IT,
Where NNI denotes Net National Income and NNP denotes Net National Product.
GDE = C + I + G + X-M
NDE = GDE - D
= C + Net I + G + X-M
GDI = GDP - IT
NDI = GDI - D
GNP = GDP - Net Investment Income Paid to Non-residents.
NNP = NDP - Net Investment Income Paid to Non-residents.
3) Issues and Problems of the Current National Income Accounting.
(1) Conceptual Problems:
Income may be considered to be the maximum that could be consumed in a given period consistent
with the maintenance of wealth or of income potential. Alternatively and essentially equivalent it
may be considered the sum of the amount that is consumed in a given period and that amount that
is added to wealth. It is taken for granted that income has a direct bearing on material welfare,
which may not be always true. For instance, the average income level of the Canadian native
people fares well in national and international comparison. However, their longevity and level of
satisfaction seem to be very low. There has a move to come up with a better and more
comprehensive indicator of the well-being of people than the current National Income Account.
The new indicator should encompass income, longevity (health), and satisfaction.
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Chapter II Appendix
(2) Missing Components of the National Income
We have already seen that the definition of GDP correctly excludes
a) Intermediate goods: They are counted in the value of final goods which are made of
intermediate goods. If the values of intermediate goods are included, in addition to the value of
final goods, they are counted twice.
b) Transfer income or Capital Gains: These items do not result from any productive services.
They do not represent any production.
c) Capital Gains and Losses: Changes in the valuation of assets/wealth are clearly income at
the personal level. However, they are usually not included in the National Income Account
unless they represent new (current) production of goods or services. Sales of old houses,
stocks, or antique may bring income to individuals, but do not increase any current production.
They were included in the national income back at the time of new production. However,
commission income of realtors is included in the current national income as the services
rendered by them are new. The same is true of an antique dealer's value-added. Capital gains
mostly arise from speculative activities. As speculation is usually a non-productive economic
activity, gains from speculation are normally excluded from the calculation of national
income.
(i) However, some capital gains do arise from what is a productive speculation. What is the
productive speculation? Speculation that transferred goods from consumption at a time when they
are plentiful and cheap to consumption at a time when they are scarce and expensive is productive.
An example is the speculation on seasonal products such as fish: Without speculation the price of
fish would show a larger degree of seasonal fluctuations and much of fish would be wasted. In
season, fish is so cheap that workers may not care too much about wastes in the processing
procedure. Out of season, the price of fish is too high for some people to have enough of. As a
speculator buys fish in season when fish is cheap, and releases it out of season when it is
expensive, the price shows smaller seasonal fluctuations. The price of fish is now higher in
season, so there will be less waste and more fish to be stored. This means a larger supply of fish
than otherwise. Out of season, fish price is lower, and there will be a larger demand for fish. This
means more expenditure on fish. The speculator's capital gains represent a larger supply and
demand or an increase in the national income.
(ii) Consumers-goods elements of job: Restaurant meals on an expense account are not included in
the National Income. Expense account items of business representatives are goods and services
which are clearly the consumption of goods and services on any reasonable interpretation, but they
are classified as productive and therefore written off from the measured incomes of the person
enjoying them. In Canada reform of tax regulations is under way to rectify this issue, which
reduces the amount to be claimed in this way.
(iii) Household Production: Over the past twenty years the rate of participation of women in the
work force has risen at an average rate of 2.2 % per year from 37.1 % of the Canadian labour force
in 1968 to 57.4 % in 1988. The rapid rates of increases are also reflected in employment growth
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Chapter II Appendix
over the same period, a compound annual rate of growth for women of 3.9 % compared to 1.5 %
for men. There are no markets or prices at which all of household production activities, such as
laundry, home-cooking, baby-sitting, cleaning and etc. can be evaluated. So they are not taken
into account of national income. As the women participate in the work force, they would now rely
on the market for those goods which they used to produce at home. The formerly non-market
activities, such as child-care and home-cooking give way to paid baby-sitters and meals in
restaurants. They will pay for the baby sitter. The family may eat out more frequently instead of
eating home-cooked meals. They may even pay for the cleaning ladies. These are counted as a net
addition to output. Part of the growth in GDP simply reflects the substitution of market activities
for non-market home production.
But growth will be more or less overstated depending on what happened to the non-market activity
previously undertaking by these new entrants to labour force. If some of the previous non-market
activity is forgone entirely, as a result of women entering the labour market, then measured GDP
growth should be reduced by an equivalent amount. If, on the other hand, the housework is not
foregone, and the women or other members of household somehow take up the slack, then
measured GDP should not be adjusted.
The difficulty, of course, is to estimate the value of household work and the degree of substitution
or replacement. In Canada, estimates have been prepared for 1971 and 1981 using data from
Census Information and time use studies for a range of household activities. Valuing these
activities at counterpart rates (prices: for instance, home-cooking is evaluated with the price of
restaurant foods) in the market produced totals equivalent to 39.5 % of GDP in 1971 and 34.0% in
1981. (30% in 1990, unofficially) This unpaid work is estimated to account for 30 % of GDP in
Canada. The decline in the relative importance no doubt reflected other factors as well as the
movement of women into the market economy, but the overall effect was considerable.
Including the measured value of household work reduced the average rate of overall economic
growth by 0.5 % per year. Alternatively put, Statistics Canada estimates that on average 0.5
percentage point of annual growth has come from the replacement of unpaid work with the market
since 1971. In other words, even if the sum of home and market production does not increase at all,
a mere substitution of market production for home production would make the GDP look as if it
were growing at 5% per annum in Canada.
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30
Chapter II Appendix
(iv) Underground Economy
Read the article entitled "Gross Deceptive Product" (GDP).
(3) False Components of the National Income
(i) Expenses of an Intermediate good nature
The current National Income Accounting System does not make any distinction between a
leisurely driving and commutation for work. Expenses on commuting back and forth between
home and work places are included in the national income. In fact they are costs for a further round
of production, and should be excluded from the national income.
(ii) Systematic Exaggeration of the Government Role in a GDP Creation.
The following excellent example illustrates the seriousness of double-counting caused by the
government: In the following two cases the real resources available for consumption, measured in
the number of pairs of shoes, are identical, but the apparent National Income measured according
to the present national income accounting system will be quite different.
Case 1. A ramp from a shoe factory to a highway is owned privately by a factory. Annually it costs a $1000 to maintain
the ramp. The factory produces $100,000 worth of shoes. The costs and expenses of the ramp services are regarded as
intermediate goods, and are already included in the values of the final goods or the shoes manufactured. Thus the ramp
maintenance cost of $1000 is included in addition to the values of the shoes. The measure national income is $ 100,000
(= Y = C).
Case 2. Now government nationalizes the ramp and maintains it. The firm is required to pay annual tax of $1000 to
government. Nothing has changed for the firm and the real economy: The firm is under the identical set of
circumstances as in the original situation. The government makes expenditures in hiring workers and resources to
upkeep the ramp. As the current National Income Accounting System values public goods provided by government on
a cost basis, these government expenditures will be taken as increasing the national income. Now the measured income
is the sum of private (shoes) and public goods (ramp services): Y = C + G = 100,000 + 1000 = 101,000. However, in
fact, the cost of road services is already embodied in the value of the final goods or shoes. It is counted twice; once in
the shoes and secondly in government expenditure (G).
How serious is this double counting in the public sector? For Canada, according to Reich (1986)
intermediate goods account for 22.9 % of government expenditure or public goods. Therefore, the
correct and true national income accounting identity, which includes various expenditures on final
goods only, should be
Y = C + I + 0.77 G + X - M in Canada.
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31
Chapter II Appendix
Appendix: How the Circular Flow Chart is obtained:
Some of you have noticed that I have jumped from the model with only consumers to the model
with consumer, firms, government and foreign sector. This appendix is for the mind which
requires some convincing as regards the transition from the simplest model with consumers only to
the complex model with consumers, firms, government, and foreign sector.
1. Economy with Consumption Only.
We have already view the simplest economy with consumers only: AE = C only. If there is only C
on the aggregate expenditure side, the equilibrium condition for the national income is Y = C.
Example I: Let's suppose that the following table shows an annual production of all industries
evaluated at the current market prices in a simplest economy. What is the current national income?
Industry
Sales Revenues
PxQ
=
Material Costs for
Intermediate Goods
Factor Costs (Value
Added)
Wheat
$5
$0
$5
Flour
$8
$5
$3
Bread
$ 17
$8
$9
Deli-Bread
$ 25
$ 17
$8
In the table, the sum of Value-Added of all industries is $ 5 + $3 + $9 + $8 = $25. Thus the current
National Income is $25.
2. Economy with Consumption and Investment: No government or Foreign Sectors
Now let’s add Firms’ demand for goods and services produced in the economy: Now AE will turn
to C + I in the following example.
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32
Chapter II Appendix
Example II:
Let's also add a machine-making industry, which produces final goods for investment.
Industry
Sales Revenues
PxQ
=
Material Costs for
Intermediate Goods
Factor Costs (Value
Added)
Wheat
$5
$0
$5
Flour
$8
$5
$3
Bread
$ 17
$8
$9
Deli-Bread
$ 25
$ 17
$8
Machine
$ 50
$0
$ 50
The supply side has Y = YS:
Y = VA's = $5 + 3 + 9 + 8 + 50 = $75
YS= Pmarket x Qfinal = 25 + 50= $75
We have so far assumed that households spend all their income: the entire Y is disposed of as
C. Let's now introduce savings: Households dispose of their income either in consumption
spending or in savings. By the amount of the savings, which is a leakage from the circular
flow, the national income does not go back to the flow of demand for goods: Y = C + S.
The demand is for deli-bread for consumption and for machines for investment: AE = C + I:
AE = C + I = 25 (Deli-Bread) + 50 (Machine) = $75
Note 1) Machines may be used in the production process. That does not make the machines an intermediate goods.
Intermediate goods are materials, which are to be embodied in their outputs. Machines may wear and tear, but will not
be made into outputs. Machine are a capital good which endures many cycles of production.
Macroeconomics
33
Chapter II Appendix
The Circular Flow Chart for this economy is modified as follows:
Note: Savings of households may be channelled by financial intermediaries, such as banks, to firms as investment.
However, there is no guarantee that investment and savings are equal to each other as they are carried out by different
economic agents: the first by households and the second by firms. For instance, when business outlook is break,
households may cash their investment and hold their assets in deposits. Now savings become larger but investment
smaller.
If they happen to be equal to each other, the circular flow will be maintained at the current level as the leakage(savings)
is the same as the injection(investment). This is the equilibrium situation, meaning that the current state will persist in
the absence of any disturbing forces.
Keynes noted that when savings exceeds investment, as leakage from the circular flow exceeds injection into it, the
circular flow or the national income flow will diminish over time. He pointed out this problem as the cause of recession.
Example III: Inventory) The National Income should include all the factor payments(=VA) for
goods produced of all the industries regardless of whether they are sold or unsold later in the
economy. Income is created through the process of producing these aggregate outputs.
The existence of inventory compounds the output approach to the National Income. We should
note that the value of inventories of final and intermediate goods should be included in the
computation of the value of aggregate output. Sold intermediate goods get their value embodied in
the value of final goods. The values of unsold intermediate goods are not reflected elsewhere and
should be taken into account. Therefore, the Total Value of Output = Sold Final Goods + Unsold
Final Goods + Unsold Intermediate Goods:
YS = P x Qfinalsold + P x Qfinalunsold + P x Qintermediateunsold.
In the expenditure approach of getting the AE, the changes in inventories or Inventory
Accumulation of final and intermediate goods are regarded as Investment on inventories:
AE = C + I.
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34
Chapter II Appendix
Numerical example: Refer to Assignment #1.
2) An Economy with Government
What complications does the introduction of government bring to the national income accounting
system?
i) The income approach national income Y (= W + R + I + P) should now include W, R, I, P paid by
the government. They are all before-income-tax figures. The disposal of income should include
direct taxes: Y = C + S + T. Consumers cannot spend taxes on final goods, and thus tax constitutes
another leakage from the circular flow of the national income.
ii) In the output approach, the value of goods and services produced by the government or public
goods should be included in the National Product. There arises a question of how to come up with
the market value of public goods? How to include the value of the Gibbon's park service on
Sunday? There is no market or market price for it. So the National Income Account calculates the
value on a cost basis: The operating costs for the park service are its value. Therefore the value of
public goods is equal to their production cost/expenditure.
Note: Problem of double counting is the most serious with government sector. According to the Output approach, the
value of final goods and services produced by the government should be included. Since there are no markets where
government goods and services are bought (or evaluated). The value of goods and services produced by government or
`public goods' are evaluated at their production costs. Whenever government makes expenditures to produce some
goods and services, the national income accounting system simply assumes that there occurs an increase in national
income by the amount of government expenditures; all government expenditure is assumed to be on final goods. The
very problem blurs the distinction between final and intermediate goods in the government sector.
iii) Indirect taxes or sales taxes will create inequality between the National Income, which is
measured at the production stage(factory), and the National Product, which measured by the
marketing stage(market). The value of output in the market is the sum of the factory value and
sales taxes:
NI + Indirect Tax = NP.
iv) The government expenditure should be added to the Aggregate Expenditure as another
injection to the system of circular flow:
Government activity involves current expenditures or G (jet fighters, judges, policemen, civil
services, etc.) and taxation. Government expenditures, which adds to the Aggregate Expenditures,
are either on consumption-nature goods and services (Gc) or investment goods (GI). The latter is
put together with Investment of the private sector to become the Total Investment of the economy.
Therefore,
AE = C + Iprivate + G = C + I + Gc + GI = C + (I + GI) + Gc = C + I + G.
Note: Government Current Expenditure or Gc or G in the National Income Account could be a very misleading indicator
of the size of government activities; Some items of government spending are not included in `G' of the national income
account, and they are substantial in Canada; old age pensions, social welfare expenditures which are transfer payments
from government to the private sector, and there are also interest payments on government bond (IB). The government
Macroeconomics
35
Chapter II Appendix
expenditure on currently produced goods and services accounts for only 44 % of the total government spending in
Canada. The interest payment accounts for 22% of the total government spending and the transfer payment which does
not bring about any production of goods and services in reciprocation of payment accounts for 34% of the total
government spending. Therefore, Government Spending > Government Expenditures or G.
Summing up, we can write
Y = C + S + T ; YS ; AE = C + I + G.
The modified Circular Flow Chart is as follows:
3) A Complete Economy with Consumers, Firms, Government, and International Sector
How does an introduction of the foreign sector compound the National Income Account?
i) There are final goods and services which are produced in a country but will not be claimed by its
nationals.
The difference between the National and Domestic concepts of the National Product or Income is
that the first is produced/ created by the nationals (citizens) and the latter is produced/created in the
country: The first focuses who produces outputs, and the second where output are produced. In a
country where there are many foreign workers (L) and foreign capital (K), the Domestic Product
(Income) is larger than the National Product (Income). Parts of the domestically produced outputs
are claimed by non-nationals who contribute production factors to the country:
Domestic Income (Product) = National Income + Income paid for Foreign Labor/ Investment.
Think about which is the larger of the two in Canada, Japan, Kuwait, and other countries.
ii) The AE should include the expenditures on goods and services by foreigners, or the value of
exports(X). For an expedience in data collection and accounting, the Canadian purchase of foreign
goods or the value of imports (M) are included in C + I + G. The value of imports (M) should be
Macroeconomics
36
Chapter II Appendix
subtracted from GDE. The expenditures on the domestic outputs are C + I + G - M.
AE = C + I + G + X - M.
Summing up, we can write
Y = C + S + T; YS; AE = C + I + G + X - M
The complete Circular Flow Chart is as follows: Exports are a new injection to the system and
imports a new leakage. By the amount of imports national income does not become AE for
domestic final goods.
Macroeconomics
37
Chapter III. Keynesian Cross Diagram
III. Keynesian Cross Diagram
1. Introduction
What determines GDP in an economy? Keynes says that the actual or equilibrium national income
is not necessarily equal to the maximum potential output (full employment income). The question
is what prevents us from enjoying the full employment income?
This is a simple Keynesian Model of Income Determination. It is ‘simple’ in the sense that it does
not have the money market, and all the consequent implications and complications: For instance,
there is no Crowding Out of government expenditure policy. We will introduce the money market
in the next chapter.
Within this chapter, depending on the specifications of components of aggregate expenditures,
there are three different cases; Case 1 has just lump-sum taxes; Case 2 has proportional as well as
lump-sum taxes; Case 3 has imports and exports as well as proportional taxes.
2. Basic Principle (Strategy for Solving for Y*)
Always go through the following steps to solve for Y*:
Step 1. Spell out the Aggregate Supply side income;
YS (=W+R+I+P+D) = Y (=C+S+T).
Step 2. Spell out Aggregate Expenditure side income;
AE = C + I + G + X-M.
And, then Substitute the functional specifications given by the question for the variables C,I,G,
X-M, and rewrite it in the form of AE = A + B Y, where A and B are specific (constant) numbers.
Step 3. At the equilibrium, we know S=D and that here YS = AE.
Y = C + I + G + X-M, or Y = A + B Y.
Therefore
(1  B)Y *  A
A
Y* 
1 B
where B is the slope of Aggregate Expenditure curve, and A is a set of Autonomous Aggregate
Expenditures.
Note that B has the terms that are associated with Y and A has a set of variables independent of Y.
Macroeconomics
38
Chapter III. Keynesian Cross Diagram
Step 4. From the above equation, get the first derivatives of various components of A;
Y *
; consumption _ exp enditre _ multiplier
C 0
Y *
; investment _ exp enditure _ multiplier
I 0
Y *
; government _ exp enditure _ multiplier
G0
Y *
; lum  sum _ tax _ multiplier
T0
3. Case 1: T = T0
1) Basic Assumptions
i) No money market; No inflation (price level is fixed): P ;
ii) All taxes are lump-sum or of a fixed amount: T  T ;
iii) There are no exports or imports (closed economy): M  X  0 .
P (the price level) is assumed to be fixed because
a) we are dealing with short-run, where prices are inflexible;
b) we have unemployment situation. So an increase in demand would lead to the increase in
production/output, not inflation;
Producers would not have any difficulties in increasing output fairly quickly without raising the
costs or prices; there are idle capacities of capital and equipment. It is almost costless to bring
them into production. And unemployed labour forces are standing by and are willing to be hired
for pittance.
c) Y (= y) adjusts rather than P with the change of Demand.
d) All variables, such as consumption, investment, and government expenditure, are expressed in
real terms. There is no distinction between real and nominal magnitude as the price level is fixed.
The interest rate here is the real interest rate.
Macroeconomics
39
Chapter III. Keynesian Cross Diagram
2) Supply Side
YS (=W+R+I+P+D) = Y(=C+S+T)
(Interpretation) The value of supply of final goods and services (=YS) will be paid out to
households (in the forms of W, R, I, P, D) to become national income (=Y). It will be disposed of
by the households either in consumption, savings, or taxes.
Graphically, in a quadrangle with YS on the vertical axis and Y on the horizontal axis, the 45
degree line from the origin represents the supply side of national income.
The horizontal distance from the origin to point A is equal to the vertical distance from the origin
to point B on the 45 % line. It has a degree of 1. YS = Y. The line can be nothing but a 45 degree
one as the firms pay out to households all of what they earn from production.
3) Demand Side: Aggregate Expenditure
(1) Consumption Function
Keynesian Consumption function:
C = C0 + c1 Yd,
where Yd is disposable income, or Yd = Y-T.
For simplicity, let us assume that T = T0 independent of income level, or that all taxes are
lump-sum.
What is the constraint on the value for C0 and c1 respectively?

C0 is an autonomous, exogenous, and independent consumption regardless of income
level;

c1 is the Marginal Propensity to Consume.
0< c1<1;
Macroeconomics
40
Chapter III. Keynesian Cross Diagram
MPC measures how much of an increase in income will be consumed. The consumption increases
as income increases (>0), but is not increasing as fast as income is (<1).
Let's quote Keynes' explanation of MPC;
"The fundamental psychological law is that men are disposed, as a rule and on average, to increase their
consumption as their income increases but not by as much as the increase in income."

Graphically, c1 or MPC is the slope of the consumption curve drawn with C on the vertical
axis and Y on the horizontal axis;
C = C0 + c1 (Y-T)
= {C0 – c1T} + c1 Y

Average and Marginal Propensity to Consume;
(Definitions)
C
Y
C
APC 
Y
MPC 
Macroeconomics
41
Chapter III. Keynesian Cross Diagram
(Questions)
What is MPC at y1 and y2 respectively? (MPC is constant over y1 and y2)  APC1 > APC2
What is APC at y1 and y2 respectively? (APC decreases as Y)
MPC = Slope
(if straight line)
Graphically, the MPC is the slope of the consumption curve, and is constant everywhere on the
straight line of the consumption curve regardless of the level of income.
The APC is the slope of the line linking the origin and the point of interest on the consumption
curve (= tangent of the angle Theta). APC at y1 is given by the slope of a hypothetical line linking
the origin and point A. APC at y2 is equal to the slope of the imaginary line liking the origin and
point B. The flatter is a curve, the smaller its slope will be. So APC at y2 is smaller than APC at y1;
the APC decreases as the national income level increases.
Also, naturally APC > MPC holds at all income level.
(2) Investment
Demand for addition to fixed capital formation and a voluntary addition to inventory.
I is for now assumed to be exogenous, such as
I = I0 ;
What it means is that we are assuming that investment is geared to long run; entrepreneurs make
investment decision based on expected future income which is independent of current income.
Even if the current income is very low, when there is a prospect that the demand for their goods
will increase in the future, they will be engaged in the expansion of production facilities.
Naturally, the dependence of investment on expectations makes investment very volatile. What
will be the impact on the output or income? As the expectations or business outlook changes,
investment decision will vary. The expectations and business outlook are very much affected by
rumours, fear, etc aroused by unexpected events. Would such variations in investment lead to
smaller or larger changes in output than the changes in investment itself?
Macroeconomics
42

Chapter III. Keynesian Cross Diagram
Investment is a
major source of
fluctuations
of Y
(3) Government Expenditures
G = G0.
Numerical Example: G= 150
(4) Foreign Sector
Let us assume that X-M = 0 for simplicity.
(5) Aggregate Expenditures
AE = C + I + G + (X-M);
Suppose that specifications of each variable are given as follows;
C = C0 + c1 (Y-T)
= C0 - c1 T + c1 Y;
I = I;
Macroeconomics
43
Chapter III. Keynesian Cross Diagram
G = G;
X-M = 0 for simplicity.
Substituting the above specifications for the variables in the equation, we get
AE = C + I + G + X-M
Note that I,G,C in the first equation are variables, and I,G in the second ones are numbers or
specific values
AE = C0 – c1 T0 + I0 + G0 + c1 Y
intercept
slope
AE consists of two parts; one is independent of Y or national income, and the other dependent on
Y. The first is called `Autonomous Aggregate Expenditures, and the latter `Induced Aggregate
Expenditure.'
AE = Autonomous AE + induced AE
= A + B Y,
where A = C0 – c1 T0 + I0 + G0, and B = c1.
AE
AE  C  I  G
C1  C 2T
II
GG
Y
Note that the slope of the Aggregate Expenditure curve is equal to that of the consumption curve
and the MPC = c1.
Macroeconomics
44
Chapter III. Keynesian Cross Diagram
3) Equilibrium Y*
(1) Graphic Solution
E
(2) Algebraic Solution
Step 1: YS = Y; Supply side.
Step 2: AE = C+I+G+X-M; Demand side.
By substituting the functional forms, given by the question, for C,I,G,X-M, and rewriting it, we get
AE
= {C0 – c1 T0 + I0 + G0} + c1 Y, or
= A + B Y,
(X – M = 0)
where A and B are numbers.
Step 3: YS = AE at equilibrium, so
Y* = {C0 – c1 T0+ I0 + G0} + c1 Y*
Solving for Y*, we get
(1 - c1 ) Y * = C 0 - c1 T0 + I 0 + G 0 .
*
Y =
Re call Y * =
1
{ C 0 - c1 T0 + I 0 + G0 }.
1 - c1
A
, where A = C 0  c1 T0 + I 0 + G 0 , B = c1
1 B
Macroeconomics
45
Chapter III. Keynesian Cross Diagram
The above is the equilibrium national income equation. If we know the values for C0, c1, T0, I0, and
G0, we can get the numerical value for Ye.
(3) The Equilibrium Condition
YS = Y = C + T + S
AE = C + I + G + X-M
Equilibrium Condition S + T = I + G + X-M;.
Without government and foreign sector, S = I.
S = I + (G-T) + X-M suggests that the private sector has three ways of disposing its savings; by
lending to the business sector which uses the funds for investment. By lending to the government
which uses the funds for financing the government deficits. By lending to foreigners who would
buy more goods and services from us than we are buying from them.
4) Comparative Statics

No change in the supply side or YS can alter the equilibrium national income.

Only change in the demand side or AE can do so. (Keynesian Idea)
AE = C0 – c1 T0 + I0 + G0 + c1Y = A+BY
= Autonomous AE + Induced AE

Alternatively, when we draw the above AE curve with Y on the horizontal axis, we get
Slope (B)
: c1
Intercept (A): C0 – c1 T0 + I0 + G0;
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Chapter III. Keynesian Cross Diagram
(1) Increases in Autonomous AE; changes in the intercept of the AE curve.
The vertical shift of the AE curve brings about the horizontal changes in Y*. The ratio of the
(horizontal) change in Y* to the (vertical) change in the AE is given by a `(generic) multiplier', and
is equal to one over one minus the slope of the AE curve. The slope of the AE curve is equal to that
of the consumption curve in this particular case;
If all taxes are lump-sum, the slope of the consumption curve is equal to MPC or c1. So the
multiplier is 1/(1-c1).
If there is a tax proportional to income, then the slope of the consumption curve is equal to c1 (1-t1)
where t denotes the tax rate. The multiplier is equal to 1/{1-c1(1-t1)}.
Y*
increase in Y * on horizontal axis
=
AE
increase in AE on vertical axis
=
1
when T = T0 : Case1
1 - c1
=
1
when T = T0 t 1Y : Case2
1 - c1 (1 - t1 )
.
Macroeconomics
47
Chapter III. Keynesian Cross Diagram
Graphic Proof of Multiplier: We are interested in getting the ratio of Δ Y* to Δ AE.
 First, along the YS=Y curve, the slope is a unit. So Δ Y = A = B.
 The AE and AE' are parallel.
 Let us called B minus Δ AE `C'; C = B-Δ AE.
 The slope of the AE curve is C over A by definition. This is equal to c 1.
c1 =
C
 Y *  AE
=
.
A
Y e
Then, c1  Y * =  Y * AE.
AE =  Y * - c1  Y * = (1 - c1 ) Y * .
So,
Y*
1
=
.
AE
1 - c1
AE // Ys
Ys  Y
AE   AE  AE
AE
AE
Y *  AE
rise
 C1 
*
run
Y
*
 Y  AE  Y *C1
2 Y  AE
○
AE
1 Y
○
Y *
*
Y
 (1  C1 )Y *  AE
(2) Individual Multipliers
What constitutes the intercept? - The components of the intercept {C0 – c1T0 + I0 + G0 + X0-M0},
that is, C0, T0, I0, G0, and X0-M0, are the components of `Autonomous Aggregate Expenditures'.
Changes in autonomous expenditures are illustrated by changes in the intercept of the AE curve.
These changes in the intercept shift up or down the AE curve in a parallel way. Then there will be
resultant changes in Y* (given by the intersection of AE and YS=Y curves. The resultant changes
in Y* is usually larger than the initial changes in AE. Therefore any change in the intercept will
bring about the multiplier effect on national income.
Macroeconomics
48
Chapter III. Keynesian Cross Diagram
C0: determined by consumers. I0: determined by firms.
G0 and T0: determined by government. A set of rules determining the level and
or T0 is called fiscal policy.
changes in G0
X-M: determined by foreign sector.
The multiplier for each component can be obtained by differentiating the equilibrium national
income equation with respect to the variable of Autonomous Aggregate Expenditure: A multiplier
of a variable should be equal to the coefficient of the variable in the equilibrium national income
equation.
*
Y =
*
Y =
1
{ C 0 - c1 T0 + I 0 + G 0 }.
1 - c1
1
c1 T + 1 I + 1 G .
0
C0 0
0
1 - c1
1 - c1
1 - c1
1 - c1
Therefore,
e
dY = 1
dC 0 1 - c1
e
dY = 1
1 - c1
dI 0
e
dY = 1
dG0 1 - c1
e
dY =  c1
dT0 1 - c1
Ye Y*
Note that all multipliers but the tax multiplier one is equal to 1/1-c1.
a) Changes in C0, I0, and/or X0-M0 can cause a change in national income. C0 varies over
time; I0 is even more volatile. These changes are beyond control by government; they constitute
shocks to aggregate expenditures. Changes in I0 are magnified into larger changes in Y through
the multiplier. If the changes are cyclical, there occurs a business cycle.
Government may try to counter the changes in the AE due to changes in C0, I0 or X0-M0 by
adjusting T 0and G0 in the opposite direction by the same amount. If the changes in AE are
successfully ironed out in this manner, there would not be any change in Y*; when I is decreasing,
government increases G and thus AE is held constant and so is the national income. This kind of
Macroeconomics
49
Chapter III. Keynesian Cross Diagram
government policy is called `Counter-Cyclical Fiscal Policy.' Can government actually fine-tune
the economy in this fashion? The answer is rather negative mainly because of Time-lags.
b) An increase in G0 (ΔG0):
ΔY* = 1/(1-c1) ΔG0
ΔG0= k ΔY* = 1/(1-c1) ΔY*

Example) c1 = 0.75, and all taxes are lump-sum. Government is increasing its expenditure
on final goods and services by $ 5 billion. What is the resultant increase in the national
income?
The government expenditure multiplier is 1 over 1 minus 0.75, that is, 4. So ΔG will be multiplied
into ΔY* by the factor of 4; k = 4. Therefore, ΔY* = 4 ΔG= 4 times $ 5 billion = $ 20 billion.
c) An increase in T (ΔT0) leads to a decrease in Y*.
ΔT = k ΔY* = - c1/(1-c1) ΔY*
-C1
Macroeconomics
50
Chapter III. Keynesian Cross Diagram
An increase in T will lead to a decrease in Disposable Income by ΔT 0 (note it does not increase Y
for now); in Yd = Y - T, 0 ΔT 0= - ΔYd. The decrease in disposable income by dT will decrease
consumption only by c2 ΔT0 (a MPC fraction of changes in disposable income = changes in
consumption). This is shown as shift up of the intercept of the consumption curve and thus AE
curve;
ΔT0  -ΔYd = -ΔT0  -ΔC = c1 x (-ΔYd) = -c1 ΔT0 =ΔAE (< -ΔT0)
This change should be classified as Autonomous, so there is multiplier effect to this increase in
consumption;
 ΔY* = k ΔAE= (1/(1-c1)) (-c1 ΔT0) = -c1/(1-c1) ΔT0.
Note that when taxation is increased by say, $1, the AE curve does come down vertically by less
than $1; In other words, one dollars increase in taxes will bring about a less-than-one-dollar
-decrease in consumption or AE.
d) Balanced Budget Multiplier;
Suppose government increases G by 1 billion dollars and at the same time taxes by 1 billion
dollars. What happens to the National Income?
From (1) and (2), in this case, there are two forces working in opposite directions; ΔG brings about
an increase in income and ΔT a decrease in income. However, the first is larger in its impact on Y*
than the second, and thus there is a net positive increase in income. The increase in Y* is equal to
the magnitude of operation, that is, the increase in government expenditure or taxation. In other
words, if government expenditure is increased by ΔG and at the same time taxes are increase by
ΔT where ΔT = ΔG, then ΔY= 1 ΔG= 1 ΔT. Balanced budget multiplier is 1 regardless of what
the MPC is.
Proof 1 of Balanced Budget Multiplier being equal to one
Government increases G and T at the same time by the same amount, say, $1. We can think of the
government operation as a sequence of two separate actions.
First, government increases its expenditure by $1. This pushes the AE curve upward by $1.
Second, government increases taxation by $1. This pushes the AE curve down by less than $1;
people are taxed $1 more, and their disposable income decreases by $1. But the decrease in
consumption will be less than $1; it will be a fraction of $1. They spend $ c1 (<$1) less than before.
So the decrease in AE is $ c1.
Macroeconomics
51
Chapter III. Keynesian Cross Diagram
Combining the first and second changes in AE, there occurs a positive net increase in AE by 1-c1.
We know that a $1 increase in AE will lead to an increase in the equilibrium national income by
the factor of a multiplier k = ΔY* /ΔAE= 1/(1-c1); the net increase in AE by 1-c2 will lead to an
increase in Y* by k time 1-c1 = 1/(1-c1) x 1-c1 = 1. The increase in G accompanied with an equal
amount of increase in T will lead to an equal amount of increase in Y*. If G and T are increased by
say, $50 billion, then Y* will increase by $50 billion.
Proof 2 of BBM =1 in Case 1
In this case, government increases G and T at the same time and by the same amount. Therefore,
the resultant Balanced Budget Multiplier is a combination of the government expenditure and tax
multipliers:

ΔY/ΔG= 1/(1-c1) = government expenditure multiplier;
An increase in G by 1 billion increases income by 1/1-c1.
 ΔY/ΔT = -c1/(1-c1) = tax multiplier;
An increase in T by 1 billion decreases income by c1/1-c1.

Combined Effect on income = 1/(1-c1) – c1/(1-c1) = 1.
ii) Change in the slope of the AE curve, which is equal to the slope of the consumption curve and
MPC.
The larger MPC, the larger Y* and the larger K will be:
AS the MPC increases not only the income level but also the multiplier will increase.
i) As c1increases, Y* increases and the multiplier increases.
When MPC ; K ;
Y*
The larger MPC leads to a steeper AE curve and a larger Y*.
Macroeconomics
52
Chapter III. Keynesian Cross Diagram
ii) the larger MPC is, the larger the multiplier will be.
4. Generalization of Keynesian Cross-Diagram of Income Determination
Recall Case 1: We have so far examined the case where all taxes are lump-sum; T= T0
*
Y =
1
( C 0 - c1 T o + I o + G o )
1 - c1
Case 2: Now there are two kinds of taxes. The one is fixed or lump-sum, and the other is
proportional to the income level; T= T0 + t1 Y.
Step 1: Supply Side: YS = Y
YS = (W + R + I + P) = Y ( = C + S + T)
; Supply Side
Step 2: Demand Side: AE = C + I + G
= C0 + c1 Yd + I 0 + G 0
;Y
is disposable income
= C0 + c1 (Y - T) + I0 + G0
;Y
=Y-T
d
d
Macroeconomics
53
Chapter III. Keynesian Cross Diagram
= C0 + c1 {Y - (T0 + t1 Y)} + I0 + G0
; recall T = T
= Co + c1 Y - c1 T0 - c1 t1 Y + I0 + G0
; expand the bracket
= C0 - c1 T0 + I 0 + G0 + c1 Y - c1 t1 Y
; separate Y terms
= C0 - c1 T0 + I0 + G0 + (c1 - c1 t1) Y
; factor Y out
= C0 - c1 T0 + I 0 + G0 + c1 (1 - t1) Y
; factor c out
0
+ t1 Y
The slope of the consumption curve is smaller in this case with proportional taxes than the
case without them; c2 (1-t) < c2. The consumption curve is flatter.
We know that the slope of the AE curve is the same as the consumption curve. Thus, we
can predict that the multiplier will be smaller in this case than in the case without
proportional tax.
Step 3. At equilibrium, Y = AE and thus
Y* = C0 - c1 T0 + I0 + G0 + c1 (1 - t1 ) Y*
{1 - c1(1 - t1 )} Y* = C0 - c1T0 + I0 + G0
; transpose Y to the left
Step 3: Equation
Y* 
1
{C0  c1T0  I 0  G0 }
1  c1 (1  t1 )
Step 4: Multipliers
The multiplier of a particular variable is obtained by differentiating the above equilibrium national
income equation with respect to that variable.

What are the multipliers for the autonomous consumption and the autonomous investment?
Y *
1
=
C 0
1 - c1 (1 - t 1 )
Y *
1
=
I 0
1 - c1 + c1 t 1
Macroeconomics

54
Chapter III. Keynesian Cross Diagram
What are the multipliers for government expenditures and lump-sum taxes? (Fiscal Policy)
Y *
1
=
G0
1 - c1 (1 - t 1 )
Y *
 c1
=
T0
1 - c1 + c1 t 1

What is the multipliers for a balanced budget multiplier for the case where an increase in
government expenditures is financed by an increase in lump=sum taxes?
 c1
1  c1
Y *
1
=


G0  T0
1 - c1 (1 - t 1 ) 1 - c1 + c1 t 1 1  c1 (1  t1 )
Is this equal to one?
What if the government does not increase T0 not by the full amount of ∆G0 in the first round but
makes the overall increase in T equal to ∆G0?
Eventually the proportional tax revenues for the government will rise as the new equilibrium
national income rise over time: In T = T0 + t1 Y, overall T increases as Y rises.
Thus in this case, the increases in proportional taxes resulting from increases in Y supplement
the initial increase in lump-sum taxes. BBM is equal to one in this case. The result is the same
as the previous Keynesian balanced budget multiplier as long as the change in the tax revenue is
made by lump-sum taxes.
Proof:
0
1
1
1
1
 c1
G0 
T0
1 - c1 (1 - t 1 )
1 - c1 + c1 t 1
1
 c1
=
1
(1  tt Y )
1 - c1 (1 - t 1 )
1 - c1 + c1 t 1
1
Y =
Remarks:
 Here again, we may note that the government expenditure multiplier is smaller with
proportional taxes than otherwise; For a given vertical shift-up of the AE curve (due to an
Macroeconomics
55
Chapter III. Keynesian Cross Diagram
increase in G), the resultant ∆Y* will be smaller with a flatter AE curve than a steeper AE
curve. When the income tax rate increases, the national income will be smaller, and the
impact of an increase in G will be smaller, too.
1
1

1 - c1 (1 - t 1 ) 1 - c1
I0 and C0 exhibit cyclical movement over time, depending on, for instance, investors’ assessment
of business outlook and consumer confidence. They are not directly controllable by the
policy-makers. Their multipliers are the factor by which cyclical changes in basic consumption C0
and autonomous investment I0 are magnified into larger fluctuations in the equilibrium national
income. Therefore, the multipliers associated with the above two variables have something to do
with business cycles.
We also have noted that these multipliers are smaller for the case with proportional taxes than for
the cases without proportional taxes (thus with only lump-sum taxes). With the presence of
proportional taxes such as income taxes, the impact of cyclical changes in C0 and I0 on national
income will be smaller than in the case with only lump-sum taxes. Therefore the proportional tax
system is called an ‘Automatic or Built-In Stabilizer’.
When national income increases in a booming stage, the proportional taxes increases too. This will
in turn decrease the disposable income and the aggregate expenditures to a certain extent. And
thus the overall increase in national income will be moderated. When income decreases in
recession, the proportional taxes will also decrease. Thus there will be a boost to disposable
income and consumption. It will offset the initial decrease in Y*. The overall decrease in national
income will be moderated. All in all, business cycles will be smaller with the proportional taxes.
Case 3: There are imports proportional to national income:
Case 3 is built upon Case 2. There are two kinds of taxes. The one is fixed or lump-sum, and the
other is proportional to the income level; T = T0 + t1 Y
T =T0 + t1 Y; and
AE = C + I + G + X – M.
The Aggregate Expenditures will have one additional element such as
NX = X – M;
Net exports = Exports – Imports.
X = X0 …………(1)
Exports are the demand for our domestic products by foreign countries. The exports are given and
thus exogenous from the viewpoint of our economy: The domestic country has no control over the
Macroeconomics
56
Chapter III. Keynesian Cross Diagram
exports. The national income of the foreign countries is the major determinant of our exports to
them.
M = M0 + m1 Y, …………(2)
where M0 is the basic import, and m1 is the Marginal Propensity to Import (MPI).
he import demand for foreign goods is the function of the entire national income, not
just the disposable income portion of it. This contrasts with the consumption function
where the consumption is a function of the disposable income. In the case of imports,
there are two agents of imports: The one is the private sector whose imports are based on
the disposable income. The other is the government whose imports are based on tax
revenues. Thus, the total imports are a function of disposable income plus taxes, the sum
of which is the national income itself.
Solution for Y*:
Step 1. YS = (W + R + I + P) = Y ( = C + S + T)
Step 2. AE = C + I + G + X - M
= C0 + c1 {Y - (T0 + t1 Y)} + I0 + G0 + X0 - (M0 + m1 Y)
= C0 + c1 Y - c1 T0 - c1 t1 Y + I0 + G0 + X0 - M0 - m1 Y
= C0 - c1 T0 + I0 + G0 + X0 - M0 + c1 Y - c1 t1 Y - m1 Y
= C0 - c1 T0 + I0 + G0 + X0 - M0 + (c1 - c1 t1 - m1) Y
= C0 - c1 T0 + I0 + G0 + X0 - M0 + {c1 (1 - t1) - m1} Y
Step 3. At equilibrium, Y = AE and thus
Y* = C0 – c1 T0 + I0 + G0 + X0 - M0 + {c1 (1 - t1) - m1} Y*
{1 - c1 (1- t1) + m1} Y* = C0 - c1 T 0+ I0 + G0 + X0 - M0
*
Y =
=
1
( C0 - c1 T0 + I 0 + G0 + X 0  M 0 )
1 - c1 (1 - t1 ) + m1
1
1 - c1 - c1 t1 + m1
( C0 - c1 T0 + I 0 + G + X 0  M 0 )
Macroeconomics
57
Chapter III. Keynesian Cross Diagram
Step 4. Multipliers – Comparative Static
The multipliers for autonomous expenditures can be obtained by differentiating the above
equation with respect to C0, T0, I0, G0, X0, and M0 respectively.
Remarks:

The multipliers are still smaller in this case than in all the previous cases; the
existence of m1 further reduces the magnitude of the multiplier. The open economy
(with international trade) has a smaller multiplier than the closed economy. The
more open the economy, the smaller the multiplier.

