Introduction to Macroeconomics
Macroeconomics
Macroeconomics: social science that studies the performance of the economy as a whole, studies
the interaction between the agents and the markets in the economics, highlighting the links
between different economic phenomena.
It has different objectives and thus methods of economics respect to microeconomics.
Macroeconomics is a recent discipline, born in 1936 with John Keynes book ‘General theories in
Employment, Interest, and Money’.
2 policy makers:
- Government: fiscal policies, decision on taxes, expenses, public debt, and others.
- Central bank: monetary policies, it’s an institution that in modern economy has the
monopoly to print legal money, that doesn’t have intrinsic value (gold) but has a given value.
4 Economic Factors:
1. Growth: general tendency of the economic systems to grow in the long run (the base of
the economic development) but differently according to the velocity of growth and the
economy considered.
2. Fluctuations: irregular alternation in the short run of phases of accelerated growth
(booms), slowdowns or contractions (recessions, depressions). Such fluctuations are called
‘Business Cycles’.
Understand fluctuation means understand the tendency of the graph, which is the
approximated slope. There are different models for studying short and long run trend of the
economy.
3. Unemployment: the economic system is unable to create jobs for all who wish to work,
and the unemployment rate fluctuates significantly.
4. Inflation: on average prices of goods and services tend to increase.
GDP (Gross Domestic Product):
GDP (Gross Domestic Product):
§ it’s an important variable that measures the performance of the economy, the most important
is the real GDP (Gross Domestic Product).
§ GDP follows the Growth principle of increase in the long run and the Fluctuation principle of
irregular up and downs in the short run (above 100 economy is growing, below 100 it’s
decreasing). GDP is sometimes criticized.
§ GDP is a quantitative value of the life that can influence qualitative aspects and levels of the
life, and is correlated positively to it, to the happiness. In addition, it is strictly correlated to the
unemployment rate.
a. Nominal GDP:
The average value of all goods and services produced in 1 year but we are not interested to
the nominal value, but to the real.
b. **Real GDP or constant price GDP:
§ It’s the measure of the level of the activity of a country in the economy,
§ It measures the value of goods and services produced in a country in a given year (NET of
goods and services consumed to produce them).
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§
It’s taken one base year and are computed the values of all the goods and services during
that year using the prices of the first taken year, to do not be influenced by inflation. In this
way GDP is evaluated not on the base of the market prices, but on the base of the first year
took in consideration.
c. Per capita GDP:
It’s the GDP divided by the overall population, indicates the wealth (Welfare) of a country.
General level of prices: an index, the ratio of nominal product to real product.
Neoclassicals and Keynesians
Neoclassicals and Keynesians
Neoclassicals:
Adam Smith is the father of the economics, has a neoclassical view.
Neoclassical economist idea: endogenous adjustment, markets are self-corrective. Keynes is
against this vision.
Invisible hand by Adam Smith: the metaphor for the unseen forces that moves the free markets
economy towards the equilibrium.
Other neoclassical economists: Marx, Pareto.
Keynesians:
Keynes is the father of the macroeconomics, he tried to explain the reasons behind the possibility
that capitalist economy can be subjected, not to recession or modernization, but to depression (USA
Great Depression).
John Keynes tried to explain the reasons behinds the Great Depression of 1929, the first big crisis
since the industry revolution in the capitalistic system in one of the main countries in the economy.
After this episode it’s started to study how to intervene in this kind of situations.
1933 New Deal from Roosevelt: changed the situation, positive interevent of the state in the
economy.
Birth of macroeconomics was generated by those empirical factors.
GDP has 2 empirical regularities:
- Fluctuations, up and downs in short run.
- Tendency to grow in long run.
The reactions of the economic policies were very different during the Great Depression and the
Pandemic crisis; the latter one was faster than the first one, the policy makers have learned from
the past mistakes
Differences Neoclassical and Keynesians
Self-correcting markets
State Intervention
Keynesian
❌
✅
Neoclassical
✅
❌
The differences between Neoclassical and Keynesians thinkers are related to 2 dimensions:
1. Structure of the markets:
2
Neoclassicals:
§ They assume the perfect competition, since economic model is a simplified version of the
reality, the distortions in the market are irrelevant, so small that are neglectable à Selfcorrecting markets. (ex while driving you don’t use a realistic Photo of Rome but a simplified
version by google maps).
§ They also sustain that there isn’t a deadweight loss: how much the consumer spends, at
the maximum, is equal to how much the worker earns.
§
§
Keynesians:
The Neoclassical perfect competition is an ideal, not the reality, which is characterized by
imperfect competition: He believes that distortions are important (this is a consequence
for the second dimension, the state intervention is requested).
In his model prices are always higher than the marginal costs, this introduces deadweight
loss for society. So the firms are not price taker but price maker, they have a monopoly
power.
The workers are less paid respect to their production. How much the consumer spends is
even more than how much the worker earns.
2. Role of the economic policy:
Neoclassicals:
They believe that the market without the state interevent can reach high welfare. Ex the
Central Bank should not try to in to influence the level of economic activity, but should only
focus on maintaining the price stability.
Keynesians:
Intervention of policy makers, thus of the government, is effective for Keynes, but not for
the Neoclassicals.
The 5 Macroeconomic questions:
1. Understand the origins of the economic fluctuation of the real GDP.
The role of the economic policies that tries to stabilize the business cycle
2. Understand the reasons for the GDP tendency to rise in the long run.
3. Understand the Unemployment Rate, subjected to fluctuation and inversely related to GDP.
4. Understand the sustainability of the state of finances, so the public Finances and of the
public budgetary policy.
5. Understand the origins and the determinants of the Inflation.
3. Unemployment and Fluctuations
The presence of unemployment from a macroeconomic perspective is a sort of market value, and
also a market failure, it’s a loss.
Determinants of Unemployment Rate:
• Labor Forces (NF): all persons who want to work.
• Employed (N): all persons who work, not the total of the population.
• Unemployed (U): all persons who want to work and do not work U = NF – N.
• Unemployment Rate (u): the percentage of the unemployed to the total labor forces
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.
The unemployment rate can change consistently over the years, is subjected to large up-down
fluctuations, but all those changes happen very slowly.
The volatility of the unemployment rate is positively correlated to the flexibility of the market.
In USA it’s easy to hire and to fire, in Europe it’s less flexible. A flexible market means that with a
shock people can end up without a work easily, but also with a boom there can be many hires and
many productions.