The smaller magnitude of the multipliers are "mixed blessings", being good and
bad.

A small open economy has a larger value for m1 than a large country or a closed
economy.

Show the impact of a $1 increase in government expenditures on the equilibrium
national income and on the import, when (1) c1 = 0.8; t1 = 0.5; m1=0.3, which may
be the case for a small open economy, and when (2) c1 = 0.8; t1 = 0.5; m1=0.1,
which may be the case for a large and less-open country, respectively. Prove
numerically that in a small open economy, compared to a large less-open economy,
an increase in government expenditures has smaller impact on the national income
but a larger impact on the import thus on the trade balance.
We also know that the balanced budget multiplier is the sum of the government
expenditure multiplier and the tax multiplier. Specifically, what will be the
balanced budget multiplier if initially an increase in government expenditures is
financed only by an increase in lump-sum taxes or ∆ T0



1  c1
1  c1
 1 , if m1 ↑ => total value of
↓, if m = 0,
1  c1  c1t1  m1
1  c1  c1t1  m1
=> very large multiplier => larger business cycle.
In this case, BBM ≠ 1; BBM < 1.
Macroeconomics
58
Chapter III. Apendix
Appendix for Chapter III.
1. Numerical Examples:
A question will specify the functional forms for consumption, investment, government
expenditure, and net exports.
What you should do is
Step 1: Write down YS [=(W+R+I+P+D)+IT] = Y
Step 2: Write down AE = C + I + G + X-M
Step 3: Invoke the equilibrium condition,
YS = AE or Y = C + I + G + X-M
Step 4: Substitute the given functional forms for the variables C,I,G, and X-M in the above
equilibrium equation.
Step 5: Solve for Y* by rearranging and rewriting the equation.
(Question 1) In a simple economy without government or foreign sector, the consumption and
investment functions are given as follows. Get the equilibrium national income.
C = 40 + 0.8 Y
I = 60
(Solution)
As there are no government or foreign sector, there is no G, T, or X-M.
Step 1: YS = Y
Step 2:
AE = C + I
Step 3:
At Equilibrium, Y = C + I (Note there is no G or X-M)
Step 4: Substitute C = 40 + 0.8 Y (Note that YD = Y as T = 0), and I = 60 for C and I in the
equilibrium equation, and thus get Y = 40 + 0.8 Y + 60
Step 5: Sending all the terms involving Y to the left hand side of the equality, we get
Y - 0.8 Y = 40 + 60
0.2 Y = 100
Therefore,
Y = 100/0.2 = 500.
Macroeconomics
59
Chapter III. Apendix
(Question 2) Now in a little more complex economy with government and foreign sector, the
consumption, investment, government expenditure, taxation, and net exports function are given as
follows. Get the equilibrium national income.
C = 50 + 0.75 Yd; Yd = Y - T
I = 70
G = 120
T = 100; all taxes are lump-sum.
X-M = 0
Step 1: YS = Y
Step 2:
AE = C + I +G + X-M
Step 3:
At Equilibrium, Y = C + I + G + X-M
Step 4: Substitute C = 50 + 0.75 (Y-T) = 50 + 0.75 (Y-100),
I = 70, G = 120, and X-M = 0 for C, I , G , X-M in the above equation, and get
Y = 50 + 0.75 (Y-100) + 70 + 120
Step 5: Sending all the terms involving Y to the left hand side of the equality, we get
Y - 0.75 Y = 50 - 75 + 70 + 120
0.25 Y = 165
Therefore,
Y = 165/0.25 = 660//.
(Question 3) If taxes are proportional to income and thus T = 0.6 Y instead of T = 100, and all other
things are identical to the above economy, what is the equilibrium national income?
Step 1: YS = Y
Step 2:
AE = C + I +G + X-M
Step 3:
At Equilibrium, Y = C + I + G + X-M
Step 4: Substitute C = 50 + 0.75 (Y-T) = 50 + 0.75 (Y-0.6Y) = 50 + 0.75 (1-0.6) Y, I = 70, G =
120, and X-M = 0 for C, I , G , X-M in the above equation, and get
Y = 50 + 0.75 x 0.4 Y + 70 + 120
Step 5: Sending all the terms involving Y to the left hand side of the equality, we get
Y - 0.75 x 0.4 Y = 50 = 70 + 120
0.7 Y = 240
Therefore,
Y = 240/0.7 = approx. 343//.
(Question 4)
C = C0 + C1 (PDI) = 50 + 2/3 PDI
Macroeconomics
60
Chapter III. Apendix
I = 70
G = 120
T = 100
(1) What is the equilibrium level of national income (Y*)?
(2) What is the consumption at the equilibrium?
(3) What is the Saving at the equilibrium?
(4) What is the APC ?
(Solution)
First, it is important to figure out what to invoke to get the equilibrium, which is not given in the
question.
Step 1. YS = Y = C + S + T
Step 2. AE = C + I + G
= C0 + c1 (Yd) + I + G
= (C0 + c1 Y - T) + I + G
= 50 + 2/3 (Y - 100) + 70 + 120
Step 3. At equilibrium YS = AE, therefore
Y* = 50 + 2/3 (Y*- 100) + 70 + 120 (Y becomes Y* now)
Putting all the terms involving Y on the left-hand side of the equation, we get
Y* - 2/3 Y* = 50 - 2/3 x 100 + 70 + 120.
1/3 Y* = -2/3 x 100 + 240
Y* = $ 520 billion.
C = 50 + 2/3 (Y - T)
= 50 + 2/3 (520 - 100)
= 330.
APC = C/PDI = 330/(520-100) = 33/42
S = Y - T - C = 520 - 100 - 330 = 90.
We can double-check the equilibrium; At equilibrium, S + T = I + G; the left hand side in this case
is 90 + 100 =190, and the right hand side in this case is 70 + 120 = 190. Here the left hand side = the
right hand side. So we can be reassured that this is an equilibrium.
(5) What will happen to Y* when the government simultaneously increases government
expenditure and tax by an equal amount, 60 billion dollars? Now T = 160, and G = 180 billion
dollars.
Macroeconomics
61
Chapter III. Apendix
Solution:
YS = Y
AE= C + I + G
At the equilibrium, Y* = C + I + G;
We substitute the above given functions of C, I, and G for the variables of C, I, and G.
Y* = 50 + 2/3 (Y* - 160) + 70 + 180
Y* = 580 (billion dollars)
Alternatively, we can answer the above question as follows;
this is a case for the balanced budget multiplier where the increase in government expenditure (G)
is accompanied by the equal amount of increase in tax (T), and thus the balance of the government
budget does not change; ΔG= ΔT. The balanced budget multiplier dictates that an increase in G
accompanied by an equal amount of increase in T will add itself, nothing more or nothing less, to
national income. In other words, the balanced budget multiplier is one. So ΔY= 1 x ΔG. With a $1
billion of increase in G accompanied by an $1 billion of increase in T will lead to an $ 1 billion of
increase in Y*. ΔG= $ 60 billion, so Y* will increase by $ 60 billion from $ 520 billion to $ 580
billion.
2. Criticism against Balanced Budget Multiplier (A Monetarists' view of government fiscal
policy)
1) Nonsensical Implication of the Keynesian Balanced Budget multiplier.
When government takes away $100 billion from the private sector in the form of taxation and puts
it back to the economy through its expenditure, there should be an increase in income by $100
billion.
Ow! Thus it seems that you are pulling yourself up by your own bootstraps; you are increasing Y
by 1 at no real cost by simply shifting resources from consumer to government.
In a hidden way, the MPC associated with government expenditure is regarded as 1, while the
MPC associated with consumption expenditure is regarded as less than one. It is related to the way
G is evaluated, i.e. on the cost (expenditure) basis; whenever there is an increase in G, it will be
counted in national income to the full (all of government expenditure is regarded as the production
of final goods).
Macroeconomics
62
Chapter III. Apendix
2) Basic Tenet:
"There is no such a thing as free lunch."
It seems strange that an increase in G should have a multiplier effect on income.
Contention: To the extent that government expenditures are on intermediate goods, the balanced
budget multiplier is less than one.
Indeed, in a special case, the Balanced Budget Multiplier may be zero.
3) Review of Multipliers
(we have already seen the illustration, which is also in the textbook in a great detail)
Remember the illustration of multiplier.
Increase in Autonomous Expenditure/Aggregate Demand
______________________________________________________
Period
Increase in
Increase in
Increase in
Demand
Production
Income
______________________________________________________
1
ΔAE
ΔAE
ΔAE
2
c1 ΔAE =
c1 ΔAE
3
c12 ΔAE
c12 ΔAE
=
c1 ΔAE
c12ΔAE
4
c13 ΔAE
c13 ΔAE
c13 ΔAE
___________________________________________________.
.
.
.
.
.
The cumulative sum of the increases in income is
ΔY = ΔAE+ c1ΔAE+ c12 ΔAE+ c13 ΔAE.........
= ΔAE (1 + c1 + c12 + c13 ...........)
=
1
---- ΔAE
1-c1
= multiplier x ΔAE
Note: If there is no net increase in AE in the first round (ΔAE= 0), there would not be anything
which can bring about the multiplier effect; ΔY= k x 0 = 0.
Macroeconomics
63
Chapter III. Apendix
Balanced Budget Financing Re-examined;
Government increases government expenditure (G) and at the same time increases tax (T) by an
equal amount; ΔG = ΔT > 0.
If there is $ 1 billion of increases in G (Δ G = $ 1 billion), now it is assumed that there is $ 1 billion
of increases in aggregate expenditures in the first round. On the other hand $ 1 billion increase in
tax leads to a decrease in consumption by "c1 (MPC)" fraction of $ 1 billion because $ 1 billion
increase in tax decreases personal disposable income by $ 1 billion, and the resultant consumption
would decrease by c2 x $ 1 billion. In the equation of AE for the first round, in AE + Δ AE = C +
ΔC + I + G + ΔG, ΔG= $ 1 billion, and Δ C = c1 x $1 billion, and thus net change in ΔAE = $ (1 –
c1) billion. This is a net increase in AE, the parallel shift-up (an increase in the intercept) of
aggregate expenditure curve. This parallel shift-up of $(1-c1) billion brings with it the multiplier
effect (by k times ΔAE) as going through the second, third...... rounds. The resulting total
cumulative increase in national income will be ΔY* = ΔAE x k = (1-c1) x 1/(1-c1) = 1.
4) A Correct National Income Accounting Identity without Double Counting
We should note the present inappropriate Definition of National Income;
In the conventional national income accounting system,
AE = C + I + G + X-M;
However, erroneously, we regard all government expenditure as increasing aggregate expenditure
or national income. But parts of government expenditures are on intermediate goods (eg. J. Carr's
example of a shoe factory's road).
But only part of ΔG, the portion of government expenditure on final goods should be included in
the 'correct' national income; In Canada 77% of ΔG are on final goods.
The correct national income account should be
AE = C + I + 0.77 G in Canada.
5) A Correct Balanced Budget Multiplier
When government increases its expenditure and taxation by the equal amount; ΔG= ΔT. Then, on
the one hand, ΔG increases AE on final goods and services by 0.77 ΔG. On the other hand, ΔT
decreases the disposable income by ΔT (ΔYd = -ΔT) and consumption by MPC times the decrease
in the disposable income or -ΔT; ΔAE = -c1 ΔT;
AE = C + I + 0.77 G + X-M, and thus
AE + ΔAE= C - ΔC + I + G + 0.77 (ΔG);


ΔG ΔAE= 0.77 ΔG
Macroeconomics

64
Chapter III. Apendix
ΔT  ΔAE= -ΔC = MPC x – ΔYd = -c1 ΔT......(2)
The net change in AE is (1) + (2);
Net ΔAE= 0.77 ΔG- ΔC = 0.77 ΔG- c1 ΔT.

As ΔT = ΔG with balanced budget fiscal policy,
Net ΔAE= (0.77 – c1) ΔG.
The resultant change in the equilibrium national income is
ΔY= k (multiplier) x ΔAE= (0.77-c1)/(1-c1) ΔG.
The Balanced Budget Multiplier is (0.77-c1)/(1-c1) and smaller than the conventional Balanced
Budget Multiplier which is equal to 1 = (1-c1)/(1-c1).
In a very special case where MPC happens to be 0.77, then the BBM = 0.
Balanced Budget Multiplier works through redistribution of income;
Income is redistributed from people whose MPC <1 to government whose MPC is assumed to be
1.
But real MPC of the government on final goods is not one.
You can have a non-zero balanced budget multiplier where expenditures by government are not a
take over of private services (i.e., not an intermediate goods, eg. military expenditure)
The above case, the only case you can get something for nothing is in the world of rigid prices and
unemployed resources.
If national income were to be Y = C + I + G - T, the balanced budget multiplier would be equal to
zero. Here all taxes would be regarded as taxes on intermediate goods, thus C > C + cY.
3. Criticism against a Naive View of the role of government
It seems strange that an increase in G should have a multiplier effect on income.
Why can't government expenditure simply be consolidated into the rest of the economy?
-i.e. we cannot view government as a giant corporation which produces goods and services and
sells (or gives) them to consumers and is owned by the citizens as shareholders of the country. The
corporation (is assumed to) acts in the interests of its shareholders.
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Chapter III. Apendix
It is true and to some extent it is recognized by people making consumption decisions that
government expenditures of a consumption nature are of value only the extent that they have a
consumption value to individual households and that under full employment the making of either
type of expenditure (C or I) reduces the total real resources currently available to households for
private consumption and addition to wealth.
If these facts were recognized and given exactly accurate weight by households in every relevant
respect, then the government can, without error, be consolidated into the private sector.
From the standpoint of economic analysis there would be no more reason for treating government
as an entity separate from the private sector than there would be for treating a company as an entity
separate from its shareholders, where the stockholders were in full and knowledgeable control of
its own affairs.
The point has generally been overlooked, the government having, habitually, and without
justification, been cast in a separate role in effect as if households placed no value whatsoever on
the goods and services supplied by government.
The truth may be somewhere between these two extremes.
If households do, after all, value government expenditures as income, as they would (meals
supplied without charge at their jobs or other such income in kind) and similarly count in their
consumption the consumption component of government expenditures then the consumption
function will be
C + Gc = C0 + c1 (Y - T + Gc)
= C0 + c1 Y if G = T (balanced budget).
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Chapter III. Apendix
i.e. government expenditure is income in kind. So consumption depends in total income. If people
decide to spend money on recreation collectively (i.e. Gc up - parks built) they will spend less in
recreation privately. You don't have to go up North for vacation if government builds national park
besides you.
Here the changes in (balanced change) Gc have no effect (zero multiplier); balanced budget
multiplier = 0 because the decrease in private consumption in C is equal to the increase in Gc. The
result for consumption happens because an increase in government consumption(expenditure) will
be matched by an equal decrease in private consumption, leaving no net increase in aggregate
expenditure. These are same results which would be obtained if government were consolidated in
private sector.
A zero multiplier for Gc, though it may appear paradoxical, is not because it simply shifts the
composition of total consumption at any given level of income.
We can view the private offset to the consumption supplied by the government as having two
components.
(1) those who are taxed to finance reduce their consumption by c2 of the taxes
(2) those who are recipients reduce private consumption by the fraction 1-c2 of their
consumption (= regular fraction saved out of any income).
(3) the sum of (1) and (2) is one, giving total re-caution in private consumption = increase in Gc.
To the extent that the above is correct, balanced budget multiplier and the effect of G and T on NI
given originally must be modified. We can also extend the above logic to Gc financed by bonds.
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IV. IS-LM Model
Chapter IV. The IS-LM Curve Model
We are starting a new paradigm, IS-LM analysis.
The IS-LM curve model gives the equilibrium level of national income (Y*) in a larger setting. We
have obtained Y* from the Keynesian Cross Diagram. The equilibrium condition of the goods
market will be condensed into a curve of IS. We will introduce the money market; the equilibrium
condition of the money market will give a one-line curve of LM. The IS and LM curves are
delineated with two explicit variables of national income and interest rates.
In the IS-LM Curve Model, the interactions between the goods (output) market and the financial
market gives the equilibrium Y* and the equilibrium interest rate i*.
As this new Y* satisfies the equilibrium condition in the goods market as well as the money market,
it is an equilibrium of a broader scope and a higher order.
We still maintain the assumption about the fixed price level: The price level P is assumed to be
fixed in the IS-LM model unless it is specified otherwise. This could be reasonable assumption
when the actual equilibrium national income Y* is below the full employment national income
level Yf. If there is such a buffer, an increase in demand would not push up the price level in any
significant way.
1. Introduction
First, we will establish an inverse relationship between interest rates and investment in the goods
market. This eventually leads us to the IS curve or the various combinations of i and Y, which
satisfy the equilibrium condition in the goods market or make the demand equal to the supply in
the goods market.
Second, we will establish an inverse relationship between interest rates and (real) money demand
in the money market. This leads us to the LM curve or the various combinations of i and Y, which
satisfy the money market equilibrium or make the demand equal to the supply in the money
market.
Third, we will solve for the national income Y* and the interest rates i*, which satisfy the goods
and money market equilibrium conditions at the same time. Basically, they are obtained from the
intersection of the IS and LM curves.
Fourth, we will examine the Crowding-Out effect. An increase in aggregate expenditures will in
general be accompanied by an increase in interest rates in the money market. This in turn will have
a negative spill-over or feedback to the goods market as an increase in interest rates shaves off
investment to an extent. Particularly when ∆G causes an increase in i and a decrease in I, it is
called ‘Crowding-Out Effect’ of government expenditures
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IV. IS-LM Model
2. Modification of Investment Function
So far the investment function has been regarded as exogenous: It is determined or given from the
outside.
Now let us endogenize the investment by making it a mathematical function of interest rates. The
following re-specification of the investment function leads to a new paradigm.
How can I establish the inverse relationship between investment I and interest rates i?
1) Marginal Efficiency of Capital Method
Investment is the demand for resources to be used for specific physical additions to the capital
stock. An increase in capital stock or investment is expected to yield ‘a stream of net income’ over
time. We can find the rate of return, which equates the present price tag of investment project on
the left side of the equality and the stream of the expected returns. This rate of return is called
‘Marginal Efficiency of Capital’. As we start investing in the most lucrative project and move
onto less profitable projects, the Marginal Efficiency of Capital declines as the amount of capital
input increases.
The cost of the fund is the cost associated with the borrowing the fund. This is the ‘Marginal Cost
of Fund’. It is generally equal to the interest rate paid on the interest bearing security, such as
government bonds. In other words, the marginal cost of fund is fixed, and thus can be delineated by
a horizontal line in the graph.
The entrepreneurs then weigh the benefit and the cost associated with the potential investment
project. They will invest up to the point where the benefit is equal to the cost at the marginal level.
Marginal Cost of Fund = Interest Rate
When the interest rate goes up, the amount of capital input or investment declines. Simply, think
of the project which is exactly making both ends, revenues and costs, meet in right now. If the
interest rate and borrowing costs go up, the project has loss and will be knocked off. The
investment volume decreases by the amount of investment.
2) Intuitively Speaking
How does a high real interest rate dampen economic activities? Actually it works in two ways; first
it reduces the investment, and thus the AE, eventually reducing Y*. It also reduces the real money
demand. At this moment ignore the second impact.
The (real) interest rate constitutes a cost of obtaining (financial) capital for additions to capital
stock or investment. A higher interest rate means a higher cost, a lower profitability and the lower
rate of return on investment projects.
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IV. IS-LM Model
Some investment projects which used to be marginally profitable or managed to make both ends
meet are no longer profitable. So the desired investment will decrease as the interest rate
increases.
3) Functional Form of Investment
I = I0 – b i,
I0 is the autonomous investment and b is the elasticity of investment with respect to interest rates. b
> 0. Here b measures the responsiveness to changes in investment to changes in the interest rate.
The larger the value of b, the more responsive the investment with respect to changes in interest
rates. In other word, the larger the value of b, the more interest-rate elastic the investment will be.
A numerical example would be I = 100 – 5i: One percentage increase in interest rates will bring
about a 5% decrease in investment.
(w.r.t. = with respect to)
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IV. IS-LM Model
3. IS Curve: Goods Market Equilibrium
The IS curve shows various combinations of national income and interest rates which bring out the
equilibrium, or the equality between demand and supply, in the goods market.
Let’s plug the aforementioned modified investment function into the aggregate expenditure
function, and solve for Y* and i*.
1) Algebraic Derivation
Recall there are three different cases of AE.
Case 1. All taxes are lump-sum or autonomous. T = T0.
(Assume NX = X- M = 0 for simplicity for now)
Suppose that we are dealing with the aggregate expenditures with only lump-sum taxes and no
exports or imports (This is Case 1 in the last chapter of the Keynesian Cross Diagram).
The AE will be
AE = C0 + c1 (Y – T0) + I0 – bi + G0
= c1 Y + (C0 - c1 T0 + I0 + G0 – bi0 )
At equilibrium,
YS = AE
Y = c1 Y + (C0 – c1 T0 + I0 + G0 – bi)
Y – c1 Y = C0 – c1 T0 + I0 + G0 – bi
Solve for Y* and i*: We can rewrite this equation as a functional relationship between Y* and the
interest rate i.
Y*=
i=
1
( C 0 - c1 T 0 + I 0 - b i + G0 )
1 - c1
1
1( C 0 - c1 T 0 + I 0 + G0 ) - c1 Y
b
b
This is the algebraic expression of the relation between (i, Y) which represents equilibrium in the
final goods market.
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IV. IS-LM Model

Note that the slope has a negative sign and thus the IS curve is downward sloping. This
means that in equilibrium, of the goods market, the interest rate and income move in the
opposite direction; if interest rate increases for some reason, in order to stay at the same
equilibrium in the goods market, national income should decrease.

Also, we can draw the IS curve by putting i on the vertical axis and Y on the horizontal
axis.
2) Intuitive Explanation of the IS curve.
We can also give the following intuitive explanation about the negative slope of the IS curve;
Let us start from one equilibrium: Y = YS = AE = C + I + G. Here let us change the interest rate
and examine the responsive changes in Y. If i and Y turn out to be moving in the same direction,
the slope of the IS curve will be positive, and vice versa.
Let us suppose that the interest rate decreases from i0 to i1. If investment is inversely related to the
interest rate, there will be an increase in investment and thus an increase in the AE. This means
that there will be an excess aggregate demand (now Y < AE’). How can we re-establish the
equality between AE and Y? The answer is by increasing Y. In the equality of AE and YS, or the
equilibrium of the goods market, when interest rates goes down and national income goes up. The
interest rate and national income should move in the opposite direction.
We can express the above relationship with a curve in a graph with Y* on the horizontal axis, and
the interest rate i* on the vertical axis. This curve is called the IS curve because, at equilibrium, AE
= Y, which means C + I + G + X – M = C + S + T. As C in both side cancels out, the equilibrium
condition of the goods market can be expressed as I + G +X = S + T + M. The first letter of each
side of the equality read ‘I’ and ‘S’. So along the IS curve, I + G + X = S + T + M. So that is how
the name, ‘IS curve’, came about.
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IV. IS-LM Model
3) Graphic Derivation of the IS curve.
Start with the Keynesian Cross- Diagram with which you are very familiar. Redefine the
Investment function in the AE curve as being inversely related to the interest rate




Suppose that the initial interest rate is i0, it gives a certain investment level in AE, which in
turn gives Y*. (see the initial equilibrium point at A in the graphs below)
Now change the interest rate up to i1. See the corresponding new Y*’  AE decreases: 
the new equilibrium point at B;
Also, change the interest rate down to i2, See the corresponding new Y*’’.  AE increases,
 the new equilibrium at C.
These combinations of i and Y* will give an IS curve.
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IV. IS-LM Model
4) Comparative Statics of the IS Curve
What can cause a change in the IS curve?
(1) The slope of the IS curve
In summary, the following factors determine the slope of the IS curve:
i)
ii)
iii)
The larger the marginal propensity to consume (c1), the flatter the IS curve.
The larger the elasticity of investment demand with respect to interest rate (b),
the flatter the IS.
The lower the income tax rate (t1), the flatter the IS.
Let us examine the second point: The more elastic the investment demand with respect to interest
rate, the flatter the IS curve. The more sensitive the investment demand is towards the interest rate,
the flatter the IS curve will be. Here the magnitude of b, or the elasticity of investment with respect
to the interest rate, determines the slope of the IS curve.
Numerical Examples: Suppose that we have the following two different investment functions,
which have different elasticity of investment with respect to the interest rate.
Case 1: Interest-rate Inelastic Investment
eg) I = I0 – 0.5 i
Here, the investment demand is inelastic with respect to interest rate: A 1% increase in the
interest rate i will bring about a 0.5% decrease in the investment demand (Δ I0). Therefore, for a
given increase in the interest rate, there occurs a relatively small decrease in AE = C + I + G ,
which will bring about a magnified but still small decrease in Y through a multiplier effect in the
cross diagram.
Case 2: Interest-rate elastic Investment
eg) I = I0 – 10.0i
A 1% increase in interest rate will bring about a 10% decrease in investment (Δ I 0). Therefore
there occurs a relatively large decrease in AE = C + I + G (Δ AE), which will bring about a
correspondingly large decrease in Y through a multiplier (Δ Y) in the cross diagram.
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IV. IS-LM Model
Ys = Y
Y*
Y*
1
0
Ys = Y
Y*
1
Y*
0
We can see that the first example of IS curve is much steeper than the second example of the IS
curve.
2) Changes in the intercept of IS curve.
Changes in the intercept of the IS curve will bring about Parallel Shifts of the IS curve. Changes in
C0, I0, T0, G0 which constitute the intercept of the IS curve, will lead to the parallel shift of the IS
curve.
i) Δ G0, Δ C0, and Δ I0 shift the IS curve to the right by the actor of their (simple) multiplier 1/(1-c1)
(times the changes in those variables).
For instance, Δ G0 will bring about a horizontal shift of the IS curve. The distance of the horizontal
shift is given by Δ G0 times 1/(1-c1).
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IV. IS-LM Model
ii) Δ T0 will shift the IS Cure to the left by the amount of its multiplier c1/(1-c1) times Δ T0.
4. LM Curve and Money Market Equilibrium
LM curve shows the combinations of the interest rate and the income (i, Y) which satisfies
the equilibrium in the money market.
1) ‘Nominal’ versus ‘Real’ Money Supply/Demand
We should make distinction between Nominal Supply or Demand and Real Supply or Demand.
The first one is in monetary terms, and the second in quantity terms.
In microeconomic analysis of equilibrium, we define the demand and supply in real terms, not in
monetary or nominal terms. For instance, if we say that $20,000 worth of hamburgers are
demanded (or supplied), the statement is not clear enough. This $20,000 is nominal demand in
monetary terms. What about the real demand or quantity? If the price is $1 per hamburger, in real
terms, 20,000 units of hamburgers are demanded. If the price is $10, in real terms 2,000
hamburgers are demanded.
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IV. IS-LM Model
In the same vein, for the analysis of the money market equilibrium, the quantity of money should
be also defined in real terms, not in nominal or monetary terms. The nominal quantity of money is
the face value of the money, and the real quantity of money is the face value divide by the price
level;
Real quantity of money = Nominal quantity of money/Price level.
m = M/ P
The real quantity of money supply m is the nominal money supply divided by the price level. For
instance, nominal money supply is $2,000,000,00 dollars or $ 2 billion. The price level is
measured by a price index. Suppose that the price index is 100 (or 1.00) right now. The real money
supply m = 20,000,000,000/100 or 20/1.0 (units do not matter as long as there is a consistency).
2) Money Supply
The nominal quantity of the money supply is determined by the monetary authority, which usually
is the central bank.
MS = M
Money supply varies depending on the scopes of money: it may include only cashes (in circulation)
in a narrow scope, and may include cashes and all deposits in a broad scope such as M2. The
different scopes of money supply will be discussed in full in the separate chapter.
For instance, M = $20,000,000,000 or $20 billion.
The monetary authority does not have to determine the nominal money supply on the basis of any
variables in any given manner over time. Thus, we regard the nominal money supply as an
exogenous variable, and regard it as arbitrarily determined by the monetary authority.
Mathematically, this means that the nominal money supply curve is vertical, being independent of
interest rates. As the money supply is independent of the interest rate, when drawn in the interest
rate and real quantity dimension, the money supply curve is vertical, being the same regardless of
the level of the interest rate.
𝑖
𝑚𝑠 =
𝑀
𝑃
𝑖1
𝑖0
𝑚𝑠
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IV. IS-LM Model
At one point of time it is fixed. However, of course, over time it can be changed by the monetary
authority. In fact, the monetary authority sets the nominal money supply in each period.
For instance, depending on circumstances, the monetary authority may increase or
decrease the nominal money supply when there is an increase in the national income. If the
monetary authority wants to accommodate the booming or growing economy, it would
increase the nominal money supply in the face of a rising national income. The logic is that
a larger economy has a larger volume of economic transactions and needs a larger amount
of medium of exchanges, i.e., money. On the other hand, if the monetary authority judges
that the rising national income may touch off inflation and thus decides to fight the
inflation, it will decrease the money supply in the face of a rising national income. This is
called ‘ leaning-against-wind’ monetary policy. All in all, the monetary authority can
choose any of these policies. Mathematically, this means that there is no consistent
functional relationship between the national income and the nominal money supply. In
fact, nominal money supply has no consistent relationship with any economic variables.
2) Real Money Demand
(1) Uniqueness of Real Money Demand
A few important things to remember about real money demand:
First, note that the money market equilibrium should be defined in terms of real money supply and
demand;
Nominal money supply is equal to nominal money demand at all times, i.e., at and out of
equilibrium. The nominal quantity of money demanded by the society as a whole is always equal
to the nominal quantity of money supplied by the government; MS = MD at all times. Suppose the
government is handing out newly printed paper monies or notes on the street. IS there anyone who
would refuse them? Every dollar of money supply will be gladly demanded.
Second, while an individual can control real money demand, the general public as opposed to the
monetary authority cannot control real money demand;
When an individual receives some new paper monies, her/his nominal (and real) balances increase.
S/he may succeed in decreasing the nominal money demanded or the real money balanced back to
the initial level by spending the excess money holdings. However, because her/his expenditures
will become someone else’s receipts, some other members are getting the increased money supply.
So from an individual’s view point the nominal money demanded may be controllable, while it is
not controllable from the entire society’s viewpoint. What is true for individuals is not necessarily
true for the society as a whole. This is the ‘fallacy of composition’ commonly founded in
macroeconomics.
As individuals are busy getting rid of the excess of money holding over the desired level of
demand (“I would like to have $200 in my pocket, but as government gives me a new $100 bill,
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IV. IS-LM Model
now I have the excess of money holding by $100. I would like to go back to the desired level of
money demanded, that is $200 by spending $100 away.”) The increased money becomes a kind of
‘hot potato’. What does this mean in terms of the real money demand? The real money demand,
which is the nominal money demand (= the nominal money supply) divided by the price level, is
going back to the initial level. The increased speed o spending and expenditure will eventually
push up the price level. The general public are collectively changing the price level and thus
controlling the real money demand.
Suppose MS = M = MD = $200 billion and P = 1.00 initially in the equilibrium; the real money
demand is MD/P = 200/1 = 200 and should be equal to the real money supply at the equilibrium.
This real money demand is at the desired level at the equilibrium in light of all the determinants of
the demand including the income level and the interest rate.
Now the monetary authority increases the nominal money supply MS to $400 billion.
First, all the increased nominal money supply will be demanded. So the nominal money demanded
is equal to the new nominal money supply; MD’ = MS’ = M’ = $400 billion.
In the short-run, the price does not change, and thus the actual amount of the real money holding
will be m’ = m’’ = M’/P = $400/1.00 = 400. This is much larger than the desired real money
demand, that is, 200. As there are no changes in the determinants of the real money demand, there
should not be any change in the level of real money balances the general public wishes to hold.
There is an excess of real cash balances over the desired real money demand; ‘actual’ real money
balances > ‘desired’ real money balances.
As individuals with excessive money balances try to recover the desired real money balances by
spending the excess money receipt, the price level is going up to P’. At this new price level, the
new ‘actual’ real money balances (M’/P’) become equal to the desired level of real money
balances.
Specifically, the price level will go up to the level of 2 (or the index number 200). The actual real
money demand will be 400/2 = 200, the same level as before any changes.
(2) Functional Form of Real Money Demand
The real money demand is given a functional form such as
md = L ( i, Y ).
The above equation defines the real money demand as a decreasing function of interest rates and
an increasing function of national income. What determines the desired level (quantity) of real
money demand? Just as the desired quantity of hamburgers is determined by the consumers’
income and the price of hamburger, the real demand for money is determined by the income level
of the economy, that is the national income, and the price of the money, that is, the interest rate.
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IV. IS-LM Model
Let us examine the second point in the above statement: the price of money is the interest rate. In
other words, the opportunity cost of holding money balances is the interest rate.
Money is one of many assets, which include bonds, stock, equities and real assets. Money and
other assets are substitutes. The major difference between money and other assets is that money
does not bring in any positive pecuniary returns. Actually it is very often subject to the erosion of
real value due to inflation, and other assets do have pecuniary returns. However money, or cash
balances in a precise term, renders a unique non-pecuniary service, which is known as ‘liquidity’.
Money is the most generally accepted medium of exchange and most ‘liquid’. So when you decide
to hold assets in the form of cash balances instead of any other, you are showing your preference
for liquidity over pecuniary returns. This is the reason why the money demand is called’ liquidity
preference and the money demand function ‘liquidity preference function.’
(Digression: Diversity of various interest rates) The pecuniary returns of other assets are, in fact,
no uniform because the risks associated with other assets differ: risky assets have higher rates of
returns an safe assets have a lower rate of return. The difference in the rate of returns is
compensation for entering the risk, in buying risky assets. However, for simplicity, let us simply
suppose that the rate of return on other assets than money can be represented by a certain
representative ‘interest rate’.
The interest rate represents the foregone pecuniary return or the economic sacrifice you have to
take when you are choosing cash balances over other assets, as your mode of holding assets; in
other words, the interest rate is the opportunity cost of holding cash balances. When the interest
rate goes up, the cost of holding cash balances increases and naturally you would like to hold less
assets in the form of cash balances and more interest bearing assets. This means that the demand
for money is inversely related to the interest rate.
Now we have another major factor to be considered, which affect the real money demand; the
income level. When real income increases, in most cases, the demand for money increases in real
terms, too. To name one reason, when real income increases, there occur more transactions, and
then more cash balances should be held to back up the increased transactions.
We can give the liquidity preference function the following specific functional form;
Md = kY – h i + u,
where K is the elasticity of real money demand with respect to the national income; h is the
elasticity of real money demand with respect to interest rates; and u is the random component of
real money demand.
The liquidity preference curve is negatively sloped when drawn with the interest rate on the
vertical axis and the amount of real money on the horizontal axis. The variables Y and u are the
shift parameters of the real money demand curve.
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IV. IS-LM Model
i1
i0
L(Y, u)
md
(Note: Y and u are shifting parameters)
Also, we can draw a set of liquid preference curves for different levels of income; the higher the
level of national income, the larger the demand for real money balances. You may remember,
from the class of introductory economics, that an increase in income shifts the demand curve to the
right.
3) Money Market Equilibrium and LM Curve
As emphasized, the money market equilibrium should be defined in real terms; the money market
is in equilibrium when real money supply is equal to real money demand ex-ante. If the demand is
larger than the supply, the price will go up. With an increased price some people will give up their
demand. The price, which adjusts to equate the supply and demand, is nothing but the interest rate.
The money market interest is set at such a level as to make the supply equal to demand ex-ante.
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IV. IS-LM Model
(1) Algebraic Solution
LM Curve: Money market equilibrium condition ms = md yields the following equations.
Rearranging the equation with ‘i’ on the left hand side and ‘Y’ on the right hand side, we get a LM
s
Curve. Real money supply = M , m d = L(i,Y,u) = kY – hi + u
P
M
= kY - h i + u
P0
h i= -
M
+k Y +u
P0
1
M
k
i = (+ u )+ Y
h
h
P0
↓
↓
intercept
slope
We can draw a LM curve with the interest rate on the vertical axis and the national income on the
horizontal axis. The LM curve is upward-sloping, or in other words, it as a positive slope. (Along
LM m s  m d )
(2) Intuitive Explanation
Why is the LM curve upward-sloping LM?

Let us start with an equilibrium, ms = md.
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
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IV. IS-LM Model
When the interest rate increases there will be a decrease in the real quantity of money
demanded, (a new md < an old md = ms).
How can we recover the equality between the real money demand and the real money
supply? The real money supply cannot change unless the government changes the nominal
money supply MS or M to a higher level, or the price level changes. So the real money
demand should rebound back to the initial level in order to re-establish the equality. One
way of doing it is to increase Y*. When the national income increases, the real money
demand will increase. This increase in real money demand offsets the previous decrease in
real money demand. So we can observe that the interest rate and the national income move
in the same direction.
(3) Graphic Derivation of LM curve:
The real money demand and supply mainly carve up the relationship between the interest rate and
the real money balances. However, we are interested in getting the LM curve which carves up the
relationship between Y and i*.
To get the relationship between the two, we have to change the value of Y and look at the
responsive change in i* or the money market equilibrium interest rate;
When Y increases from Y1 to Y2 the real money demand curve shifts to the right. Here the Y
variable is a shift parameter I the real money demand function.
When the real money supply remains unchanged, the increased real money demand will push up
the equilibrium price of the money in the market, that is, the equilibrium interest rate I the money
market. Previously Y1 corresponded to i1, and now a higher Y2 to i2.
i
ms 
M
P
i
LM (
M
, u)
P
i2
i1
md (Y2 , u)
i
m d (Y1 , u )
ms / md
Y
Y
Y2
So a higher level of income means a higher level of interest rate. Y and i are moving in the same
direction. The LM curve should be upward sloping.
Y1
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IV. IS-LM Model
4) Comparative Statics of LM curve
(1) Change in the Slope of LM curve.
i) Elasticity of real money demand with respect to Income, or income elasticity of real money
demand (K):
The larger the income elasticity of real demand, the steeper the LM curve.
For instance, when Δ Y = 1% for the following two cases:
Case I with K = 1: md = Y – 20 i+ u
i
ms 
M
P
i
LM (
M
, u)
P
i2
i
md (Y2 , u)
i1
m d (Y1 , u )
Y
ms / md
Y1
Y2
Y
Case II with K = 0.5: md = 0.5 Y – 20 i + u
i
ms 
M
P
i
LM (
M
, u)
P
i2
i1
md (Y2 , u)
Y
m d (Y1 , u )
ms / md
Y1
Y2
Y
ii) Elasticity of real money demand with respect to Interest rate, or Interest rate elasticity of real
money demand (h): the elasticity of real money demand with respect to the interest rate, or in
short interest elasticity of money demanded.
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84
IV. IS-LM Model
In general, the larger the value of h, or the more (interest rate) elastic the real money demand, the
flatter the real money demand.
In the following two cases, assuming that K = 0.5 and u = 20 for both in the money demand
function md = K Y – h i + u,
Case 1 with h=0.5; Inelastic money demand, md = 0.5 Y – 0.5i = 200
ms 
i
M
P
i
LM (
M
, u)
P
i2
md (Y2 , u)
i1
i
m d (Y1 , u )
Y
ms / md
Y1
Y
Y2
Case II with h =20; Elastic money demand, md = 0.5 Y – 20 i +200
ms 
i
M
P
i
LM (
M
, u)
P
i2
i1
md (Y2 , u)
m d (Y1 , u )
Y
ms / md
Y
Y2
In the above graphs, we can see that with a flat m curve with a large interest-rate elasticity, a very
small drop in the interest rate will bring about a very large increase in md. We may also review
some extreme cases.
Y1
d

When the real money demand is perfectly inelastic with respect to interest rate (the interest
elasticity h = 0)
M
 KY  hi  KY
P
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85
IV. IS-LM Model
This is the case where interest rates do not enter the real money demand or liquidity preference
function. In other words, real money demand is not responsive to the change in interest rate all;
real money demand is completely inelastic with respect to the interest rate; real money or liquidity
preference function is drawn as a vertical line, and the derived LM curve is also vertical.
m d  kY
i
LM
ms
i
ms / md
Y
Under what conditions will the elasticity of real money demand with respect to its own price, that
is, the interest rate become equal to zero?
The magnitude of the (own price) elasticity is determined by the availability of alternatives or
substitutes. If people regard non-money assets, such as bonds, equities, and so on, as completely
useless as substitutes for money, the (own price) elasticity of real money demand should be equal
to zero. As there are no substitutes for money, regardless of the cost of holding money (whether it
is high or low), there would be a certain amount of real money balances that they think they must
absolutely hold.
At the equilibrium in the money market, where real money supply is equal to real money demand
as:
Ms
 KY
P
Thus Y 
Ms
KP
In this case, there is a strict proportionality between the National Income (Y) and the Real Money
Supply (ms). Only money supply determines the equilibrium national income. The goods market
is completely irrelevant in the determination of the equilibrium national income.

When the real money demand is perfectly elastic with respect to the interest rate (h is
infinitely large): the Keynesian ‘Liquidity Trap’.
When a small change interest rate leads to a very large change in real money demand; real money
demand is extremely responsive to a change in interest rate; real money demand is infinitely
interest rate elastic. Graphically, the real money curve is horizontal. With a horizontal money
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86
IV. IS-LM Model
demand curve, changes in money supply would not affect the interest rate at all. The interest rate
will be stuck at the same level. The derived LM curve is also horizontal at that level of interest
rate.


i
i
ms ms m s
For these different money market
equilibrium a, b and c, the money market
equilibrium interest rate is the same, and
is fixed.
a


b
c
md
i
LM
ms / md
Y
Here monetary policy is ineffective, as any increased money supply will be gobbled up as
soon as it is injected into the economy. The public has a hefty appetite for liquidity, or
money, and thus, it will swallow it up even with little incentive to do so, that is, a very
small drop of interest rate. Therefore, the increased money supply would not have had
much of a change to exert any downward pressures on interest rates. This situation is
called a ‘liquidity trap’. It could have been named ‘liquidity blackhole’ if Keynes had been
well versed in astronomy.
Interest Pegging Monetary Policy: When the monetary policy which involves changes in
money supply is completely ineffective, the LM curve is horizontal. However, the reverse
is not necessarily true. The horizontal LM curve does not necessarily mean that monetary
policy is ineffective. Even if the real money demand curve is downward sloping in a
normal way, when the monetary authority or the central bank is dedicated to maintaining a
fixed interest rate at all cost, the LM curve will be horizontal.
Let us illustrate this point. There are a set of money demand curves which correspond to different
levels of income. This gives the LM curve, linking different levels of Y and i. Let’s suppose that
now changes in some factors other than Y and i cause a decrease in money demand: the money
demanded decreases at a given level of interest rate and income, and thus real money demand
curves with different level of national income shift all down or to the left at the same time.
In this situation, if the government is not doing anything, thus the money supply is fixed, obviously
this decrease in real money demand will bring about the decrease in the
money-market-equilibrium interest rate at all level of income: ms = md. Initially, and md i – md’ <
m’ – i'. Therefore the LM curve shifts to the right. This will be an ordinary case.
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87
m
i
IV. IS-LM Model
s
i
LM (
M
, u)
P
LM (
M
, u )
P
m d (Y2 , u )
m d (Y2 , u)
m d (Y1 , u )
md (Y1,u)
ms / md
Y1
Y2
Y
However, if the central bank stands ready to offset any change in the interest rate, as is assumed in
this question, it should decrease the money supply. If the money supply is changed exactly by the
same amount as the changes in the money demand, there will be no change in the money-market
equilibrium interest rate. The interest rate will be always constant at a fixed level. This implies
that the LM curve is horizontal at that level of interest rate.
We can also think of the reverse case. The interest rate will be still kept at the target level. In this
monetary policy regime, monetary policy is effective in pegging the interest rate. Here the policy
target is the fixed interest rate, and the monetary authority changes money supply in response to
the uncontrollable changes in real money demand.
ms
m
s

ms

i
i
LM (
i
M
, u)
P
md (Y2 , u)
md (Y2 , u)
md (Y1 , u)
ms / md
Y
(2) Shift of the LM curve.
i) Change in nominal Money Supply; Δ MS
The LM curve shifts to the right when the monetary authority increases the nominal money supply:
An increase in nominal money supply leads to the increase in real money supply when the price
level is fixed.
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i
ms
88
ms
IV. IS-LM Model

LM (
i
M
, u)
P
LM (

M
, u)
P
md (Y2 , u)
m d (Y1 , u )
ms / md
Y1
Y
Y2
ii)Change in Real Money Demand unrelated to any changes in the interest rate or the income level:
∆u
The LM curve shifts to the right when the real money demand decreases at the given interest rate
and income level.
Under what circumstances could this happen? Think about the case where people lose their
confidence in currency due to the imminent currency reform. The domestic residents will decrease
the demand for money and seek safe haven for their wealth elsewhere. Also, in an open economy
situation, the demand for domestic currency could decrease as the foreigners wish to convert the
domestic currency that they are holding into foreign currencies.
Suppose that due to a decrease in the residual term of the money demand function, an initial money
demand md = K Y – h i + u (eg: md = 0.5 Y – 20 i +200, and here u = 200) is reduced to md’ = K Y
– h i + u’ (eg: md = 0.5 Y – 20 i +100, and here u’ = 100). The entire set of money demand curves
for different levels of income should decrease.
Note: md (Y2, u) and md’(Y2, u’) have the same Y2; and md (Y1) and md’ (Y1) have the same Y1.
Initially, Y1 corresponds to i1, and Y2 to i2. With a decrease in real money demand and consequent
shift of the demand curves, Y1 corresponds to i1,and Y2 to i2. When md decreases as u decreases to
u’, the LM curve shifts to the right.
i
ms 
M
P
i
LM (
M
, u)
P
LM (
m d (Y2 , u )
m d (Y2 , u )
m d (Y1 , u )
md (Y1, u)
ms / md
Y1
Y2
Y
M
, u )
P
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89
IV. IS-LM Model
5. Equilibrium National Income and Interest Rate in the IS-LM Framework
The intersection of the IS and LM Curves give the equilibrium national income and the interest
rate that satisfy the market clearing condition in both goods markets and money markets; ex-ante
all the goods produced are demanded, and real money supply is equal to the real money demand.
1) Graphic Solution
2) Algebraic Solution
Steps
1.
2.
3.
4.
Get the IS and LM curve
Equate the IS and LM curve
Solve for Y*
Substitute the solution of the Y* for the variable Y and the LM
equation to get the value for i*;
5. Differentiate the above equations for multipliers.
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90
IV. IS-LM Model
Case 1. All taxes are lump-sum or autonomous. T = T0.
(Assume NX= 0 for simplicity)
 Recall the IS Curve: Goods market equilibrium condition AE = Y yields
1
Y=
( C0 - c1 T 0 + I 0 - b i + G0 )
1 - c1
1
1i = ( C0 - c1 T 0 + I 0 + G0 ) - c1 Y
b
b
1  c1
) = slope of IS Curve}
b
Recall the LM Curve: Money market equilibrium condition ms = md yields
{Note: (
M
= ky - h i + u
P0
h i= -
M
+k Y +u
P0
1
M
k
i = (+ u )+ Y
h
h
P0
(Note:
k
k
= slope of LM curve, h↑ ↓, thus, LM gets flatter)
h
h
where K is the elasticity of real money demand with respect to the national income; h is the
elasticity of real money demand with respect to interest rates; and u is the random component of
real money demand.

Equate the above two equations for i or Y: The Simultaneous Equilibrium of Goods and
Money Markets yields
*
Y =
h
b
M
( C 0 - c1 T 0 + I 0 + G 0 ) +
(
- u)
h(1 - c1 ) + kb
(1 - c1 ) + kb P0
Rewriting the above we get,
*
Y =
1
kb
1 - c1 +
h
( C 0 - c1 T 0 + I 0 + G 0 ) +
b
h
(
M
kb P0
1 - c1 +
h
- u)
Macroeconomics
91
IV. IS-LM Model
Multipliers:
i)Impacts on Y*
We may remember that in the simple Keynesian model of income determination (the
Cross-Diagram with Y = YS and AE) the multipliers were obtained by differentiating the
equilibrium national income equation.
Now, in the IS-LM curve model, another set of the multipliers can be obtained by differentiating
the first equation, which describes the equilibrium national income in the goods and money
market, with respect to the Autonomous components of AE ( C, T, I, G and M). The result of
differentiation is the coefficient of each variable in the above equation.
Y
=
C0
*
Y
=
I 0
*
1
1 - c1 +
kb
h
1
kb
h
(Note: the above two are business cycles)
1 - c1 +
Y
=
G0
*
1
1 - c1 +
kb
h
Y *
(Note:
= “Fiscal Policy Multiplier”)
G 0

The first two multipliers have something to do with business cycles as the C0 and I0 show
cyclical movements over time beyond the control by government.

The third one is called the ‘Fiscal Policy Multiplier’. It measures the ratio of the change in
the goods and money market equilibrium national income to a change in government
expenditure. Note that this new multiplier or the fiscal policy multiplier in the IS-LM
framework is smaller than the government expenditure multiplier in the Cross-Diagram
setting. Both measure ∆Y* due to ∆G. However, the fiscal policy multiplier takes account
of the resultant change in interest rate and the consequent crowding out effect while the
government expenditure multiplier does not; the difference between the government
expenditure multiplier and the fiscal policy multiplier is the crowding-out effect which
results from an increase in interest rates and its suppression of private investment. Because
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92
IV. IS-LM Model
of the secondary feedback in the money market, the magnitude of fiscal policy multiplier is
smaller and thus ∆G has a smaller impact on Y*.
i
LM
e
1
*
1
Crow ding out eff ect
i
i0
e0
*
IS 
IS
Y 0*

Y1*
The following multiplier measures the change in income to a change in a lump-sum tax
responsible for it.
Y
=
T0
*

Y 2*
 c1
1 - c1 +
kb
h
The following multiplier is called the ‘Monetary Policy Multiplier’. It measures the ratio
of the increase in income to an increase in money supply.
b
h
Y *

M
kb

1 - c1 +
p
h
“Monetary Policy Multiplier”
ii) Impacts on Interest Rates:
Remarks:
 Note that compared with the equilibrium national income equation without the LM curve
(in the previous handout), there is an additional term kb/h in the multiplier for the
autonomous expenditures.

A $1 increase in G shifts the IS curve by $1/(1 - c1), and y* by $1/(1-c1 +kb/h). What makes
the difference?
Now, let’s extend our model to more complex cases of aggregate expenditures as we have seen
before.
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93
IV. IS-LM Model
Case 2. There are Autonomous and Proportional Taxes. T = T0 + t1Y,
 IS Curve: Goods market equilibrium condition AE = Y yields
1
( C 0 - c1 T 0 + I 0 - b i + G 0 )
Y =
1 - c1 (1 - t 1 )
i=

1
1 - c1 (1 - t 1 )
( C 0 - c1 T 0 + I 0 + G0 ) Y
b
c1 (1 - t 1 )
LM Curve: Money market equilibrium condition ms = md yields
M
= ky - h i + u
P0
h i= -
M
+k y+u
P0
1 M
k
i = (+ u )+ y
h P0
h
 Simultaneous Equilibrium of Goods and Money Markets
*
Y =
h
b
M
( C 0 - c1 T 0 + I 0 + G0 ) +
(
- u)
h(1 - c1(1 - t 1 )) + kb
(1 - c1(1 - t 1 )) + kb P0
Rewriting the above we get,
*
Y =

1
kb
1 - c1(1 - t 1 ) +
h
( C 0 - c1 T 0 + I 0 + G0 ) +
b
h
(
M
kb P0
1 - c1(1 - t 1 ) +
h
- u)
Note: compared with the equilibrium national income equation without the LM curve
(in the previous handout), there is an additional term kb/h in the multiplier for the
autonomous expenditures.
Case 3. There are proportional taxes, and Imports are proportional to national income.
NX = X - M;
M = M0 + m1 Y;
X = X0,
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94
IV. IS-LM Model
where M0 denotes the Autonomous imports and m1 denotes the Marginal Propensity to Import.
IS Curve: Goods market equilibrium condition AE = Y yields
1
( C0 - c1 T 0 + I 0 - b i + G0 + X 0 - M 0 )
Y =
1 - c1 (1 - t 1 ) + m1

i=

1
c1 (1 - t 1 ) + m1
( C0 - c1 T 0 + I 0 + G0 + X 0 - M 0 ) -
1 - c1 (1 - t 1 ) + m1
Y
b
LM Curve: Money market equilibrium condition ms = md yields
M
= kY - h i + u
P0
h i= -
M
+k Y +u
P0
1 M
k
i = (+ u )+ Y
h P0
h
 Simultaneous Equilibrium of Goods and Money Markets
*
Y =
h
b
M
( C 0 - c1 T 0 + I 0 + G 0 + X 0 - M 0 ) +
(
- u)
h(1 - c1 (1 - t 1 ) + m1 ) + kb
1 - c1 (1 - t 1 ) + m1 + kb P0
Rewriting the above, we get
*
Y =

1
( C 0 - c1 T 0 + I 0 + G 0 + X 0 - M 0 ) +
b
h
(
M
- u)
kb
kb P0
1 - c1 (1 - t 1 ) + m1 +
1 - c1 (1 - t 1 ) + m1 +
h
h
Note: compared with the equilibrium national income equation without the LM curve (in the
previous handout), there is an additional term kb/h in the multiplier for the autonomous
expenditures.
3) Comparative Statistics: Business Cycle, Fiscal and Monetary Policies
The above equilibrium equations for Y* and i* indicate that
(1) Business Cycles
∆I0, and ∆C0 are beyond direct control by government and cause undesirable fluctuations in Y*:
The factor by which the changes in autonomous investment and consumption are multiplier into
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95
IV. IS-LM Model
larger changes in Y* is given by the coefficient of I0 and C0 in the above equilibrium income
equation.
(2) Fiscal Policy:
i) ∆G0 leads to an increase in Y* and an increase in i*
ii) ∆T0 leads to a decrease in Y* and an decrease in i*.
(3) Monetary Policy
i) An increase in money supply leads to an increase in national income:
ii) An increase in money supply leads to a decrease in the interest rate.
Let us examine the above (2) and (3) in a formal and rigorous way:
5. Fiscal and Monetary Policies in the Conventional IS-LM Curve Model
1) Fiscal Policies
Government expenditures may be financed either by taxes or by deficits. In the latter, the deficits
should be made up by issuing bonds. Perversely, a bond-financed increase in government
expenditures has a larger impact on national income than a tax-financed increase in government
expenditures. This inequivalence in terms of financing is a main feature of the conventional
IS-LM model. We will later discuss the problem of this view and present an alternative view
developed by Barro-Richardo. For now, we are simply having a review of fiscal policies in the
IS-LM model.
(1) A Bond-Financed Increase in Government Expenditure: ∆G = ∆B
When government increases its expenditure without increasing tax revenues, there occur deficits.
The government has to make up for deficits by borrowing funds. The certificates of borrowing by
the government are bonds. So deficit-financing is the same as bond-financing. There is no
corresponding increase in taxes when government expenditures increase.
In the Keynsian Cross-Diagram, ∆G0 shifts the AE curve up by ∆G0 and the Y (note that there is no
longer * on Y because this Y is just an equilibrium in the goods market as opposed to the Y* which
is the equilibrium in the goods and money markets) increases by ∆G0 times 1/(1-c1).
Accordingly, in the IS-LM curve model, there occurs a parallel shift of the IS curve to the right by
∆G0/(1-c1). This results into the increase in Y* by ∆G0 times 1/(1-c1 + Kb/h) which is smaller than
∆G0 (1-c1).
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96
IV. IS-LM Model
A: the horizontal distance of IS curve shift
B: Y*
C:  i*
The increase in Y*, shown as the rightward movement of Y*in the graph, is smaller than the
rightward shift of the IS curve. The reason is that ∆G0 leads to ∆Y*and this increased income
increases real money demand. An increase in real money demand pushes up the interest rate when
real money supply is fixed. A higher interest rate decreases investment and through the multiplier,
income falls. This mechanism partially offsets the initial increase in the income due to ∆G0. This
is called ‘Crowding Out’. The increased government expenditure crowds out the private
investment by raising the interest rate.
(2) A Tax-Financed Increase Government Expenditure: ∆G = ∆T
When government is increasing its expenditure with revenues raised through taxation, it is
engaged in balanced budget operation.
In the Cross Diagram, ∆G = ∆T leads to a rightward shift of Y or the goods market equilibrium
national income by ∆G times 1.
Accordingly, in the IS-LM curve model, the IS curve shifts to the right by ∆G. This results into the
rightward shift of Y*, goods and money market equilibrium national income by ∆G times (1c1)/(1- c1 + Kb/h) which is less than ∆G. Also the interest rate goes up.
2) Issues of Monetary Policies
We will examine some relevant issues in the separate chapter.
3) Policy Mix
The crowding out effect shows that as long as the IS and LM curves are normally shaped, a change
in G will bring about undesirable side effect of a higher interest rate and a smaller investment.
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97
IV. IS-LM Model
Now the policy mix enables a desired Y* and a desired I* to achieved simultaneously if and only if
Y* is below Y1 or the full employment national income (maximum potential national income).

CASE STUDY: “House or Gun” for the Americans during the Vietnam war
(Credited to Professor R. Gordon, Northwestern University)
The 1965-67 period, during which U.S. government spending expanded rapidly as our
involvement in the Vietnam war deepened, provides an unusual case study of the
consequences of fiscal expansion while the real money supply remains fixed. In the fourth
quarter of 1966 (October through December), written as 1966:Q4, the real money supply was
almost exactly the same as five quarters earlier, in 1965:Q3. An LM curve corresponding to
this fixed level of Ms/P is drawn in the figure. During this five-quarter interval the level of real
government purchases grew by 12.2 percent, represented in the figure by the rightward shift in
the IS curve from IS0 to IS1.
How did real income and the interest rate behave over the five-quarter interval? Real income
increased by $129.9 billion, more than the $60.2 billion increase in government spending,
because of the (fiscal policy) multiplier effect. And the higher demand for money forced an
increase in the interest rate from 4.7 to 6.0 percent to keep the total demand for money equal to
the fixed real money supply.
The immediate victim of the higher interest rates was investment in residential housing. By
1966:Q4 this component of investment had declined 17.9 percent from the level reached in
1965:Q3. This is the Crowding out effect. (Nonresidential investment including inventory
change and expenditures on plant and equipment-continued to grow despite the increase in
interest rates through 1966:Q4. The reason for this growth stems from the delay between the
increase in the interest rate and the subsequent decline in nonresidential investment, a factor
our IS-LM model does not take into account.)
A basic principle of economics holds that a wartime economy cannot boost military spending
without decreasing civilian expenditures; that is, the economy “cannot have both guns and
butter”. In this case the economy could not have both “guns and houses”.
The principle is not true in a recession or depression which has some buffer in productive
capacity and has the actual national income below the full employment income level. With
expansionary monetary policy which shifted the LM curve, the interest rate was brought down.
This is the policy mix. In 1967 and the early 1968 the economy tried to have both “guns and
butter” due to this policy mix of the simultaneous use of expansionary fiscal and monetary
policies.
President Lyndon Johnston delayed proposing a tax increase, which was not finally approved
by Congress until Jul 1968. Consequently, the money supply began to grow rapidly, and this
allowed private spending as well as defense spending to grow.
The problem arose when the resultant Y*exceeded the full employment income Y*. The
excessive spending growth of 1967 –68 in an economy that was straining at the limit of its
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98
IV. IS-LM Model
productive capacity unleashed a serious inflation. Many analysts think that an underlying
cause of the inflation suffered by the United States sine the late 1960s dates back to President
Johnston’s refusal to “pay for” the Vietnam war in 1966.
The IS-LM curve model shows that there could be a number of policy mixes or the
combinations of fiscal and monetary policies to achieve a certain level of national income. For
instance, when the economy is stuck at the equilibrium with Y* and i* which is below Yf or full
employment equilibrium, the government can attain Yf by entirely relying on ‘expansionary
fiscal policy’ (case I), by entirely relying on ‘easy money policy’ (case II), or even the
combination of the two policies (case III).
Although the equilibrium income is the same for both cases, the relative composition of private
and government sectors will be different. In the first case, at the given level of income, the
share of private investment and consumption compared to that of the government sector is
smaller than in the second case. The reason being, the increased government expenditure
raises the interest rate and thus decreases private investment. In other words, the relative share
of the public sector rises at the expense of the private sector.
(4) Effectiveness of Fiscal and Monetary Policies
The degree of effectiveness of fiscal and monetary policies depends upon the magnitude of the
underlying parameters.
1) Effectiveness of Fiscal Policies
Depending on the magnitude of the elasticity of real money demand with respect to interest rate
(=h), the LM curve could be vertical (h=0), upward sloping (0<h<infinity), and horizontal (b is
infinitely large).
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IV. IS-LM Model
An expansionary fiscal policy (∆G or ∆T) shifts the IS curve to the right. The same shift of the IS
curve could bring about different degrees of ∆Y* depending on the slope of the LM curve.
classical (complete crowding out)
LM1
i
LM 2
normal (partial crowding out)
*
i1
*
i2
i0
keynesian (no crowding out)
LM 3
*
IS
IS
Y 3*
Y
Cf. Now you may remember that the Interest Pegging Monetary Policy leads to a horizontal LM
curve: The interest rate is constant at a fixed level. In this case of the horizontal LM curve, the
fiscal policy will be very effective because there is no crowding out; the expansionary fiscal policy
does not increase the interest rate and thus does not have any dampening effect on investment or
partially offsetting effect on national income. However, the bad side of the horizontal LM curve
(which would not have any crowding out effect) is that a decrease in consumption or investment
will bring about a larger decrease in national income in this horizontal LM curve than when the
LM curve is upward sloping.
.
2) Effectiveness of Monetary Policies
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IV. IS-LM Model
6. Controversies and Pitfalls of the IS-LM curve analysis:
1) Ricardian Equivalence
IS-LM curve model suggests, “Bond-financed government expenditures have a larger impact on
the national income than the same amount of tax-financed government expenditures.”
“A tax cut without an equal decrease in government expenditures leads to an increase in
government budget deficits. This switching from one method of financing government
expenditures to another should alone increase the national income.”
“An increase in government deficits due to tax cuts will lead to an increase in national income.”
(1) Illustration: What does the IS-LM model imply?
This is just to paraphrase the Keynesian position that in the simplified Keynesian model the
government expenditure multiplier ∆Y/∆G = 1/(1-c2) is larger than the balanced budget multiplier
∆Y/∆G + ∆Y/∆T = 1 or that in the IS-LM model the fiscal policy multiplier ∆Y*/∆G = 1/(1-c2 +
Kb/h) is larger than the balanced budget multiplier (1- c2/ (1-c2 + Kb/h).
Graphically,
Keynesian school gives a very clear answer: when the bond-financed government expenditure
increases, the AE increases, and thus IS curve shifts to the right which results in an increase in Y*
and i*.
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IV. IS-LM Model
The upshot of the Keynesian theory is that ∆G will have different impacts on Y* depending on how
∆G is financed, or the method of financing ∆G. ∆G financed by bonds does shift the AE and the IS
curves more to the right than ∆G financed by taxes.
To corollary is that the switching of revenue sources from taxation to bond-issues without any
changes in G will lead to a net increase in Y*: A tax-cut increases disposable income, which in turn
increases consumption by a lesser amount, AE, and finally Y*.
A gullible mind would conclude that deficit financing is more effective and thus better than
tax-financing. We are now experiencing the legacy of this line of thinking by having the problem
of the accumulated amount of deficits. That is a huge amount of public debts.
(2) Uncertainty from Intergenerational Transfer and Bequest
Whether the above statement is correct or not depends on (1) the degree of farsightedness of the
consumers, and (2) their sense of responsibility towards the welfare of the future generation. The
crucial problem is that the beneficiary of the present tax cut may be different from those who will
eventually pick up the tap in the form of an increased tax in the future.
Let us examine the following concrete real world examples faced by consumers:

As soon as the NDP party came to power in the province of Ontario in 1989, it increased
government expenditures drastically. Sensible and far-sighted people predicted that as the
government did not hit any bonanza, it would soon have to increase taxes. In 1992, in fact,
the government proposes major tax hikes. It has turned out that the government was riding
a fiscal time-machine, and simply playing the game of transferring resources from 1992 to
1990. Back in 1990, what would be the impact of the increased government expenditures
on those who benefited directly from it and correctly foresaw the future tax-liability
attached to it?

In the year 1992, the government announces that it will decrease taxes in 1992-93, and
issue bonds with a maturity of 100 years. It will raise taxes to retire the bonds in the year
2092. Let us suppose that the average life expectancy is 75 years. What will be the impact
of this proposed tax-cut on Y*?
The following two scenarios are possible:
First, if the consumers are short-sighted or myopic, or have no concerns about the welfare of the
future generation on whom the tax burden will be imposed after their death: they will be just
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IV. IS-LM Model
concerned about their life-time income. The tax-cut increases disposable income now, but the
corresponding tax increase will come after their death in 2092. So this tax-cut is free lunch for
these people. They will spend the part of increased disposable income on consumption, which
increases AE, and eventually, through the multiplier effect of the A, Y*.
Alternatively, if the consumers are far-sighted and responsible for the welfare of the future
generation: They foresee the price tag of an increased future tax liability attached to the goody of
the present tax cut. They do not want the future generation to be affected by the tax-hike. They
would not spend their increased current disposable income on consumption. They save it and
leave the savings as the bequest to the future generation so that the future generation may cash the
savings to pay for an increased tax liability in the future. The consumption by the current
generation does not change, and thus neither the AE nor Y* change. The IS curve will not shift to
the right.
(3) Ricardo-Barro Equivalance
Ricardian Equivalence states that there is equivalence between bond and tax-financed issuing
bonds instead of increasing taxes, the Canadians used increases in disposable income in raising
their standard of living rather than increasing savings for the future generation. The present
generation cannot help feeling that they are forced to pick up the lunch bill for the past generation.
To that extent, Ricardian Equivalence failed. This failure does not reduce the need to learn the
theory itself, but rather strengthens it: it will help the current generation to remember that there is
no such a thing as free lunch in the economy and that the tax-cut for the current generation comes
at the expenses of an increased tax liability of the future generation.
2) Timing and Expectations
The IS-LM curve model simply suggests, “Investment tax cut will boost economy.”
According to the Keynesian theory, ∆Y*/∆I = 1 /(1- c1) in the simple cross diagram model without
the crowding out, and ∆Y*/∆I = 1/(1- c1 + Kb/h) in the IS-LM model with the crowding out.
When we introduce the element of time and expectations, the results could be uncertain.

Example: Carefully analyze the following economic situation.
The Canadian economy is caught in a serious recession. Some measures to boost investment are
needed. Now in January of year 2010, the concerned Canadian government announces that it will
give an investment tax credit, which will last only for four months. But it says that it will take
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IV. IS-LM Model
eight months from now to pass through the parliament.

What will be the instant impact of this supposedly ‘expansionary measure’ on the economy
during January to August?
The firms will delay the preplanned and newly planned investment until the bill passes through the
parliament. During January to September, there will be very little investment to be made. This
decrease in investment will decrease Y* through the multiplier effect.

Would this measure more expansionary between September and December than a
permanent investment-tax-break at the same rate? Why?
If the tax break is only for a limited time, then the investors would like to take advantage of it by
rushing investment during the period of the tax break. They will delay and forward the investment
projects. In the case of a permanent tax break, there is no reason to forward investment projects
along the time scale: the tax cut will be effective forever, so why hurry to invest? There will be
only delaying investment projects from the time of the announcement to the time of the tax break
coming into effect. In other words, as far as investment is concerned, a temporary tax break has a
larger expansionary impact on the economy than a permanent investment tax break.
3) Time-lags
It takes time for any economic problem to get recognized, for any remedial decisions to be made,
and for the policies to be formulated and executed. These are Recognition Lag, Decision Lag, and
Execution Lag of an economic policy. It also take time for the economy to respond to an applied
policy; this is the Effectiveness Lag. The former is Inside Lag, and the latter Outside Lag.
Due to time lags, contradictory fiscal or monetary policies may come into effect at a wrong time.
4) Lucas’ Critique of Economic Policy Evaluation
Government economists use some version of the IS-LM model in order to predict and to evaluate a
proposed economic policy.
The equilibrium national income equation shows the quantitative relationship between Y* and
various variables such as G, I, C and T: they are related through the coefficients, such as 1/(1- c1 +
Kb/h), which in turn consist of many parameters, such as h, b, K, c1, and so on.
Econometrics enables us to estimate the magnitude of h, b, K, c1 with past data. We use these
estimated values of parameters in the IS-LM model, and thus make some quantitative evaluation of
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IV. IS-LM Model
newly proposed policy. For instance, if c1 is estimated from past data to be equal to 0.8, K to be
equal to 0.5, b to be equal to 20, h to be equal to 20, a proposed decrease in government
expenditures by $50 billion will lead to a decrease in national income by $ 75 billion, that is, 50
times the multiplier of 1.5 (1 over 1 minus c1 plus Kb/h) in case of no crowing-out.
This use of econometrics along with the IS-LM curves could lead to problems under certain
circumstances.
When government changes its whole set of rules of the game, there occurs a ‘regime change’. This
is different from a mere ‘policy change’, a quantitative change in government expenditures or
money supply. If the general public takes a regime change as permanent and credible, they will
accordingly change their behavior. This change in behavior is reflected in the parameters of
behavioral equations such as consumption function. This is a ‘parameter drift’ due to regime
change. The use of estimated parameters under the old regime to a new policy under the new
regime would give a wrong prediction of the proposed policy. This is the core of Professor Lucas’
Critique against Econometric Policy Evaluation: when there is a regime change which causes a
parameter drift, the use of estimated parameters from the past regime would give the wrong
evaluation of the new proposed policy.

Case I (a mere policy change). There is no regime change. Now government is going to
decrease its expenditure by $50 billion. The econometric technique gives you that the
marginal propensity to consume is estimated to be 0.8 from the past 10 year data. In this
case, the use of the old parameter 0.8 for a new policy is justifiable as there was no change
in government’s rule of game or regime change and thus the consumers have no reason to
change their behavior. The IS curve will shift to the left by ∆G times 1 over 1 minus 0.8 or
$250 billion. There will be a decrease in Y* by a less amount.

Case II. (a regime change). Government announces that it will change the rules of game
entirely. It will turn away from the past ‘spending’ regime to a new ‘saving’ one. Now as
part of such fundamental change, the government is decreasing its expenditure by $50
billion. What will be the change in Y*? The past behavior of the consumers under the old
regime was that a $1 increase in disposable income increased consumption by $1 time the
marginal propensity to consume, say, 0.8. Now as they expect leaner days ahead of them,
they would like to practice thrift, too. This change in consumers’ behavior will be reflected
in the change in the marginal propensity to consume or c2, say 0.6, will be smaller than the
c2 before the regime change. The IS curve will move to the left by ∆G times 1 over 1 minus
0.6, that is, %50 times 4 = $200 billion, not by $50 times 1 over 1 minus 0.8 = $250 billion.
Of course, the resultant decrease in the equilibrium Y* will be smaller due to the crowding
out effect.
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Chapter IV. Appendix I
Appendix I. Review Questions
In the IS-LM curve model, the general price level is assumed to be fixed. This is a
reasonable assumption if the economy is operating under the full employment income level.
The IS Curve
1. From the Keynesian cross diagram, derive the IS curve, which shows various combinations of
interest rate and national income in the goods market equilibrium, 1) when the investment function
is independent of interest rate, and 2) when investment is inversely related to interest rate.
The LM Curve
2. Derive the LM curve, which shows various combinations of interest rate and national income in
the money market, 1) when the money demand is independent of interest rate (h = 0 in the real
money demand function Md/P = KY – hi), 2) when the money demand is inversely related to
interest rate, and 3) when the money demand is infinitely elastic with respect to interest rate (h is
infinitely large): Draw money demand and supply curves in a graph, and the LM curve in the other.
3. Show graphically what happens to the LM curve when the central bank increases money supply.
4. The following question shows what happens to the LM curve when there occurs a decrease in
money demand which is caused by other things than changes in income or interest rate:
Suppose that in a country called ‘Erehwon’ there breaks out a rumor of the currency reform which
would penalize the holders of money balances. People naturally scramble to make a flight from
cash balances and to buy up alternative assets. Describe the situation with the graphs of the
liquidity preference function and the LM curve. What will be its impact on national income?
5. Let’s suppose that the money supply and demand curves are normally shaped, and that the Bank
of Canada is committed to maintaining interest rate at a certain level. This means that the Bank of
Canada stands ready to change the nominal money supply in response to changes in the real money
demand which could affect interest rate. What will be the resultant shape of the LM curve in this
case? Explain why, under this monetary regime, the impact of a reduction in investment on
national income would be felt more painfully than under alternative monetary regime?
Equilibrium of IS-LM: Crowding-Out Taken into Account
[Can you tell the difference between Fiscal Policy Multiplier and Government Expenditure
Multiplier: the first takes Crowding-out Effects into account while the second does not.
Accordingly, the first is usually smaller in magnitude than the first.]
6. Suppose that the following report was made by an economist who offers consultation to an
opposition party ‘Libertarian’ in a country called ‘Erewhon’. If you ar the opposition leader who
is properly trained in economics, why would you feel like switching to another consulting
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Chapter IV. Appendix I
company? – Let’s assume that the facts used are all correct. Indicate the missing points which lead
to the drawing of the underlined wrong conclusion from the correct facts.
“My econometric analysis using a very sophisticated programme and the data of the past 10 years
shows that the marginal propensity to consume is 0.67 in this country (fact). Now the government
treasury is cleaning its house, and ready to cut down on its expenditures by 50 billion this year
(fact). Therefore, I can forecast that the accumulated total decrease in national income over time
will amount to 50 billion dollar times the implied multiplier equal to 1 over 1 minus 0.67, that is,
about 150 billion dollars. (opinion). Everyday the news media is pounding into the head of the
citizens that the idea that the citizens should be prepared for lean days (fact). However, one social
study show that the thresh-hold point is a 100-billion-dollar reduction beyond which the citizens
will prefer a political regime change to the economic sacrifice however necessary it might be
(fact). Therefore, it is my prediction that with the reduction of national income by 150 million
dollars the present ruling party ‘Troy’ will most likely lose the next election (opinion).”
7. Answer the following questions:
1) Let’s suppose that the IS-LM curves are normally shaped: the first is downward-sloping and the
second upward-sloping. Evaluate the following argument within the Keynesian framework:
“The government spending raises interest rate, which chokes off private investment. As now the
Canadian economy is heading toward recession, the government spending should be reduced,
thereby lowering the interest rate and preventing recession from taking its toll any further.”
2) In each possible case of the LM curves given in Question 3 on Page 3, what is the extent of
Crowding-out effect when government increases its expenditures?
Policy Mix
8. Suppose that two administrations, one the Liberal and the other Socialists, all use fiscal and
monetary policies to raise the national income to a target level which is still below the maximum
potential national income, and that the Liberal administration relies relatively more on the
expansionary policy while the Socialists relies more on fiscal policy.
1) On a single graph, show how the IS and LM curves of these two administration differ.
2) Indicate whether the following variables will be higher under the Liberal or Socialist
administration: interest rate, private investment, and government spending.
Alternative Frames of Reference
9. Keynesian ‘Non-equivalence’ and Ricardian Equivalence.
At time t, the government announces that it will decrease taxes on consumers’ income, and issues
bonds to make up for the decrease in government revenues. The bonds will be paid back in 90
years with an increase in taxes at that time. The average life expectancy is 75 years, which means
that the current generation of consumers will not be hit with the tax-hike in their life-time.
Note that government expenditure has not changed, but some part which used to be financed by
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Chapter IV. Appendix I
taxes is now financed by bond issues.
1) The Keynesian framework assumes that the consumers are near-sighted or selfish, and thus do
not have any concern for the welfare of the future generation. What will be the impact of such a
tax cut on national income? Illustrate it with the IS-LM model.
2) Now let us assume that the consumers are far-sighted and responsible for the welfare of the
future generation, and thus do have bequest motive for their descendants. What will be the impact
of the tax cut on the national income at time t and time t + 4?
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Chapter IV. Appendix II
Appendix II: Summary of Chapter
1. Fiscal Policies: G
(Case 1: all taxes are lump sum)
A
B
A: y =
*
B: y =
1
b
( C0 - c1 T 0 + I 0 + G0 ) 
i
1 - c1
1  c1
1
kb
1 - c1 +
h
( C 0 - c1 T 0 + I 0 + G 0 ) +
b
h
(
M
k b P0
1 - c1 +
h
- u)
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Chapter IV. Appendix II
2. Monetary Policies: M
(Case 1: all taxes are lump sum)
i
A
B
Y
M
= ky - h i + u
P0
h
1
i 
u
k
k
kP0
1
M
k
i=
(
+ u )+
y
h
h
P0
A: y =
*
B: y =
M
1
kb
1 - c1 +
h
+
( C 0 - c1 T 0 + I 0 + G 0 ) +
b
h
kb
1 - c1 +
h
(
M
P0
- u)
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Chapter IV. Appendix II
3. Effectiveness of Monetary Policies in Various Settings: How much Y results from M
b=0
normal b
b->
(h = 0)
LM
LM
IS
LM
IS
IS
IS & LM is perfectly inelastic
(Normal h)
IS
LM
LM
LM
IS
IS
( h   )
IS
LM
IS
LM
IS
LM
LM is perfectly elastic
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Chapter IV. Appendix II
4. Effectiveness of Fiscal Policies in Various Settings: How much Y results from G
b=0
h = 0
normal h
h ->
normal b
b - > 
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Chapter V. AS-AD Model
Chapter V. Aggregate Supply & Aggregate Demand Curve Analysis
1. Aggregate Demand
1) Algebraic Derivation
You may remember that the equilibrium national income from the IS-LM curve is
*
Y =
h
b
M
( C 0 - c1 T 0 + I 0 + G0 ) +
(
- u)
h(1 - c1 ) + kb
1 - c1 + kb P0
Let’s focus on the relationship between Y and P.
If all variables are constant except for Y and P, we can get an equation showing the relationship
between the two variables Y and P, such as Y = 500 + 200/P. This equation carves up the
relationship between two variables, Y and P, is called the Aggregate
Demand Curve.
P
( C 0 ; T 0 ; I 0 ; G 0 ; M ) s h i f t p a r a m e t e r s
AD
YP
In the discussion of monetary policy which involves a change in money supply M and its impact
on P and Y, we deliberately drop the intercept A, which is related to fiscal policies, and frequently
use Y = B/P = B’ (M/P) to carve up the relationship between the three key variables, M, P, and Y
(real income).
If we draw the graph of the above equation with Y on the horizontal axis and P on the
vertical axis, this is a hyperbola.
We know that Y = 1/X is a rectangular hyperbola. Y = A + B/X is simply Y = 1/X shifted
up by A and outward along the Y =X line by B.
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Chapter V. AS-AD Model
The quantity theory of money postulates that the equation of exchange is M V = P Y, or
Y = V (M/P), where M is the supply of money, and V the velocity of circulation of
money. This equation is exactly the same as Y = B’ (M/P). This is a special case,
featuring monetary aspects, of the AD curve which embodies the impact of fiscal
policies along the others (∆C, ∆I) in the first term and that of monetary policies along
with monetary shocks (∆u) in the second term of the equation Y
2) Graphic Derivation
We derive the AD curve by examining the impact of a changing price level on the LM curve and
consequently on the AD.

When the price level falls from P1 to P2, the real money supply rises from M/P1 to M/P2.
This shifts the LM curve to the right.

The equilibrium national income level rises in the IS-LM curve.
The corresponding point shifts in the AD setting. By linking the two points, we get the AD
curve.

LM (M/P1)
LM (M/P2)
P1
P2
AD
3) Shift of AD curve

∆ C0, ∆I0, ∆G0, - ∆T0  ∆IS  ∆AD

∆ M ∆LM  ∆AD

∆ md = ∆u  ∆LM  ∆AD
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Chapter V. AS-AD Model
In summary, the AD has six shift-parameters, C0, I0, G0, T0, M, and u.
 Out of them, C0, I0 and u are beyond the control of the government;

C0, I0 and u are called Aggregate Demand Shocks;
specifically, C0 and I0 (X0 and M0 as well in the open economy) are goods
market shocks, and
u is a monetary shock;

G and T are fiscal policy instruments;

M is monetary policy instrument.
To countervail the Aggregate Demand Shocks and thus to eliminate any impact on the equilibrium
national income, the government may control G, T, and M in counter-cyclical ways. This is called
‘the Counter-cyclical policy’ or ‘Income stabilization policy’.
2. Aggregate Supply
1) What is the aggregate supply?
AS versus YS
The aggregate output is the sum of all the supplies of goods and services in the economy. You may
remember the 45 degree line of YS = Y in the Keynesian Cross Diagram. When the aggregate
output YS is drawn against a particular price level, that is the aggregate supply. The only
difference is that the AS is drawn again at the price level while YS is not. In a sense, AS comes
from YS. Then, our next question is, what determines YS?
2) Aggregate Production Function
AS is the aggregate outputs at a particular price level. Output results through production process
from inputs. The production function shows the relationship between the inputs and the outputs:
production combines production factors with a certain technology. The production function
summarizes all three aspects of the supply: Inputs, outputs, and technology.
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Chapter V. AS-AD Model
(1) Functional Form
In microeconomics theories, an individual production function, say, a hamburger or i th industry, is
given by
Qi = f (K,L),
where K and L are capital and labor inputs, and Q output at the firm or industry level. Technology
is implied in the functional form.
The aggregate production function is obtained by summing up the production functions of all
industries. The aggregate production function shows the aggregate output YS as an increasing
function of capital and labor inputs. Again technology is implied in the functional form. We use
notation K for the capital stock or the amount of capital, and N for labor input at the aggregate level
of economy.
YS = F (K, N; T ).
Note that unlike the microeconomics which uses L for labor input, we use N for the aggregate
labor inputs, which is called the ‘level of employment’ in an economy. N may be measured in total
hours worked for a given period of time, which is equal to the number of workers employed times
the number of hours worked by each worker. Here T stands for Technology employed in
production.
(2) Derivation of the Aggregate Production Curve
Note that in the short-run, K remains fixed and T does not change. Thus the short-run aggregate
production function can be expressed as an increasing function of one variable N or the level of
employment of existing workers: the more workers employed for longer hours, and then more
aggregate output.
YS
Aggregate Production Curve
N
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116
Chapter V. AS-AD Model
Let’s take a numerical example for the Short-run Aggregate Production Function:
YS = 100N – 0.3 N2
If the level of employment is given at 40 (say, million hours worked for a year), what is
YS? The answer is YS = 100 x 40 – 0.3 (40)2 = 3520.
If N increases up to N = 60, then the aggregate outputs rise to a new level: 100X60 – 0.3
(60)2 = 4920.
These two points give us an aggregate production curve. It is upward sloping, and is
convex upwards. In the short-run, there is a one-to-one relationship between the level of
employment and the aggregate outputs: N*’ – AS* t in the short-run. An increase in the
level of employment leads to a movement along the given aggregate production function.