The Okun Law:
The unemployment rate is inversely related to GDP value, it’s an empirical regularity.
This empirical regularity, and stylized fact, is called Okun Law:
- It’s the interactions between good markets and labors market,
- It shows the inverse correlation between the percentage of GDP and of the unemployment
rate. They are mirror Curves (scatter plot in photo). It is the first kind of co-movement
across Macroeconomic variables.
The intercept with the vertical axis indicates the GDP growth above which unemployment
decreases (about 3.6%). The slope of the straight line measures the reduction in
unemployment associated, on average, to a one-point increase in GDP (about 0.6%). This
is an elasticity:
.
4. State of Public Finances
Mixed economy: the state intervenes (even in USA which is the most liberal country, in fact the
intervention is after the Great Depression). When the state intervenes there are problem, especially
fiscal ones.
The allocation of budgetary policy, thus public finance, is measured by 2 variables:
1. Public deficit:
(Overall Expenditure – Revenues) It’s the difference between the overall expenditure by the
government (universities, bridges, roads) and what government collects through taxes.
Usually the deficit is evaluated in terms of the size of the economy, and the size of the economy
is evaluated by the GDP. When we think about the stance of budgetary policy, we think always
to the so-called deficit to GDP ratio: the ratio between the deficit and the size of the economy
(GDP).
Positive Public deficit: whenever overall expenditures overcome overall revenues (ex in
Finland it’s negative because of more revenues than expenditures). Whenever there is a Public
Deficit, like in majority of countries, it must be financed by issuing public bonds in absence of
seigniorage.
When the deficit tends to increase must be allocated the deficit spending policies, that
consists in spending more than the revenues.
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The deficit spending policies has been adopted for the 1° time by Roosevelt at 6%, and then
by Obama at 10%.
The deficit increases in 2 cases: during military wars and after big recession.
But during the Regan period in 80s: even without a war or a recession, the deficit level was high.
Regan implemented a tax cut and Berlusconi proposed a flat tax. Those policies of cutting taxes
were issued to let people work more for having a better income, but it revealed the opposite.
2. Public debt:
It’s the overall value not fully repaid from the state to independent central bank. During a
recession there is less production, people pay less taxes, and there is less income to the country,
it automatically creates a cyclical debt.
Debt problem: a state can occur in a bankruptcy, that for the states is called default (actually
it’s present in Lebanon, partially in Argentina, in ‘98 in Russia), and in case of a crisis there is
for sure a default.
2 ways to Finance a Debt:
1. Seigniorage: power of the public sector to print new money for financing (not possible in
EU because the central bank is independent from the government since the Maastricht
treaty). If the central bank can’t print more money you have to create the debt.
2. Institution of Public Bonds: issue a debt, finance a deficit by buying public bonds, but
to make it possible it’s necessary to trust the credibility of the government to pay back the
debt, or nobody would finance it.
It consists in paying an interest rate and have major consequence, but it increases the
public debt.
The sustainability of the fiscal policies is an important problem (Latin America, Lebanon).
5. Inflation and Deflation
Inflation:
The general tendency of prices of goods and services to increase overtime, historically inflation
is almost always positive. Consequently, with the continuous increase in the prices of goods, the
purchasing power of money continuously decreases.
Phillips Curve: the inverse correlation between the inflation rate (u) and the the unemployment
" ).
rate (!
70s Great inflation:
It was a double-digit inflation caused by the increasing of oil prices in 1970s, which took the name
of the Great Inflation.
The inflation was different in each country, even if they were subjected to the same problem, in Italy
it was higher than in Germany, because of their Great Moderation.
It led to an increase of the raw materials and firms’ products, which developed into high prices.
When prices go up, the budget constraint of the consumer shift downwards.
People’s Behavior:
In those cases, when inflation is so high people try to anticipate purchases, then the demand
increase and prices increases. It’s a self-fulfilling process: the expectations become fulfilling,
the future prospects are anticipated, so people don’t want to keep money, they want to let them
circulate more, and it’s worse, money become a piece of paper.
The inflation recovery depends to the growth rate on the money supply. Usually it’s increased
the level of interest rate in order to fight the inflation (ex today in EU).
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Hyperinflation:
When the inflation is very high, like it’s double digit, it’s very easy to transit to a hyperinflation,
during this period it could happen an increase in the prices of 15% per month. The most famous
example is the German Weimar Republic during 1920s, here the average time for prices to double
was about 18 hours.
The inflation in the Weimar Republic was due to the excessive amount of money that circulated
because of the attempt to repair the debts established in the Versailles Treaty.
With hyperinflation the monetary economy is destroyed, people come back to barter ex
Argentina 2001.
Inflation Today:
Today the inflation problem is coming back, actually in Italy and EU 8%, it’s the highest inflation
rate in 40 years.
Actually, Germany is very scared of the inflation because of the hyperinflation during the Weimar
Republic, that degenerated in the Nazism (which could be a usual pattern in those crisis periods
of time). Inflation is the worst enemy for Germany: nowadays the Bundesbank is credibly committed
to price stability. Since their back history, the first condition of the Bundesbank is to ensure price
stability, the same as the EU Central Bank. It isn’t the same in USA where the 2 main objectives
are price stability and full employment.
Deflation:
The negative variation of the prices, rarer phenomenon (ex. only in Japan in 90s).
The Economic System
3 pillars for the Methodology of Economics
1. Rely on economic models:
Constructa model: simplified representation of the reality. All the irrelevant aspects are
isolated to focus the attention on the problem of our interest.
It implies that doesn’t exist a model for each question, all questions require a specific and better
fitting model. This model is not understood by all the institutions. Since all models are not
realistic, the simpler the model, the better it is. It’s also used to predict future tendencies and
changes.
2. Assumption of rationality:
People in economics are assumed to be rational. It’s not even a realistic assumption, we can
make mistakes, but at least we can learn from them, converging in this way to rationality.
3. Rely on notion of equilibrium, only if the equilibrium is stable:
The equilibrium requires 2 conditions:
1. Absence of reaction by agents: people are satisfied for they choices, they don’t have to
change, to react.
2. Behaviors are compatible, ex it happens when the demand is equal to the supply.
Economists focus on the equilibrium, if and only if they can show that the equilibrium is
dynamically stable.
If you are not in equilibrium, a more realistic assumption, there are 2 possible paths: the system
converges to the equilibrium or it diverges even more.