Note that the slope of the tangent line to the Aggregate Production Curve is the Marginal
Product of Labor.
The shape of the above Aggregate Production Curve is part of a so-called ‘S curve’ of the total
(aggregate) production curve:
YS
N
The first phase or Phase I shows the concave upward and implies that as the input of labor force or
the level of employment goes up, the output increases by more than proportion due to an increase
in efficiency coming from specialization and cooperation, etc. That is an increasing marginal
product of labor or MPL increases in this phase.
Then there occurs a point of inflection. The curve become convex upwards and implies that as the
input(labor forces or level of employment) rises, the output increases by less than proportion: This
is the area where the diminishing marginal product of labor takes place. As the level of N
increases by one unit, the output increases but it does so by less and less. It is called ‘Decreasing
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Chapter V. AS-AD Model
Marginal Product of Labor’. This is due to some imbalance between the size of (given) capital
(equipment and facilities) and the number of workers working in and with them, and the resultant
inefficiency such as congestion(too many workers collide and crowd, free-riders(some workers are
not carrying their fair work load) etc.
Our earlier aggregate product curve is a cut out of the above S curve from and beyond the
inflection point. Why cut here? Because Phase I is important and beneficial for the producer, but
it is uninteresting. All the decision to be made is trivially to keep expanding the employment (N
up). When the inflection point comes, now the entrepreneur has to start thinking of a very critical
question: When to stop? He has to weigh the inefficiency, which has started setting in, against
other benefits, and has to make a decision to stop at the right level of N. Thus, this part of S curve
is important in terms of the entrepreneur’s corporate decision making, and we are only looking at
this part of the S curve of the total production curve.
YS
N
(3) Shift of Aggregate Production Function
In the long-run, i) an increase in N, ii) an increase in K, and iii) the enhanced level of technology
are all possible, leading to an increase in Aggregate Output. However, an increase in N leads to a
movement along the Aggregate Output Curve, and the two others, such as an increase in K or/and
T leads to a shift of the Aggregate Output Curve.
i) Capital Accumulation: ∆K
With more capital inputs, each level of employment will lead to a larger amount of aggregate
outputs: With more capital equipment, each worker can produce more outputs.
This will send the Aggregate Production Curve outward, or upward.
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Chapter V. AS-AD Model
YS
N

Let’s take a numerical example,
Before: Y* = 100 N – 0.3 N2 (a Old production function)
N = 40 – Y* = 3520; N = 60 – Y* = 4920.
After: Y* = 250 N – 0.2 N2 (a New production function)
N = 40 – Y* = 5680; N = 60 – Y* = 8280.


Therefore, capital accumulation (∆K) leads to a upward shift of the production curve.
When the Aggregate Production Curve shifts up, at each level of N, the slope of the tangent
line gets steeper: The slope is equal to the marginal product of labor, and thus the MP of
labor rises.
Think about the decrease in capital, which will send the Aggregate Production Curve downward.


Capital naturally wears and tears over time and it is called ‘Depreciation’
Capital can be destroyed during a war.
ii) Technical Innovation, or Technological Advances: ∆T
With an improved production technology, each level of employment will lead to a larger amount
of aggregate outputs.
Let’s take a numerical example:
Before: Y* = 100 N – 0.3 N2 ( a Old production function)
N = 40 – Y* = 3520; N = 60 – Y* = 4920.
After: Y* = 150 N – 0.2 N2 ( a New production function)
N = 40 – Y* = 5680; N = 60 – Y* = 8280.
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Chapter V. AS-AD Model
Therefore, technological advances also lead to a upward shift of the production curve. The
marginal product of labor rises, too.
YS
N
iii) A Growing Number of Workers: ∆Ns
This is a rightward shift of the labor supply curve. The equilibrium nominal wage rates fall: So
does the real wage rate. The equilibrium level of employment rises, which increases the aggregate
outputs along the aggregate production function.
This can happen in the long run due to population growth, or open-door immigration policies. As
N is on the horizontal axis, this leads to a movement along the aggregate production curve.
3) Aggregate Labor Supply and Demand Curve: Labor Market
Then, the question in order is how the level of employment or N* is determined to enter the
aggregate production function. N* is determined in the labor market through the interplay of the
aggregate labor supply and aggregate labor demand. Now, we note that we are introducing one
more market into the picture, and that is the labor market.
The supply of labor is an increasing function of real wages, which are money wage over the price
level ( w = W/P), and the demand for labor a decreasing function of real wages.
(1) Aggregate Labor Supply
The labor supply is an increasing function of real wages, which are equal to nominal wages
divided by the price level;
Ns = f (W/P; other variables)
For a given level of P, as W rises, Ns rises as well.
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If you put Ns on the horizontal axis and W on the vertical axis, the curve should be positively
sloped. And P becomes a shift parameter.
𝑊/𝑃
𝑁𝑠

Numerical Example:
Ns = 100 + 3 (W/P).
If the nominal wage or money wage (rate per hour) is $10 per hour and the price level is
equal to 1, then the real wage (rate per hour) is 10/1 = 10, and the aggregate labor supply
would be 100+ 3 times 10/1 = 130.
The above is sufficient for the labor supply curve in macro. Note that the vertical axis is in the real
wage W/P. The labor supply is an increasing function of real wage.
However, in the macroeconomics, we would further separate real wage W/P into nominal wage W
and price level P. If we draw the aggregate labor supply curve Ns against the nominal wage W, we
can see impacts of P more clearly.
How can we do that? First, hold P = 1 constant, then W/P becomes W, and draw the N s curve of
the same shape:
𝑊 ⁄1 = 𝑊
𝑁 𝑠 (for P=1)
𝑁𝑠
Note that now the vertical axis is W or nominal wage, and the horizontal axis is the level of
employment or N, and finally that the Ns curve or the aggregate labor supply curve is drawn with
the fixed price level of 1. Thus we should note that the price level is now the shift variable of the
Ns curve.
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What will happen to the Ns curve for P =1 if the price level rises from 1 to, say, 2 while the nominal
wage (rate for hour) is held constant?
A Shift of the Ns curve:

In the short-run, a change in the price level shifts the Ns curve. As P rises, the Ns curve
shifts up as well; As P rises, for a given level of W, the real wage of W/P falls, and thus
labor supply falls.
When P rises from P=1 to P=2,
Ns (for P=2)
Ns (for P=1)
W
Ns decreases
There are other variables that shift the Ns curve.

For example, in the long-run, as population grows, the aggregate labor supply curve shifts
to the right.
When population grows or more immigrants come, the Ns shifts to the right
Ns
Ns’
W
Ns increases
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In summary, for the dimension of W and N, we can write the aggregate labor supply curve as:
Ns = f (W(+) : P(-) , other variables such as population, immigration, etc.)
All other variables, except W and Ns, become shift variables. A change in these shift variables
leads to a shift of the Ns curve.
Remember that an increase in the price level or P leads to the visually upward movement of the Ns
curve or a decrease in Ns.
(2) Aggregate Labor Demand:
Let us examine the labor demand first:
The aggregate labor demand is a decreasing function of real wages:
Nd = g (W/P; other variables).
If we draw a curve which shows the relationship between Nd and W. It will be downward-sloping;
as W goes up, the entrepreneurs demand for labor falls. The third variable P becomes a shift
parameter.
W/P
Nd
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By holding P = 1 constant, we can get a Nd curve corresponding to P=1.
W/1
Nd (P=1)
Nd
Background-You may recall the following Microeconomics theory of labor demand:
The entrepreneur does demand labor and hires workers. If s/he is maximizing profits, at
the margin or for the last worker hire, the cost is equal to the benefit. The cost of hiring the
last worker in monetary terms is the money wage W, and the benefit from hiring the worker
is the marginal product MP (units of output the worker produces) times the price of the
output P. So at the profit maximizing level of employment, W = P x MPL.
Numerical example) It costs $10 to hire a worker because W = $10. The last worker
increases the total products or outputs by 5 (5 units of outputs), and each unit of output has
the price of $2 in the market. The cost of hiring the last worker is $10, and the benefit from
hiring her/him is 5 times $2, being equal to $1.
We now know that at the equilibrium for the profit maximizing firm
W = P x MPL in dollar terms, or W/P = MPL in physical terms.
MPL is a decreasing function of the amount of labor inputs.
The real wage w= W/P is set by market forces, and is paid uniformly to all workers,
regardless of whether there are many or few workers.
When the real w = W/P is set at a certain level in the labor market, the entrepreneur who is
a price taker will hire workers in such a number that the last worker’s marginal product is
equal to the real wage set in the market. The entrepreneur is making profits from hiring
intra-marginal workers (all the workers except the last worker hired) as their marginal
products are higher than the real wage. S/he is not marking any profit from hiring the last
or marginal worker (MP = W/P) This implies that the MPL curve itself drawn against real
wages is the labor demand curve.
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A Shift of the Nd curve:

As P or the price level rises, the real wages (W/P) falls for a given level of W. And thus Nd
rises: this is a rightward movement or upward movement of Nd curve.
As P rises, say from 1 to 2, while W is held constant,
W
Nd(P’)
Nd(P)
N
Nd rises
where P =1, and P’ = 2 in this case.
There are other variables that shift the Nd curve:

In the long run, ∆K or an enhanced technology increases each worker’s productivity or
marginal product. The MPL shifts up, and the labor demand curve shifts up (or to the right):
some workers who used to be unproductive and thus unemployable become now
productive due to technical innovations and become employable. There is an increase in
the aggregate labor demand by the entrepreneurs.
W
Nd’
Nd
N
Nd rises
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In summary, for the dimension of W and N, we can write the aggregate labor supply curve as:
Nd = g(W (-) : P(+) , other variables such as population, immigration, etc.)
All other variables, except W and Ns, become shift variables. A change in these shift variables
leads to a shift of the Nd curve.
Remember that an increase in the price level leads to the visually upward movement of both
Nd and Ns curves.
(3) Labor Market Equilibrium
The interplay of the Nd and NS determines the equilibrium level of employment N* and the
equilibrium level of real wages w*;
At equilibrium,
f(W/P) = g(W/P), or
f(W: P ) = g (W: P)
We can solve for the real wages or W/P at this equilibrium in the labor market.
And then, for a given price level, we can also get the nominal wages W for this equilibrium.
Graphically,
W
W*
N*
Nd
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By plugging the value of W* back into the aggregate labor supply or demand function, we can get
N*
In summary, As – YS – N*- w* - W for a given level of P.
(4) Responses of Nominal Wages to Changing Price Levels: Flexible or Not?
We would revisit the question of what will happen to the equilibrium real wage W/P = w when the
price level rises? This depends on what will happen to nominal wage or W when the price level
rises.
In the microeconomics, which belongs to the world of classical economics, there is an assumption
of flexibility of nominal wage. In other words, the nominal wage W will rise in an exact proportion
to the increase in P. As P rises, W rises by the same amount. Thus, W/P = w or real wage does not
change. There will be no change in the level of employment N, and thereby no change in
aggregate output YS or real national income Y.
The flexibility of nominal wage W ensure the separation of the world of nominal variables such as
W and P, and the world of the real variables such as N, YS, and Y. There is a dichotomy between
the real and the nominal variables.
However, in macroeconomics, there are different schools which have different assumptions about
the degree of flexibility of nominal wage. And the different degrees of flexibility of nominal wage
opens up the possibility of W not exactly following the movement of P and thus lead to a change in
real wage or w =W/P, level of employment N, aggregate output YS, and real national income Y.
An increase in the price level, which is a change in nominal variable, can affect the real
variables.
Let’s elaborate on this point:

If W is viewed to be flexible, just as assumed in the classical economics, and follows the
movement of P, a change in P will be accompanied by an equal movement of W, leaving w
unchanged.
First, the rising P shifts both the labor supply and demand curves up;
The new equilibrium occurs at E;
The new equilibrium nominal wages are proportionally higher than the previous one: In
other words, the increase in W is proportional to the increase in P;
Therefore the real wages (w= W/P) do not change;
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The level of employment is the same as before.
W
E
W1
W0
Nd
This flexibility of money wages and thus the consequent constancy of real wages belong to the
classical world, where i) there is no information asymmetry between the entrepreneurs and the
workers: There is no money illusion on the part of workers (it goes without saying that any
working, let along successful, entrepreneurs should NOT have any money illusion at all); ii) there
is no structural rigidity which hinders flexible changes of money wages in response to a change in
price level, particularly of downwards changes or falls to a falling price level in the case of
recession, such as labour unions, and finally iii) it is in the long-run – enough of time has passed to
make a full adjustment of money wages to a changing price level.
However, John Maynard Keynes saw the real world differently: First, he argues that yes, in the
long-run, the money wages will adjust fully to a changing price level and everything will be fair
and square, but that in the long-run ‘we are all dead’. We may live through a series of short-terms,
and constant changes in equilibrium. In the short-run, money wages can be rigid for many reasons.
For one thing, it may be confusion on the part of the workers, such as money illusion. Even in the
long-run, money wages can be rigid even amid recession, and they are so mainly due to
institutional elements such as labor unions. Why did the Great Depression last for such a long
period of time – 10 years or so? It was mainly due to the rigidity of money wages backed by labor
unions, and also due to ‘confusion’ by a political leader. Let’s listen to Professor G. Smiley in her
contribution of ‘The Great Depression” in the Concise Encyclopedia of Economics:
“….In previous depressions, wage rates typically fell 9-10 percent during a one- to
two-year contraction; these falling wages made it possible for more workers than otherwise
to keep their jobs. However, in the Great Depression, manufacturing firms kept wage rates
nearly constant into 1931, something commentators considered quite unusual. With falling
prices and constant wage rates, real hourly wages rose sharply in 1930 and 1931. Though
some spreading of work did occur, firms primarily laid off workers. As a result,
unemployment began to soar amid plummeting production, particularly in the durable
manufacturing sector, where production fell 36 percent between the end of 1929 and the
end of 1930 and then fell another 36 percent between the end of 1930 and the end of 1931.
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Why had wages not fallen as they had in previous contractions? One reason was that
President Herbert Hoover prevented them from falling. He had been appalled by the wage
rate cuts in the 1920-1921 depression and had preached a “high wage” policy throughout
the 1920s. By the late 1920s, many business and labor leaders and academic economists
believed that policies to keep wage rates high would maintain workers’ level of purchasing,
providing the “steadier” markets necessary to thwart economic contractions. When
President Hoover organized conferences in December 1929 to urge business, industrial,
and labor leaders to hold the line on wage rates and dividends, he found a willing
audience……”
Perhaps, it wasn’t Mr. Hoover who found the audience, but it was the general public (workers) that
found Mr. Hoover as a populist politician. He meant to have represented the workers by
supporting an artificially high money wages, but in the end, he prolonged the depression into the
Great one in history.
Thus the Keynesian world goes as follows:

If W is fixed, particulary downwardly rigid: An increase in P may or may not be
accompanied with a commensurate increase in money wages or W, and thus may lead to a
decrease in real wages or w. However, more apparently, a decrease in P during the
recession may not lead to a corresponding fall in money wages or W. It may be due to three
things: money illusion on the part of workers; labor unions, and/or in the short-run. In any
case, it will lead to an increase in real wages or w: an increase in the real labor cost on the
part of entrepreneurs and thus their demand for labor decreases.
First, the increasing P shifts both the labor supply and demand curves visually up.
However, the nominal wages are set at a fixed level, shown by the horizontal line; nominal
wages cannot be nothing other than the fixed level.
The new equilibrium should come at E where the labor demand curve and the horizontal
nominal wage line (effective labor supply curve) intersect.
At the new equilibrium, compared with the previous equilibrium, the nominal wages are
the same, and the equilibrium level of employment N is lower.
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Ns
W
E
E
(effective labour supply)
Nd
N
*
N
*
0
Nd
The first position is taken by the classical economics, which is the same as the
microeconomics, and the second is by the Keynesian economists. The second is true when
there is structural impediment to the flexible mobility of W or nominal wage. This is the case
when there is a union which insists on having fixed nominal or monetary amount of wage. In
other words, when workers’ unions have ‘money illusion’ and thereby focus on the nominal
value of wage instead of real value or purchasing power of the wage. This is also the case
when the time-period of observation is too short. In a very short-run, the change in the price
level is not reflected in the wage level. The third possibility is when the people (= the workers)
have some kind of ‘money illusion’. The money illusion refers to the situation where, being
faced with a changing price level P, the people really should focus on the real wages w = W/P
but they in fact have ‘hang-up’ on the nominal wages, and thus they try to stick to the fixed
nominal wage( W bar). The end result is that real wage instead changes and so do N*, YS, and
Y.
On the other hand, if there are no impediments on the mobility of nominal wage W and
workers are more or less fully employed W will move in the same direction as the changing P
in the long-run. ∆P means an increase in living –costs for workers, and workers will eventually
demand a higher money wage or ∆W.
Basically, the AS analysis hinges upon what is happening when the price level changes: What is
the impact of a change in the price level on real wages and on the equilibrium employment level?
4) Derivation of Aggregate Supply Curve
(1)Different Aggregate Supply Curves
You may remember that the AS is assumed to be vertical in the classical economics, and horizontal
or upward sloping in the Keynesian economics.
You may recall that the classical AS curve is vertical; the AS is fixed at a certain level. The fixed
level of AS is called ‘the full employment level’.
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Note: The full employment does not mean zero unemployment, but a low yet positive rate
of unemployment. A certain positive rate of unemployment is inevitable for an economy
where new comers are looking for best-fitting jobs and some workers are upgrading their
skills and consequently searching for another jobs. Some unemployment is even desirable
as it provides some reserves in the economy; without it the man/women-power situation is
too tight, and a firm which is faced with even temporary rise in the demand for its products
would have extreme difficulties in hiring extra workers. As a consequence, we will
observe a shortage of the good or a rise in its price. We need a small ‘buffer’ of
unemployed workers. This positive rate of unemployment compatible with a smooth
working economy at the ‘full employment level’ is called ‘the natural rate of
unemployment’. The corresponding national income is the ‘natural real national income.’
In the short-run, there may be some temporary deviation of the actual national income from the full
employment N.I., but the price level will adjust to push the economy back to the equilibrium. The
Business Cycles can occur due to the demand shocks. However, it is only temporary, and is of no
big concern as the economy, if left alone, automatically gravitates toward a unique equilibrium
N.I.
What is the role of the government in the economy?
If there is no factor in the economy which blocks the above tatonnement, the government should
not create anything which can get in the way of this natural adjustment process of recovering the
equilibrium. Actually it should eliminate any impediments in this process and facilitate the
adjustment process by promoting competition.
You may also recall that the Keynesian Aggregate Supply curve is upward-sloping; the AS
responds positively to the (output) price level.
(2) Fundamental Cause of Different AS curves.
Flexible Nominal/Money Wages  A vertical AS curve.
(Neo Classical)
Rigid Nominal./Money Wages  a Positively Sloping AS curve. (Keynesian)
The reasons for rigidity:
Money Illusion; a kind of stupidity at the individual level
Union, etc: a kind of ‘social’ and ‘structural’ rigidity
To derive the Aggregate Supply Curve, first you need a Four-Panel graph of AS-AD, Ns and Nd,
and Aggregate Production Curve and a 45 degree-line of converting YS into Y.
The AS curve shows the relationship between the different levels of prices, or Ps, and the
corresponding levels of real national income, orYs. Thus, you have to kick up and down the price
level or P, and to find the corresponding Y.
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(3) Classical Aggregate Supply Curve: A Vertical AS Curve
Under what circumstances would the money wage be flexible?
i)
The economy is at full employment level: all available workers are fully employed;
there are no other workers who are willing to work for the real wage lower than the
prevailing rate;
ii)
There is no structural rigidity of money wage: no impediment on the equilibrating force
in the labor market;
iii)
The workers are free of ‘Money Illusion’;
iv)
In the long-run: an enough amount of time has elapsed since ∆P.
This is a graphic and somewhat mechanical derivation:

1.) Choose a price level, say, P1.

2.) For this given price level, we can have the labor supply and demand curves;
Ns = f (W/P); and Nd = g (W/P) become
Ns = f (W: P1); and Nd = g (W: P1).
Or, by simply showing the shift variables, we can write down
Ns (P1); and Nd (P1).

3.) The intersection of the labor supply and demand curves gives the equilibrium real wage
w= W/P, in the labor market; N* and W* for a given P (thus w*).

4.) The equilibrium N* feeds into the aggregate production function of
YS = F (K, N*; T) for a given K and T in the short-run.

5.) YS = Y the third panel.

6.) Y goes down to the fourth panel and matches the starting price level P1.

7.) Suppose that the price level goes up to P2.

8.) As P rises, both labor supply and demand curves shift up.
Now we get Ns (P2); and Nd (P2).
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These are shown with broken lines in the graph below.

9.) We get the new equilibrium. At this new equilibrium, the new nominal wages are higher
than the previous nominal wage by the same proportion of the increase in P. And thus, the
real wages do not change; the level of employment does not change, either.

10.) The same level of employment feeds into the aggregate production function, and leads
to the same level of YS.

11.) The same level of Y in the third panel.

12.) The same Y goes down to the fourth panel and matches the new price level P2.

13.) By linking the two points in the fourth panel, we get the AS curve.
𝑌𝑆
𝑌𝑆
𝑁
𝑊
𝑌
𝑃
𝐴𝑆(𝑊)
𝑊2∗
𝑁 𝑠 (𝑃1 )
𝑊1∗
𝑃2
2
𝑃1
1
𝑁 𝑑 (𝑃1 )
𝑁∗
𝑌∗
Note that along this AS curve the real wage is constant but money wage is not: at point 1
the corresponding money wage is W*1, and at point 2 the corresponding money wage is
W*2. However, at both points, the real wage is equal to w.
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An intuitive explanation is as follows:
When P rises, W will rise proportionately. The revenues (P Q) and the costs (W L) are
increasing proportionately, and thus the profit margin does not change. There is no reason
for entrepreneurs to attempt to expand production scale. The AS remains constant at the
macroeconomic level, too.
P increases and W increases  W/P remains unchanged  N remains unchanged YS
remains unchanged  Y remains unchanged, and thus a vertical AS we get.
(Supplement: Why does W/P determine the profit margin?)
Production decisions are made ultimately by producers, or entrepreneurs who weigh the
situations in the output market (which determines revenues) and the input market (which
determines costs).
Entrepreneurs make supply decisions by weighing the ratio of output price to input price,
which is the key variable for their profits which constitute their prime motivation.
Entrepreneurs are orchestrating production processes (borrowing capital, hiring workers,
etc.) in order to earn profits.
Formally, the aggregate production function shows the relationship between inputs such as
capital (K) and labor (L), and outputs. These aggregate outputs are the aggregate supply or
Y in Y – YS: Y = F (K,L)
We know that an increase in K and L leads to an increase in Y. However, it does not happen
by itself. In order to have a larger amount of inputs and consequently more outputs,
entrepreneurs should exert themselves to organize more K and L. What would be the
incentive for entrepreneurs to produce more? They respond to a larger profit margin. Profit
is revenues minus costs. Revenues are Output Price times Quantity.
Costs are Input Price times Input Quantity. Profit = Total Revenue – Total Cost = P Q – ( r
K + W L). In the short-run, P and W determine the magnitude of profits; an increase in P
increases profits, and an increase in W decreases profits.
(4) Keynesian Aggregate Supply Curve
Basic assumptions are as follows:
i)
ii)
iii)
The time is too short for W to change, or
There are impediments on the flexibility of W, or
There is unemployment; there are other workers other than the present employees, who
are willing to work for less than the present real wage.
Graphic Derivation is as follows:
Macroeconomics
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
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

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Chapter V. AS-AD Model
Start with P1.
For the given price level, get the labor supply and labor demand curve in the second panel.
The intersection of the labor supply and demand curves gives the equilibrium level of
employment N1.
This feeds into YS1 in the aggregate production function.
YS1 = Y1 in the third panel.
Now in the fourth panel, Y1 matches with P1.
Suppose that the price level goes up to P2.
This sends both the labor supply and demand curves up.
However, the level of nominal wages does not change due to unions or money illusion. It is
the effective labor supply curve; note that it replaces the shift labor supply curve, which is
meaningless.
The new equilibrium level of employment is given at N2.
This feeds into the aggregate production function to give YS2 = Y2.
Y2 goes down to match P2.
By linking the two points of Y in the fourth panel, we get the Keynesian Aggregate Supply
Curve. It is upward-sloping.
𝑌𝑆
𝑌𝑆
𝑁
𝑊
𝑌
𝑃
(𝑊)
𝑃2
𝐸′
𝐹𝑖𝑥𝑒𝑑 𝑊 ∗
𝑁1∗

𝑁2∗ 𝑁 ∗
𝑃1
𝑌1 𝑌2
𝑌∗
Along the Keynesian AS curve, the nominal wage rates are fixed at W*. However, real
wages vary along the AS curve. That is because the money wage is fixed along the AS
curve, but the price level varies: The real wage (=W/P) must vary along the curve.
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Chapter V. AS-AD Model
This contrasts with the fact that along the previous classical AS curve, which is vertical, the
real wage is fixed but money wage varies.
Suppose that there is a huge excess capacity of production: this is possible as the economy
is just coming out of a big recession. Even a very small increase in the price level leads to
some increase in the revenues of companies (= P x Q), and the entrepreneurs will respond
to this increase in revenues in a big way by hiring a lot of new workers back to the
production process. We can have a very flat AS curve as well.
Depending on the elasticity of the supply side, we can get the almost horizontal SAS curve
as we have seen in Chapter 1.
𝑌𝑆
𝑌𝑆
𝑁
𝑊
𝑌
𝑃
(𝑊)
𝐸′
𝐹𝑖𝑥𝑒𝑑 𝑊 ∗
𝑁1∗
𝑁2∗ 𝑁 ∗
𝑃2
𝑃1
𝑌1 𝑌2
𝑌∗
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Chapter V. AS-AD Model
Intuitive Explanation for the upward sloping AS curve is as follows:
When P rises, W remains constant. The revenues increase while the costs are fixed, and thus the
profits increases. The larger profits will give a greater incentive for entrepreneurs or employers to
expand production scale by hiring more workers. If this expansion of output happens to all firms,
the aggregate supply will increase.
P increases with W being fixed  w(=W/P) decreases  Nd increases  N* increases 
AS = y = F (K, N) increases
The opposite can happen, too.
P decreases with fixed W w(=W/P) increases  Nd decreases  N* decreases  AS =
y = F (K, N) decreases
Let us explain the same thing in terms of real wages, which is nothing but the ratio of W and P or
W/P. The profitability is related to the ratio of W to P (=W/P), which is real wage or constitutes
‘real’ cost of hiring workers.
1) When W/P falls, the real cost of hiring workers is falling, the profit margin widens, and
thus more (incentive for) production (on the part of the entrepreneurs):
Real wage (W/P) decreases  Nd increases  Actual N* increases  AS = y = F (K, N)
increases
2) When W/P rises, the real cost of hiring workers is rising, the profit margin is reduced,
and thus less (incentive for) production (on the part of the entrepreneurs).
W/P increases  Nd decreases  Actual N* decrease  AS = y = F (K, N) decreases
Note: a larger W/P sounds like good news for the workers. You may be wrongly
reasoning: “a larger W/P means a larger incentive for the workers to work. The longer and
harder the workers are working, the larger the output. And the workers will have more
money to spend.” (This is the very wrong idea that Mr. Hoover had during the Great
Depression).
But it is not workers but entrepreneurs that make production decision. In the above case,
who will hire the larger number of more willing workers at such a high real wage level?
The willing workers will not be hired as they cannot force the entrepreneurs to hire them
above and beyond the latter want to.
So we are assuming that the actual amount of employment is determined along an
entrepreneur’s labor demand curve, not along the worker’s labor supply curve, and the
effective labor supply curve, which is basically the horizontal line from the fixed money
wage or W.
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Can you mathematically express the AS curves of the Keynesian and the Classical
economists?

Classical AS curve: Y = F(K, Nf) = Yf, say, 1000.
Keynesian AS curve: Y = F(K, Nf + dN) = Y – a (W/P), say = 1500 – 100 (W/P):
(W/P) increase then dN <0, so N < Nf and Y decrease,
(W/P) decrease then dN >0, so N > Nf and Y increase.
If W/P goes up, the real cost of hiring workers is higher now, and thus entrepreneurs would
like to hire less workers. The resultant output or AS will be smaller. If W/P falls, the real
cost of hiring workers is lower now, and thus more workers will be put into production
process and the resultant AS will be larger than the previous equilibrium or the full
employment level national income.
Some may argue that the Classical AS curve is valid in the long-run; and the Keynesian AS curve
is valid in the short-run;
Short-run AS = Keynesian AS
Long-run AS = Classical AS
One might have the SAS curve in the short-run when the time is too short for W to change and the
LAS curve in the long-run when enough time elapses for the adjustment of W.
5) Shift of Aggregate Supply Curves

i)
ii)
iii)
iv)
The Long-run AS shifts(to the right) when
∆K
∆Technology
∆Population
Positive Supply shocks
As the long-run AS shifts to the right, the level of long-run real national income or
full-employment real income rises.
The first two shifts the Aggregate Production Curve up and, at the same time, the
Aggregate Labor Demand curve up.
Population growth shifts the aggregate labor supply curve to the right (downward visually).
The last one, positive supply shocks, may send the aggregate production curve up.
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Chapter V. AS-AD Model
Combined or not, the shifts of the aggregate production curve and the corresponding
aggregate labor supply or demand lead to an increase in YS and Y as we can easily
illustrate on the 4 panel graph.
Over time, the first three happen to a growing economy. And it is called ‘economic growth’,
and the annual economic growth rate is measured by a percentage change in real national
income.
These issues will be examined in details in a later chapter of economic growth theories.

The Short-run AS shifts (to the right) when
The above four shift factors, and
v) ∆ Decreases in Money Wage
When the LRAS curve moves, the SRAS shifts, too, at all times.
However, it is not necessarily the case that when the SRAS shifts, the LRAS shifts: When there is
an increase in money wages, the SRAS shifts to the left (visually up), but the LRAS stays put.
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Chapter V. AS-AD Model
(1)An Increases in Money Wages or W:
Suppose that unions raise the fixed nominal wages to a higher level;
𝑌𝑆
𝑌𝑆
𝑁
𝑊
𝑃
𝑁𝑒𝑤
𝐹𝑖𝑥𝑒𝑑 𝑊 ∗′
𝑃2
𝐹𝑖𝑥𝑒𝑑 𝑊 ∗
𝑃1
𝑁 𝑑 (𝑃2 )
𝑁𝑠
(𝑊 ∗ )
(𝑊 ∗′ )
𝑁 𝑑 (𝑃1 )
𝑁1∗

𝑌
𝑁2∗ 𝑁 ∗
Along the AS curve, the nominal wage rates are fixed at W*.
𝑌1 𝑌2
𝑌∗
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Chapter V. AS-AD Model
(2)Technical Innovation
If we assume that there is no change in labor demand, but the technical innovation shifts up the
aggregate production function only, then N1* remains to be the equilibrium level of employment in
the labor market. However, the corresponding out level is higher and thus the long-run AS curve as
well as the SR AS will shift to the right to a new point of Y2.
(𝑊 )
𝐹𝑖𝑥𝑒𝑑 𝑊
𝐸′
∗
𝑁1∗
𝑁2∗
𝑃1
𝑌1
𝑌2 𝑌3
We can see that the LAS and SAS curves all shift to the right by the same amount and at the same
time: the height of the intersection of the SAS and LAS curves stays the same.
However, most technical innovations increases the productivity of labor forces as well. Thus the
demand for labor forces increases. In other words, technical innovation shifts up the aggregate
production function as well as labour demand curve. In this case, the equilibrium level of
employment will be at N2, and the corresponding level of national income is Y3. And thus the SAS
and LAS shift more to the right than the previous case.
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Chapter V. AS-AD Model
(3)An Increase in Production Cost(except for money wages) such as Oil Shock
In general, this is called ‘adverse or negative supply shock’. It shifts the aggregate production
function downward.
This permanently shifts the LRAS and SRAS to the left by the same amount.
𝑌𝑆
𝑌𝑆
𝑁
𝑊
𝑌
𝑃
(𝑊)
𝐸′
𝐹𝑖𝑥𝑒𝑑 𝑊 ∗
𝑁1∗
𝑃1
𝑁∗
𝑌1 𝑌2
𝑌∗
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Chapter V. AS-AD Model
3. ‘Grand Equilibrium’ of Aggregate Demand and Supply
1) Grand Equilibrium
Long-run AS
Short-run AS
P
P*
AD curve
Y*
Y
The intersection of the AD curve and the Long-run Aggregate Supply curve gives the
long-run equilibrium.
The intersection of the AD curve and the Short-run Aggregate Supply curve gives the
short-run equilibrium.
There are the corresponding equilibrium national income and the equilibrium price level
for the short-run and the long-run equilibrium respectively.
2)Short-run Adjustment to the Long-run equilibrium
What if the long-run equilibrium and the short-run equilibrium do not coincide with each other?
The long-run adjustment depends on the flexibility of Money Wage: If nominal wage or W is
flexible, then the SAS curve will move around so that the intersection of all three curves, i.e., LAS,
SAS, and AD, come to one point.
However, please note that the above adjustment of the SAS to the LAS is not automatic. It
critically depends on the background of the economy, particularly on the flexibility versus rigidity
of nominal wages.
If for some reasons money wage or nominal wage is not flexible in the long-run, the SAS will stay
suspended. This was the case of the Great Depression.
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Chapter V. AS-AD Model
Suppose that the short-run equilibrium Y < long-run equilibrium Yf;
P
AD
Y1
LAS
SAS
-- deflationary gap  Y leads to more competition among workers
For instance, Yf is below the long-run equilibrium or full employment income Yf. The
deflationary gap leads to a competition among unemployed workers and thus lower
nominal wages. The falling nominal wages shift the short-run aggregate supply curve to
the right. Eventually, a new short-run equilibrium will coincide with the long-run
equilibrium.
However, if there is an impediment to the flexibility of money wages, the SAS will stay
suspended, and will not move to the new position given by the solid broken line as shown
above. And the equilibrium national income Y1 will last for a long period of time, which is
below the full employment national income Yf. It is a sustained economic recession.

If initially short-run Y*>long-run Yf* and money wages are flexible, then there will
be an inflation gap developing, which will lead to upward pressure on money wage.
As money wage goes up, the SAS goes up as well. Eventually all the three curves of
SAS, LAS and AD, intersect at one point:
P
---
inflationary gap
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Chapter V. AS-AD Model
The short-run equilibrium national income exceeds the long-run or full employment
national income. This inflationary gap leads to an increase in the price level. The labor
supply in the market is tight. The competition for workers leads to a rising nominal wage.
Thus the labor supply curve will shift to the left until it passes through the long-run
equilibrium point where the AD and the Long-run AS curves intersect.
3) Applications of the AS-AD Curve Model: Economic History of the U.S.
(1) Industrial Revolution (1869 – 1897)
Statistical data shows:
Y*
100.00
299.00
Y*
1869
1897
P
LAS0
LAS1
P*
100.00
63.40
P*
SAS0
SAS1
SAS2
P1869
(100.00)
P1897
(63.40)
Yf1869
(100.00)
-
Yf1897
AD
Y
(299.00)
mainly due to LAS (SAS), which was in turn due to K, L, T during the American
Industrial Revolution
AD was stable due to no (slow) increase in (gold) money supply
An increase in population might have added, through an increase in C, I, and so forth, but
the overall it is no stronger than an increase in AS.
When LAS0 moves to LAS1, SAS0 moves to SAS1 by the same amount at the same
time(note that the intersections of the LAS and SAS before and after have the same height).
That is not the end of the story.
Note that the SAS moves once again from SAS1 to SAS2: Because the short-run
equilibrium national income given by the intersection of SAS1 and AD leads to a short-run
equilibrium national income Y (not indicated above: you may do so), and it is below the
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Chapter V. AS-AD Model
new full employment or long-run equilibrium national income Yf 1987.
In this case, just as we have learned, the SAS should move to the long-run equilibrium. As
SAS moves to the right for this reason, there is an additional increase in Y and a fall in P.
(2) The Great Depression (1929 – 1939)
Y*
100.00
70.00
105.00
1929
1933
1939
P
LAS
P*
100.00
75.00
100.00
SAS
AD193
Y*
<<
Yf
AD193
AD9192
3
9
Y
- puzzling question: Why SAS did not shift to the right when P level fell between 1929
and 1933?
The answer lies in the institutional downward rigidity of money wages that kept the SAS
there for a long period of time.
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Chapter V. AS-AD Model
If the money wages had fallen, YSR* would not have stayed below Yf for such a long period
of time:
LAS
P
SAS09
9
SAS1
AD39
AD29
Y
Y f  YSR  YLR
*
*
(This situation did not happen in 1929-1939)
(3) Pax Americana (1945 – 1962)
-
a resumed economic growth, shifting LAS and SAS (and is coupled with an increase in AD
due to the post-war expansion of government expenditures, consumption, and investment)
LAS 0
L A S1
P
SAS 0
SAS1
E'
e
Y 1*
Yf
Y f'
Y
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Chapter V. AS-AD Model
(4) Evolution of Inflationary Spiral (1968 – 1969 – 1980’s)
-:
:
:
P
Where people to do not have inflationary expectations, the economy
moves from (a) to (b) in the SR. As the general public catch on what is
happening to the price level, they demand a higher money wage and the
higher wage is reflected in the shift of the SAS curve from (b) to (c) in
the LR.
When people revise inflation expectations at the same time along with
the actual increase in the price level: one movement is from (c) to (d).
When inflation expectations are excessive, being higher than the actual
increase in the price level, and, in addition, the excessively higher
money wages are actually obtained by strong labour unions, one
movement is from (a) to (e)  The result is a decrease in Y below Yf,
and it is called STAGFLATION, which is the combination of
STAG(nation) plub (in)FLATION.
LA S 0
SAS3 LAS1
e

SAS2

d
SAS1
SAS 0

c
b
a
AD3



AD0
Y
*

Yf
AD2
AD1
Y
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Chapter V. AS-AD Model
(5)Oil Shocks (1972 – 1975)
:
:
P
Oil shocks – permanent (negative) AS shocks, shift LAS and SAS to the
left
Additional adjustment of AS curve
LAS1
LA S 0

SAS2

SAS1
 SAS 0
AD0
Yf'
Yf
Y
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Chapter V. AS-AD Model
4. Rational Expectations Revolution and New Classical Model
1) Assumptions
(1) Revised Labor Supply and Demand Curves
The entrepreneurs make a decision on labor demand on the basis of the actual real wages, which
are equal to nominal wages divided by the actual price level;
Nd = f (W: P, other variables).
This is the same as any previous models.
On the other hand, the workers make a labor-supply decision on the basis of their ‘perceived real
wages’, which are equal to nominal wages divided by the ‘expected price level’ of the current
period, being carried from the last period.
Ns = g (W: Pe, other variables).
We draw Ns curve with W or money wages on the vertical axis and N on the horizontal axis. P e
becomes a shift parameter.
W
Ns (Pe1)
W1
Nd (P1)
N1
Y
(2) Information Asymmetry is a norm for Unannounced Policies.
At time period t-1, workers and employers do form expectations as to the price level to prevail at
time period t, that is, Pe.
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Chapter V. AS-AD Model
At time t, the actual price level turns out to be equal to P. Of course, there is no guarantee that Pe =
P.
As soon as the price level reveals, the employers or entrepreneurs are updated, and do have correct
information about the current price level P. On the other hand, the workers do not have
information about it. The workers do have just the expected price level Pe, which is carried from
the last period.
Derivation of Lucas Aggregate Supply Curve for a fixed Price Expectations on the part of
Workers:
i) Information Asymmetry and the New Classical Labor Supply and Demand Curve:
Suppose that there is an increase in P, which the entrepreneurs recognize but the workers do not.
In other words, let us assume that there is information asymmetry between the employers and
the employees about the price level.
In this case, what will happen to the Nd (P1) and Ns (Pe1) curves?

This increase in P is unexpected on the part of workers, and thus Pe remains unchanged.
Thus the labor supply curve stays put.