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When we draw a model, we must be sure that if exist an equilibrium, the equilibrium must be
stable. If the economy is in equilibrium, but it’s not stable, and there is a shock (Pandemic) the
economy diverges. If the economy is stable and there is a shock, the equilibrium falls in
disequilibrium but then comes back to the equilibrium because of endogenous forces.
Aggregation - Simplified model:
For an effective macroeconomic study, it’s assumed a simplification of the system by reducing the
number of agents, markets, prices and goods. this is the aggregation of agents and markets in
the economy.
All generally because what’s the matter in Macroeconomics is the interaction between the agents,
and not the actions of the agent itself.
The simplest macroeconomic model considers only in 2 markets:
• The goods market (Y), whose price is P.
• The labor market (N), whose price is W.
The simplest macroeconomic model considers only 2 aggregate agents:
• Firms: produce the good (Y = F(N)), buy labor (Nd), sell the goods (Ys), distribute the profits
(#) to the households.
The firms’ budget constraint is: WNd+ π = PYs.
• Households: buy the goods (Yd), sell the labor to the firms (Ns), obtain the profits (#).
The households’ budget constraint is: PYd = WNs+ π.
a. Aggregations of Agents
The agents to consider in a model:
a. Households: the interaction of them with the behavior of other players, such as the government
or the firms, but not them alone, and then assume there exists one household which is the
representative of all the other households.
b. Firms: based on the assumption that there is only one firm operating in the given market. It’s
studied the interaction between the choices of households and firms.
c. Banks: collect savings of the households, and lend to firms which finance investments, thus
bunks translate savings to investments.
d. Government: conducts fiscal policies.
e. Central Bank: conducts monetary policy, decides how much money to print, to introduce in
the monetary market, it has the main power and responsibility.
f. Rest of the world: since we live in a global economy with international transactions, exports
and imports. Based on the assumption that a macroeconomist considers only 2 countries: the
domestic country and the Rest of the world, like in a match.
b. Aggregations of Markets
There is a market whenever we can identify a demand and a supply. Markets to consider:
a. Goods Market (Y): the market for goods and services, assumed to produce only one good,
represented by Y, which is also the real GDP. Price of goods is P.
b. Labor Market (N): we assume only one type of labor, and the price of labor is the wage (W).
c. Bonds Market (B): different risk levels and maturity times are associated to only one type of
Bond. B is the quantity of bonds sold at a given price (Pb).
d. Money Market (M): paper commonly accepted, partially consists of currency like coins and
bills (physical and external money) but the majority consists in bank deposit (not tangible, called
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internal money or bank money) with legal money. Price of money is 1, because money is the
numberer, all the other factors are meant in function of the money, the price of 1 euro is 1 euro.
e. Currency Market ($): way of payment for international transaction. Quantity of currency that
circulate in the world is defined by the dollar. Price of the dollar in international currency is the
exchange rate, the price for foreign currency (e), number of domestic money to buy domestic
currency, thus one dollar.
Y: Goods
P: Price of goods
N: Labor
W: Wages, Price of Labor
B: Bonds
Pb: Price of Bonds
M: Money
1: Money is the Numberer
$: Currency
e: Exchange rate, price for Foreign Currency
The Markets Equilibrium
Agents’ Budget Constraint
Starting point: set up the number of agents and markets to consider.
In this model:
• 2 agents: Households and firms.
• 2 markets: goods market and labor market.
What’s the outcome, when we assume initial competition in 2 markets and there is a standard
production function, in which the output depends positively on the only input of this simple economy
which is the quantity of labor by the firms, thus the labor market.
Production Function: level of output producing the overall economy. It’s increasing and concave
(especially in the short run), the marginal productivity of the input is decreasing.
Y = F (N)
Budget Constraint in economics: an identity between the overall revenues of the agents and the
overall expenditures of the agents, which must be equal. It’s all the combinations goods and
services that a consumer may purchase or afford, given his income.
There are 2 budget constraints for the 2 types of agents.
a. Households:
The Households in economics supply labor, the labor input to firms.
The Households are the owners of firms, for example they buy shares, so they receive dividends
payments from the firms, will get profit from the production activity.
All profits are distributed to households as a form of dividends (simplified assumption).
The overall revenues must be employed only in one way: to buy the final goods produced by firms.
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The dialectics of the system: Households supply labor à get the wage from working à get the
dividends à they use the overall income to buy goods produced by the firms.
Households Budget Constraint:
PYd = WNs + 0
PYd = expenditures
WNs + # = revenues
b. Firms:
The firms supply final goods and receive the payments from them selling à they demand labor,
pay wages for the labor, and they distribute the profit paying the dividends to the households.
Firms Budget Constraint:
WNd + 0 = PYs
PYs = revenues by firms who supply the final goods
WNd + # = expenditures
Y: quantity of final good, final output.
Yd: demand for the final good.
Ys: supply for the final good.
N: number of workers that wish to work for a given salary.
Ns: labor supply by households, number of hours worked used by the firms
Nd: labor demanded by firms.
P: price of goods produced by the firms.
W: Wage, the price of labor.
0 = profits = overall dividends
Walras’ Law:
Excess Demand: difference between demand and supply.
Positive excess demand: demand higher than the supply.
Negative excess demand: demand lower than the supply.
P (Yd – Ys) = value of the excess demand in the goods market, times the goods price.
Difference between the demand for labor and the supply for labor.
W (Nd – Ns) = value of the excess demand in the labor market, times the relevant price.
The Overall Budget Constraint of the 2 agents:
WNd+ π = PYs (firms’ budget constraint)
PYd = WNs+ π (households’ budget constraint)
PYd + WNd + # = WNs + # + PYs
P (Yd – Ys) + W (Nd – Ns) = 0, It must be equal to zero à Walras’ Law
Walras’ Law: if we have 2 markets (Goods and Labors) it’s always true that the sum of the values
of the excess demand is equal to zero.
In order to verify the law, the 2 budget constraints are insert in an equation = 0.
If for some reasons there is equilibrium in one market, there must be equilibrium in the other
market, in order to maintain the equation valid.
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If for some reasons there is an excess demand in the goods market (positive term), there must be
an excess supply in the labor market (negative term) to balance the equation, and vice versa.
It’s a very important equation because it describes and catches very well the interaction between
goods market and labor market, it also allows to concentrate only on one of the 2 markets took in
consideration.
It’s a very general law, It’s also true for the equilibrium of 3 markets, or even n-markets.
Functioning of the Goods Market
4 ingredients for defying a Market:
In this case is analyzed the Goods Market, but any market in the economics (goods, labor, financial,
monetary, …) is defined by 4 ingredients:
1. Describes behaviors of buyers, in this case behavior of households.
Yd = D(P) D’ < 0, the demand depends negatively on the price (Demand Function).
2. Describes behaviors of sellers, in this case firms.
Ys = S(P) S’ > 0, the supply depends positively to the price (Supply Function).
3. A case in which there is an equilibrium, thus the compatibility between the 2 behaviors.
Yd = Ys ⟺ D(P) = S(P) General equilibrium or Neoclassical equilibrium
.
4. What happen outside the equilibrium, thus the reaction if the demand is not equal to the
supply.
!"
= !̇ = ;P [D(P) – S(P)] The law demand and supply translated in mathematical terms.
!#
L: equilibrium point
PL and YL: the only combination between price and quantity that ensures the equilibrium, thus the
equality between demand and supply. There exists only 1 equilibrium point, other way for any other
price there is exit equilibrium.
Markets in Equilibrium – Neoclassical Equilibrium:
By the Walras’ Law if there is equilibrium in the goods market, there is equilibrium also in the labor
market, which means that the demand for labor and the supply is equal, balanced, not that the
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unemployment rate is equal to zero, it’s never zero, because there always be people not satisfied
for their wage.
Thus, automatically this will happen Yd = Ys ⟺ Nd = Ns.
It’s the general equilibrium or Neoclassical equilibrium, which is the only part of microeconomics
that binds all the market together.
In macroeconomics if there is perfect competition, if the prices are flexible, the law of demand and
supply generates a simultaneous equilibrium in all the markets, in the book ‘Principle of
Economics’ by the neoclassical economist Alfred Marshall, the same book used by Keynes.
In the Market Equilibrium:
Point L, P = PL, so the quantity demanded is equal to the quantity supply (Yd = Ys = YL).
Markets Outside the Equilibrium - Law of Demand and Supply:
Law of Demand and Supply: sellers and buyers’ reaction outside the Equilibrium.
Since the market are perfectly competitive (the essential condition), in case of incompatibility
between the behaviors, there are 2 possible events outside the equilibrium (P ≠ PL):
•
In case of higher price (P > PL) there is an excess supply respect to the demand (this graph).
This leads to a reaction: a competition between the sellers, in order to sell the good it’s
decreased the price.
Thus, there is a tendency of the price to go down.
•
In case of lower price (P < PL) there is an excess demand respect to the supply.
This leads to a reaction: a competition between the buyers, in order to buy the good some
buyers will pay more to get the goods.
Thus, there is a tendency for the price to go up.
Conclusion: the model used by the markets is dynamically stable, converging towards the
equilibrium. This means that the equilibrium is stable, because even if we aren’t in equilibrium,
there are endogenous market forces, which is the competition between agents, that enables the
economy to go towards the equilibrium.
Thus, the equilibrium is the arrival point of these dynamic mechanisms.
The most important macroeconomics implication: the system converges automatically to the
equilibrium point, without any policy makers intervention by the state. Only thanks to the Law of
Demand and Supply.
$%(')
>̇ = $' = f(x)
Solve this, for a given specification of f, means find a path, a trajectory, for x(t), for ∀B. Where x(t)
is a variable x in function of the time, and evolves over time, like the prices.
Law Demand and Supply: !̇ =
!"
= ;P [D(P) – S(P)]
!#
Only if the demand is equal to the supply !̇ = 0, it means that the price is fixed, we are in
equilibrium, there is no dynamics, because the equilibrium is a static situation.
The market system is stable and converges towards the equilibrium, mathematically we
proceed in one way:
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!"̇
!"
= ;P [D’(P) – S’(P)] < 0 Negative because the prime is positive but there is the minus.
D’(P): slope of the demand schedule, which is negative.
S’(P): slope of the supply function, which is positive.
;P: a given coefficient
!̇: derivative to P respect the time, Ċ depend on P, is a function of P.
Ḋ = f(x) the function of Ċ belongs to the group of differential equation: the derivative of the variable
over the time depends to the variable itself.
$%(')
f(x) = $' : It’s the change over time of the x variable, as a function of the variable itself.
If the change over time of a variable is a function of the variable itself, we
have a differential equation.
Differential equation:
• Captures the dynamics of the model outside the equilibrium.
• Equazione in cui l’incognita da trovare è una funzione, e in cui sono presenti una o più derivate
della funzione incognita.
Phase Diagram of the goods market:
Phase Diagram: we can visualize the time path of the variable.
It’s a dynamic equation graphically represented in terms or differential equation.
It is decreasing because the derivative is negative.
The intersection of the function with the horizontal axis gives exactly the equilibrium point PL, in
which there is no dynamics.
!̇ = 0 there is no dynamics when the demand is equal to the supply, it means that the price doesn’t
change over time.
In all other point there is disequilibrium:
In PH, !̇ < 0, it means that P decreases over time.
In PK, !̇ > 0, it means that P increases over time.
Then the prices, tend to converge towards the equilibrium, because of the demand supply law, the
velocity of the convergence towards the equilibrium point depends on E P, so the equilibrium is
stable.
Implication: The equilibrium in the goods markets implies the equilibrium in the labor market.
The equilibrium in the labor market implies the absence of involuntary unemployment.
Compute the derivative, draw the diagram. If the derivative is negative the system is always
stable.
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Functioning of the Labor Market:
For the Neoclassical model:
If there is an excess supply in the labor market, in the goods market there must be an excess
demand, by the Walras’ Law.
But in case of excess demand in the goods market, the price level P increases, and this generates
a sharp decrease in the real wage, until we go back to the equilibrium between the labor demand
and supply.
The law demand supply (translation of the invisible hand) says that decentralized decisions by
egoistic agents that care only to their objectives and not at all to the social welfare, will bring the
system automatically to the first best.
The first best: all markets in equilibrium, included labor market, so there is full employment. In
case of a shock that brings temporally the system in disequilibrium, the equilibrium will be
restored by himself.
For Keynesians:
For Keynes the Neoclassical equilibrium is unsatisfying, doesn’t describe the properties of the
real word, especially in the short run or in case of depressions or recessions.
For Keynes it’s unrealistic, after the Great Depression this didn’t happen, there was even deflation,
not the reduction in wages. This is the reason why that Keynes believe that the markets in the
long run tend to the equilibrium, but in the short run not.