However, the entrepreneurs are updated on the increase in P. Thus the labor demand curve
shifts up.
W
Ns (Pe1)
Nd (P2)
Nd (P1)
Y
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Chapter V. AS-AD Model
ii) Information Asymmetry and the New Classical AS Curve:
P > 0
Pe = 0
W* >0
P > W* > Pe = 0
𝑌𝑆
𝑌𝑆
45°
𝑁
𝑊
𝑌
𝑃
𝑃2
∆𝑊 ∗
𝑃1
𝑁1∗ 𝑁2∗

Lucas’s
AS
𝑁∗
𝑌1𝑌2
𝑌∗
Along the Keynesian AS curve, the nominal wage rates are fixed at W*.
The resultant AS is called “Lucas’s AS curve” or “Expectations-Augmented AS curve”.

Note that along this Lucas AS curve, the expectations about the price level are constant. In
other word, the expected price level is the shift variable for Lucas Aggregate Supply Curve.
As the workers or the general public revise their expectations as to the price level (up: it is
a numerical increase), Lucas’s AS curve shifts (it is visually a upward movement, but a
numerical decrease in AS).

Note that the increase in the nominal wages W is smaller than the increase in P.
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

152
Chapter V. AS-AD Model
As a result, in the mind of a worker, the perceived real wages have gone up: The expected
price level remains unchanged while the actual nominal wages have gone up somehow.
The labor supply rises along the curve.
However, the actual real wages, the nominal wages divided by the actual price level, have
gone down; the numerator has changed less than the denominator has.
iii) Revised Expectations and the Shift of Lucas Aggregate Supply Curve
Recall that, as P1 goes up to P2, Nd curve shifts up on the part of entrepreneurs but Ns remains
constant reflecting a constant Pe on the part of workers: This is needed to derive LAS(Pe1 ) curve.
Now what will happen if the workers revise their expectations? The Ns will shift up as shown
below, there will be two corresponding points to the two different price level P1 and P2.
𝑌𝑆
𝑌𝑆
45°
𝑁
𝑊
𝑌
𝑃
𝑃2𝑒
𝑃1𝑒
𝑃2
∆𝑊 ∗
𝑃2
𝑃1
Lucas AS (𝑃2𝑒 )
Lucas AS (𝑃1𝑒 )
𝑃1
𝑁3∗ 𝑁1∗ 𝑁2∗
𝑁∗
𝑌3 𝑌1𝑌2
𝑌∗
Note that Y1 here coincides with the full employment national income.
iv)A vertical Long-Run Aggregate Supply Curve or LRAS is still valid here as well. This is the
line passing through the points where expected price levels are the same as actual price level. In
the long-run the perception will come in line with the reality.
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Chapter V. AS-AD Model
(3) Policy Invariance Theorem for Fully Anticipated Government Policies
How convincing is the assumption of Information Asymmetry as assumed above?
Generally it did make a sense prior to the 1980s. However, in today’s world of the
post-information-revolution society where the general public has access to all kinds of information
including government policies, information asymmetry may not be sustainable. The general
public has the same access to information of the government’s policy model and all the input data.
With this parity-of-information between the general public and the government or the policy
maker, the assumption of information asymmetry between the employers(entrepreneurs) and
employees(workers) is unsustainable. It is all the more so in a democratic society where every has
equal access to all kinds of information and information is efficiently propagated. This is
particularly so when government announces its proposed policy and its forecast economic impacts
in advance. The ‘honest’ government may be educating the general public in this case.
A well-announced economic policy with deterministic rules will not have any impact on the
real variables such as real national income- Policy Invariance Theorem
Suppose that even the workers are fully updated on a change in the price level: The government
announces its policy well in advance to the general public and carries out the policy in the honest
and open way. The general public have time to understand the impact of the proposed policy on
the price level and thus to revise their expectations about the price level. What will happen to the
labor supply and demand curves?
Ns (Pe2)
W
Ns (Pe1)
Nd (P2)
Nd (P2)
P
Note that P = Pe = W* > 0 in this case.
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Chapter V. AS-AD Model
What is the resultant AS curve in this case?
𝑌𝑆
𝑌𝑆
45°
𝑁
𝑊
𝑌
𝑃
AS
𝑃2
∆𝑊 ∗
𝑃1
𝑁1∗
𝑁∗
𝑌1
𝑌∗

Along the Keynesian AS curve, the nominal wage rates are fixed at W*.
The resultant AS is the same as the long-run AS curve.

Note that the increase in the nominal wages W is proportional to the increase in P.

This happens in the long-run when the workers are fully updated on what is happening to
the price level, and the money wages become flexible even if they are not so in the
short-run.

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Chapter V. AS-AD Model
Another way of looking at the above is as follows:

We can think of the above vertical long-run AS curve as Lucas’s AS curve shifts up as the
expectations are revised as given below:.
𝑌𝑆
𝑌𝑆
45°
𝑁
𝑊
𝑌
𝑃
LAS (𝑃2𝑒 )
𝑃2
LAS (𝑃1𝑒 )
∆𝑊 ∗
𝑃1
𝑁1∗

𝑁∗
𝑌1
Along the Keynesian AS curve, the nominal wage rates are fixed at W*.
𝑌∗
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Chapter V. AS-AD Model
4. New Keynesian AS curves
1) Assumptions
i)Rigidity of Nominal Wages;
In the New Keynesian model of labor market, the nominal wage is set at t-1 through labor
contracts, and the level of employment is to be determined at time period t.
ii) Long-term Non-indexed Labor Contract: Just like the Keynesian AS curve model, the
wages are set in advance through the long-term non-indexed contract.
iii) The labor contract sets nominal wages at time t-1. The workers are bound by the contract to
work at the set wage rates as much as is required by the entrepreneurs. The level of
employment is flexible to be determined according to the labor demand at time t.
Ex-post revisions of expected price levels do happen, and shift the labor supply and demand
curves around. However, the labor supply curve is redundant as it is effectively replaced with
the wage line, which is set through the contract. The equilibrium takes place where the
horizontal nominal wage line intersects the newly shifted labor demand curve.
2) Derivation of New Keynesian AS curve
Graphic Derivation is as follows:












Start with P1.
For the given price level, get the labor supply and labor demand curve in the second panel.
The intersection of the labor supply and demand curves gives the equilibrium level of
employment N1.
This feeds into YS1 in the aggregate production function.
YS1 = Y1 in the third panel.
Now in the fourth panel, Y1 matches with P1.
Suppose that the price level goes up to P2.
This sends both the labor supply and demand curves up.
However, the level of nominal wages does not change due to unions or money illusion. It is
the effective labor supply curve; note that it replaces the shift labor supply curve, which is
meaningless.
The new equilibrium level of employment is given at N2.
This feeds into the aggregate production function to give YS2 = Y2.
Y2 goes down to match P2.
By linking the two points of Y in the fourth panel, we get the New Keynesian Aggregate
Supply Curve. It is upward-sloping.
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Chapter V. AS-AD Model
YS = Y
450
P2
(New
Classical)
Fixed W*
P1
N1*
NKAS
N2*
Y1
Y2
3) Comparison of the New Classical and the New Keynesian AS curves

Note that the slope of New Keynesian AS curve is flatter than the corresponding New
Classical AS curve: if we look at the labor market only for a unexpected rise in the price
level, the comparison is as follows:
New Classical Eq.
Ns (Pe1)
New Keynesian Eq.
Nd (P2)
Nd (P1)
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
158
Chapter V. AS-AD Model
Comparison of New Classical and New Keynesian equilibriums:
YS = Y
450
P2
New
Classical
Fixed W*
P1
N1*

N2*
NKAS
Y1
Y2
Note that the slope of New Keynesian AS curve is flatter than the corresponding New
Classical AS curve: if we look at the labor market only for a unexpected rise in the price
level, the comparison is as follows:
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Chapter V. AS-AD Model
5. Putting them all together in a complete macroeconomic model with the AS and AD curves.
So far we just assume that there is an increase in the price level P. Why or how does it happen, or
what causes this rise in the price level?
In reality a rise in the price level or inflation is most likely the result of government’s expansionary
fiscal or monetary policies, which shift the AD curve.
Suppose that government increases nominal money supply or MS. It will put a train of economic
sectors in motion:
First, the real money supply curve ms will shift to the right.
Second, the LM curve will shift to the right.
Third, the AD curve will shift to the right.
Now, when it comes to the response of the AS side, there are different assumptions for different
circumstances:
1) If the increase in Money Supply is unanticipated or unexpected for the workers or
the general public, then the SAS curve does not move at all in the short-run.
2) Even if the expansionary monetary policy is unexpected, eventually in the long-run
the general public will figure out the consequent increase in the price level. Suppose
that there is no institutional wage rigidity in the labour market. As they demand a
higher money wage so as to recover the real wage, the money wage will rise and the
SAS will reflect the wage(labour cost) increase and thus decrease(shifting to the left
or up visually).
3) If the expansionary monetary policy is announced well in advance and is executed by
the monetary authority as announced, and at the same time, if there is no
institutional money wage rigidity, then there is the Policy Ineffectiveness Theorem
holding once-for-all, i.e., in the short-run as well as in the long-run.
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Ch VI. Consumption
Sectoral Analysis
Chapter VI. Consumption Function
1. Keynesian Theory
1) Background
We have learned that the Keynesian consumption function in general takes the form
C = C 0 + c1 Yd
= C 0 + c1 ( Y - T ),
where C0 is the basic consumption, c1 the marginal propensity to consume, and Yd the
disposable income which is equal to income minus taxes. Implicit herein is the assumption that
changes in income and changes in consumption are contemporaneous.
Ct = C0
+ c1 Yd t
= C 0 + c1 ( Y t - T t ).
So by introducing time subscript, we can rewrite the above as
Keynesian economists estimated consumption function by obtaining a best fitting line with
time-series data of disposable income and consumption.
For instance, with the U.S. yearly data of the period 1929-1941, the consumption function for
the whole U.S. economy was estimated as
Ct = 47.6 +0.73 Ydt
(unit: in 1972 Billion U.S. dollars);
With the Canadian yearly data of 1926-1940, the consumption function for Canada was
estimated as
Ct = 3.0 + 0.69 Ydt
(in 1972 Billion Canadian dollars).
So we can make a prediction as to the magnitude of consumption if we have a reasonable
forecast about income. Alternatively, as we have seen in the above Question #1, we can get
the value of the APC for a predicted level of national disposable income

Question #1: Suppose we have obtained the consumption function in Question #1 from
the past data. What is the APC for a personal disposable income of $ 150 billions in
1972 dollars?
The answer is 0.71; the consumption is 3.0 + 0.69 times 150 from the equation, and is
equal to 106.5. The APC is this consumption $ 106.5 billions divided by the total
disposable income $ 150 billions.
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
161
Ch VI. Consumption
Question #2: Suppose we have obtained the consumption function in Question #1 from
the past data. What is the APC for an personal disposable income of $ 200 billions in
1972 dollars?
The answer is 0.705; the consumption is 3.0 + 0.69 times 200 from the equation, and is
equal to 141. The APC is this consumption $141 biiions divided by the total disposable
income $ 150 billions.
2) Implications of Keynesian Consumption Model
Two corollaries we can draw from the above equation are

Average Propensity to Consume (APC) is larger than Marginal Propensity to Consume
(MPC); more importantly, the APC decreases as income increases. This implies a
non-proportionality between an increase in income and the responsive increase in
consumption. As income rises, a smaller and smaller portion of income will be spent as
consumption. The above questions #1 and 2 illustrate the APC falls as income
increases.

The estimation of the Marginal Propensity to Consume (MPC) enables government
policy makers to compute the multiplier and thus to know exactly how much
government expenditures or taxes should be adjusted in order to increase the national
income by the target amount.
Quite important implications behind the two points are as follows:

The first point is a terrible prognosis for a growing economy.
The APC shows the proportion of the total income to be consumed. A small APC
means a small portion of income to be transformed into expenditures.
Savings are, in the circular flow model of the Keynesian theory, a leakage, which
lowers the Aggregate Expenditures and subsequently the level of the national income in
the next round.
As the APC decreases in a growing economy, an increasingly larger proportion of
income is saved away and thus there occurs a deficiency of aggregate expenditures.
The aggregate output continues to grow while the aggregate expenditures stagnate due
to an increasingly larger proportion of income to be saved away. The result is a secular
stagnation. This implication that a growing economy will be inevitably faced with
Secular Stagnation due to a deficiency of aggregate expenditure or an excessive saving
is in line with Marxists' argument that the capitalist economy is bound for general glut
due to excessive savings by stingy capitalists.

In the Keynesian view, the second point is a miracle cure for the problem of a falling
APC: By using the multiplier government may know exactly how much it has to
supplement the aggregate expenditure which is not sufficient if left to the private sector.
3) Keynesian Justification
The Keynesian Proof of the first point of a declining APC in the face of a growing income is as
follows:
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Ch VI. Consumption
By definition, in general, the marginal propensity to consume (MPC) is the ratio of the
responsive increase in consumption to a unit increase in income. It measures what proportion
of an incremental increase in income is consumed. The average propensity to consume (APC)
is the ratio of the total consumption to the total income. It measures what proportion of the
total income is consumed.
APC =
C
dC
, and MPC =
.
Y
dY
(1) Illustration
Graphically, the MPC is the slope of the consumption curve and is constant over the entire
range of income.
The APC measured at a certain level of income is the slope of the ray which links the origin and
the corresponding point on the consumption curve.
R1
R2
0
At Y1, MPC = c1; APC = Slope of the OR1 ray.
At Y2, MPC = c1; APC = Slope of the OR2 ray.
(Note: the OR1 is steeper than the OR2, and therefore; APC at Y1 >> APC at Y2.)
Algebraically, we can also show that
As Ct = C1 + c2 Ydt,
C t C0
Yd
=
+ c1 t = C 0 + c1 .
Yd t Yd t
Yd t Yd t
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Ch VI. Consumption
So the APC is the MPC plus a positive term. And thus APC - MPC = C0/Ydt which is positive.
Therefore, APC >> MPC.
We note that the term C0/Ydt is a decreasing function of income level; the numerator C0 is
constant regardless of the level of Yd. As Yd increases in the denominator, the ratio falls.
Therefore, the APC falls as income increases. A smaller and smaller proportion of
income will be spent and thus be transformed into the aggregate expenditures. This
means that the average propensity to save rises as income increases.
Ydt = Ct + St
Dividing the both sides of the above equation by Ydt, we get
1 =
Ct
Yd
+
t
St
Yd
.
t
As the income is increasing, the APC is falling and the APS is rising.
(2) Numerical Example
The consumption equation (unit: in 1971 Billion dollars) is given as
Ct = 3.0 + 0.69 Ydt.

What is the MPC?

What is the APS at Ydt = $ 150 billion? What is the APS at Ydt = $ 200 billion?

These feature,
i) "dAPC/dYd < 0" or the APC falls as income increases, and
ii) "APC > MPC", basically the same results from the fact that the
consumption function has an intercept.
If the consumption function is a ray from the origin and thus without any intercept, the APC
will be equal to the MPC and the APC would be constant all the time just like the MPC. The
APS will be constant over the entire range of income. As income rises, the increase in
consumption is proportional to the increase in income.
4) Two Empirical Anomalies
Upon the Keynesian theory, economists who have been working on historical data have found
two empirical anomalies:
1) "The estimated consumption function underpredicted the consumption for a higher level of
income";
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Ch VI. Consumption
For instance, income has grown over time after World War II. We have seen that by
substituting the forecasted level of national income into the estimated consumption function,
we can get the predicted value of consumption and thus the APC. Economists did so in the
pre-war time for the post-war era. Over time it was revealed that the consumption level
predicted in the pre-war time for the post-war era was smaller than the actual post-war
consumption. Also the predicted APC turned out to be smaller than the actual APC. For
instance, when we predict the APC for the disposal national income level of $150 billions, it is
about 0.71. However, historically, when the actual income was equal to $150 billions in
Canada, the actual APC was about 0.85 rather than 0.71.
A few possibilities;
The first one is people have become more prodigal in the post-war period. The MPC might
have increased in the post-war period compared to the MPC of the pre-war period. And thus
the APC might have increased over time, too.
The second possible scenario is that the average and marginal propensities might have been
wrongly measured in the estimation process. And there might have been a systematic error in
estimating consumption.
If the first is true of the two possibilities, the Keynesian consumption function would be
preserved, and there would be no further need for research geared to improving economic
theory. This is an academically uninteresting case.
2) "The long-term APC thus APS were constant over a long period of time"
Professor Simon Kuznets estimated the long-run APC by observing the changes in
consumption and income during a considerable long period of 1869 to 1933, and found that the
long-run APC was constant at 0.89 over time. This result contrasts with the estimation result
from a relatively short-period data.
This implies that there are two kinds of consumption curve, short-term and long-term:

The long-run consumption curve can be drawn as a ray from the origin;

There, long-run APC = long-run MPC as there is no intercept; the APC and APS are
constant over the entire range of income.

long-run MPC >> short-run MPC if the short-run consumption curve is based on the
yearly changes in income as shown above.
In attempts to resolve these anomalies, some alternative hypotheses about the consumption
behaviour were proposed. These alternative consumption theories differ in the length of the
time-horizon over which consumers are assumed to make consumption decision.
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Ch VI. Consumption
2. Permanent Income Hypothesis
1) Basic Ideas
M. Friedman says that the current consumption is a function of permanent income Yp.
Ct = ctrue Y p ........ (1).
Permanent income is a sort of income stable in the long run. Its calculation requires an
observation over multiple periods of time. ctrue is a true value of marginal propensity to
consume measured out of permanent income. This contrasts with c 1 or the simple and
conventional Keynesian type of marginal propensity to consume measured out of current
income.
2) Fictitious Keynesian Consumption Function
He argues that in order to get the correct consumption function we should lengthen the period
of observation, or should observe income and consumption for a sufficiently long time. Trying
to attribute changes in current consumption to changes in current income would lead to a
fictitious or erroneous consumption function.
The following example will be helpful in your understanding his point;
For instance, suppose that in an economy all the people are identical and homogeneous
who are all paid $ 110 per week. The only inter-personal difference is that the one sixth
of workers are paid on each day of the weekdays. So 1/6 are paid on Monday, another
1/6 on Tuesday, and so on... Let suppose that the workers spend more, say $ 40, on the
pay day, than on other days of the week, say $10 per day. So they save $ 10 each week.
A Keynesian economist would like to examine the relationship between current income
and current consumption. And s/he chooses a day of the week, say, Monday, and
observes the receipts and expenditures of the workers on the very day.
S/he will find two groups of people with different income and consumption;
─────────────────────────────────────────────
Monday’s Income
Consumption
─────────────────────────────────────────────
1/7 of the workers
$ 110
$ 40
The rest of them
$ 0
$ 10
────────────────────────────────────────────
The economist would (wrongly) reason that the basic consumption (C1), which is
necessary even there is no income, is $ 10, and calculate the MPC = dC/dYd =
approximately 0.3 because dY = 110 and dC = 30 between the two groups of the
workers. So s/he will get a Keynesian consumption function C = 10 + 0.3 Y.
However, when lengthening the period of observation or time span for the calculation
of income and consumption from a day to a week, the above fictitious Keynesian
consumption function will disappear; there is only one kind of workers who are all paid
$ 110 and consume $ 100: about 90% of income is spent on consumption. The resulting
consumption function will be C = 0.9 x Y (which has no intercept). Friedman thinks
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Ch VI. Consumption
that extending the time horizon to a year would not completely eliminate the above
error. He does not specify the time horizon.
3) Two Period Model of Permanent Income Hypothesis
Permanent income is a weighted average of the past and current incomes. How far back into
the past? The PIH itself is silent as to the specific length of time-horizon the consumer look
over in making consumption decision. For practicality's sake, we have to cut it off somewhere
in the time-point of the past. In a simplified version of the two-period model;
Y p = Y t -1 + ( Y t - Y t -1 )
=  Y t - (1 -  ) Y t -1 ....... ( 2 ),
where θ is in the range between zero and one, and indicates the extent to which people regard
the current increase in income as permanent.
For instance, people assign 1 to θ when they regard the entire increase in income as permanent
or persisting in the future. Then all the change in the current income will become the change in
permanent income, and the c1 (=MPC) fraction of the increase in permanent income will
translate into a change in consumption.
However, they will assign 0 to θ when they regard the entire increase in income as transitory or
temporary. The increase in current income will not affect the permanent income, and therefore
there would not be any change in consumption.
What is the MPC? There are multiple MPC's depending on what income to use in measuring
the MPC.

When the MPC is measured against the permanent income: MPC measured out of
permanent income = dCt /dYp .
Differentiating both sides of equation (1) with respect to Yp, we get
dCt / dYp = cture.

The MPC measured out of current income (Yt) = c1= dCt / dYt;
Substituting equation (2) into equation (1), we get
C t = ctrue Y p
= ctrue {  Y t + (1 -  ) Y t -1 }
= ctrue  Y t + ctrue (1 -  ) Y t -1 .
Differentiating the above equation with respect to Yt, we can get
c1 = d Ct/dYt = ctrue θ.
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Ch VI. Consumption
Obviously, ctrue > ctrue θ, because 1 > θ and thus cture x 1 > ctrue x θ.
The larger θ is, the larger the impact of changes in current income on permanent income and
consumption;
(1) When θ is equal to one, the MPC measured out of permanent income will be just
equal to the MPC as is the case of the Simple Keynesian consumption function.
(2) When θ is equal to zero, the MPC measure out of permanent income will be zero
because there is no change in permanent income and thus no change in consumption.
The increase in income will be mostly saved, and thus the ratio of saving to income will
rise.
(3) Usually 0 < θ < 1. The MPC is measured out of.
Historical Evidence that a transitory increase in income or windfall of income does not increase
consumption very much.
(1) There was a one-time restitution payment from Germany to the Israeli citizens. The
payment was equal to the average annual income per household. Only 20 % of the
amount received was spent out as consumption.
(2) In 1950, there was a unanticipated, one-time payment of life insurance dividends to
the U.S. Word War Two veterans. It was $ 175, which amounted to 4 % of annual
household income. Consumption rose only by 1 % that year (less than 30 % of the
windfall increase in income was spent).
4) Life Cycle Hypothesis
Life Cycle Hypothesis specifies (1) the time horizon, which the consumer consider in
making consumption decision, as her/his life time, and (2) include wealth in the income and
thereby regarding wealth as making differences in consumption for a given level of labor
income.
(1) A consumer's time horizon is equal to her/his life time;
the consumer will first figure out the total amount of resources available for consumption
during his/her entire life time. This total amount of resources available during the life time is
called 'Life-time Budget Constraint', which is specified, assuming life span is 75 years, as
( Y t+2 - Tt  2 )
(
)
Disposable Y lcbc = ( Y t - T t ) + Y t+1 T t+1 +
+ .......
(1 + r t )
(1 + r t )(1 + rt+1 )
+
( Y t+75 - T t+75 )
.
(1 + r t )(1 + rt+1 ).......(1 + rt+75 )
Note that the Life-time Budget Constraint is the Present Discounted Value of all income over
the life span; the future income is discounted with the relevant interest rates for the time
interval between the present and the future time points; So the life cycle budget constraint is the
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Ch VI. Consumption
Present Discounted Value of the present and future income over the entire life span.
The consumption will be given as
Ct =
C t+1
C t +2
=
(1 + r t ) (1 + r t )(1 + r t+1
= ....... =
C t+75
.
(1 + r t )(1 + r t+1 ).......(1 + r t+75 )
If we assume that r = 0 at all time periods, fist the life-time budget constraint becomes
Disposable Y lcbc = ( Y t - T t ) + ( Y t+1 - T t+1 ) + ( Y t+2 - T t+2 ) + ....... + ( Y t+75 - T t+75 ).
Secondly, consumption function becomes
C t = C t+1 = C t+2 = ....... = C t+75= C .
Note that consumption is equalized over time, and the actual level of consumption depends on
the life-cycle budget constraint which in turn is a function of the current and future income over
life time. Broadly speaking consumption function is given as
Ct = f ( Y t , T t , Y t+1,T t+1,.......,Y t+75,T t+75 )........(c).
Let us examine some implicit assumptions behind this life-cycle hypothesis before making
more realistic modifications to them;
(1) There is No Uncertainty. The L.C.H. assumes perfect foresight for the consumer;
s/he is assumed to know the entire profile of current and future incomes. When s/he is
born at time t, s/he knows what the current and future personal disposable incomes are
and what the current and future taxes are. Government is acting along a preannounce
path of policies.
(2) The preference of the consumer is that s/he can maximize her/his utility over time
by smoothing the consumption profile or by spreading consumption evenly over time.
The equal amount of consumption for each period will maximize the total utility,
because of the decreasing marginal utility of consumption.
Here a tax cut or decrease in tax (dTt+25), say, at time t+25, does bring about no increase in
consumption at time t+25 compared to that at time t+24 or dCt+25 = Ct+25 - Ct+24. It means
dCt+25/dTt+25=0. That is because the tax cut was already correctly and completely predicted and
thus consumption was already adjusted (at time t or at the beginning).
(2) Wealth matters;
Consumption is a function of life-time labor income and wealth;
Ct = c YL + a WL, where
YL is the (life-time) labor income and WL wealth.
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Ch VI. Consumption
For a given level of labor income, at a personal level, the larger wealth one has, the
larger APC will be when it is measured against (conventional labor) income;
Ct/Yt = c YL/Yt + a WL/Yt.
5) Modern Frontier Consumption Theory
(1) In the real economy, there is uncertainty to the future. The best one can do is to make an
educated guess, or to form expectations by efficiently utilizing information contained in 'news'.
Now consumption depends on the current and all the expected future incomes during the life
time; A revision of expectations provoked by the receipt of news about the occurrence of shock
or unanticipated events involving future disposable income will lead to changes in
consumption; the modified Life Cycle Model in the presence of uncertainty will be
*
*
*
*
C t = f ( Y t , T t , Y t+1 , T t+1 , .......,Y t+75 ,T t+75 )........(d).
where * means expected future variables.
Example:
For instance, government may suddenly announce at time t that it will decrease tax at
time t+25. This comes as surprise or shock as it was an unanticipated, unforeseen,
unpredicted event. The 'news' leads to the revision of the expectations of the future
income (Tt+25*). Therefore, the Expected Life-cycle Budget Constraint will be revised
upward at time t, and accordingly consumption level will be raised once-and-for-all at
time t.
When actually the tax is raised at time t+25, nothing is out of blue. The event has been
fully anticipated, and perhaps by this time all the necessary adjustments have been
made. Thus the tax cut at t+25 would not bring about any adjustment in consumption at
time t+25.
The changes in tax and consumption are not contemporaneous any more; at time t,
consumption changes even if there is no change in tax or current disposable income. At
time t+25, there will be no change in consumption while there occurs changes in
disposable income due to the tax cut. Probably, by now, all the necessary adjustments
have been made in response to this fully anticipated tax cut.
(2) The time-horizon may extend beyond life-time if the consumer cared about the welfare of
her/his descendant(s), and so on for each subsequent generation.
Suppose there is a tax cut at time t+25, and the decrease in government revenue due to
the tax cut will be offset by an increase in the revenues from issues of bonds. As the
bonds have maturity and should be retired sometime in the future. Let us also suppose
that government is planning to retire these bonds by increasing tax at the year t+76, a
year after the death of a particular consumer. Within the framework of L.C.M. which
regards the time horizon of a consumer as being limited to her/his life time, the
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Ch VI. Consumption
consumer can enjoy the benefit of tax cut and avoid the future tax-liability (s/he dies at
the year t+25). So the tax cut will be regarded as bonanza or windfall gains and lead to
increases in consumption.
However, it s/he cares about the future generation, s/he will give weight to the
disposable income and expenses of the future generation. In the above case, s/he would
like to lessen the future tax liability to be imposed upon her/his children. So s/he will
save the benefits from tax cut by buying bonds newly issued, and bequeath bonds to the
descendant. At the year t+76, the descendants will cash the bonds and pay the increase
in tax-liability which is necessitated for the repayment of government debts. In this case,
all the government does is to move tax over the time horizon, and thus to delay taxation.
That kind of `intertemporal reallocation of taxation' does not alter the total amount of
resources available for a consumer. The consumer will not change her/his consumption
behaviour. Therefore there is no further impact on economy. So the Ricardian
Equivalence holds (which says that switching from one method of financing to another
does not matter, or that deficit-financed and tax-financed government fiscal policies are
equivalent, unlike the Keynesian argument that there is no equivalence between the two
because the former is more effective with the associated multiplier (=1/{1-c}) having a
larger magnitude than the latter with the corresponding multiplier which is equal to
one). Here the consumer acts as if s/he would live an infinite life. The
inter-generational link is the bequest (motive).
Now in the infinite time horizon model, a general form of consumption function should be
again modified as a function of income and tax variables of the current and all the future time
points up to the infinity;
*
*
*
*
C t = f ( Y t , T t , Y t+1 , T t+1 , ......,Y t+75 ,T t+75 .... ).....(e).
(3) Liquidity Constraint
L.C.H. assumes that the consumer can completely smooth the consumption profile by
effectively financing current consumption with future income. This is possible when
one has an unconstrained access to credit market, and thus can borrow or lend freely.
In reality, a lot of people have only limited access to credit market. Particularly this is
the case for those who have wealth in the form of human capital. For instance, most
people agree that students will earn more income in the future. But risk-averse people
will not give unlimited credit to students. The students are faced with liquidity
constraint and their consumption is below the desired level. When the liquidity
constraint is lifted up, there will be increase in consumption because the previous
consumption is somehow suppressed.
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Ch VI. Consumption
Application:
1) Consumption Function and Tax Cut (Fiscal Policy)
Why does the specification of consumption function make difference in fiscal policy
implications?
The consumption function is important because it characterizes a most important link within
the mechanism of fiscal policy.
Once a renowned economist Professor Edmund Phelps asked in the class, “What is the ultimate
purpose of tax?". The answer is that through Taxation and consequent changes in disposable
income the government can affect Consumption. Changes in consumption, which is the
largest component in the Autonomous Expenditure or YD, will bring about changes in
equilibrium national income. So the sequence of fiscal policy involving tax cut is that dT
(changes in T)  dPDI  dC  dYD = dAE  dYe.
It can be explained in the following details;
The tax multiplier or dYe/dT can be broken into the chain of functional relationships such as
e
e
dY
dY dYD dC dPDI
=
.
dT dYD dC dPDI T
Note that the first component is the multiplier which is equal to 1/{1-c1}. The second
one is always one because YD = C + I + G; C will increase YD at the one dollar-to-one
dollar ratio. The third is the MPC whose magnitude depends on the specification of
consumption function. The last component dPDI/dT = d(Y-T)/dT is one in the
Keynesian consumption theory, while in the PIH dPDI/dT = dYp/dT = θ.
The purpose of this chapter is that depending on the link dC/dPDI and dPDI/dT, the
impact of tax cut on national income is not that simple, and varies much. We will examine
how the modification of the simple Keynesian consumption function could alter the
implications of fiscal policy, particularly tax-cut.
2) Permanent Income Hypothesis
In the context of the PIH, the tax multiplier which indicated the impact of tax cut on
equilibrium national income can be broken into
e
e
dY
dY dYD dC dPDI
=



.
dT dYD dC dPDI
T
We can show the following:
Y t = Ct + I t + Gt .
Permanent Yd t = (Y - T ) p =  ( Y t - T t ) + (1 -  ) ( Y t -1 - T t -1 ).
Yd t = c x permanent PDI t + I t + Gt
= c {  ( Y t - T t ) + (1 -  ) ( Y t -1 - T t -1 } + I t + Gt .
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Ch VI. Consumption
At equilibrium YS = YD, where YS = Y and YD is as given as above,
Y t = c {  ( Y t - T t ) + (1 -  ) ( Y t -1 - T t -1 )} + I t + G t
= c  ( Y t - T t ) + B + I t + Gt ,
where B = (1 -  ) ( Y t - 1 - T t - 1 ) .
( 1 - c  ) Y t = -c  T t + I t + Gt, so
e
Y t=
1
{-c  T t + I t + Gt }.
1- c
The PIH suggests that the tax cut will shift the IS curve only by the θ fraction of the distance of
shift of IS as is suggested by the Keynesian model.
3) Life-cycle Income Hypothesis
We know that the present tax cut leads to budget deficit at the margin, and necessitates the issue
of bond. The crucial point is when the bond will have to be retired sometime in the future, and
that this retirement will be done by a tax increase. So basically all the government does in
cutting tax is to delay tax over time. The crucial matter for the consumer is whether the bond
will be retired and at the same time tax will be increased for that purpose; if the present tax cut
has a tax increase within the life time, the consumer knows that s/he cannot escape the future
tax liability and thus will not regard the present tax-cut as `free lunch.' S/he saves the increase
in income which results from the decrease in tax by buying bonds, and will keep them until the
tax raise. Then s/he will cash the bonds and pay the increased tax. In this way her/his
consumption is kept smooth, and needs not be swayed by the whimsical government policies
against her/his preferences.
4) Modern Frontier Consumption Function
(1) If the L.C.H is true and correct, and if the government will correct the future tax after
her/his death, then the present tax cut is regarded as `free lunch,' whose bill will have to be
picked up by the future generation s/he does not care about. Her/his consumption will increase
upon the news that there will be a tax cut. So in this case of finite time-horizon model, the
Ricardian Equivalence fails to hold.
If the time horizon is infinite because a generation cares about its subsequent generation, the
consumer will behave as if s/he lives an infinite life; s/he equally weighs the present tax cut and
the future tax liability. S/he will save the benefit from the present tax cut and bequeath the
saving to the future generation or ‘bequest’, which will be cashed to pay the (future) tax
liability, which originated from the tax cut. The bequest motive is the operational link between
generations.
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Ch VI. Consumption
(2) Rational expectations theory says that in the real world with uncertainty, consumption is a
function of the current and all expected future incomes. Therefore expectations about the
future affect current consumption behaviour. Whenever there is a revision of expectations
about the future, which is prompted by the receipt of news about unanticipated event, there will
be changes in consumption.
Anticipated changes in income, or fully foreseen tax cuts would not bring out any concurrent
changes in consumption, when actually the tax cuts happen. Because the tax cuts were fully
anticipated in the past and were acted upon it at that time of perception, by the time when
actually the even occurs, all actions have been taken and no further actions will be left to be
taken.
In summary, only unanticipated shocks will bring about changes in consumption, and therefore
the changes in consumption will be unpredictable or 'random walk.'

Example: There is no actual tax cut now at time t. But there is 'news' about the future
tax cut of time period t+5. The consumer will revise expectations about the future
income upward. The extent to which s/he revises expectations also depends upon
her/his judgement as to whether the tax cut is permanent or temporary, or in other
words, whether it is for one period or for multiple periods. As her/his expected future
income increases, her/his consumption will increase now at time t. At time t+5 when
actually the fully anticipated tax cut happens, there would not be any change in
consumption.
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Ch VII. Investment
Chapter VII. Investment Function
1. Definition
Investment consists of



Fixed Capital Investment: Machinery, Equipment,
Non-residential Building, and Residential Construction
Addition to Inventory: finished goods and materials on the pipeline, and also buffer stock
of finished goods.
We can also divide the total or gross investment into replacement investment or capital
consumption allowances and net investment;
Gross Investment = Net Investment + Depreciation
There are suggestions to include Consumer Expenditures for Durables in Investment.
2. Biggest Issue: Volatility of Investment
Investment is much more volatile than income or consumption; Inventory Investment is still more
volatile.
3. Explanations for Volatility of Investment.
1) Keynesian Accelerator Model of Investment
(1) Model
Inverting the following Aggregate Production Function with labor input being held constant
Y t = F ( K t , N t ).
we can rewrite the above equation into;
K t =  Y t , > 1.
We can also apply this to the last period;
K t -1 = Y t -1 .
Investment is the increase in capital stock which is proportional to the increase in (the
production of aggregate output, which is equal to) national income;
I t = K t - K t -1 =  ( Y t - Y t -1 ).
Differentiating both sides with respect to time t, we get
( )
dI t
=  Y t Y t -1 .
dt
dt
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Ch VII. Investment
The rate of change in investment depends on the acceleration/deceleration of the growth rate of
income, or the change in the rate of change in income.
(2) Numerical Example:
Assumption: Ct = 50 + 0.8 Yt, It = 3 (Yt - Yt-1).
Note that v =3 here.
──────────────────────────────────────────────────
Year Yt
% change
Ct
% change
Kt
It
% change
──────────────────────────────────────────────────
450
410
1350
2
500
11 %
450
10 %
1500
150
3
600
20 %
530
17 %
1800
300
100 %
4
660
10 %
580
9.5%
1980
180
-40 %
5
726
10 %
630
8.6%
2178
190
5%
─────────────────────────────────────────────────
1
Note that the % change in income and the % change in consumption go hand in hand in a
similar proportion. However, the % changes in investment are much more volatile than those
in national income or consumption.
In fact it is in a proportion to the % change of the % change in income; the % change in the %
change in Y between years 2 and 3 (from 11% to 20%) is 82%. The % change in the % change
in Y between years 3 and 4 (from 20% to 10%) is -50%. The % change for the subsequent
period is 0%. These numbers, 82%, -50%, and 0%, are in line with the % changes in
investment, 100%, -40%, and 5%.
Therefore,

Acceleration in Y (an increase in the growth rate of national income)  I

Deceleration in Y (a slow-down of the growth rate)  I

Whether investment will increase or decrease this year in comparison to the last
year's investment depends on whether the growth rate of this year is larger or
smaller than the growth rate of the last year;
For instance, suppose that the real income grew 3% last year, and grows 1% this year.
The economy is still growing; income increases this year and so does the consumption.
But the investment will decrease compared to the last year's level because the growth
rate drops from 3 to 1 % or the growth decelerates.
(3) Implications of the Keynesian Accelerator Model;
i) When the above investment function as a function of changes in income is substituted
in the equilibrium national income equation, the only exogenous variables left over are
autonomous consumption (C) and government expenditure (G). So what ultimately
determines the equilibrium national income is G.
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176
Ch VII. Investment
ii) Substituting the above investment function into the equilibrium income function, we
get a first-order difference equation; Yt = A (G + C) + B Yt-1. Depending on the value
of B, there could be different patterns of business cycles.
(4) Problems
i) This is a circular argument; Y changes as I changes, which changes as Y changes.
Therefore this is rather a mechanical illustration than a explanation which touches the
fundamental causes of volatility of investment.
ii) There is some factor which attenuates the volatility of investment; the adjustment
cost makes actual fixed capital, investment or increases in fixed capital, take place over
time in a gradual fashion rather than over night. But the adjustment cost is minimal for
inventory investment.
The actual change in capital stock or dK cannot take place overnight. The time lag
involved in increasing K is fairly long (think about the construction period, and the time
lag between the order and the shipment of equipment and machinery). Inventory
Investment does not involve any significant lag.
2) Neoclassical Model of Investment
Investment is the demand for new capital stock (dK). The demand for dK is determined by
weighing the cost (Present Price) and the benefit (PDV) of the capital good;
so It = dKt = f (Cost versus Benefit of New Capital Stock)
The cost is equal to the present price of New Capital Stock.
The benefit comes over time in the form of the stream of revenues generated from the capital
stock over its life-time. To compare it with the present price of new capital stock, we should get
the present value equivalence of the revenue streams by discounting the revenues with interest
rate of the times and summing them up. This leads to the Present Discounted Value of the
stream of future revenues. So the Benefit of New Capital Stock is a function of the stream of
future revenues and future interest rates. In reality where there is uncertainty, the future values
are unknown. The best the investor can do is to make a rational guess about the future variables.
This means that the PDV becomes the function of expected future variables such as expected
future revenues and expected future interest rates;
*
PDV =
Rt +
Rt+1
+ ......
(1 + r) (1 + r t )( 1 + r t+1* )
*
+
Rt+20
.
(1 + r t )(1 + r t+1* )......( 1 + r t+20* )
where * denotes expected future variables, Rt+i is the stream of revenues from the investment
project, r interest rate.
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177
Ch VII. Investment
*
*
*
*
I t = f ( Rt , r t , Rt+1 , r t+1 , Rt+2 , r t+2 ..... ).
The revenue is the value of sales of output (= the price of output multiplied by the amount of
output demanded and thus produced) minus tax, and so on;
I t = f ( Pt ,Qt ,T t , r t ,
*
*
*
*
Pt+1 ,Qt+1 , T t+1 , r t+1 ,
*
*
*
*
Pt+2 ,Qt+2 , T t+2 , r t+2 ....).
Implications:
(1) There are a lot more expected variables in the investment function than in any other
function; the expectations matter more in the investment function than in other
functions.
(2) The expectations change all the time, reacting to 'News', which may not be
necessarily correct.
(3) Among the expected variables which affect the PDV of the investment project, in
percentage terms, the interest rate is the most volatile. For instance, at the aggregate
level, revenues rarely change by 50% (due to such changes in sales or price) while the
interest rate often changes by 50 % (from the 11 % to 15 % level or the other way
around). So ultimately, a substantial part of the volatility of investment can be
explained by the volatility of interest rate. What makes interest rate volatile? It
should be considered in the context of Money Supply and Demand. Naturally this has a
lot to do with the next topic of this course.
3) Rental Cost of Capital
Investment is the demand for new capital stock or an increase in capital stock (ΔK). The
demand for ΔK is determined by weighing the cost and the benefit (or revenue) of the capital
good at the margin.
Marginal Revenue = Marginal Cost.
Let's suppose that you are an investor or entrepreneur. You are borrowing money from a bank
at the interest rate of i for a year and buy a capital good. You produce outputs from the use of
the capital good, and sell it in a year to repay your loan from the bank.
Your revenues come from two sources: During the year, there will be product generated from
the machine. At the end of year when you sell the machine you will have gains or loss as the
price of the machine has changed.
The marginal revenue is the sum of the marginal product of capital MPK (for a year) and the
capital gains or loss due to the changes in price of the capital good (when you are selling your
company at the end of a year):

MR = MP K + P K .
PK
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Ch VII. Investment
You incur two kinds of cost: one is the interest ("i") you pay to the bank. The other is that the
machine needs repairs, that is, depreciation. Let's suppose that with the payment for
depreciation the machine is maintained in as good a condition as a new one:
MC = i +  .
Here the interest rate i is determined in the money market. The percentage change in the price
of the capital good may be in line with the rise of the general price level:
 PK
= .
PK
MPK is primarily a decreasing function of capital stock. It is also an increasing function of
technical innovation and a decreasing function of any event which adversely affects
productivity of capital (for instance, oil shocks).
By transposing the rate of inflation, we rewrite the equilibrium condition as follows:
MP K (K,
L
, T) = i -  +  .
K
We call the right-hand side express the user (rental) cost of capital.
Note that the interest rate minus the rate of inflation is the real interest rate. Therefore, the
equilibrium condition is that the marginal product of capital is equalized with the user cost of
capital, the sum of the real interest rate and the depreciation rate.
Applications of Rental Cost of Capital Model: How does this model work in respond to
variety of changes?