The Labor Market:
The wages are a cost for the firms, so the labor demand (Nd) is negatively sloped.
The leisure is substituted by the worktime, which is positive for the firms, so the labor supply (Ns) is
positively sloped.
We must consider the real wage, not the nominal wages.
*
Labor demand and supply depend on the real wage ( ).
+
Situation of the Great Depression: labor supply is higher than the demand, the difference is the
involuntary unemployment.
-,
-Ns > Nd ⇒ Yd > Ys ⇒ ΔP > 0 ⇒ Δ < 0 ⇒ Nd = Ns
"↑
I =1
Assumption: W=H
In the labor market the wages are fixed, exogenous and equal to 1, I’s the numberer.
It means that the wages can’t change in the short run, and it implies that the wages don’t react to
excess demand.
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The law of Demand and Supply, which is operative in the goods market, leads to the
equilibrium also in the labor market, even with fixed wages.
Even if the wages are fix, the prices are flexible, so the prices increase by the law of demand
and supply. But the increase in the price generates a reduction in the real wage, that take place
until we converge towards the equilibrium point.
General Equilibrium Theory by Keynes
Neoclassical Equilibrium Confutation by Keynes
At this point Keynes, looking at the Great Depression, started to think about some mistakes, at least
in the short run.
Goods Market:
L: neoclassical equilibrium
YM: macroeconomic equilibrium.
For Keynes this neoclassical equilibrium is valid only in the long run.
Suppose a supply of goods higher than the demand, this is a sign behind the crisis. For Keynes in
the short run there isn’t a movement in the prices, but a movement in the quantity.
This dynamic mechanism for him is horizontal, in the short run the prices are rigid (P = I
!). Prices
can change for many reasons but not because of the law of demand and supply.
If Ys > Yd the excessive production is not sell for less, but the next month will be produced less,
keeping the prices at the same cost as before.
The reduce in production won’t converge in L but it will converge in E (Ym; I
!): the short run
macroeconomic equilibrium for Keynes. The exogenous variable is the price, the endogenous
variable is the quantity.
But the reduced production implies less labor, this implies workers firings, in fact NM > NL.
Effective Demand Principle
I . The firms’ behavior is described by the
Let E = Yd be the quantity demanded at a given price P = !
Effective Demand Principle equation:
!"
= ;Y (Yd – Ys) (prof)
K̇ =
!#
!$
= ;Y (E – Y); ;Y > 0
!#
14
In case of disequilibrium the firms react by changing the output produced:
• Whenever there is an access supply, then Q̇ < 0, firms reduce the quantity produced.
• Whenever there is an access demand, then Q̇ > 0, firms increase the quantity produced.
• In case of demand equal to the supply, then the quantity produced remains the same.
Keynes conclusion: In the economic system there could be bad equilibria E in which there is
involuntary unemployment. And the market is not able to self-correct it, so there is a market
failure for the involuntary unemployment.
Next step: the system in the short run converges to E, in which there is involuntary
unemployment. The economic policy in the short run can bring the system to YL, the full
employment. So we introduce the public sector, with monetary and fiscal policies.
Neoclassical approach ≠ Keynesian approach:
In the short run prices and wages are rigid, and the dynamic adjustment is not about Ċ but Ṙ.
Neoclassicals: Law of Demand and Supply (always).
Keynesians: Effective Demand Principle (short run) Law of Demand and Supply (long run).
The equilibrium with the Demand and Supply Law (L) and the equilibrium in the Effective
Demand Principle (E) are 2 different points of equilibrium.
The Keynesian Macroeconomic Model
The Keynesian macroeconomic model is the Keynes critics’ to the Neoclassical equilibrium,
not yet an actual Keynesian model.
The assumptions of all the Keynesian models:
• Rigid Wages in the short run.
• Rigid Prices in the short run.
%&
• Effective demand principle is verified Ṙ =
= E Y (Yd – Ys).
%'
Rigid meant as that they are exogenous, they can change, but for other reasons, different from
the neoclassical reasons.
3 Keynesian models:
1. Income expenditure model.
2. IS-ML model.
3. AD-AS model.
Each model is an extension of the previous one.
Neoclassicals respond to Keynesian model producing new models.
Production and Income (GDP, NDP)
Production and income are strictly linked.
Value of production:
All final goods and services produced and is measured broadly by the GDP. It’s identically equal
to the sum of all income. This means that this value must be distributed to all agents of the
economy as a form of income. So the level of production and level of income are treated in the
same way.
15
GDP (Gross Domestic Product):
Value of the overall quantity of goods and services produced in an economy in a year, net of the
intermediate goods consumed to produce them (Gross of the Depreciation).
It’s used the GDP since it’s very difficult to compute S.
NDP (Net Domestic Product):
Gross Domestic Product net of the depreciation of capital.
Net Value of production, Net National income.
Level of production: quantity of final goods and services minus the intermediate goods.
ex for who sells the bread, only the bread (final) will be took in consideration in GDP and NDP, not
the flour (intermediate).
But if I want to make the bread by myself the final good is the flour, not the bread, since I will acquire
the flour and not sell the bread.
So the GDP is an imperfect measure of the level of production since it doesn’t internalize the
human firm.
π = Rt - Ct
π = PQ – WN – (r+δ) PK – PMr
P (Q - Mr – δK) = WN + rPK + π
Y = P (Q - Mr – δK)
Y = WN + rPK + π
Y = NDP
GDP = NDP + δK
GDP = Q – Mr
NDP = GDP - Depreciation
π: profit
C: consumption
I: investments
K: capital goods, the goods and labor productions accumulated in the past.
Q: all the quantity of goods produced.
M: only means for payment
B: bond, fixed income purchased by who saved.
S(delta): depreciation rate (ammottamento), amount of the capital that is consumed, deteriorates,
over the production process.
Mr: raw materials.
NDP: Net Domestic Product.
GDP: Gross Domestic Products.
.
Income Expenditure Model
Income Expenditure Model without the state
Income Expenditure Model: the first Keynesian model.
16
Simplified version of the model with only 2 agents: households and firms, without the
government or the central bank. It explains the origins and consequences of economic recessions
and crisis.
1. First assumption in the Keynesian model: In the short run both wages and prices are rigid,
they don’t adjust in excess demand or supply, so the real wage is completely exogenous. Prices
and wages vary only in the long run, it means that the law of demand and supply doesn’t apply
in the short run, but only in the long run.
Since the real wage is completely exogenous, in the Walras law there isn’t a labor market, so
not a labor demand or supply. We focus only on the goods market. The quantity of labor that
prevails in this economy, corresponds to the equilibrium level of output decided by the firms.
By normalizing the price level, the wages and the prices for bonds correspond to 1.
Keynes uses a linear function, that represents a line.
P = Cc = 1
I =1
W=H
c
Pb = Cd = 1
2. Second assumption in the Keynesian model: There are 2 agents (households and firms)
and 2 markets (goods and bonds). It’s introduced the possibility for agents to save.
Savings: part of income not consumed. In the bonds market, saving is the bond accumulation
over time. These bonds are supplied by firms to finance their investments.
Domestic Income = Domestic Production.
Income can be used in only 2 ways: consume or save.
Households budget constraint:
Expenditures = Incomes
C + ΔBd = Y
Firms budget constraint:
Expenditures = Incomes
I = ΔBs
Firms supply bonds, demanded by households, to finance investments.
Firms have 2 opportunities:
1. Use the internal finance: use retained profits, which are the profits not distributed to households
as a form of dividends.
2. Use the external finance: firms can issue bonds, shares or stocks.
Budget constraint for firms is a bit complicated, but it can be taken in consideration the relevant
budget constraint: the simplified version, by the condition of nominal level of production = the
sum of all income.
Combining the 2 budget constraints, I get the overall budget constraint for the whole economy.
The relevant Walras’ Law for 2 markets (bonds and goods):
C + ΔBd + I (goods)
Y + ΔBs (bonds)
C + ΔBd + I = Y + ΔBs
C + I - Y + (ΔBd - ΔBs) = 0
17
The 2 markets are correlated, an excess demand in one of them, implies an excess demand in the
other. So If one market is in equilibrium, also the other market must be in equilibrium.
Income expenditure model focus the attention to the determination of the GDP, focusing on the
goods market, and using the Walras’ Law there is also the representation of the bonds market.
The 1° Keynesian model, the Income Expenditure Model:
k = l + m
⎧
!"
⎪l = lc + nQ; 0 < c < 1; !#
m = m̅
⎨
⎪k = Q
⎩Q̇ = pq (k − Q)
Like every model, it is a system of equations:
E = C + I: definition of the aggregate expenditures
C = s̅ + cY: consumption function, behavior of the households
I = t ̅ : investment function, behavior of the firms
u = R: in equilibrium
Ṙ = Ev(u − R): outside the equilibrium
E: aggregate demand, demands coming from firms and households, since prices are fixed, it can
also be called aggregate expenditures.
B: overall stock of bonds.
ΔBd: variation of the stock of bonds demanded by the households.
ΔBs – ΔBd: excess demand in the bonds market.
C: consumption, demand for goods and services coming from households, largest part of the
aggregate demand.
I: autonomous consumptions, part of consumption that doesn’t depend on the level of income, but
w
depends on external variables, it’s the households’ wealth.
c: marginal propensity to consume.
I: variation overall level of investments, overall means of production.
I – Y: excess demand in the goods market.
ccccccccccccc): the variable can change for reasons outside the model.
Exogenous (xyz{y|}~
marginal: implies an incremental ratio or a derivative behind
ex if c = 0,8 and the households income increase by 1€, then the households consumption
increases by 0,80 €.
Consumption function in the time
I ):
For Keynes 2 external variables affect the autonomous consumption (w
For Keynes it exists the state of long-term expectations:
behind the consumption there are also expectations about the future level of income. In a wave
of optimism, more consumption, in a wave of pessimism, less consumption.
It’s the index of the level of trust in the future economy.
18
Keynes assumes that investments are completely exogenous, determined by variables outside
the model, and are affected by the state of future expectations, in function of future profits.
Scatterplot: every point is one particular year.
Microfoundation: the choice of the macroeconomic agent is derived aggregating the rational
choice of the individual agent.
The consumption function C = C (Yd) can be Microfounded:
Consumption dynamics strictly follow GDP dynamics.
Consumption decision are intrinsically intertemporal decisions, so consumption choice is an
intertemporal choice.
It must be computed the budget constraint for each period, and then combined by substituting
the S.
Present: income can be used to consume or to save, which can also be negative.
Assume only 2 periods:
Present: C + S = Y
Future: CF = YF + S (1+r)
Lifetime Budget Constraint:
C+
()
$)
=Y+
)*+
)*+
It’s the lifetime income. It’s a budget constraint because it gives me all the possible combinations.
It’s this kind of equation P1 Y1 + P2 Y2 = m.
Lifetime budget constraint as the equation of a straight line:
CF = [(1+r)Y + YF] – (1+r)C
Intertemporal budget constraint that includes present and future.
Slope m = - (1+r)
Intersection points:
y axis: [0; (1+r)Y+YF]
$!
x axis: (Y+%&'
; 0)
19
The consumer will choose points along the budget line, between the intersection point. The
choice follows the preferences over current and future consumptions.
Preferences are expressed on the base of the utility function, which depends on C and CF.
Utility function is increasing and concave, like the logarithmic function.
We assume the preferences for time: today and tomorrow preferences are different
(
Utility function: U = U (C, CF) = log C + (&) log CF
The consumption today is different from the future consumption, this is the reason why introduce Ñ.
Ñ(gamma): rate of time preference, measure the degree of impatience
Assume positive gamma, Ö > 0.
(
⎧max U = log C + (&) log C*
{C, C* }
⎨
""
#"
⎩àâdäãåB Bç C + (&+ = Y + (&+
Choose the 2 variables C and CF to maximize the utilities, subject to the lifetime budget constraint.
Microeconomic principle:
To solve this problem you can use whatever method preferred:
a. Tangency condition:
At the optimum the marginal rate of substitution MRS between future and present
consumption must equal to the marginal rate of transformation MRT, the relative price,
which is the slope of the budget line (1+r). à MRS = 1+r
b. Lagrangian method:
Computing the constrained maximum of the utility function doing the ratio between the 2
%,
.
marginal utilities. à %, %-
.%/
é
a. MRS = slope of the budget line (1+r):
MRS,-/, = 1 + r
"
#
"
"
C + (&+
= Y + (&+
The optimality condition: the Marginal Rate of Substitution MRS is the slope of the indifference
curve (convex), that must be equal to the slope of the budget line.
Any other point or indifference curve is not optimal.