For some reason of external shocks (such as an increase in real interest rate) the MC
may rise. To ensure the equality between the user cost and the MPK, the MPK should
rise to re-establish the equality. MPK will rise when K decreases. Investment should
decrease. Intuitive explanation is that when the user cost of capital rises, the least
productive project of investment should go to enhance the marginal productivity of
capital of the existing project. We will observe that the negative correlation between
the interest rate and investment: An increase in the real interest rate will lead to a
decrease in investment.

For some reason (such as oil shocks, which lead to cumbersome and disruptive energy
saving measures) the MPK may decrease. The two forces will start working. In order to
re-establish the equality, the MPK of the left-hand side should rise back. The capital
stock should decrease to have an increase in MPK. The least productive project should
go to enhance the productivity of capital. This decrease in the demand for capital will
lead to a fall in the interest rate or th lending rate of the bank. In the right-hand side of
the equality, the real interest starts falling. We will observe a positive correlation
between the interest rate and investment.

A decrease in the nominal interest rate will not necessarily lead to an increase in
investment; For instance, in 1990, the nominal interest rate was about 12% and the rate
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Ch VII. Investment
of inflation stood around 7%. The user cost of capital was then 12 minus 7 % plus
depreciation rate. Now the nominal interest rate is only 8%, and the inflation rate is
2%. The current user cost of capital is 8 minus 2 % plus depreciation rate. The current
user cost is higher than that of 1990. What matters to the investor is not the nominal
but the real interest rate.
4) Tobin's Q Theory
According to James Tobin, the `Q' index larger than one is a green-light signal for expansion of
facilities or new investment. The Q index is equal to the market value of a firm over the
replacement cost of a firm: The market price incorporates the market’s expectations as to the
prospect of future business returns to the firm, while the replacement cost is simply the present
market price of capital required to set up the firm.
Tobin's Q shows how or through what transmission mechanism, for instance, an increase in
money supply leads to an increase in investment. If money supply increases, other things being
equal, expenditures on all assets will rise. As the demand for stocks rises, the stock prices will
go up. The market value of a firm is the stock volume times the stock price. As the market
value of stocks rises, Tobin's Q exceeds one. There occurs a new physical investment.
5) Permanent versus Temporary Investment Tax Credits?
By nature, investment can be done in the discrete manner; investment spurts, making the best
use of an auspicious investment environment, which comes occasionally ("Make hay while the
sun shines").
Implication: A temporary tax cut on investment will have a larger expansionary impact on
investment than a permanent tax cut. This contrasted with the case of tax cut on income; a
permanent income-tax cut has a larger impact on consumption and aggregate expenditures than
a temporary income-tax cut.
"....... Congress may revive the investment tax credit (ITC) in hopes of boosting
spending on factories and equipment. Bush would probably sign on. Experts caution
that ITC would be truly helpful only if the credit is temporary...." (The Times, "Does
America Need a New Deal for the Nineties?", January 13, 1992).
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Ch VIII. Money
Chapter VIII. Money
We have already learned that the LM curve shows the combinations of interest rate and income (i,
Y), which satisfy the equilibrium in the money market. It comes from the money supply and
demand curves: The equilibrium in the money market, that is, the money supply being equal to the
money demand, yields the interest rate.
1. Nominal versus Real Quantity of Money
In economics we define the demand and supply in real terms, not in nominal terms. It is in line
with the microeconomics expression of demand and supply. Let's take an example of the demand
and supply of hamburgers. We say that 5000 units of hamburgers are demanded at the price of $4.
If we say that $20,000 worth of hamburgers are demanded, the statement is not clear enough. If
the price is $1, 20,000 units of hamburgers are demanded in real terms. If the price is $10, the
demand for hamburgers in real terms is 2,000 units. We can dispel any ambiguity by expressing
the volume of demand and supply in real terms- here `real' means no change in response to
changes in prices. The nominal quantity of money (supply or demand) is the face value of
the total amount of money, and the real quantity of money is the face value divided by price
level;
Real quantity of money = Nominal quantity of money / Price level:
m = M/P
At the equilibrium in the money market, the money supply in real terms is equal to the money
demand in real terms:
ms = md.
Nothing further will happen to national income, interest rate, and so forth. At disequilibrium,
there occurs an excess supply of or demand for money. The equilibrating forces come in to push
back the economy to the equilibrium. In this process there occur changes in such variables as
income, and interest rate.
It is of great importance to understand the operation of the above equation describing the
equilibrium money market condition. Unlike the usual demand and supply case, where the
left-side supply is determined by the supplier(s) and the right-side demand by the demander(s).
The left-side can be determined by the interaction of the supplier and demander(s). The above
equation can be rewritten as
M/P = md
ms = M/P as will be seen shortly.
In case the right-side md is constant, an increase in nominal money supply M by the monetary
authority can lead to an increase in the price level P: If the demanders have a very clear idea as to
how much money they want to hold in real terms, an increase in nominal money supply will
simply lead to a rise of the price level. The above equation can be rewritten as
M = P md.
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Ch VIII. Money
When the left-side variable, that is, nominal money supply M increases, the price level will go up
proportionally if the real money demand is constant. What it implies is that the monetary
authority or government determines only the nominal money supply. The real money supply and
the price level are both determined by the demanders of money.
2. Money Supply
1) Exogeneity of Money Supply
The nominal quantity of the money supply is determined by the monetary authority, which
usually is the central bank.
MS = M
As just mentioned, the monetary authority does not determine the real money supply as it does not
control the price level. The demanders of money or the general public determine the price level.
To recap, the monetary authority determines the nominal money supply not the real money
supply.
How does the monetary authority determine the nominal quantity of money supply? The
monetary authority determines the money supply on the basis of a variety of variables. For
instance, in the face of a high level of unemployment rate it may increase money supply (of the
next period). In this case the money supply is positively related to the unemployment rate.
Alternatively, the government may change money supply by accommodating money demand. In
the booming stage of business cycles where more money is needed to back up a higher volume of
transactions, the government may increase money supply. In that case the money supply is
inversely correlated with the unemployment rate. The money supply must be positively
correlated with government deficits if part of deficits is monetized or financed through printing of
paper money. If deficits are financed through issues of bonds or taxation, they are uncorrelated
with money supply. All these suggest that there is no clear-cut unchanging hard-and-fast relation
of a great significance between any macroeconomic variables and the money supply. Depending
on the government's current monetary and fiscal policies, the macroeconomic variables and
nominal money supply could have different relationship. It is impossible to define any
unchanging specific relationship between money supply and any variables. In this sense, we say
that basically, the nominal money supply is exogenously determined, meaning that it is a good
approximation to say that the nominal money supply is independent of any macroeconomic
variables. Precisely speaking, the nominal money supply is also affected by interest rates, and so
forth. However, their impacts are so small as to be dominated by the government's decision as to
the money supply. At one point of time it is fixed, but over time it can be changed by the
monetary authority.
The real quantity of money supply (ms) is the nominal money supply divided by the price level;
ms = MS/P = M/P
As the money supply is independent of the interest rate, when drawn in the interest rate and real
quantity dimension, the money supply curve is vertical, being the same regardless of the level of
the interest rate.
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Ch VIII. Money
2) Detailed Studies of Money Supply: Money Multiplier
Here we would like to show that while there are determinants of money supply their impacts on
money supply is all buried under the dominating factor, that is, the government decision of money
supply. Roughly speaking, the money supply is independent of all variables including interest
rates.
(1) Different scopes of money
There are a variety of alternative scopes of money. As you expand the scope of money, you are
moving from a more liquid form of money to a less liquid one.

Monetary Base or High-powered money is the sum of Currency outside banks + Vault
cashes in commercial banks and the reserve deposits at the Central Bank. This is close to
the total amount of money that government or the monetary authority directly supplies to
economy.

Cashes or Currency outside the banks or the banking institutions.

M1 = Currency + Demand Deposit

M2 = Currency + Demand Deposit + Time Deposit
The time deposits include personal notice and fixed-term deposits and non-personal notice
deposits.

M3 = M2 + Non personal fixed term deposits + Foreign currency deposits
cf. There are some differences in terminologies between the U.S. and Canada:
For the American terminologies, refer to Table 1 in Handout #1.
For the Canadian terminologies, refer to Table 2.
As of November 1975, the Bank of Canada set a target of money supply defined as M2: M2 is
regarded as the aggregate money supply variable which has the most direct impact on the
aggregate expenditures. In the present Canadian setting `money' means M2.
(2) Money Multiplier Analysis
How the fundamental change in money supply, that is, a change in the monetary base or
high-powered money (ΔMB or ΔH)lead to a change in M2 (ΔM2)?
Let's simply call the ratio of MB (H) to M2 the money multiplier. Money supply M2 is equal to
the product of the money supply multiplier and the high-powered money;
𝑀2
=𝜇
𝐻
(1)
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Ch VIII. Money
𝑀2 = 𝜇𝐻
(1')
We recall that
𝑀2 = 𝐶 + 𝐷,
where 𝐷 = 𝐷𝐷 + 𝑇𝐷
(2)
𝐻 = 𝐶 + 𝑅,
and
where 𝑅 = Required/Legal Reserves + Excess Reserves
(3)
Therefore, plugging (2) and (3) into (1), we get
𝜇=
(2) 𝐶 + 𝐷
=
(3) 𝐶 + 𝑅
(4)
By dividing both the numerator and the denominator by D, we can rewrite equation (4):
𝜇=
𝐶 ⁄𝐷 + 1
𝐶 ⁄𝐷 + 𝑅 ⁄𝐷
(5)
Therefore, by plugging (5) into (1'), we can see that the money supply M2 is a function of
high-powered money H and the determinants of the money supply multiplier such as C/D and
R/D:
𝑅 𝐶
𝑅 𝐶
𝑀2 = 𝜇𝐻 = 𝜇 ( , ) 𝐻 = 𝑓 (𝐻, , )
𝐷 𝐷
𝐷 𝐷

(6)
Questions:
i) What will happen to money supply around Christmas when people would like to hold
more cashes for small transactions? Refer to the handout. The key is that as C/D ratio
rises, as dμ /d(C/D) has a negative sign and thus μ declines, which leads to a fall in M2.
ii) What the impact on money supply would the zero reserve requirement system have?
The R/D ration declines which leads to a rise in μ.
Equation (6) implies that government (monetary authority) can mostly control money supply but
in a precise way. The interaction among the government, the general public and banks determines
the money supply:

The government can fully control H: as will be seen, the monetary authority affects H
mostly through the Open Market Operation (OMO). The central bank does have other
means of controlling H such as the `Switching Operation' (= Withdrawal and Re-deposits
of the central bank's account with the commercial banks), and so forth. However, we will
just focus on the OMO.
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Ch VIII. Money
The government has a printing machine with which to print money. Under the current fiat
money system where no paper money is convertible into gold, silver, or any commodities,
there is virtually no limit, except the self-restraint on the part of the monetary authority, to
the supply of H by the government. Money has not much intrinsic values, and its value is
just guaranteed by 'fiat' (decree) of the government.
It is under the fiat or fiduciary money system that paper money replaces commodity
money and releases resources for other useful purposes. Gold and silver which is `locked
up' for transactions purposes under the metallic standard system can now be used for other
purposes under the fiat money system. Paper money or notes are now being used for
transactions, which have very small intrinsic values. Only by the values of paper and ink
used for the production of money, resources are being diverted from other useful purposes.
This is the cheapest possible way of meeting the demand for media of exchange in an
economy. This is a good side of the fiat money system: (paper) money is
resource-releasing or resource-saving.
However, the bad side of the fiat money system is that there is no more discipline on
money supply, except for the self-restraint by the government. Historical experiences
reveal that under the fiat money system the printing machine tends to overwork. There
frequently occurs an excess supply of money. It brings about inflation, which erodes the
real values of money and thus implicitly transfers real resources from the holder of money
to the producer of money. Inflation is a form of taxation for the government. This
government revenue from inflation taxation is called 'seigniorage.'
Some epistemology may help us understand the term seigniorage. Coins of precious
metals were capable of being debased. So arouse the need for certification. In the
medieval age, the monarch stamped coins to certify their purity. The coins were made of
bullion presented to be stamped The revenues from certification were collected by
serrating the edges of coins. These revenues were called seigniorage. The seigniorage in
general refers to some due taken by the `Senior' or lord by virtue of the prerogative of
sovereign. It refers to government revenues from inflation taxation.

The government and the commercial banks together determine the R/D ratio: the fist sets
the required or legal reserve ratio and the second the excess reserve ratio. Under the new
Canadian system of zero required reserve system, the R/D ratio is controlled by chartered
banks only.

The general public determines the C/D ratio by making decision as to the relative share of
their money balances between cashes and deposits.
3) Control of Monetary Base and Interest Rate
Monetary policies involve changes in money supply and interest rate by the monetary authorities.
How does the Canadian government control the money supply and the interest rate, particularly
the Bank Rate? The Keynesian ideas are well illustrated in the IS-LM framework, with which we
are all very familiar. We would like to look into detailed processes beyond the IS-LM picture.
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Ch VIII. Money
(1) How does the government control the money supply? Open Market Operation
The government can control money supply (M2) indirectly by controlling the supply of
high-powered money (H). The money multiplier, which is affected by many factors beyond
control by the government, comes in between the two. To that extent the controllability of money
supply by government is limited.
The open market operation is defined as the controlling of high-powered money and thus money
supply through the government's purchase (H  and M2) or the sales (H and M2) of securities
or financial assets in the financial market.
There is no idiosyncrasy about the open market operation. First, it does not have to be financial
assets or securities that the government buys and sells. For instance, it could be 'wheat.' When the
government buys wheat from farmers, it pays them for the wheat with money it prints with the
printing machine in the central bank. So there will be a flow of money from the government to the
private sector, and the stock of money supply in the private sector increases.
One of the reasons why the government does not deal in wheat is that such operation will lock up
wheat which has intrinsic values and uses - consumption as food. Another reason is that wheat is
bulky and perishable, and thus it is costly to handle -transportation and storage costs. The
financial assets do not have intrinsic values - except the small values as printed paper; they can be
only used for igniting fire if the face value is gone-, and does not incur any considerable costs of
storage or transportation.
In this spirit, it may sound a rather odd suggestion, but what about the government buying birth
certificates from the public, thereby increasing the money supply? At least, it does not bring
about any distributional problems.
We can summarize the principle of the government operation affecting the money supply as
follows:

Whenever the government buys "things", in fact anything, from the private sector which
includes the public and the commercial banks, it pays for the things it buys with money it
prints. Money flows from the government to the private sector. Therefore, the stock of
money supply in the private sector increases.

Whenever the government sells "things", in fact anything, from the private sector
including the public and the commercial banks, it receives money. Money flows out from
the private sector, and the stock of money supply decreases in the private sector.
The above principle can be also obtained by studying the T-accounts of the banks in succession of
transactions as are given in a handout distributed in the class.

Case I: The Canadian government participates in the Gulf War. Let's suppose that the
Ministry of Finance sells newly issued bonds to the Bank of Canada and spends the
acquired funds mostly on buying weapons from the American companies. Show the
impact of the government action step by step on the money supply and other variables
with the use of the IS-LM model. Please note that there are two stages of the government
actions which affect the money supply: the open market operation or deals in financial
assets and the fiscal activity or deal in weapons.
Macroeconomics

186
Ch VIII. Money
Case II: What will be the impact on the money supply when the Ministry of Finance sells
newly issued bonds to the public and spends the acquired funds on Canadian wheat?
Let’s discuss the above two cases: First these questions do have two dimensions: (1) the sales of
bonds or open market operation in a narrow sense, and (2) the purchase of goods and services
from the private sector or the government expenditures.

Case I: When things are sold or bought among bureaus within the government sector, it
does not affect the money supply: although some printed money moves from the Bank of
Canada to the Ministry of Finance, it can be still regarded as the inventory of money
which has not left the producer (of money) or the government. The MS does not change
when the Bank of Canada buys bonds from the Ministry of Finance.
cf. Money residing in the government sector including the central bank is not `money
supply'. It is inventory. In the microeconomics, products stockpiled in the warehouse of a
factory are not called supply, but called inventory. Only when the products leave the
factory or firm and enter the market where demanders are, then they are called supply.
Therefore, the shift of stock of money from the central bank to the ministry of finance
does not change the money supply. Precisely speaking, money supply is money supply in
the private sector outside the supplier of money.
When the Ministry of Finance is engaged in fiscal activities or expenditure policy, buying
domestically produced final goods and services and paying for them with the acquired
fund, there will be an increase in the money supply in the domestic private sector. The MS
increases as G increases. In the case, at hand, however, the acquired fund or newly
created money is spent or injected into the American economy, leaving the money supply
in the Canadian private sector unchanged.
The overall impact is no change in the MS. Therefore, the LM curve does not move.
Neither does the IS curve, which has a shift parameter of the Aggregate Expenditures on
the domestically produced goods and services or AE = C + I + G + X-M: In fact, G or
government expenditures on goods, domestic and foreign, increases but M or imports
increases, too, and thus they cancel out each other in the end.

Case II: In the first step of dealing in financial assets or the `open market operation,' the
Ministry of Finance sells bonds to the general public. As it receives money from the
public in return, for them, the MS in the private sector decreases.
In the second step of fiscal activities, the Ministry of Finance buys goods or wheat from
the private sector with the acquired fund. The fund in payment for the wheat flows from
the government to the private sector, and there will be an increase in the money supply in
the private sector.
The combined impact of the two steps on the money supply is nil, leaving the money
supply unchanged. The LM curve does not move.
The IS curve moves to the right as G in AE = C + I + G + X-M increases.
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Ch VIII. Money
(2) How does the Bank of Canada control the short-term interest rate?
The Bank of Canada controls the Bank Rate indirectly by controlling the yields on Treasury Bills
(T-bills hereafter) or short-term certificate of government borrowing through its `controlled
auction' of the T-bills. The Bank Rate is pegged at 25 basis point or a quarter percentage point
(0.25%) above the average weighted yields on the most recently auctioned Treasury Bills of the
maturity of 91 days. The detailed procedure of the auction is provided in the separate hand-out.
The Bank Rate subsequently forms the basis for all other interest rates. To this extent the
government can control interest rates.
This is the short-term interest rate as opposed to the long-term interest rate of bonds with one year
or longer term of maturity. The relationship between the short-term and the long-term interest
rates needs more scrutiny, and will be dealt under the heading of "Term Structure."
The principle is that if the Bank closes the auction at a relatively high bid, the (discounted) last
bidding price of the T-bills is quite high and the corresponding yields should be low: you may
remember that the discounted bidding price and the yield(rate of return) are inversely related
when the face value at the maturity is fixed.
Consequently, the Bank Rate, automatically set at the rate of the yields plus 0.25%, will be
relatively low, too. As the auction is closed at a relatively high bid, a relatively small amount of
money in the private sector flows into the government. The left-over or not-auctioned-off bills
will be absorbed by the Bank of Canada that makes payment drawing on its holding of existing
stock of money or issuing new notes.
How does this affect the money supply? The Bank's purchase of T-bills itself does not increase
the money supply (in the private sector): simply money flows between bureaus within
government. As we have seen in part I, only when the fund, shifted from the Bank to the Ministry
as the payment for the bills, is spent through fiscal activities on domestic goods, there will be
increases in money supply (H).
In addition, the more of T-bills the Bank of Canada buys from the Ministry of Finance, the less of
T-bills are purchased by the general public and thus the less squeeze is made on the private
sector's liquidity or the stock of money supply. In other words, the Bank indirectly affects the
amount of liquidity or money supply of the private sector in the process of controlling the yields
and interest rate.
In this case we may observe that lower interest rates are usually associated with a larger amount of
money printing on the part of the Bank of Canada and more liquidity or larger amounts of the
money supply on the part of the private sector (liquidity effect).
Secondly, the Bank Rate may determine the amount of borrowing by the commercial banks from
the central bank, which may constitute the reserves of the first in the creation of demand deposits:
a low Bank Rate may lead to a large borrowing by the commercial banks from the central bank.
The commercial banks may use the borrowed fund as the reserves (R) against which loans and
deposits money are created (M2: M2 = m H = m (C+R), where H is high-powered money, and m
the money supply multiplier). However, the Bank of Canada has discouraged the commercial
banks from borrowing to replenish their reserves and applied a very high penalty rate to the
borrowing for reserves. In other words, in Canada the reserves of the commercial banks and
consequent creation of deposit money as part of M2 do not respond to changes in the Bank Rate.
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This contrasts with the American situations: the (re)discount rate or the American counterpart of
the Bank Rate is a major determinant of the money supply of the private sector.
One qualification we should keep in our mind is that the government sets the nominal interest rate
or the observed interest rate but not the real interest rate. As we have seen in the early chapter of
investment, the real interest rate is determined mainly by the marginal productivity of capital,
which is in turn a function of capital stock.
2. Money Demand
1) Introduction
The demand for money or the demand for holding of real money balances should be expressed in
real terms or the quantity (of goods the money balance can buy), not in monetary terms. We have
already shown that there is little point in talking about the nominal money demand for an
economy as a whole, and that the nominal money demand is always and thus trivially equal to the
nominal money supply at the aggregate level.
What determines the desired level (quantity) of real money demand? Just as the desired quantity
of hamburgers is determined by the consumers' income and the price of hamburger, according to
some economists, the real demand for money is determined by the income level of the economy,
that is, the national income, and the price of money, that is, the interest rate. Just like any other
goods, Keynesians argue that the real money demand is related positively with real national
income and inversely with the interest rate, which is the price of money from the Keynesian
viewpoint.
Let us examine the second point in the above statement: the price of money is the interest rate. In
other words, the opportunity cost of holding money balances is the interest rate. Money is one of
many assets which range from financial assets, such as bonds, stock, equities to real assets such as
land and gold. Money and other assets are substitutes. The major difference between money and
other assets is that money does not bring in any positive pecuniary (monetary) returns - actually it
is subject to the erosion of real values from inflation-, and other assets do have pecuniary returns.
However money, or money balances in a precise term, renders a unique non-pecuniary service,
which is known as `liquidity'. Money is the most generally accepted medium of exchange and
thus the most `liquid' out of all forms of assets. So when you decide to hold assets in the form of
money balances instead of any other, you are showing your preference for liquidity over
pecuniary returns. This is the reason why the money demand is called `liquidity preference', and
the Keynesian money demand function, or the `liquidity preference function.'
The interest rate represents the foregone pecuniary return or the economic sacrifice you have to
take when you choose to hold your wealth in the form of money balances rather than in the forms
of other assets: the interest rate is the opportunity cost of holding cash balances. When the interest
rate goes up, the cost of holding cash balances increases and naturally you would like to hold less
assets in the form of cash balances and more interest bearing assets. This means that the demand
for money is inversely related to the interest rate.
Now we have another major factor to be considered, which affects the real money demand: When
real income increases, as money is a normal good, the demand for real money balances increases,
too. When real income increases, there occur more transactions and thus more money balances
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are needed to back up the increased transactions.
Random monetary shocks do affect the real money demand as well. They include not only truly
turbulent shocks to the money or financial market, but also financial innovations which affect
money demand.
2) Mathematical Presentation of Real Money Demand Function
d
M = d = L [ y, i, u ],
m
P
where y is the real national income, i the nominal interest rate, and u the random term. K and h are
all constants.
d
M = d = K y - h i +u .
m
P
For simplicity we can specify the function in the linear form such as
In the log-log function, K is the elasticity of real money demand with respect to real national
income, and h the elasticity of real money demand with respect to interest rate. The liquidity
preference curve is negatively sloped when drawn with the interest rate on the vertical axis and the
amount of real money on the horizontal axis. The variables y and u are the shift parameters of the
real money demand curve.
In the case where money is defined in the narrowest scope, that is, cashes, the so-called `inventory
theoretic approach' by Keynesians do have specific numbers assigned to K and h such as
md = 0.5 y - 0.5 i + u.
Now we can see the reason why dmd/di or -h <0 , and dmd/dy or K > 0 in greater details:
i) Interest rate [Substitution Effect]:
How much money you would like to hold depends, among other things, on the sacrifice of
pecuniary returns that resulted from holding money instead of interest-bearing assets. The
foregone returns are the opportunity cost of holding money. They can be represented by the
interest rate. So the higher the interest rate, the higher the opportunity cost is and thus the lower
md will be.
ii) Income [Income Effect]:
When real income rises, households will add to all assets including money. Also, as real income
increases, the volume of transactions increases and thus there is a need for more money balances.
Keynes specified his money demand function such as Md = L1 +L2, where L1 = `Active
Balances' due to transactions motives and L2 = `Idle Balances" due to speculative
motives.
Our criticism against his idea is that one can think of different motives for holding money
balances without dividing the actual holding of money into these two motives. Every
dollar of money balances serves more than one function. Why can't the same dollar
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provide some transaction services, some precautionary services, some speculative
services? Operationally Keynes's distinction is not meaningful as we cannot attach
specific numbers to L1, and L2.
3) The Major Issues of Real Money Demand Function: Magnitude of Interest Rate
Elasticity
We would like to make two major points: i) The magnitude of the interest rate elasticity of real
money demand varies depending on the scope of money. ii) The magnitude also determines the
relative effectiveness of monetary and fiscal polices.
The interest elasticity of 'money' will be all different depending on whether the `money' includes
cash alone or other categories of money; cash does not bring any interest payment to the holder,
while time deposit does. When there is an increase in interest rate, there will be a decrease in the
demand for cash. If money includes both, the impact of the change in the interest rate on the
demand for money will cancel out and thus the demand for that concept of money (= C + TD)
could be rather constant.
First, what would be the benchmark? There is an old theory for the elasticity of real money
demand with respect to interest and income. This would be a theoretical benchmark. However,
the actual magnitudes of elasticity do change over time particularly with respect to interest rates.
Ultimately, it is an empirical issue which employs data analysis and econometric regression of
(1) The Benchmark: Cash Inventory Theoretic Approach
Can we derive the sensitivity of the demand for cash with respect to interest rate?
The Inventory Theoretic Approach developed by W, Baumol has its own answer: K = 0.5 and -h =
-0.5
Suppose that you are making and spending $ Y each month. The monthly income of $ Y comes at
the beginning of the month and, as being spent, gradually runs down to zero toward the end of the
month. During the interim period you are faced with two choices: you can hold your income
either in deposits which pay the interest rate i(in fractional terms) or in money or cash that does
not carry any pecuniary returns. Suppose you deposit the entire monthly income with a bank
which pays interest on the deposit at the beginning of the month, and you make trips to the bank to
withdraw $ Z each time. This trip is not without cost as it takes time or other resources. Suppose
that each trip costs $ tc.
The first question you may ask is: How may trips would you make to the bank per month? Y/Z
trips per month. The total cost of making trips to the banks to get cash withdrawal is $ tc (cost per
one trip) x Y/Z (the number of trips). For instance, if you have $ 800 monthly income which you
deposit in the bank at the beginning and withdraw $ 160 per trip to the bank, you will have to go to
the bank 5 times per month. If each trip costs $10 including loss of wages and use of other
resources, the total cost involved in trips is $50.
The next question you may ask is: What is the average balance of cashes or money in you pocket?
The amount of withdrawal of $ Z will slowly runs down to zero as you spend money. Therefore at
the most you have $Z and at the least you have $0. The average cash balance is $(Z + 0)/2 or $Z/2.
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As 1/2 of $Z is always in you pocket rather than in the bank, you are foregoing the possible
interest payment on it by $Z/2 x i: this is the opportunity cost of holding cash balances in your
pocket instead of bank deposits. In the above case, the opportunity cost of the average cash
balance of $80 is, if the interest rate is 0.1 (10%) per month, $8.
Therefore, the total cost is the sum of the costs of having money in the pocket and the costs of
making trips to the bank:
Total Cost =
Z/2 x i + Y/Z x tc.
You as a holder of cash balances would like to minimize the total cost by choosing an optimal
value of Z;
Minimizing Z/2 x i + Y/Z x tc.
You are choosing $ Z here ( $ Y is given by your boss; i set by the bank; tc set by other things,
such as bus fairs or your loss of wages for the time spent on trips) to minimize the total cost. The
optimal value of Z* can be obtained from the first order condition: Differentiate the total cost with
respect to Z and equate the first derivative with zero.
(f.o.c.) 1/2 i + Y x tc {-(1/Z)2} = 0.
as we know that d(1/Z)/dZ = - 1/Z2.
Solving the above for Z*, we get
1/Z2 = 1/2 x i x 1/Y x 1/tc
Z2 = 2 Y tc / i
Z = [(2 Y tc)/ i]½ , and
Md = Z/2 = [(Y tc)/ 2i]½

What is the income elasticity of the demand for cash balances?
Answer: 1/2.

What is the interest elasticity of the demand for cash balances?
Answer:-1/2.
(2) Changing Interest rate Elasticity, and Effectiveness of Monetary/Fiscal policies:
As we have discussed, alternative concepts of money have different demand elasticities with
respect to interest rate. When money is defined as M2 = Cashes in circulation + Demand Deposits
+ Time Deposits, the interest rate elasticity of money demand will be very small. One may think
that if the interest rate or the rate of returns on short-term T-bills goes up, the demand for all the
components of money M2 will decrease. It is not true. Because of competition that induces the
banks to bid up their interest rate on deposits, the demand for deposits does not have to decrease.
In this case, what determines the money demand is not a particular interest rate, but the difference
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between the interest rate on bonds or T-bills and the interest rate on deposits. As they tend to
move together, the interest rate itself does not lead to a large change in money demand.
Keynesians argue that h is quite large while classical economists and Monetarists argue that it is
very small.
A large value of h means that the elasticity of real money demand with respect to interest rate is
quite high: graphically the elastic real money demand curve is quite flat. The LM curve derived
from the flat money demand curve along with the vertical money supply curve is quite flat, too.
You may recall that the flatter the LM, the smaller the Crowding-out. Fiscal policies are quite
effective. In this case monetary policies are not so effective. These conclusions are in line with
the Keynesian basic doctrine that advocates fiscal policies and is skeptical of monetary policies:
A small value of h means that the elasticity of real money demand with respect to interest rate is
quite low: graphically the inelastic real money demand curve is quite steep. The LM curve
derived from the steep money demand curve along with the vertical money supply curve is quite
steep, too. You may recall that the steeper the LM, the larger the Crowding-out. Fiscal policies
are not so effective. In this case monetary policies are quite effective. These conclusions are in
line with the Monetarists's basic doctrine that advocates monetary policies and is sceptical of
fiscal policies:
The so-called Re-entry Problem illustrates skepticism of monetary policies: It states that once
the government turned around from expansionary to stringent monetary policies, it is difficult to
go back to use money to boost the economy and to raise the national income. In the stage of
monetary policies as a means of boosting the economy, there is a `re-entry problem'. Once you go
out of it, you may have difficulty in re-entering it.
It occurs under the following two conditions:
i) the money demand is quite interest rate elastic; and
ii) the nominal interest rate is falling.
it can be explained as follows: The money demand equation can be expressed in terms of
percentage changes such as
ΔM/P = K Δy - h Δi + Δu
When the interest rate is falling, the term -h i is positive. Thus
ΔM > K Δy .
So when there is the re-entry problem the rate of monetary expansion is larger than K Δy. This
means that the same rate of money creation would lead to a smaller increase in the national
income. Put differently, in order to have the same rate of economic growth, the rate of money
creation should be a lot higher with the re-entry problem than otherwise. The re-entry problem
makes monetary policies quite ineffective.
eg) Let's assume that K=1 and h=0.5, and that interest rates have been falling from 15% to
7.5% (this is a 50% decrease as (7.5-15)/15 is equal to -50%). To have a 5% growth of
national income, at what rate the money supply should be increased?
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(Answer) ΔM/P = K Δy - h Δi = Δy - 0.5 Δ = 5 % - 0.5 (-50%) = 30 %.
A 30% increase in money supply will only lead to a 5% increase in national income. Under the
given two conditions the effectiveness of monetary policy is smaller for a given rate of money
creation than otherwise. The reason is that as the interest rate falls, the opportunity cost of holding
money falls and thus the demand for real money demand increases. Put differently, when interest
rates fall, people let money holding grow in their pocket or bank accounts. So a large part of the
newly injected money supply will be held by an increased money balances rather than being spent
around to boost the economy.
(4) In Search of Stable Money amid Financial Innovations
One of the main reason why real money demand is elastic with respect to interest rates is that
money does not bring in any interest payment but its substitutes do. In the U.S., there has been
so-called “Regulation Q”, which forbids any interest payment to money or cash balances. The
U.S. financial institutions cannot pay interest payment to balances of checking account or demand
deposits. On the other hand, when it comes to the means of payment, money or cash has the
unique services of ‘liquidity’ as opposed other financial assets do not have ‘immediate’ liquidity.
Thus, whether or not, and how much the real money demand is sensitive to changes in interest
rates depends on whether there are any other substitutes for money which at the same time carry
interest payment. If there is a non-money financial asset which must carry interest payment, and it
also provides a comparable service of liquidity, then the demand for money will be highly
sensitive to changes in interest rates as there will be an active substitution between money and the
financial asset.
Over time, the banks have been engaged in financial innovation, and came up with
interest-bearing financial assets which can also be accepted as a means of payment. For an
example, some investment companies have come up with a checking account based on the
balance of ‘money market mutual funds’. The customer earns interest payments as this is an
investment on financial securities, and at the same time, he can write a check against the balance
of his mutual funds. In this situation, when interest rate or rate of return on financial securities
goes up in the financial market, people will move their wealth from money or cash to the money
market mutual funds. The real money demand becomes large and unstable.
In the illustration of the ‘Re-entry Problem’, we have already illustrated that the monetary
authority would like to secure a stable real money demand for the sake of control of economy via
monetary policies. The controllability of economy depends positively on the stability of real
money demand and negatively on the magnitude of the interest rate elasticity of real money
demand.
From the viewpoint of policy makers, there is a simple solution to the problem of the real money
demand becoming unstable due to financial innovations: Expand the scope of money for
consideration. For the example at hand, due to the financial innovation of the checking account of
money market mutual funds, the real money demand defined in terms of M2 has become
‘unstable’ and more sensitive to changes in interest rates. Now, if the policy maker expands his
horizon so as to make a new definition of ‘money’ include the balance of the checking accounts of
money market mutual funds, now the new real money demand will be less sensitive to interest
rates. When interest rates go up, financial wealth will move from M2 to the checking account of
money market mutual funds. However, that is still a flow within the scope of the newly expanded
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concept of money. In fact, the policy makers call the new scope of money ‘M2 +’. Now the real
money demand, defined in terms of M2+ will be stable and be less sensitive to changes in interest
rates. The monetary policy based on M2+ will have a clear impact on economic variables such as
Y or P. Thus we can say that the monetary policy makers are always in search of ‘stable money’.
3. Equilibrium and Disequilibrium in the Money Market: Mathematical Analysis:
Quantity Equation of Exchange
The relations between Money, Income, and Price Level can be viewed in light of the equilibrium
and disequilibrium of real money demand and real money supply such as
M/P = K y - h i + u:
The left-hand side of the equal sign is real money supply, and the right-hand side is real money
demand. At the equilibrium, nothing changes and the equilibrium levels of y, P, and i are shown in
the equation.
In fact, the relationship between money supply M and income y and price level P can be best – in
the sense that it is not clouded by the interest rate variable - with the Quantity Equation of
Exchange. This is a very old model. It overlaps with the mathematical model of real money
demand equation that we have examined. Compared to the mathematical version of the demand
curve, the Quantity Equation of Exchange is simpler and thus has strength and weakness: It is
easier and quicker to use in figuring out the impact of money on y or P. It is, however, not for a
sophisticated analysis.
There are different versions of the quantity equation. However, the most common one is the
Income Version of the Quantity Equation of Exchange such as
M V = P y,
where V is called the `income velocity of money' which means how many times a dollar changes
hands for a given period of time.
There are also the `Transactions Version of the Quantity Equation' such as M V = P
T, where T denotes the total volume of transactions, and the so-called Cambridge
Cash-Balance Equation such as M = k P y where k = 1/V.
We can transform the above equation into;
Δ%M + Δ%V = Δ%P + Δ%y
If we look at the equation just mechanically, we can ask and answer the following questions very
easily:

If the nominal money supply grows by 8%, the general price level rises by 6%,
and velocity rises by 1%, what would happen to real income?
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
If income is growing at the annual rate of 4%, the money supply at 6%, and the
prices at 1%, what must be the change in velocity?

If in the Canadian economy real income is growing along the long-run trend of 3%
per annum, the velocity is expected to fall by 1%, what monetary growth rate is
required to produce `a zero inflation'?

The aggregate demand and supply are given by the following equations:
AD: P y = 3 M (no fiscal policies); AS: y = yf =300.
Presently M = 100. What is the AD? Now if ΔMSe for the next time period t+1 is 30,
what is ΔPe for t+1? Suppose that actually ΔMS at t+1 turns out to be only 20. What
are actual ΔP at t+1, and forecast error respectively? What is going to happen to y in
the short- and long-run?

The above equation itself does not specify what impact ΔM would have on P, V, or y. There are
alternative views of causality and relationship among the variables appearing in the quantity
equation.
Comparison to the mathematical version of real money demand is possible:
MV = P y
M/P = K y - h i + u
Basically, V or the velocity corresponds to the part of – hi + u. In other words, the velocity of the
quantity equation of exchange corresponds to the interest rate elasticity of real money demand and
other random effects. Thus V reflects a lot of things without showing breakdown of the effects:
V= V(i, u, other economics customs related to payments and money use).
We know that the above nominal interest rate i= r+ : the nominal interest rate is equal to real
interest rate plus expected rate of inflation. Thus the velocity of circulation V is a function:
V = V(real interest rate, expected inflation, random monetary shocks, other economic customs
related to payments and money use).
For one thing, if people expect a higher rate of inflation, then V rises as they would like to spend
their money before it loses real value. A higher expected inflation pushes up the nominal interest
rate i, and in the mathematical real money demand function, a higher interest rate leads to a
reduced real money demand.
4. What Does Money Do?: Relationship between Money and Real Income, Price Level, and
Interest Rates.
Here we will look at what money does with respect to i) real national income(y), ii) price
level and inflation, and iii) interest rates. The bridge between a change in money supply
and changes in other variables is called the `Monetary Transmission Mechanism'.
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Basically, the Classical School saw no connection between the real sector of economy to
which investment, consumption and national income in real terms belong and the nominal
sector of money and price level. They saw ‘Dichotomy’ or a big separation between the
two worlds. Money is a veil and has impacts on nominal variables such as price level. As
money increases, in the long-run the price level(P) goes up, and the nominal
expenditures(=P times y) may increase but the real variables(y) do not change.
1) Relationship between Money and Real National Income: Neutrality versus
Non-Neutrality of Money
There are two descriptions for the relationship between Money and Real National Income:

Neutrality versus Non-neutrality: If an increase in money supply does not have any
impact on real national income or any other real variables such as investment, we say that
money is ‘neutral’. If an increase in money supply leads to an increase in real variables
such as investment and national income, money is ‘non-neutral’.
Note that this concept of ‘neutrality of money’ is in line with the tradition of ‘classical
economics’ which sees the ‘dichotomy’ between the nominal sector variables such as
money and price level, and the real sector variables such as ‘real’ interest rates, investment
in real terms, consumption in real terms, and real national income.