The second condition: the point must be in the budget line.
The endowment point (Y, YF) (rotazione) is important because if the tangency point occurs to the
left or to the right, it tells me the present and future behave of the consumer.
20
•
In S point the consumer is a saver, who consumes today less, saves, and tomorrow more of
his income.
In B point the consumer is a borrower, who consumes today more of his income and tomorrow
less, will pay the debts.
•
We want the optimal solution for C, the optimal consumption:
b. MRS = Ratio between the 2 marginal utilities:
⎧
01/
02 =
01/
03
1/
2
1 1
1+ # -.
= (1 + r)
⎨
""
#"
⎩C + (&+ = Y + (&+
(&+
C* = 1+ ) C
è
C+
""
(&+
=Y+
#"
(&+
Substituting C* :
(&+
C* = 1+ ) C.
è
"
#"
C + 1+ ) = Y + (&+
Solving the microeconomic problem for the representative consume, with both the methods I obtain
the optimal consumption function:
Optimal consumption function: C ="
C = Cc + cY
c = ì1+ 9 YF î
C
2+ 9 1+;
1+ <
c=
2+ <
/+ 7 8/
/+ 7
#+
Y
2+ 7 )*+
2+ 7
Time profile for the consumption at the optimum: C= =
>*?
1+ <
C
• If r = Ñ it’s optimal for the consumer to smooth consumption over time.
• If r > Ñ it’s higher the optimal future consumption, it’s better to save, better future consumption.
• If r < Ñ it’s lower the optimal future consumption, the consumer is more impatient to spend.
Consumption smoothing: consume in every period the same quantity of consumption.
Suggested in case of high level of income ex win the lottery.
I + cY
Keynes linear function: C = w
C ="
1+ < @0
1+ <
#+
Y
2+ < >*?
2+ <
1+ 9 YF
s̅ = 2+ 9 1+;
1+ <
c=
2+ <
It’s a linear function in which the intercept is s̅ , which is directly influenced by the expectations.
21
Consumption depends to expectations:
• The more optimistic is the expectation for the future level of income, then implies higher
consumption.
• The more pessimistic is the expectation for the future level of income, implies lower
consumption.
MRS and MRT: is that the former determines the D (demand) side of the market while the latter
determines the S (supply) side of the market.
The Keynesian Multiplier
The Keynesian Multiplier
Starting from the Keynesian income expenditure model:
E=C+I
⎧ C = Cc + cY
⎪
I = I̅
⎨E = Y
⎪
⎩ Ẏ = βy(E − Y)
c + cY + I̅
C+I=C
C + I − cY = Cc + I̅
c + I̅
E − cY = C
c + I̅
Y − cY = C
(1 − c)Y = Cc + I̅
E=Y
⎧C + I = Y
⎪
c + cY + I̅ = Y
C
⎨(1 − c)Y = Cc + I̅
⎪
⎩Ẏ = βy(E − Y).
Y*=
)
(lc + m̅)
)AB
I
Y*= mò
>
= m > 1 always
>AC
I = Cc + I̅
A
Keynes new: the endogenous variable that solves the model is a function of endogenous and
exogenous variables, that are the expectations determined outside the model.
For Keynes expectations are exogenous, for Neoclassicals endogenous.
Y*: solution of the model, equilibrium level of output macroeconomic equilibrium, the only point
in which there is equilibrium in both markets, also called national product in the exercises.
*: equilibrium level of output.
ccccccccccccc: fixed, exogenous.
õúùûúü†°
I : autonomous expenditure that doesn’t depend on the level of income, but depends on other
ò
variables, which are exogenous.
m: Keynesian multiplier.
22
Keynesian cross
It’s the graph of the income expenditure model.
Since we have imposed the equilibrium at the beginning, we have to check preliminary that this
solution is dynamically stable, it means that if we are outside the equilibrium Y*, then Y should
converge towards Y*.
In order to verify that the solution is dynamically stable, here it is the graphical representation of
the Keynesian cross:
E = Y: 45° bisector line, with slope=1. All the equilibrium solutions are one point along this line.
Relationship between the aggregate expenditures and the level of income:
c
¢C = C + cY
E = C + I̅
c + cY +I̅
E=C
¢
E = Cc + I̅ + cY
I=C
c + I̅
A
I + nQ
k=ò
Since 0 < c < 1, the slope of the expenditure line is lower than the bisector, lower than 1.
Y*: the macroeconomic equilibrium point, the only point in which there is equilibrium in both the
markets (goods and bonds).
In case of not equilibrium there is excess demand or excess supply. ex Y(0) excess supply.
Then the Y in disequilibrium will converge towards the equilibrium point Y*.
In this case E > Y, Y(0): expenditures < level of outputs à excess supply.
Firms reaction: produce less in order converge towards the equilibrium.
So we have shown that the equilibrium is stable, since it will converge from disequilibrium to
equilibrium. Stable equilibrium: the ending point of a dynamic process.
Since the equilibrium is stable, we can compare different types of equilibria.
The Multiplier Effect
I
Y*= mA
I =Cc + I̅
A
23
D$∗
G
DF
D$∗
m= I
DH
D$∗
m= ̅
DJ
m=
I tells me that the equilibrium value of the GDP is the multiplier of the autonomous
Y* = m ò
expenditure. Ex GDP is 5 time the autonomous expenditures.
The Keynesian multiplier (m) is:
I)
• The variation in the equilibrium level of output (Y*) if the autonomous expenditure (ò
I increases by 1€, then the GDP increases by m-€. Ex GDP is 5 time the
increases by 1€. If A
autonomous expenditures.
I , or one
• The incremental ratio, for the derivative. It’s the derivative of Y with respect to the ò
I (lc, m̅). The multiplier (m) also measures:
component of ò
o The equilibrium level of output (Y*) if the autonomous consumption (lc) increases by
1€.
o The equilibrium level of output (Y*) if the autonomous investments (m)̅ increases by 1€.
Waves Effect - Economic mechanism behind the Keynesian multiplier
1°Wave (by firms):
£m̅ = 1 ⟹ £• = 1 ⟹ £K = 1 ⟹ £w = ¶
Suppose a positive shock by optimistic firms, that increase the level of investments (I)̅ by €1
million, then there is an increase in the aggregate demand (E) by €1 million, according to the
effective demand principle, then there is an increase in the production (Y) by €1 million.
The increased value of production will be distributed as a form of income (paid workers and
dividends) Thus Y is not only the value of production, but also the value of income.