Super-neutrality versus Super-non neutrality: If an increase in the rate of changes in
money supply does not have any impacts on real national income, we say that money is
‘super-neutral’. If an increase in the rate of changes in money supply affects real variables,
money is ‘super-non neutral’.
Note that here an increase in the rate of changes in money supply is the same as an
increase in the speed of money creation, or in shorter terms, an acceleration of money
creation. The accelerating money creation is different from a simple once-and-for-all
increase in money supply which is related to ‘neutrality’ issues.
Here we will examine a few different schools of macroeconomics: First, the ‘Original Keynes’s
view of money’, the Neo-Classical Synthesis, Monetarists, and New Classical or Rational
Expectations.
(1) The Original Keynes’s Ideas on Money and Income
The Keynesian transmission mechanism is well illustrated by the IS-LM model which is the basic
analytical tool for the Neo-classic Synthesis or `American Keynesians'. An increase in money
supply shifts the real money supply curve. The interest rate falls in the money market. The falling
interest rate favourable affects the investment in the goods market, and the rising investment leads
to an increase in the aggregate expenditures and the national income.
Keynes came up with a ‘new’ economics against the back drop of the Great Depression or a most
severe recession or deflation in history. In the specific setting of the severe recession, Keynes was
skeptical of any effective transmission of an increase in money supply to an increase in any
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variables: (i) If the money demand is almost perfectly interest-elastic, a given amount of an
increase in money supply will lead to a very small fall in interest rate. This will be particularly
true when the current interest rate is so low at the rock bottom that it cannot fall any further. And
in addition (ii) If investment is not quite sensitive to interest rate, a falling interest rate will have
hardly any impact on aggregate demand. In Keynes's view the investment is mainly determined
by expectations of businessmen or `animal spirits' rather than by interest rates.
In the Quantity Equation of Exchange MV = P y, any increase in M will be completely offset by
the opposite movement of V. On the net, the left-hand side does not change, nor does the
right-hand side: P or y does not change. Keynes empathetically said that during a severe
recession “Money Does Not Matter”. This is what we have many times, by now, gone over as
‘Liquidity Trap’. Needless today, in this case money is ‘neutral’ in its strongest sense of the
word.
(2)Neo-Classical Synthesis on Money and Income
This view is well illustrated with the standard IS-LM and AD-AD(long-run and short-run) curves.
When the monetary authority pours money supply or M into economy, then there occurs a
dynamics of disequilibrium: for a moment at the beginning, the left-hand side of real money
supply M/P exceeds the real money demand on the right-hand side. This inequality may – and
may not- put a train of variables in motion. The disequilibrium in the money market makes the
borrowing cost of money go down, and the (nominal) interest rate may fall. If the price level is
constant for the moment, this will lead to a reduction in real interest rate which boosts real
investment. Thus an increased investment will increase the aggregate demand of the economy.
Thus, the national income measuring the expenditure side, that is, Gross Domestic Expenditures
will automatically rise. This is the demand side of national income. Whether the increase in the
demand side of national income leads to an increase in the supply side of national income such as
Gross Domestic Products(GDP) depends on the size of room in the economy. If there is a room
for an expanded production in the economy, the supply side of national income will increase.
That is an increase in real national income ‘y’ or the aggregated quantities of goods and services.
Going back to the above equation, as i falls and y rises, the right-hand side of real money demand
rises. This dynamic change keeps happening until the right-hand side rises up to the equal level of
the left-hand side of real money supply. Then, the economy has reached a new equilibrium and
there would be no further changes. In this case, money is non-neutral.
A pure sense of non-neutrality may take place when M affects y only, but not P. This is possible
when the economy has the almost perfect price(level) elasticity of (aggregate) supply: A small
increase in the price level leads to an almost infinite increase in the aggregate supply. The
short-run AS curve is horizontal.
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In a hybrid case of non-neutrality, an increase in M would lead to an increase in both y and P. In
this case, the short-run AD curve is upward-sloping. This is a true sense of ‘Synthesis’ befitting its
name of school ‘Neo-classical Synthesis’.
If there is no room in the supply side, however, the increased aggregate expenditures or GDE will
simply push up the price level of national income. The right hand side does not change. The result
is an increase in P. Going back to the above equation, P on the left-hand side roses up until M/P
goes back to the initial level. At the time when it is completed, the resultant change in P will be
proportional to the change in P as long as there is no change in inflation expectations which will
be shown as no changes in i (=r + as you may recall). In this case, money is neutral.
If we really want to split a hair, we will have to be exact here. Even when the economy is at the
full employment level, the national income may rise for a short term. People may overwork and
facilities may be put into use beyond capacity. In the short-run real national income rises. So we
can say that even at the full employment level, money could be non-neutral for a short-term.
However, in the long-run, people cannot overwork and facilities cannot be over-utilized.
Eventually everything will come back to the full employment level. In the long-run, the increase
in money supply will result into the only permanent increase in the price level. In the long-run,
there will be neutrality of money. So remember that in this case there will be first a short-run
non-neutrality and then a long-run neutrality.
Let’s have a look at the quantitative equations. This view basically believes that the velocity of
circulation of money or V in MV = Py is stable. As M goes up and if y < yf , then y goes up. This
is non-neutrality of money.
If y = yf, then M leads to an increase in y in the short-run, and an increase in P in the long-run. This
is non-neutrality of money in the short-run to be followed by neutrality of money in the long-run.
(3) Monetarists' Ideas
The Monetarists are those who believe that money matters and money has the most far-reaching
impacts on macroeconomic variables. They are headed by the late Professor Milton Friedman.
His innovative ideas are summarized as ‘Monetarism’ and those who follow his ideas are called
‘Monetarists’.
Monetarists' transmission mechanism is direct and thus powerful. The money supply affects the
aggregate expenditures directly. However, Milton Friedman did not say that the duration of the
transmission is short. While it is direct, the transmission can take a varying length of time
depending on the situation. In other words, there is a time-varying time-lag between a change in
money supply and the manifest impacts on the economy. Thus, Professor Friedman was, for
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practical reasons, against the use of money as an instrument for an ‘active’ monetary policy
geared to stabilizing the national income in the short-run. The ideal ‘monetary policy’ is,
according to him, of the long-term nature, and is to be devoted to stabilizing the price level. The
focus shifts from the national income to the price level. And then he took one step further to
distinguish a simple increase in the price level and sustaining inflation. He analyses them in the
context of real money demand, and their impacts on interest rates as well. Thus, Professor
Friedman is known for his unique contribution of ‘real money demand’. M. Friedman should be
heard in his voice:
"The quantity theory is in the first instance a theory of the demand for money. It is not a
theory of output, or of money income, or of the price level. Any statement about these
variables requires combining the quantity equation with some specifications about the
condition of supply of money and perhaps about other variables as well." (M. Friedman,
"The Quantity Theory of Money - Restatement, Studies in the Quantity Theory of Money,
University of Chicago, 1956.)
Let’s run the risk of repetition and boredom, we may describe the transmission mechanism of
money to other economic variables for the last time:
The nominal quantity of money demanded by the society as a whole is always equal to the
nominal quantity of money supplied by the government; MS = MD at all times. The general
public as a whole cannot control the nominal money supply but it can control the real money
supply through their collective control of price level.
Suppose the government is handing out newly printed paper monies or notes on the street. Is there
anyone who would refuse them? Every dollar of money supply will be gladly demanded. When
an individual receives some new paper monies, her/his nominal (and real) balances increase. S/he
may succeed in decreasing the nominal money demand or the real money balanced back to the
initial level by spending the excess money holdings. However, because her/his expenditures will
become someone else's receipts, some other members are getting the money being dumped on
them by the first recipient. So from an individual's view point the nominal money demand may be
controllable, while it is not controllable from the society's viewpoint. What is true for individuals
is not necessarily true for the society as a whole. This is the `fallacy of composition' commonly
found in macroeconomics.
As individuals are busy getting rid of the excess money over the desired level of demand("I would
like to have $200 in my pocket, but as government gives me a new $100 bill, now I have the
excess money holding by $100. I would like to go back to the initial level of desired money
demand, that is, $200 by spending $100 away.") The increased money becomes a hot potato. I
dump money on you, you do on him, he does on her, and so forth. The total quantity of the
nominal money demand of the society as a whole, which includes my money as well as yours, and
theirs, remains constant. So we say that an individual can control nominal money demand but the
society cannot.
Depending on the situations surrounding the aggregate supply, the increased speed of spending or
aggregate expenditures can do two different things to the economy:
(i) an increase in aggregate expenditures may stimulate the aggregate supply of goods and
services if there is room in the economy as the current national income is below the full
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employment level. The majority of impact will be on the real national income. The
increase in the national income will consequently induce people to hold more money,
which restores an equilibrium in the money market. In this case the real money demand
rises up to the new higher level of real money supply: in M/P = md, an increase in M
raises M/P to create a disequilibrium. The economy goes back to equilibrium as an
increase in y leads to an increase in md. P remains constant.
(ii) If the economy is around the full employment level, an increase in the aggregate
expenditures will eventually push up the price level. The general public are collectively
changing the price level and thus controlling the real money demand, which is equal to the
nominal money demand divided by the price level. What does this mean in terms of the
real money demand of the society? The real money demand of the society as a whole or
the macroeconomic real money demand is going back to the initial level.
Suppose an economy is around the full employment level, and MS =MD = $200 billion
and P =1.00 initially in the equilibrium. Now the monetary authority increases the
nominal money supply MS to $400 billion. What will happen to the economy?
The (macroeconomic) real money supply is MS/P = 200/1 = 200 for the society at the
initial equilibrium. The MS in the numerator can be replaced with MD as they are always
equal to each other. Let's us not have any distinction between nominal money supply and
demand by using just M: MS/P = MD/P = M/P. At the equilibrium the real money supply
is equal to the real money demand: M/P = md. This real money demand is at the desired
level at the equilibrium in light of all the determinants of the demand including the income
level and the interest rate.
What will happen as the nominal money supply doubles? First, all the increased nominal
money supply will be demanded. So the nominal money demand is equal to the new
nominal money supply(note that this equality of nominal money supply and demand does
not mean at all as the equality of real money supply and demand is the condition for
equilibrium): MD' = MS' = M' = $400 billion.
In the short-run, the price does not change, and thus the actual amount of real money
holding will be M'/P = $400/1.00 = 400. This real money supply is much larger than the
desired real money demand, that is, 200. As there are no change in the determinants of the
real money demand such as interest rate and national income, there should not be any
change in the level of real money balances the general public wish to hold. There is an
excess of real cash balances over the desired real money demand: `actual' real money
balances > `desired' real money balances.
As individuals with excessive money balances try to recover the desired real money
balances by spending the excess money receipts, the price level is pushed up to P'. At this
new price level, the new `actual' real money balances (M'/P') become equal to the desired
level of real money balances.
Specifically, the price level will go up to the level of 2 (or the index number 200). The
actual real money demand will be 400/2 = 200, the same level as before any changes.
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Ch VIII. Money
If you think that up to this part it seems to be, by and large, a repetition of what we have discussed
elsewhere, you are missing a subtle but very important point. Indeed, there is some uniqueness to
the Monetarists’ view. All explanations evolve around the real money demand, and its functional
stability: If there is no change in the equilibrium level of real money demand, a change in
money supply will be met by changes in such a way that the real money balance is to be
restored. The functional stability of real money demand is the key to Professor M. Friedman’s
ideas. The real money demand can change if there are changes in relevant determinants of
variables such as y or i. However, the functional form is stable, and it is the Monetarism’s essence.
Which out of the two paths, an increased money supply go depends on a completely separate
(auxiliary) assumption as to the aggregate supply condition. Some people think that the
Monetarism always argues for neutrality of money. They erroneously think that in the Monetarists’
view an increase in M would just lead to an increase in P, and that it is the major part of the
Monetarism. Simply it is a common misperception. The Monetarism itself is silent and neutral as
to which one is correct. It requires a quite separate auxiliary assumption. We have already
discussed the whole range of arguments as to the impact of an increase in aggregate expenditures
or aggregate demand on the real income versus the price level: Classical school believes that the
As curve is vertical and thus an increase in the AD or AE leads to a rise of the price level only, and
Keynesians argue that it is upward-sloping and thus a higher AE leads to a higher equilibrium real
national income. The New Classical economists argue that the unanticipated increase in the AD
or AE leads to an increase in the real national income only in the short-run and that any
anticipated change will have impacts only on the price level, not on real variables. Monetarism
itself does not necessarily side with any particular argument.
(4) Rational Expectations Theory: New Classical Theory
The bottom line is that only unanticipated ΔM affects Y or national income in the short-run. This
has been discussed in earlier chapters in relation to ‘Policy Invariance Theorem’.
Empirical studies on the Canadian economy of the last twenty years or so indicate the following
conclusions:
i) Monetarist's transmission mechanism is correct for the entire period in question: Whenever
monetary policies went against fiscal policies, monetary policies determined the changes in the
aggregate demand and the nominal national income. For instance, in the case when monetary
policies were expansionary and fiscal policies contractionary, the nominal income increased.
ii) As a result, V or the income velocity was quite stable at least until the early 1980s. This means
a proportionality in changes in the nominal income and the money supply for the most period of
time: ΔM V = Δ Y.
iii) In the early 1980, V rose. This means that in the early 1980s the changes in the nominal
income started to exceed the rate of changes in money supply: ΔM Δ V = Δ Y, and here M is
defined as M1. This is not evidence against Monetarism, which does not preclude the possible
changes in V. In the early 1980 inflation in Canada accelerated and the general public expected a
continued acceleration. So people speeded up spending, and the income velocity rose. The
income velocity changed in a systematic response to a changing opportunity cost of money
holding. When they measured the velocity as a ratio of the nominal income to M2 as opposed to
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Ch VIII. Money
M1, the proportionality between the nominal income and money supply or the constancy of the
velocity V (= Y/M) could be verified again. The most important determinant of the nominal
income and the aggregate demand seemed to be M2. The Bank of Canada has changed its major
money aggregate from M1 to M2 in managing the aggregate demand.
The New Classical Theory has brought a new dimension in out debate to “Neutrality” versus
“Non-neutrality”. It argues that only unanticipated changes in money supply leads to a surprise
inflation and consequently changes in real national income. This is called the (Monetary)
“Policy Ineffectiveness Theorem”. They make a very clear distinction between Anticipated
and Unanticipated Changes in the Money Supply.
(i) Short-run Neutrality for Anticipated Changes in Money Supply
Ultimately the question of whether a change in the money supply would affect national income
depends on whether or not the monetary policy which involves the change in the money supply
is anticipated by the public.
We have already examine this case in the section of the AS. In that graph, the economy moves
from 1 to 3 directly, not through 2. Even in the short-run there is no change or increase in y.
Now let’s introduce some mathematical model as follow:
Remember that two kinds of random factors can make the actual national income deviate from
the full employment income: the forecast error as to the future money supply, and aggregate
supply and demand shocks.
Y t = Y f + ½(M t – t 1 Met)+ ½(  t  t ),
where M t is the actual money supply of period t,
time t-1 to prevail at time t.
t 1
M te denotes the money supply expected at
Some authors may use different notation such as t 1 M te  t 1 M t*  Et 1 M t , They all denote the
same thing: M t expected at time t-1.
 t and t are aggregate demand and supply shocks following a random walk process. The
examples of the aggregate supply shocks are war destruction(of negative value; -), drought(-),
oil shocks(-), discovery of natural resources(+), and so forth. The example of the aggregate
demand shocks may be something like a sudden foreign demand for domestic goods(of
positive value; +), and so forth.
Anticipated changes in the money supply lead to anticipated changes in the price level there is
no forecast error about the price level; there is no divergence, except for the one due to the
aggregate supply and demand shocks, between the anticipated price level, which form the basis
of setting nominal wages, and the actual price level; there is no change in real wages from the
ones corresponding the full employment; there is no change in the level of employment from
the natural rate of unemployment; there is no change in the national income from the initial Y t .
If there is a fluctuation in the national income, that is due to aggregate supply and demand
shocks.
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Ch VIII. Money
An anticipated monetary policy means
Mt=
t 1
M *t and thus M t -
t 1
M *t = 0.
Therefore
Y t = Y f + ½(0) + ½(  t  t ); Y t = Y f + ½(  t  t ).
Note that the monetary variables have disappeared from the income equation. Money is neutral
in the short-run as well as in the long-run.
(ii) Short-run Non-Neutraility of a Unanticipated Change in Money Supply.
In the above equation, a unanticipated change in money supply leads to M t 
t 1
M *t and
thus M t - t 1 M *t (forecast error)  0.
Here money could be non-neutral. There will be a possible forecast error as to money supply of
the next period, which creates room for the national income to deviate from the full
employment level in the short run. Unanticipated changes in the monetary supply lead to
changes in real national income.
However, this does not mean that monetary policies should be used to control the national
income. The forecast errors are random and thus the short-term deviation of national income
from the long-run equilibrium value will be random as well.
An unanticipated change in the money supply increases the degree of variability of the national
income: in order to defeat the general public’s expectations, the money supply should be
changed in a random fashion. If so, the national income would also change in a random way.
As stability of the national income is an important element of society’s material welfare, the
increase volatility decreases social welfare. This kind of nondeterministic or random monetary
policy is not useful.
When there turns out to be a positive shock or surprise, the actual money supply increases more
than what was anticipated in the last period, and the actual price level rises more than
anticipated: M t - E t 1 M t  0 (>0) and P t - E t 1 P t  0 (>0); the nominal wages for the period
t or t 1 W t was determined on the basis of E t 1 P t at the t-1. And thus the realized real wages
W
Wt
( t ) will be smaller than the desired or anticipated one (
), which is equal to the full
Pt
E t 1 Pt
employment equilibrium; this relatively low wage will provide employers with an incentive to
hire more labor; as the labor input increases, the output will increase and the national income
will increase above the full employment level in the short run.
These are all beyond the control by the monetary authority or the government.
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Ch VIII. Money
(iii) In the long run
Three alternative situations are possible:
First, if there is no further change in the monetary policy, in the long run, the general public
will catch up with the reality and revise their expectations as to the money supply and the price
level in line with the actual ones. Workers will demand a new level of nominal wages which
recovers the equilibrium real wages. Then everything goes back to the initial full employment
equilibrium.
Second, if the monetary authorities are engaged in nondeterministic ‘surprise’ monetary
policies and thus changing the money supply in a purely random fashion, the general public
will be continued to be ‘fooled’ and there will be always a deviation of the actual national
income from the full employment one. However, the direction of the deviation, up above or
down below the full employment one, is unpredictable as the deviation of
Y t from Y f is the weighted average of the forecast error and the aggregate shocks, both of
which are intrinsically unpredictable under the rational expectations.
Third, when there are some structural rigidifies which hinder the flexible adjustment of
nominal wages, actual wages do not return to the ones corresponding to full employment even
if the general public may revise their expectations. An example is a legally binding
non-indexed multi-period wage contract which carries to the current and future periods the
previously set nominal wages based on the earlier expectations. In this case, the short-run
deviation persists as long as the contract remains valid.
(vi) Empirical Evidence:
Early research on the United States and Canada, such as Robert J. Barro, “Unanticipated
Money, Output, and the Price Level in the United States,” Journal of Political Economy, 1977,
Vol. 86, and Gillian Wogin, “Unemployment and Monetary policy Under Rational
Expectations: Some Canadian Evidence,” Journal of Monetary Economics, 1980, Vol. 6,
indicated that money surprises were important - even more important than actual or forecasted
money supply – in explaining the departure of the real aggregate output from the potential
output.
In addition, in Y t - Y f =    (M t - E t 1 M t ) +  (M t - E t  2 M t 1 ), by using the data from
the U.S. economy of 1941 – 1977, Barro has found the econometrics test result that   0 and
 = 0, which means that M t - E t 1 M t has explanatory power while M t - E t  2 M t 1 does not.
The first is the forecast error which is included in the information set or I t 1 . This confirms the
prediction of rational expectations theory: only unanticipated changed in the money supply can
affect the national income.
However, Barro’s findings might not stand up to attempts to deal with the longer-run
movement in money in the 1970’s. In fact, his results have been brought into question by later
researchers who have found that actual money supply explains the residual of the fluctuations
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Ch VIII. Money
of the national income from the potential one which cannot be explained by money surprise (F.
Mishikin, “Does Unanticipated Money Matter? An Econometric Investigation,” JPE, 1982,
Vol. 91; M. Askari, “A Non-nested Test of the New Classical Neutrality Proposition for
Canada,” Applied Economics, 1986, Vol. 18).
Let’s take off from money supply and national income, and move on to the relationship
between money supply and inflation.
2) Money Supply and Inflation
Real money (cash) demand has direct bearing on the social welfare. The change in real money
demand is important. Real money demand is the ratio of nominal money supply to the price
level. Therefore the relative movements or a relative change of the money supply and the price
level determines the size of real money demand.
In this analysis, we would like to see whether an increase in the money supply would be
accompanied with constancy of real money demand (M/P), or with a decrease in real money
demand [(M/P) ↓].
In the first case, the price level increase in the same proportion as the money supply so M/P
does not change. This can only happen when there is no change in nominal interest rate which
determines the real money demand.
In the second case, the decrease in M/P with increasing money supply means that P rises more
rapidly than M. So M/P decreases. This happens when the nominal interest rate increase.
(1) Once-and-for-all increase in money supply
If we believe neutrality, the only result is the proportional increase in the price level.
The holding of real balances does not change.
M ↑ and P ↑ proportionately → M/P does not change.
The once-and-for-all increase in money supply does not increase interest rate unless it raises
the inflation expectations. By definition, if the increases in real money supply is
once-and-for-all, the moneys supply will only increase once and in the long-run it will never
increase again, so the long-run rate of inflation or the expected rate of inflation does not
change.
dP e
  e  0.
P
Therefore, a once-and-for-all increase in money supply will not result in a continuous rise in
price level or the true sense of inflation, and will not induce the public to economize on the
holdings of money and waste resources on the replacement of paper money. Thus, it does not
impose any permanent cost on the economy.
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Ch VIII. Money
Graphically:
P
M
Ti m e
Ti m e


i  r  
r
Ti m e
Ti m e
(2) Continuous but Steady Increase in the Money Supply (dM > 0 but d 2 M = 0)
The repetition of an once-and-for-all increase in money supply will result in the continuous
increase in the price level. This is a constant or steady rate of inflation. Inflation occurs only
with a sustained or continuous increase in money supply.
As long as the money supply increases at a steady rate, there is no complicating dynamics. The
only problem is that compared to zero inflation there is a discrepancy between the social
optimum and the private optimum in terms of money holdings; because the opportunity cost of
holding money is positive, the public is trying to economize on the holding of paper money and
this wasting resources and time.
As long as the rate at which the monetary authority increase money is constant, the rate of
money creation is steady. In addition, if we accept the neutrality theorem, the steady rate of
money creation will result in an equal and steady rate of inflation; dM/M = dP/P. The price
level and the money supply increase at the same rate. The nominal interest rate, which is equal
to the sum of the real interest rate and the rate of inflation, will be constant, too. So the
opportunity cost of holding real money balance is constant and there is no reason why the real
money demand should change. There is no worsening of the social welfare or no increase in
social deadweight loss.
In this state, also  e =
dP e
> 0, but constant.
P
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Ch VIII. Money
Graphically:
M
P
slope =  % M
slope =  % P
= 
Time
Time
i = r +

Time
Time
(3) Continuous and Accelerating Increases in the Money Supply (dM > 0, and d 2 M > 0)
An acceleration of continuous increases in money supply will increase the rate of inflation.
This will in turn decrease the demand for real cash balances or the real money demand.
Although M and P are increasing at the same time, the real balances should decrease. This in
turn means that the speed at which P rises will exceed that at which M is increased.
Not only  > 0, also d  > 0; and  e > 0 and d  e > 0.
So, i = r +  e ↑
Numeric Example:
Time
M/P
t
Money Stock
%change
Price Level
Inflation rate
Y
t + 1
10
1
t + 2
10
0.86
t + 3
40
t + 4
0.86
100
Note:
t +Y
5 is constant in
20
100
1
100
110
100
121
100
145
0.86
100
174
100
10%
110
10%
121
20%
169
20%
202
the209
assumption of neutrality
and superneutrality.
20%
242
0.86
100
20
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208
Ch VIII. Money
Graphic Illustration:
M
III

P
II
II
II
*
I
I
III
Time
Time
I
Time
M
=m
P
i
II
I
I
*
II
III
Time
Time
In stage I (a steady stage), the rate of money creation is 10%. If Y is constant, the rate of
inflation is constant at 10%. So the nominal interest rate is constant at i =  + r = 10% + r.
In stage II (another steady stage), the rate of money creation is 20%. If Y is constant and does
not change (i.e. if superneutrality holds), the rate if inflation is 20%. There is no acceleration of
inflation. The nominal interest rate is constant at i =  + r = 20% + r.
In stage III (transition from a rate of inflation to higher rate), as the rate of inflation rises, the
nominal interest rate rises, and thus the real money demand decreases [(M/P) ↓]. As the money
supply (M) is increasing now, the price level (P) should increase more than the money supply
to have M/P go down. As real money demand or real money balances decrease, the social
welfare decreases and the social deadweight loss increases.
(Neutrality Revisited) The neutrality debates takes on another dimension. OK, we may
accept the neutrality of a once-and-for-all increases in money. How about the accelerating
increase in money? Would it still have n impact on the real national income? Those in favor of
‘superneutrality’ states that sustained and accelerating (/ decelerating) increases in money
supply (  M) will just lead to an increase (/decrease) in the rate of changes in the price level or
an increase (/decrease) in the rate of inflation (  P =   ) but not the national income (Y kept
being constant). On the contrary, those arguing for ‘Non-superneutrality’ states that an
increase in the rate of growth of money supply (the acceleration of the rate at which to create
money) will increase the real national income level.
The increase in the rate of growth of money supply will increase the rate of inflation. We all
know by now that the increase in the rate of inflation will increase the opportunity cost of
holding cash balances or money balances (m d = (M/P) falls). We know that the general public
holds savings (S = Y – C) in the form of either increases in money holdings or in demand for
physical goods or capital. In the face of the accelerating inflation rates, the public switches
from money holdings, which are subject to inflationary erosion, to other assets including
capital, K, which are not vulnerable to inflationary erosion. If the supply of K is elastic, then
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Ch VIII. Money
there will be an increase in the equilibrium K stock in the economy. The increased stock of K
will lead to a larger national income. This impact of the acceleration of inflation rates on the
capital stock is called ‘Tobin’ effect.
(Summary)
M↑ and accelerates →  ↑ → i ↑ → m d = M/P ↓ → demand for K ↑ → Y = F (K, N) ↑
(If the Tobin effect is correct.)
The major problem of the Tobin effect is that if focuses only on the ‘substitution effect’ of
inflation, namely, the switching by the public from money holdings to the demand for capital;
given the size of savings; the relative size of money holdings will decrease while that of K will
increase. Inflation has also an ‘income effect’: inflation would decrease national income which
is net of the resources to be wasted on transactions and this purely available for consumption.
It will then crease savings (S = Y – C), which decrease the absolute sizes of money holdings
and demand for K.
With the substitution effect (K↑; m d ↓) and the income effect (K↓; m d ↓), the overall size of K
may not change while the real cash balances will surely decrease. If K, the stock of capital,
does not change, there will be no change in national income. This is the superneutrality; an
increase in the rate of growth of money supply will lead to an increase in the rate of inflation,
but no change in national income.
Under superneutrality, whatever the rate of money creation might be, say 10% or 1000%, and
whatever the rate of inflation might be, national income level dose not change.
3) Money and Interest Rate: Two Tales of Money and Interest Rate
Does an increase in money supply lead to a decrease or an increase in interest rate?
There are two opposite views of this matter:
(1) IS-LM Model: Liquidity Effect: M and i move in the opposite direction
For a given money demand, an increase in money supply will lead to an excess supply of
money and thus the interest rate will fall. Note that according to this view, the interest rate and
money supply move in the opposite direction.
Graphically, in the real money supply and demand, and the IS-LM settings, the above case can
be illustrated as
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p
210
i=r
Ch VIII. Money
LM
LM 
i0
i1
i
IS
(2) Expectations’ Theory or Monetarists’ View: M and i move in the same direction
Fisher’s equation says
i = r +  e ; and
i = r +  in the long-run,
The nominal interest rate is equal to the real interest rate, which is independent of monetary
variables, and the expected rate of inflation. If any change in money supply increases the
expected rate of inflation (  e ), or the long-run actual rate of inflation (  ), then there will be a
change in the interest rate. The implications are as follows:
i)the monetary authority can control only the nominal interest rate, not the real interest
rate. The real interest rate r depends on the marginal product of capital which in turn
depends on the amount of capital stock in the economy, the quantity and quality of
labor forces to be combined with capital, and the level of technology and, over time,
technical innovations. These are not what the monetary authority can control through
monetary policy.
ii) The net impact of an increase in money supply on the nominal interest rate is the sum
of liquidity and expectations’ effects.
The natural question is what kind of increase in the money supply would lead to an increase in
the expected or actual rate of inflation. For example, a truly once-and-for-all blip of increase in
money supply does not change the expected or long-run rate of inflation. So only the liquidity
effect works. Only an accelerating money creation will touch off a revision of the general
public’s expectations to a higher level.
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5. Advanced Theories of Monetary Economics
1) Revisiting the Relationship between Money and Income
Professor James Tobin sees the relationship between the relationship between money and real
income in a different light. He has no problem with the neutrality of money: a once-and-for-all
increase in money supply may lead to no change in the national income in the long-run. From
there, what will happen if the rate of money creation increases or money supply increases in an
accelerating fashion?
If the rate of money creation rises, the rate of inflation rises as well. Thus, the Fisher equation
i = r + tells us that the nominal interest rate will go up.
Then the real money demand falls and the demand for all other assets rises. Particularly,
people would substitute physical assets for money balances. As the demand for physical
products increases, their supply and production will rise. The real national income will
increase. This is called ‘Super Non-neutrality of Money’.
If Tobin’s argument is right, a mild yet ever-increasing inflation is beneficial for the economy.
In some developing countries, people would like to minimize holdings of money for their
assets and wealth, and to replace them with holdings of anything which is supposed to be
protected from inflationary erosion of value.
However, the Monetarists have different view. Tobin’s idea focuses only on the substitution
effect of inflation, and ignores the income effect. Inflation reduces overall national income.
Why? It may not immediately and visibly decreases the nominal dollar value of national
income. However, over time, inflation reduces efficiency of economy by increasing
shoe-leather cost and menu cost. Eventually the real national income will decline. This is the
negative income effect of inflation. Thus, if we look at the overall impact of inflation on the
real national income, the positive substitution effect and the negative income effect cancel each
other and, to say the least, the net result is uncertain. We may restore the dictum that an
increase in the rate of changes in money supply or an accelerated increase in money supply has
no impact on real national income. It is called ‘Super Neutrality’ of money.
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2)Revisiting Inflation: The Phillips Curve
(1)The original Phillips curve and its Policy Implications
Phillips Curve shows the trade off relationship between the rate of inflation and unemployment
rates. In other words, according to William Phillips’s empirical observation of the British
economy of 1861 to 1957, there was a negative correlation between the rate of inflation and
unemployment rate. In this Phillips curve, in order to achieve a lower unemployment or a
higher level of national income, a policy-maker must pay the cost of a higher rate of inflation.
(2) How do you relate it to the Short-run Aggregate Supply curve?
We also know that there is a negative correlation between unemployment rate and national
income. Thus, we can infer that according to the Phillips curve there is a negative correlation
between the rate of inflation and national income. That is ‘almost’ the same as the short-run
aggregate supply curve (SAS) except that the SAS shows the trade-off between the level of
price and national income while the Phillips curve implies the negative correlation between the
rate of change in price level and national income. Just as we can mark the full employment
national income or Yf in the SAS, we can mark down the corresponding natural rate of
unemployment or the non-accelerating inflation rate of unemployment(NAIRU), which means
that as long as the actual unemployment does not exceed this threshold there is no pressure on
inflation.
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(3) Modification to the Expectation-augmented Phillips Curve
Later studies showed that the trade-off between inflation and unemployment rates became
fuzzy and doubted the validity of the Phillips curve.
Edmond Phelps won the Nobel Prize(2006) for adding a third variable of inflation expectations
by the general public and rescuing the Phillips curve: There is not one Phillips curve, but are
many Phillips curves which correspond to different rates of expected inflation. In other words,
an expected rate of inflation is a shift variable for the Phillips curve.
In this ‘Expectations-augmented Phillips curves, at the natural rate of unemployment or
NAIRU(do you recall what it stands for?), the expected rate of inflation, as the shift variable of
a Phillips curve, is the same as the actual rate of inflation on the vertical axis. In other word,
when the expected and actual rates of inflation are equal to each other, regardless of what the
numerical rates are, the national income is at the full employment level. The idea here is
similar to the expectation-augmented aggregate supply curve or Lucas’s aggregate supply
curve while the Expectations-augmented Phillips curves are shown in terms of the trade-off
between ‘inflation rates’ and unemployment rates and the EAS or Lucas’s AS is described in
terms of the negative relationship between ‘the Price Level’ and national income. Thus, we can
have a vertical line above the NAIRU which passes through all Phillips curves of different
expected-inflation rates (and the corresponding same actual rates of inflation respectively).
Some may call this ‘the Long-run Phillips curve’ in contrast to Expectations-augmented
Phillips curves.
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(4) Application of Expectation-Augmented Phillips Curves
The application of EAPC is similar to that of EAS.
When government accelerates money creation and thus the rate of inflation goes up, the
unemployment rate may or may not come down depending on the inflation expectation of the
general public:
When the rate of inflation goes up and if the general public’s expected inflation does not
change, the unemployment rate will fall.
However, it is for only short-run until the general public figure out what is happening to
inflation rates. Eventually, as they revise their expectations of inflation rates, the Phillips curve
shifts up. The unemployment will come back to the NAIRU.
1
2
3
When the rate of inflation goes up and if the general public’s expected inflation change in line
with it, the unemployment rate will not change.
We can put this change in a reverse gear:
When government lowers the rate of inflation, the national income may or may not fall. If the
people revise their inflation expectation down in line with the government policy, then there
will be no changes in national income. However, if the people hold onto their current inflation
expectation, which is higher than the rate of inflation to be realized, recession will take place
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with a higher rate of unemployment and a lower level of national income at least in the
short-run.
When government lowers the rate of money creation and thus the rate of inflation, it may lead
to ‘painless’ only when the general public revise their inflation expectation in line with the
government policy. This is a successful ‘Disinflation Policy’, which means a lower inflation
without a recession and thus an enhanced efficiency of resource allocation for the economy.
(5) In the Short- and Long-run, and the New Keynesian Histeresis.
According to the above theory, in the long-run, as people figure out the reality and revise their
expectations in line with reality, there is no trade-off between rates of inflation and rate of
unemployment. In the long-run, economy moves along the Long-Run Phillips Curve.
However, some new Keynesians have come up with a different idea from their empirical
observation of some European countries of the 1980s.
Suppose that an economy is initially at the full employment level, but with a high rate of
inflation.
Suppose that the government decides to have a disinflation policy. When the rate of inflation
comes down and if initially people do not revise their expected inflation in line with the actual
rate of inflation, the economy should first experience a recession. And then, eventually in the
long-run as people revise their expectations, the economy should go back to the full
employment level of national income or the NAIRU.
However, if the economy has a ‘memory’ and is ‘path-dependent’, it may not go all the way
back to the full employment level. This would be particularly the case if the recession has
lasted for a while. This phenomenon is called ‘histeresis’: a supposed short-run increase of
unemployment rates becomes permanently embedded in the economy as an additional part of
NAIRU. Thus after recession as a result of disinflation, a new NAIRU is now higher than the
previous NAIRU. In this case, the Long-Run Phillips Curve is not vertical but slanted. In this
case, it will be very difficult to lower the rate of unemployment through a macroeconomic
policy. The government may have to break up the hard core part of unemployment, that is, the
NAIRU, through labor market policies.
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3) Revisiting Milton Friedman: The Optimal Inflation
Whatever the constant rate of money creation might be, say 10% or 1000%, and whatever the
constant rate of inflation might be, national income level dose not change as long as it is fully
anticipated and thus the PIT holds – Neutrality of Money.
Even anticipated changes in the rates of money creation, acceleration or deceleration, may
not alter the national income – Super neutrality of Money.
If so, can we safely afford to be indifferent to the rate of inflation or the rate of money creation?
The answer is ‘no’ when the social welfare or social efficiency is taken into account; inflation
is resource-wasting and welfare-reducing.
Here we would like to introduce Professor Milton Friedman’s theory of optimal inflation. It is
the quintessential Milton Friedman Theory. It tells us what is the optimal economic condition,
and has so many lessons and inspiration.
(1) Social Welfare Analysis of Money
First of all, let us examine the proportion that “Inflation creates a wedge between the social
optimum and the private optimum in terms of money holdings”:
Social Optimum in the use of money is achieved when the Social Marginal Cost of (producing)
money = MB. In fact, SMC = 0. Therefore, money should be held or used up to the point
where MB = 0 which is the saturation point of money holdings.
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Illustration
i
md  MU  MB
i0  0
PMC
Private Optimum for i
0
Social Optimum
SMC = 0
PMC = 0
i1  0
Time
Private Optimum for
i1
1) When i0  0 , PMC > SMC = 0
Private Optimum falls short of S.O.
2) When i1  0 , PMC  = SMC = 0
Private Optimum = S.O.
Private Optimum in the holding of money is achieved when the Private Marginal Cost of
(holding) money = MB. In reality, the PMC = nominal interest rate i. Therefore, any positive
nominal interest rate prevents the public to hold money up to the saturation point. Only when i
= 0, then the Private Marginal Cost of holding money becomes zero (PMC = 0). Then the
public will increase money holdings up to the point where the PMC = 0 = MB. The private
optimum coincides with the social optimum. This is the saturation point of holding money. At
this point, nobody in the economy foolishly wastes any resources including his/her own mental
energies on economizing on the holding of money because the holding of money incurs no
opportunity cost. Money is a cheap way of having transactions than other means of payment
such as gold, silver, and other arrangements. How can the government make the nominal
interest rate equal to zero, and therefore induce the general public to hold real balances up to
the saturation point? Fisher’s equation says that i = r +  . When  = -r, i = 0. The optimal
rate of inflation is equal to the minus real interest rate. Thus the socially optimal rate of money
creation is the one which leads to  = -r or i = 0.
The optimal rate of inflation, optimal in the sense that the social welfare is maximized, is equal
to minus real interest rate. This is the first best world. In the second best world, among the
positive rates of inflation, the lower rate of inflation is better than the higher rate of inflation.
As for the above question, we can say that 10% rate of inflation is clearly and far better than
100% rate of inflation from the standpoint of the social welfare. The loss of social welfare is
larger with 10% rate of inflation then with 1000% rate of inflation.
(2) Social Welfares for Different Levels of Inflation:
The Social Welfare or the welfare associated with the use of money for a given real money
demand is the integral or sum of the marginal benefit over the social marginal cost from the
origin to the point of the real money demand or the holding of real cash balances: the area
below the marginal benefit above the social marginal cost line (= horizontal line).
The private sector’s welfare for a given real money demand is the integral or sum of the
marginal benefit over the private marginal cost from the origin to the point of the holding of
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real cash balances: the area below the marginal benefit above the private marginal cost line (=
the given nominal interest rate).
What is the difference between the two and who gets it? Why the social welfare is larger than
the private welfare? The difference between the two is obtained by the government as its
revenue from inflation. It is inflation-tax revenue or seigniorage. It is the rectangular = i  md
(and is equal to   md if real interest r = 0).
The area of the rectangular changes as the rate of inflation changes. When is the area of the
rectangular maximized for a given MB or money demand curve? The answer is when the
rectangular becomes a square. When inflation rate is at the point corresponding to the midpoint
of the money demand function or the MB line, the rectangular has the largest area being a
square. This is called the inflation-tax-revenue maximizing the rate of inflation.
i
consumer surplus
i
(Social welfare =
consumer surplus + producer surplus)
0
social dead
weight loss
(seigniorage) producer
surplus
Let us compare zero inflation, 10% inflation, and 1000% inflation.
The difference in the social welfare between zero inflation and 10% inflation is the social
deadweight welfare loss. The difference is larger between zero and 1000% inflations. This
means that the social deadweight loss increases as the rate of inflation increases.
i
i
r  1000  i1
DWL
r 10  r   i0
DWL
The welfare loss represents resources wasted in efforts to economize on real cash balances.
From a slightly different angle, the welfare loss can be described as the sum of shoe-leather and
menu costs.
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Ch VIII. Money
(3) Reality check- Time Inconsistency of Disinflation Policy
Now if the optimal rate of inflation is the negative of real interest rate, why do we in reality
observe mostly positive rates of inflation all around the world?
The first answer is found in the political economy surrounding the seigniorage. Many
countries rely on the seigniorage for financing government expenditures. This forces them to
set the date of money creation above the Friedman’s optimal rate.
The second answer is to be found in the dynamic game of the ‘Time Inconsistency’ of the
optimal (low inflation) policy. The monetary authorities know that a low inflation is the
optimal policy, but once it is announced and trusted by the general public, they all too often
deviate from the professed policy and use ‘money surprises’ as a means of boosting the
national income. In other words, the disinflation policy has an innate or built-in incentive for
the policy maker to break or to renege on. This kind of policy in general is called ‘Time
Inconsistent’: At one point of time, the policy is optimal as it is, but over time, it becomes
optimal not to follow the policy.
A bigger problem of a ‘Time Inconsistent’ policy is that the general public will figure this out
and will not trust the policy maker. Most likely it will happen over time. As the policy maker
announces a target of a lower inflation. People base their wages settlement and so forth on
those expectations of inflation. Then, however, the policy maker will generate a larger amount
of money supply and a higher rate of inflation. This surprise inflation will lower the real wages
for the economy, and thus helps entrepreneurs to expand production and employment. The
national income rises. The government may have lied but it will say that it was a necessary evil
by quoting, “All is well that ends well”. The problem is that in the mind of the general public it
is not the end, and there will be a next time.
The next time when the policy maker announces a certain target rate of inflation, the general
public will not trust the announcement. People will form their own expectations of inflation,
which will be certainly higher than the publicly announced target rate of inflation. The rest of
the course will be ‘self-realizing prophecy’, and the economic system is settled at the rate of
inflation higher than the optimal rate. Professors Finn Kydland and Edward Prescott have
developed a dynamic theory of ‘Time Inconsistency’ and have got the Nobel Prize in
economics.
Time inconsistency of the policy refers to the situation where the optimality of policies is
inconsistent over time: first it is optimal to have a certain policy, and later it becomes optimal
not to follow the policy. The examples are numerous beside the above disinflation policy:
Example 1) The U.S. government keeps announcing that it will vigorously prosecute illegal
immigrants. However, the government is tempted to give ‘general amnesty’ to illegal
immigrants as they alleviate the shortage of labor forces particularly in the fields which many
American workers shun away from. The potential illegal immigrants are ‘rational’ enough to
know this time-inconsistency of the government, and they try to enter the U.S. in any way. So
the announced policy against illegal immigration is not credible and has no effects in deterring
potential illegal immigrants.
Example 2) The government may announce that it will not render any help to those who are
building houses in an area which is constantly flooded. However, once an area is flooded or
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keeps being flooded, it is in the best interest of the government to come to its rescue and to help
its residents. That is because such an action increases the popularity of the government and
enhances the change for re-election. The rational economic agents figure out this ahead of
time. They will not regard the announced policy as being credible from the beginning, and will
build the houses in the flooded area anyways. The announced government policy has no forces
at all.
How can the government resolve this time inconsistency problem? One solution is to eliminate
discretion (for a policy change) on the part of the policy-maker so that the policy once made
cannot be easily altered. The policy-makers should follow rules as opposed to discretion. It
can enhance the credibility by making it difficult to change any policy. Alternatively, the
policy-makers can build up their reputation over time.
This theory will be fully covered in the next sequel of this course, that is, Advanced
Macroeconomics.
5. Applications to Canada
1) Setting
The Bank of Canada announced the plan to lower the rate of inflation step by step by lowering
the rate of money creation: It is planning to lower the rate of money creation over time so that
as a consequence to the rate of inflation will be lowered from 7% now to 3% per annum by the
end of 1992, and 2.5% by the middle of 1994, and finally to 2% by the end of 1995.
2) Justification of disinflation policy: Anticipated decrease in the rate of inflation
If the policy is carried out in a fully anticipated and credible way, all the economic agents will
act upon a lower expected rate of inflation: new labor contracts will be written in advance, and
so on. In this situation, there will not be any change in the national income. We have also seen
that disinflation will lower the nominal interest only (not the real interest rate) and that does not
reduce the real cost of borrowing capital for the Canadian firms. The question is, why should
the government bother to lower the rate of inflation?
We have seen that the lower the rate of inflation, the better in terms of social welfare. Fewer
resources will be wasted on economizing on the holdings of real cash balances. This gain in
efficiency can be redistributed to the constituents of society and make them better-off.
3) Why Gradualism over ‘Cold Turkey’?
The above-announced policy is ‘Gradualism’ as opposed to a ‘cold turkey’ prescription in
achieving a lower rate of inflation through several stages.
Of course, if the policy invariance theorem is correct, even without gradualism the disinflation
policy would not cause any cost in terms of a reduction in the national income under the
following set of conditions:
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Ch VIII. Money
i) Rational Expectations
The general public should form rational expectations as to money supplies and the price level.
This is a reasonable assumption.
On the contrary, if the economic agents form adaptive expectations, there would be a persistent
difference between the anticipated monetary policy and the actual one, a systematic forecast
error. The worker’s revision of expectations in to a lower one will lag behind the actual
disinflation. The downward adjustment of the rate of nominal wage raise, which is based on
the worker’s expectations of inflation rates, will lag behind the actual disinflation. As a result,
the real wage will be higher than the market-clearing one and there will be unemployment and
a decrease in the national income.
ii) a Fully Anticipated Policy
A policy change should be fully anticipated and acted upon by the economic agents, workers
and employers alike.
First, the policy should be announced far in advance and in detail, sending a clear signal to the
public in general and leaving no room for uncertainty, speculation or misinterpretation.
Second, the policy should be ‘credible’. No credible policy will be believed by the public in
the first place, and subsequently will be acted upon. Some policies are not believed as the
government has no credibility. In this case the government should build up a ‘reputation’ by
demonstrating its will power. Other policies are not credible as they contain an incentive for
the policy maker to renege on. Those policies are said to be ‘time inconsistent’.
If the above conditions are all met and thus all monetary policy should be announced and
credible, and the economic agent or the general public is rational, then the PIT should hold.
The public will be very swift in readjusting their expectations and there will not be any forecast
error about the price level or about the money supply even in the short-run, and thus there
should not be any change (decrease) in the national income.
iii) The above i) and ii) may hold. However, if the workers are locked-up in a multiple-period
and non-indexed labor contract which was set up before this change in government policy,
the rational workers cannot react to this new policy during the interim period of the contract.
During this period, the policy invariance theorem does not hold and the disinflation policy
would take toll on the national income.
The rapid disinflation would cause changes in real wages of those whose nominal wages are
fixed by the non-indexed multi-period labor contract: the existing non-indexed multi-period
W
contract incorporates a previous higher expected rate of inflation ( t -1 e t ). After the
t -1 P t
disinflation policy comes into effect, the new rate of inflation is lower than the previous one.
So under the contract which was signed before the announcement of the new and lower rate of
inflation, the predetermined (negotiated and previously set) increase in normal wages will be
larger, and so will be the increase in real wages. Thus there will be a decrease in the demand
for labor. The level of employment will drop and there will be a decrease in the national
income.
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Ch VIII. Money
It is important to give time for the workers to exit the existing contract and to have a new
contract which incorporates a lower rate of inflation.
Friedman argues that the most important device for mitigating the side effects is to slow
inflation gradually but steadily under the circumstances where workers are locked up in
long-term or multi-period and non-indexed contracts: The government should announce the
policy in advance so that the public in general can prepare itself for the change and adjust its
expectations about the monetary policy and the new inflation. It also should adhere to the
policy (should not make a U-turn) so that the policy should be shown to be credible and any
uncertainty should be dispelled. This gradualness and advance announcement is to give people
time to readjust their arrangements (M. Friedman, Free to Choose, p. 273).
We note that the announced disinflation policy intends to decrease the rate of inflation over
next four years in a gradual fashion; the present 7-8% inflation in March 1991 will be lowered
to 2% by the end of 1995.
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Ch IX. Open Macroeconomics
Chapter IX. Open Macroeconomics: IS-LM-BP Model
1. Introduction
1) Assumption: Price level (domestic: P; foreign P*) is fixed.
2) Definition:
S denotes exchange rate. It is defined as the price of foreign currency in terms of domestic
currency.

If the Canadian dollar price of U.S. $1 is 1.50, we take this as an exchange rate. Note that
the news paper uses different exchange rate, that is, how much of foreign currencies a unit
of domestic dollar can fetch. For instance, if Cdn $1 can fetch U.S. $0.67, the exchange
rate is 0.65. All throughout this course, we will use the first definition, which is
convenient and consistent: Just like any other goods such as a hamburger, the price of a
unit of foreign currency is the exchange rate.
An increase in exchange rate or S due to market forces under the flexible exchange rate system is
called an appreciation of foreign currency and a depreciation of domestic currency.
When government raises exchange rates or S under the fixed exchange rate system, it is called a
‘devaluation’ of domestic currency. The opposite is called an ‘evaluation’.
2. IS Curve
1) Modification of the IS curve in the Open Macroeconomics setting
The IS is derived by equating Y with AE = C + I + G + X-M. Whenever there is a change in AE
or its components, the IS curve shifts around. Now the X-M has to be specified.
X-M is the Net exports (NX), which is approximate equal to the Current Account balance: X-M =
NX = CA.
So we can rewrite into AE = C + I + G + CA. Whatever affects the components of the AE shifts
the IS curve: Now an improving current account will shift the IS to the right, and a deteriorating
current account to the left.
2) What determines the Net Exports or Current Account Balance?
X = M*(Y*, SP*/P)
Our exports are the imports by the foreign country. How much the foreign country
imports from us depends on their income (foreign country's national income), and the
relative price level of the foreign country to our country (SP*/P).
P* is the price level of the foreign country in terms of the foreign currency. S is `our' price
of `their' dollar. So the product of S P* is the relative price level of the foreign country to
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Ch IX. Open Macroeconomics
our (the domestic country) in our currency terms. For instance, suppose that a hamburger
in the U.S. is $1.00 in U.S. dollar terms (P*), a Canadian hamburger is $1.30 in Canadian
dollar terms (P), and the Canadian dollar price of U.S. $1 is $1.40 (S). The U.S.
hamburger costs Canadian $1.40 as S times P* = 1.4 X 1. The Canadian hamburger costs
Canadian $1.30. So the relative price level of the foreign to the domestic country is 1.4 to
1.3, that is, 1.076. The foreign price level is 1.076 times as high as the domestic price
level. In our model we assume that the price level, domestic and foreign, is fixed. An
increase in the exchange rate or S makes the foreign good dearer and more expensive, and
raises the foreign price level compared to the domestic price level. This will in turn make
consumers, domestic and foreign, switch from foreign to domestic goods: our exports of
domestic goods rise and our imports of foreign goods fall. Our current account and the
balance of payment will improve: S  SP*  SP*/P  Foreign price level  
Demand for domestic goods  and Demand for foreign goods  X and M 
Net Exports(X-M) (doubly improving)  CA.
M = M(Y, SP*/P)
Our imports are an increasing function of our national income, and a decreasing function
of the relative price level of the foreign to the domestic country: The more money we have,
the more of foreign goods we can afford to import. The higher the foreign price level, the
less we would like to import.
Combining the above two as CA = NX = X-M, we get
CA = X(Y*, SP*/P) - M(Y, SP*/P)
Ultimately, the current account is a function of Y, Y*, SP*/P;
CA = f(Y, Y*, SP*/P)
Let's review the impact of each variable on the net exports or current account:
i) Y  M  NX = CA
ii) Y*  X  NX = CA 
iii) S  SP*/P   M and X  NX = CA
This suggests that the IS curve becomes endogenous under the flexible exchange rate
system. A changing exchange rate leads to a change in the AE curve, which in turn shifts
the IS curve around.
In short, the IS curve has shift parameters of C, I. G and CA(=X-M), and CA becomes
endogenous under the flexbile foreign exchange rate system.
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Ch IX. Open Macroeconomics
3. LM Curve
LM curve has shift parameters the real money supply (=MS/P) and the random term in the money
demand u. The price level is fixed. The only shift parameters are the nominal money supply MS
and the random money demand term u.
As the nominal money supply MS changes (increases/decreases), LM shifts around (to the
right/left).
As will be seen in details later, under the Fixed Exchange Rate System, government intervention
into the foreign exchange market has a side-effect of a changing money supply and thus the
nominal money supply becomes endogenous and the LM curve moves around beyond the control
of government.
Money supply becomes endogenous, and the LM curve shifts around under the fixed
foreign exchange rate system.
4. BP Curve
1) Definition
There are two concepts of the Balance of Payment. The broad sense of the Balance of Payment
includes all the external transactions in the private as well as public sectors. The narrow sense of
the BP with which we are mainly concerned in economics is the account of the private sector's
transactions with other countries. This is called `the Above-the-Line' Balance of Payment, where
the line of demarcation divides the transactions of the private sector from those of the public
sector or the government:
I. Current Account (CA)
Trade
Remittances
Transfers
Exports
Imports
II. Capital Account of the Private Sector (KA)
Capital Flows
Inflows
Outflows
______________________________________________
III. Capital Account of the Public Sector
Official Financing
Inflows
Outflows
The double entry bookkeeping makes the broad sense of the BP, which is the sum of I, II and III,
equals zero all the time. So it is rather uninteresting.
Our BP, the narrow sense of BP, or the Above-the-Line BP is the sum of I + II:
BP
=X–M
= CI – CO
= CA + KA.
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It can take on any value. When it happens to be equal to zero, it is said, the BP is in equilibrium:
BP = 0. Otherwise, the BP is in disequilibrium. We also say that the economy is in the external
equilibrium. When BP<0, the BP is in deficits. When BP>0, the BP is in surplus.
The BP curve is the locus of the combinations of the national income and interest rate (y, i) which
bring about the BP equilibrium: BP = 0 along this BP curve.
2) Determinants of BP = CA + KA
i) CA
We have already examined the determinants of the current account. Recall that CA = NX
(Y, Y*, SP*/P);
-when domestic national income rises, CA falls.
-when foreign national income rises, CA rises.
-when foreign exchange rate rises, foreign currency becomes more expensive in terms of
domestic currency, and thus the domestic prices of foreign goods goes up. Therefore, less
imports and more exports, and CA rises.
ii) KA = Net Private Capital Inflows = CI - CO
KA = NCI ( r - r*), where r (real) interest rate or real rate of returns on domestic bonds; r-r*
is the interest differential between domestic and foreign countries or how higher domestic
interest rate is than foreign one. This signifies the relative attractiveness of investment in
the domestic country to investment in the foreign country. The larger the interest
differential, the larger the capital inflows into the domestic country.
When r-r*, international investors bring foreign currencies to convert into domestic
currency: KA, and BP
The above will happen either when domestic interest rate r rises, or when foreign interest
rate r* falls.
iii) Now BP is the sum of the current and the capital accounts
BP = CA(Y, Y*, SP*/P) + KA(r-r*)
Therefore, BP = BP(Y, Y*, SP*/P, r-r*)
3) Derivation of BP curve
The BP curve shows different combinations of interest rates and income which all bring
about external equilibrium or BP=0. In general the BP curve is upward sloping, meaning
that along the external equilibrium BP=0 the interest rate and income are changing in the
same direction.
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Step 1: Start with a point where BP = 0 (@ a)
Step 2: Now suppose that national income rises. The current account and thus BP will
deteriorate:
Y rises  M   CA   BP < 0 (@ b)
Step 3: How to restore the external equilibrium BP=0?
There should be an improvement of KA by the same amount of the decrease in CA, and
then they will cancel each other. In order to have KA improve, the domestic interest rate
should be raised:
KA by r (@ c). Then BP = CA + KA = 0 again.
Step 4: Link a and c to get `BP = 0 Curve.
Note that the region above or to the left of the BP curve the BP is in surplus and the region below
or to the right of the BP curve the BP is in deficits:
Let's suppose that the BP = 0 at point a in the following graph. Point b means less national income
and thus less demand for foreign goods: the better current account and thus now the BP is in
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surplus: BP= CA () + KA >0. Note that as this point lies at the same height of point a, the interest
rate remains unchanged and thus there is no change in the capital account. Point c means more
income and thus less CA and BP<0.
Point d lies straight above point a of BP=0, meaning the same national income but a higher
domestic interest rate. The better capital account and thus now the BP is in surplus: BP= CA +
KA () >0. Point e lies straight below point a, meaning the same national income but a lower
domestic interest rate. The capital account at point e is smaller than that at point a, and thus now
the BP is in deficits at point e: BP= CA + KA () <0.
4) Different Slopes of BP curve
The slopes of BP curve depend on the Degree of Capital Mobility across countries or the
sensitivity of capital flow with respect to interest rate differentials. The principle is that the
more mobile the capital (the freer capital flows), the flatter the BP curve.
Illustration
In the above two graphs, the same increase in Y causes the same decrease in CA at b. As BP = CA
+ KA, in order to get back to BP = 0, the same amount of increase in KA through capital inflows is
required.
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However, to induce the same increase in KA, Case I requires a more raise of interest rate than
Case II: When capital is not so mobile like Case I, a relatively large increase in interest rate is
needed to induce the same increase in KA. On the contrary, when capital is very mobile, only a
small rise in the interest rate will bring about the same amount of capital inflows and thus the
needed KA improvement.
There are four different slopes of the BP curves depending on the degree of mobility of capital:
5) Shift of BP Curve
All determinants of BP = BP(Y, Y*, SP*/P, r-r*) other than r and Y shift the BP curve: Y*, S, and r*
are shift parameters. The first two variables which affect the Current Account shift the BP curve
horizontally (to the right/left). The last variable r* or the foreign interest rate which primarily
affects the Capital Account shifts the BP curve vertically (up/down).
Case I: S  BP shifts to the right
Recall that to the left of the BP curve, BP > 0 (surplus); to
the right of BP curve, BP < 0 (deficit).
i)Suppose that initially BP =0 at point a
ii) S  SP*/P (relative foreign price level)  X and
M  CA 
So now point a should have BP>0 at the same interest rate (no change in KA). Point a should lie
to the left of the new BP curve BP', which is the BP surplus region in the graph. To restore the
external equilibrium BP = 0, the national income should rise to have a deterioration of the current
account which offsets the initial improvement in CA. Point a moves to point b. From the
viewpoint of the BP curve, we can say that the BP curve shifts to the right.
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Case II: Y*  BP shifts to the right
Case III: r*  BP shifts up
i) Initially BP = 0 at point a
ii) r*  Capital Outflows   KA ; So now point a
should have BP <0 at the same Y (which means no change
in CA as there is no change in income). Point a should lie
below the new BP.
We note that Cases I and II affect the CA favourably, and shift the BP curve to the right, and Case
III affects the KA adversely and shifts the BP curve up. The emerging principle is that whatever
affects the CA favourably shifts the BP curve to the right, and whatever affects the KA favourably
shifts the BP curve down.
In general cases of an upward sloping BP curve, the rightward shift is virtually the same as the
downward shift: all expands the BP surplus region in the graph. However, they are quite different
in the following extreme cases:
r=i
In the case of perfect capital mobility, an increase in exchange rate or S would not affect
the BP curve at all. The horizontal BP curve shifts to the right without any substantive
change.
r=i
Y
Y
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In the case of perfect capital immobility, an increase in foreign interest rate would not
affect the BP curve at all. The vertical BP curve shifts up without any substantive change.
r=i
Y
Y
5. Exchange Rate
Depending on what exchange rate system the government adopts, either IS-BP or LM may
become endogenous.
1) Imbalance of Payment and Pressures on Exchange Rates (SR)
BP > 0
(surplus)
Excess Supply of
Currency
Foreign
Downward Pressure on
Exchange Rate
Foreign
BP < 0
(deficit)
Excess Demand for
Currency
Foreign
Upward Pressure on
Exchange Rate
Foreign
BP > 0 means that the Balance of Payment is in surplus. This implies that BP = CA + KA > 0 and
that the total receipt of foreign currency (exchange) through exports(X) and capital inflows(CI)
exceeds the total payment of foreign currency through imports(M) and capital outflows(CO).
X + CI > M + CO; X-M + CI -CO > 0 ;
NX + NCI > 0, where NCI denotes Net Capital Inflows.
CA + KA > 0; BP > 0
So the Supply of foreign currency exceeds the Demand for foreign currency. When S>D, there is
Excess Supply and there occurs downward pressures on the price of foreign currency, that is,
foreign exchange rate. Left alone, foreign exchange rate will fall.
2) Fixed Exchange Rate System:


" Money Supply becomes Endogenous"
“LM Curve moves around to restore the balance of payment equilibrium”
The Fixed Exchange Rate System means the government's standing commitment to maintain
foreign exchange rate at a fixed level through unlimited sales/purchases of foreign currency.
Under the fixed exchange rate system, government should buy/sell foreign currency whenever
there occurs BP surplus/deficit.
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In the above example, to diffuse the downward pressure on exchange rate and to fix the exchange
rate, government should eliminate the Excess Supply of foreign currency by moping it up.
Government should buy excess supply of foreign currency.
Under the fixed exchange rate system, there is a very important side effect to this operation. You
may remember whenever government buys anything from the general public, it should make
payment in domestic currency from them. As Money flows from the government to the general
public, Money Supply increases. The LM curve shifts to the right. Under the fixed exchange rate
system, money supply becomes endogenous (meaning that government loses control over MS).
BP
Gov't action to fix S
Side Effect (LM) (in the LR)
surplus
buys foreign currency
MS increases()
deficit
sells foreign currency
MS decreases()
Sterilization Policy
Actually there is a way of regaining the control of MS: at least in the short-run;
The government may take a counteraction in the open market operation in order to offset any
change in MS due to its purchase of foreign currency.
For instance, in the case of BP surplus under the fixed exchange rate system, the government has
to buy foreign exchanges. This will increase the money supply in the private sector. This in turn
may put upward pressures on the price level and inflationary trends. If the government would like
to reign in the money supply, then it should do something .The government may sell bonds. These
sales of bonds or securities are in exchange for domestic money as their payment. Thus all in all,
the money supply comes back to the initial level. There will not be any net change in money
supply.
This counteraction designed to offset the impact of government intervention in the foreign
exchange market is called `Sterilization' policy.
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The short-term nature of sterilization is more obvious with the case of BP deficits.
The BP deficits will exert an upward pressure on foreign exchange rates. To diffuse the upward
pressures on exchange rates, the government will have to sell foreign currencies. This
government action has a side-effect of decreasing the money supply as the private sector’s buyers
of the foreign exchanges will make payments with domestic currency. Thus the money supply
falls, exerting a contractionary impact on the economy. The sterilization policy in the case dictates
that the government may buy bonds or securities. As the government makes payments in
domestic currency, money flows from government to private sector. The money supply of the
private sector rises. This offsets the initial decrease in money supply which has resulted from the
government sales of foreign exchanges. Overall, there will be no net change in the money supply.
Graphically, the BP deficits shift the LM curve to the left in its gravitation to restore the new
equilibrium. However, the sterilization policy puts the LM back to the state where the BP takes
place. In this way, the sterilization policy perpetuates the BP balance of payment disequilibrium,
or BP deficits in this particular case. This forces the government to intervene in the foreign
exchange market and the sales of foreign exchanges. The government will continue to do so until
it runs out of foreign exchanges. Thus the sterilization is only a short-term measure of gaining the
control of money supply.
Without Sterilization
LM’
i
With Sterilization
LM
i
LM
BP
BP
IS
IS
Y
Y
3) Flexible Exchange Rate System:


“Exchange rates change”.
"IS and BP curves becomes endogenous to restore the balance of payment equilibrium."
BP
Exchange Rate
Current Account
BP
Curve
(LR)
IS
Curve
(LR)
surplus
S
CA 
to left
to left
deficit
S
CA 
to right
to right
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When BP > 0 and government does not do anything to diffuse the downward pressure on
exchange rate, the exchange rate will fall (S). The falling exchange rate means a lower relative
foreign price level (SP*/P). Exports decrease and imports increases, and thus the net export NX
= X-M or current account CA falls. AE = C + I + G + X-M falls and the IS curve shifts to the left.
6. Applications
Let us familiarize ourselves with the terminologies such as the internal (domestic) and external
equilibrium: The intersection of the IS and LM curves is called the `Internal Equilibrium'. The
External Equilibrium is achieved along the BP curve where BP=0. At the `Grand Equilibrium'
both the internal and external equilibria are achieved at the same time. Graphically the
intersection of the IS and LM curves should be on the BP curve.
Shocks can create a discrepancy between the internal equilibrium (intersection of IS and LM) and
the external equilibrium (BP curve): the intersection of IS-LM is no longer on BP curve. BP is in
disequilibrium: BP>0 or BP<0. There occurs an adjustment process of internal and external
equilibrium converging to each other. Alternative exchange rate systems do have different
adjustment processes. After the process is over, the economy restores external and internal
equilibrium: BP=0. Under the Fixed Exchange Rate System, the MS changes endogenously, and
thus the LM curve shifts to restore the external equilibrium. Under the Flexible Exchange Rate
System: S (goes up/down) changes endogenously and thus IS and BP curves shift (to the
right/left).
1) Inevitability of Competitive Devaluation in the 1930s
If an economy has unemployment and BP deficits at the same time under the fixed exchange rate
system and no capital mobility, it is impossible to resolve any problems, of the domestic and
international sector, through fiscal or monetary polices. The two policies will be completely
incapable of any solution. The only possible way out is devaluation.
i
BP
i
E0
Y*
Y1
BP
i
LM
LM
IS
IS
Y
Fiscal Policy
Y
BP
LM
IS
Monetary Policy Y
In the above graph, let's suppose that the initial condition of an economy is at point E0 with
unemployment (y < yf) and BP deficits (to the right of the BP curve is the BP negative region).
If government raises its expenditures in the hopes of eliminating unemployment, the balance of
payment will deteriorate further. The BP deficits require the government sell foreign currencies
under the fixed exchange rate system. The side-effect will be a decrease in the money supply and
the LM curve will shift to the left. An expansionary monetary policy or the government's attempt
to increase money supply and thus to shift the LM to the right will be also futile under the fixed
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exchange rate system: the BP deficits require the government to sell foreign currencies and thus to
reduce money supply. As a result the LM curve continues to shift to the left.
The only solution is to shift the BP curve and the IS curve at the same time so that the intersection
of the new IS and LM curves are on the new vertical BP curve. This can be done only when the
exchange rate is raised by the government. We may recall that this administered raise in the
exchange rate is called `devaluation'.
In the 1920s and 1930s, the prevailing exchange rate system was the fixed one, and the
international capital mobility was very limited at least outside economic blocs. Many countries
suffered from recession and balance of payment deficits. They tried all kinds of economic
policies with no success and finally entered competitive devaluations, which resulted into a total
collapse of the international fixed exchange rate system.
2) Impacts of Fiscal and Monetary Policies on BP

An expansionary monetary policy has a clear-cut negative impact on the balance of
payment;
The expansionary monetary policy increases the national income Y and decreases interest
rate i.
The first leads to a deterioration of the current account balance as an increased national
income leads to more imports. The second leads to the deterioration of the capital account
as the lower interest rate means capital outflows. The combined impact is clearly negative
on the BP.
Capital is immobile
Capital is mobile
BP
LM
LM
BP
BP<0
BP<0
IS

As shown in the graph below, an expansionary fiscal policy has an ambiguous impact on
the balance of payment;
An expansionary fiscal policy leads to a larger Y and a higher interest rate or i. The first
leads to a deterioration of the current account of BP, and the second to the improvement of
the capital account of BP. The first negative and the second positive impacts work against
each other. The overall impact depends on the relative magnitude of the two effects.
When capital is mobile, the improvement of the capital account may be substantial, and be
large enough to more than offset the first negative impact. The net BP will improve.
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i
IS
e
BP>0
BP
LM
Y
Mobile
When capital is immobile, the improvement of the capital account may be small, and thus
be not large enough to offset the BP deterioration resulting from an increasing national
income and imports. All in all, the BP will deteriorate on the net basis.
i
BP
LM
BP<0
e
IS
Immobile
Y
3) Modified Effectiveness of Fiscal and Monetary Policies
We have just seen that, in certain cases with added international dimensions, the IS-LM model
developed for a closed economy should be greatly modified.
Effectiveness of fiscal and monetary policies in the open macroeconomics (IS-LM-BP model)
will be significantly different from the prediction for the closed economy (IS-LM model).
(1) Effectiveness of Fiscal Policies
Case I. Capital is relatively immobile: The BP curve is steeper than the LM curve.
Expansionary fiscal policy leads to the BP deficit: a rightward shift of the IS curve in the IS-LM
setting means a higher equilibrium national income and a higher interest rate. A higher national
income means a fall in CA. A higher interest rate means a rise in KA. The assumed capital
immobility means that the second is smaller than the first, and thus the net impact on the BP is
negative. The BP deficit means the excess demand for foreign currencies (exchanges). There
occurs upward pressure on exchange rates.
Under the Fixed exchange rate system, as government diffuses the foreign currency shortage by
selling foreign currencies, the payment for them in domestic currency flows into the government
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and thus the money supply in the private sector decreases. The LM curve shifts to the left, exerting
recessionary impacts on the economy and thus partially offsetting the initial expansionary fiscal
policy. Here the fiscal policy is being hampered.
(Note: Fixed Forex, Immobile Capital)
Under the Flexible exchange rate system, the exchange rate will rise. As a result the price level of
the foreign country expressed in terms of domestic currency rises, which leads to international
demand switch from foreign to domestic goods. CA improves. The IS curve will shift further to
the right, and the BP curve will shift to the right, too. The resultant equilibrium income is still
larger. Here the fiscal policy is reinforced by the international factor.
(Note: Flexible Forex. Capital Relatively Immobile)
Under a relative capital immobility, the fiscal policy and the flexible exchange rate system are a
good combination.
Case II. Capital is relatively mobile: The BP curve is flatter than the LM curve.
Expansionary fiscal policies lead to the BP surplus. Why? When the IS curve shifts to the right as
a result of the expansionary fiscal policy, two things will happen to affect the BP: an increase in
Y* at the new internal equilibrium or the new intersection of the IS-LM leads to more imports and
thus a decrease in CA. On the other hand, the interest rate goes up as a result of crowing-out and
this rise in the interest rate attracts more international funds into the country, which leads to an
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increase in KA. The net change in the BP is the difference between the decrease in CA and an
increase in KA. The assumption of the highly mobile capital implies that the increase in KA is
larger than the decrease in CA: a higher interest rate will attract an avalanche of massive capital
inflows which will more than dominate the deteriorating current account due to a higher income.
The BP surplus means an excess supply (`too much of foreign currencies').
Under the Fixed exchange rate system, as government mops up the foreign currency surplus by
buying foreign currencies, the payment for them in domestic currency flows from the government
to the private sector and thus the money supply in the private sector increases. The LM curve
shifts to the right, exerting expansionary impacts on the economy and thus reinforcing the initial
expansionary fiscal policy. Here the fiscal policy is being reinforced.
Under the Flexible exchange rate system, the exchange rate will fall. As a result the price level of
the foreign country expressed in terms of domestic currency falls, which leads to international
demand switch from domestic to foreign goods. CA falls. The IS curve will shift to the left,
partially offsetting its initial rightward shift, and the BP curve will shift up too. The resultant
equilibrium income is not as large as that in the simple IS-LM setting. Here the fiscal policy is
partially offset by the international factor.
Under a relative capital mobility, the fiscal policy and the fixed exchange rate system are a good
combination. When international capital flows are quite brisk in and out of a country, and
government is now being engaged in fiscal policy, it should not allow the exchange rate to
fluctuate. The fluctuation exchange rate will offset the current fiscal policy.
For instance, the capital mobility between Canada and U.S. is very high. Let's suppose
that the Canadian government wants to get out of recession by increasing government
expenditures. The resultant higher interest rate will attract international funds into Canada
(KA) and thus the BP will improve. There occurs a downward pressure on foreign
exchange rate (upward pressure on the external value of the Canadian dollar). The point is
that if the government wants to boost the economy, it cannot afford to let the exchange
rate fall. Because the falling exchange rate will hamper exports and encourage imports.
The CA will fall and thus the AE (=C + I + G + CA) will fall. There will be a recessionary
impact on the export industry, which nullifies the initial expansionary fiscal policy. If
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government instead engages itself in fixing the exchange rate (keeping the Canadian
dollar artificially low), government ends up selling the Canadian dollars and buying the
U.S. dollars. The money supply (Canadian dollars) in the private sector rises. It will exert
expansionary impacts on the economy, furthering the initial fiscal policy. The fiscal
policy and the fixed exchange rate system is a good combination.
You may think of the opposite case where the Canadian government wants to fight against
inflationary pressure by cutting government expenditures. Still the fixed exchange rate
system or some attempt to fix the exchange rate at the current level is a better choice than
the flexible exchange rate system.
(2) Effectiveness of Monetary Policies
Regardless of the degrees of capital mobility, an expansionary monetary policy invariably leads to
a deterioration of the BP: When the LM curve shifts to the right, the equilibrium income rises and
equilibrium interest rate falls. a rising income leads to more imports and thus a fall in CA. A
falling interest rate leads to a fall in KA. If we start with an initial equilibrium of BP=0, an
expansionary monetary policy will lead to the BP deficit or BP <0.
Under the fixed exchange rate system, the BP<0 requires the government sell foreign currencies
(simultaneously taking in domestic money as their payments). The money supply in the private
sector decreases and thus the LM curve will shift to the left. The initial expansionary monetary
policy is now hampered.
Under the flexible exchange rate system, the BP<0 will lead to a rise in the exchange rate. The
rising exchange rate will bring about an increase in exports and a decrease in imports: CA The
IS as well as the BP curves will shift to the right and meet the already-shifted LM curve.
Regardless of the capital mobility, the monetary policy and the flexible exchange rate system are a
good combination.
For instance, when the first priority of the Canadian government is a tight monetary policy,
it cannot afford to intervene into the foreign exchange market. It should take its hands off
from it, and had better let the exchange rate go freely. If the government makes a wrong
choice of the fixed exchange rate system, the BP surplus as a result of the tight monetary
policy will require the government to buy foreign currencies, which leads to a
self-defeating rise in the money supply.
Let’s illustrate the above points.
An expansionary monetary policy is intended to increase the national income. Depending on the
capital mobility of the economy, the initial impact of the expansionary monetary policy is as
follows:
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Both lead to a balance of payment deficit. This deficit will have a contractionary impact under the
fixed exchange rate system. And thus the LM will shift back to the left.
Under Flexible Exchange Rate System:
Under the flexible exchange rate system, the BP deficit leads to an increase in exchange rates,
which in turn leads to a CA increase. A rising CA shifts the IS and BP curves to the right. The
new equilibrium is now on the BP curve. We can say that the flexible exchange rate system
magnifies the initial changes in the national income, and thus reinforces the expansionary
monetary policy.
Fixed Exchange Rate System
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The balance of payment deficit will lead to a contractionary impact under the fixed exchange rate
system. And thus the LM curve will shift back to the left.
You can see that the secondary endogenous movement of the LM curve shifts the equilibrium
national income back against the direction to which the initial monetary policy has changed Y.
Thus, we can say that the fixed foreign exchange rate system offsets the monetary policy
regardless of degrees of capital mobility.
4) Exchange Rate System as an Insulator against Shocks
Exchange rate system could be a built-in stabilizer or an amplifier of economic shocks or
disturbances. Under what conditions which exchange rate system becomes a magnifier or a
pacifier of troubles? As will see below, it all depends on the degree of capital mobility and the
nature of shocks. One thing which clearly emerges from discussion will be that there is no
insulator from foreign monetary shocks at all: no exchange rate system will serve as a buffer from
the foreign monetary shocks.
For instance, if the U.S. government raises interest rate, which is a foreign monetary shock, its
impact will be inevitable felt on the Canadian economy no matter which exchange rate system
Canada adopts. What still matter is that such an impact could be expansionary or contractionary
on the Canadian economy depending on the exchange rate system. A higher interest rate will lead
to capital outflows from Canada, a KA deterioration and thus a BP deficit in Canada. If the fixed
exchange rate system is adopted (the Canadian government tries to depend the external value of
the Canadian dollars which are loosing values against the U.S. dollars), the very government's
attempt to fix the exchange rate by selling the U.S. dollars in exchange for the Canadian dollars
will lead to a decrease in the money supply in Canada. The LM curve shifts to the left, exerting a
contractionary impact on the Canadian economy. Alternatively, if the Canadian government
simply lets the exchange rate go, the falling exchange rate will lead to the improvement of the CA
(recall S and CA move in the same direction all the time). The IS and BP curve will shift to the
left, exerting a contractionary impact. One more thing we should keep in mind is that the
expansionary impact is not necessarily a better one than the contractionary impact. Which is the
better depends on what government wants for now. If government targets at boosting an economy
amid recession, yes, the expansionary impact helps. However, if the government's first priority is
to restrain the overheated economy, the expansionary impact will hurt.
In order to figure out the correct impact, we have to specify three important things very clearly
before plunging into analysis:
(a) The Nature of Initial Shocks; "Do the initial troubles or shocks shift which curve(s)? IS,
LM, and/or BP?"
(b) The Degree of Capital Mobility; "Is capital perfectly immobile, relatively immobile,
relatively mobile or perfectly mobile?" Alternatively, "Is the BP curve in question
vertical, steeper than the LM, flatter than the LM, or horizontal?" In the modern world,
the vertical BP is hard to find except for a very few exceptional cases (for instance,
between North Korea and any other country), which accordingly are uninteresting. The
perfect capital mobility is not general either, yet it shares basic features with the case of a
relatively mobile capital with a few minor modifications. The example of perfect capital
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Ch IX. Open Macroeconomics
mobility is between Canada and U.S. in the age of free trades, and the current situation is
quite close to it. So we should examine at least the last two possible cases: a relatively
mobile capital, and a relatively immobile capital.
(c) The Exchange Rate System; "What exchange rate system the government is
adopting?" Alternatively, in the age of dirty floating where government mixes elements of
fixed and flexible exchange rate systems as expediency dictates, "Is the government trying
to intervene in the foreign exchange market and to influence the exchange rate or to let
exchange rates go?"
(1) Internal Goods Market Shocks:
These are ΔC or ΔI which shifts the IS curve around.
Case I. Relatively Immobile Capital
In both graphs, the initial goods market shocks shift the IS to the right as the single-line arrow
indicates. The internal equilibrium, which is the intersection of the new IS and LM curve, is now
at E1. E1 lies to the right of the steep BP curve, belonging to a BP deficit region:
Under the fixed exchange rate system, the BP deficit leads automatically to a contractionary
decrease in the money supply and the leftward shift of the LM curve, which is indicated by the
double-line arrow. The new equilibrium E2 is now on the BP curve. Comparing E1 with the
initial troubles only and E2 with the working fixed exchange rate system, we can say that the fixed
exchange rate system partially offset the initial changes in income. Here clearly the fixed
exchange rate system works as a moderator to fluctuations in income, and thus serves as a built-in
stabilizer or insulator.
Under the flexible exchange rate system, the BP deficit leads to an increase in exchange rates
which in turn leads to a CA increase. A rising CA shifts the IS and BP curves to the right, which
are indicated by the double-line arrow. The new equilibrium E2 is now on the BP curve.
Comparing E1 with the initial troubles only and E2 with the working fixed exchange rate system,
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we can say that the flexible exchange rate system magnifies the initial changes in income. Here
clearly the flexible exchange rate system works as an amplifier of fluctuations in income.
Case II. Relatively Mobile Capital
Suppose that consumption or investment rises: Initially, only IS curve shifts to the right.
(2) Domestic Money Market Shocks:
Δu which shifts the LM curve around
First of all, we should note that the domestic monetary shocks do have unambiguous impact on
the BP regardless of capital mobility. This contrasts with the domestic goods market shocks
which can lead to either a BP surplus or deficit depending on capital mobility. You may recall
because of this difference, in the previous section as to the effective of policies, the analysis of
the fiscal policy was a lot more complicated than that of the monetary policy.
We know that a decrease in the money demand due to a random factor (u) shifts the LM curve
to the right: md = K y - h i + u.
Fixed Forex
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Both lead to a balance of payment deficit. This deficit will have a contractionary impact under the
fixed exchange rate system. And thus the LM will shift back to the left.
Flexible Exchange Rate System
Under the flexible exchange rate system, the BP deficit leads to an increase in exchange rates,
which in turn leads to a CA increase. A rising CA shifts the IS and BP curves to the right. The
new equilibrium is now on the BP curve. We can say that the flexible exchange rate system
magnifies the initial changes in income.
Fixed Exchange Rate System
The balance of payment deficit will lead to a contractionary impact under the fixed exchange rate
system. And thus the LM curve will shift back to the left.
You can see that the secondary endogenous movement of the LM curve shifts the equilibrium
national income back against the direction to which the initial monetary shock has changed Y.
Thus, we can say that the fixed foreign exchange rate system offsets the monetary shock
regardless of degrees of capital mobility.
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(3) External Goods Market Shocks
Good market shocks: ΔCA (resulting from ΔY* and thus ΔX), which shifts the IS and BP curves
around.
Suppose X rises, or Exchange rates rises: Initially, not only IS but also BP shift to the right.
We can think of the external goods market shock in the setting of perfect capital mobility. This is
simpler to think of as the BP curve is horizontal.
Flexible Exchange Rate
Fixed Exchange Rate
I
LM
BP>0
LM
BP
BP
IS
IS
(4) External Monetary Shocks:
Δr* (resulting from MS*) which affects KA only, so that only the BP curve moves around,
particularly up or down..
Here again the rise in the foreign interest has unambiguous impact on the BP: A higher interest
rate of the foreign country will lead to capital outflows from the domestic country and thus KA
and BP deteriorates no matter what the exchange rate system might be. Recall that graphically
the rise in foreign interest rate shifts the BP curve up: r*  BP. The BP deficit region expands:
the area above the BP curve is now smaller after the shift than before. The intersection of
IS-LM curves lies below the BP curve, which means that the economy is now with BP deficits.
We will discuss this case in a specific setting of a perfect capital mobility:
Cast this issue in the case of Perfect Capital Mobility, or horizontal BP
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Fixed Exchange Rate
Flexible Exchange Rate
LM
LM
BP’
BP
IS
BP
IS
For instance, if the U.S. government raises interest rate, which is a foreign monetary shock, its
impact will be inevitably felt on the Canadian economy no matter which exchange rate system
Canada adopts.
What still matter is that such an impact could be expansionary or contractionary on the
Canadian economy depending on the exchange rate system. A higher interest rate will lead to
capital outflows from Canada, a KA deterioration and thus a BP deficit in Canada.
If the Canadian government simply lets the exchange rate go, The BP deficits put upward
pressure on foreign exchange rates.
The rising exchange rate will lead to the improvement of the CA (recall S and CA move in the
same direction all the time). The IS and BP curve will shift to the right, exerting an
expansionary impact. The national income rises.
Alternatively, if the fixed exchange rate system is adopted (the Canadian government tries to
depend the external value of the Canadian dollars which are losing values against the U.S.
dollars), the very government's attempt to fix the exchange rate by selling the U.S. dollars in
exchange for the Canadian dollars will lead to a decrease in the money supply in Canada. The
LM curve shifts to the left, exerting a contractionary impact on the Canadian economy.