The workers will spend what they earn in other goods and services, so the increase in the income
induces an increase in consumption by c-time €1 million, because c is the marginal propensity
to consume.
2° Wave (by consumers):
£w = ¶0 ⟹ £• = ¶0 ⟹ £K = ¶0
The aggregate demand (E) coming from consumers, will increase by c, and then the output will
increase by c.
3° Wave: £w = ¶1 ⟹ £• = ¶1 ⟹ £R = ¶1
⋮
n° Wave: £w = ¶2 ⟹ £• = ¶2 ⟹ £R = ¶2
These waves can go to the infinite.
The overall increase in the GDP = 1 + c + n 0 + n 1 +…+ n 3 .
Since 0 < c < 1, as the power of c increases, then the value of the powered c decreases, and the
geometric progression: c > n 0 > n 1 >…> n 3 converges to
)
)AB
, which is the multiplier (m), that
measures this waves effect, induced by an initial shock, which has an endogenous propagation
effect.
Problem: in case of negative shock, like pessimism because a recession or depression, then there
is the same process but with the sign minus, so less investments means less production, that means
24
that workers spend less, and the GDP decreases more than proportionally. This is the situation
that Keynes wanted to explain during the Great Depression.
Conclusion:
• All the markets are linked.
• GDP is very volatile because of this wave effect, propagation effect.
Great Depression - Wallstreet crash reasons
Income expenditure model:
Premises:
In US during 1929, it was a positive period: there was an high growth in GDP, full employment
and all the markets were in equilibrium, at the same time there was an increase in the assets
prices, like houses price. So there were speculators who bought houses in order to obtain a
capital gains selling them.
The Bubble:
The houses prices were self-fulfilling: the increase happened not because of the fundamental
reasons of population growth, but because people expected that the prices will increase.
The higher demand let the prices increase, but this increasing trend is a bubble: it doesn’t reflect
the fundamentals of the economics, only the expectations. The bubble for sure will burst
when people will reverse the expectations, but the exact moment is unpredictable.
The Crisis:
In this case of pessimistic expectations the prices for houses can potentially converge to zero, in
1929 the prices of assets immediately decreased by 80%. Once that the expectations are
reversed, everyone will sell and the prices will go down, it leads to a financial crisis that become
an economic crisis.
This is the reason for the Wallstreet crash: bubble burst, an immediate plunge in assets price,
a financial crisis, thus an economic crisis.
c < 0 and ©I̅ < 0 ⟹ £ò
I>0
©C
Since the household’s wealth decreases, also the autonomous consumption decreased: ©Cc < 0
(households)
In case of a crisis there is also a banking crisis, and when this happens, banks won’t lend money
to households and firms, so also the autonomous investments decreased: ©I̅ < 0.
The decrease in autonomous consumption and autonomous investments is reinforced by the
pessimist expectations.
25
This determines the decrease in the autonomous expenditures à the expenditure line
translates downwards.
Since the equilibrium is dynamically stable, after the shock the economy will converge to the new
equilibrium.
The equilibrium is no more L (full employment), but the new equilibrium is M (involuntary
unemployment inducted by firms that produce less and requires less labor).
The financial crisis becomes an economic crisis: the level of employment and GDP has fallen.
In 1929-1933 the GDP decreased by 30% and the unemployment rate increased by 25%.
Here there is nothing to do, it is a trapping point (YM) because there is equilibrium in all markets,
except for the labor market.
The same mechanism with some small variations occurs during the global financial crisis 20072008, it was a plunge in the asset prices, following the bubbling behavior in the house market.
The pandemic crisis was induced by the pessimism and by the lockdown because people
couldn’t consume, it means no demand, so the firms couldn’t produce and there weren’t
investments. It wasn’t a financial crisis.
In the long run we will be back to YL, but for Keynes matters the short run.
The state can immediately act during the crisis in the short run.
When there is a reduction in GDP in case of shock, it’s suggested to implement the fiscal policy.
But the income expenditure model above isn’t appropriate because there are only households
and firms, there isn’t the state. It can explain the consequences and the origins of a financial crisis
that becomes an economic crisis, but cannot be used for policy proposes.
Income Expenditure model with the State
Government and Fiscal Policies
Income Expenditure model with the State
When there is the state, households, as aggregate agents, receive public transfers from the
government. So the income expenditure model is extended, there is a new agent: the
government state.
Fiscal variables: variables decided by the government.
Households budget constraint:
C + ΔBd + T = Y + Tr (Expenditures)=(Revenues)
C + ΔBd = Y + Tr - T
Yd = Y + Tr – T
C + ΔBd = Yd
Public transfers: are a class of public expenditures, from the government to the households.
They include 3 components:
1. Pensions
2. Unemployment subsidies
3. Interest payments of public bonds: government must pay a positive interest rate in public
bonds.
26
Firms budget constraint:
I = ΔBSF (Expenditures)=(Revenues)
State budget constraint:
G + Tr = T + ΔBSG (Expenditures)=(Revenues)
G + Tr - T = ΔBSG
D = G + Tr – T
D = ΔBSG
C: Consumption.
c: marginal propensity to consume.
Y: income that can be spend (revenues).
Yd: Disposable Income, after receiving Transfers and net of Taxes, what can actually be spent.
T: overall taxation, both revenue for government and expenditure for households
Ï = autonomous taxation, thus that don’t depend to the income.
Tr: Public Transfers (Revenues)
ΔB: increase in the stock of public
ΔBd: Bonds demanded, that can be issued by firms and government.
ΔBSG = Public Bonds of the state
BG: overall stock of public debt, the value of all bonds issued not yet repaid (high in Italy).
G: public spending for goods and services.
!
"
: Fiscal pressure, percentage of income taken by the government (important), in italy very high.
D: Public deficit.
t: (small) marginal tax rate.
Summing up the 3 budget constraints by the Walras’ Law, I obtain the overall budget constraint:
C + I - Yd + D + ΔBd – ΔBSF – ΔBSG = 0
Yd = Y + Tr – T
D = G + Tr – T
ΔBs = ΔBSF + ΔBSG
(C + I + G – Y) + (ΔBd – ΔBs) = 0
E=C+I+G
(E – Y) + (ΔBd – ΔBs) = 0
Focus the attention on goods market. If there is equilibrium in one market, there must be the
equilibrium also in the other market.
Income expenditure model with the State:
u =C+I+G
⎧ C = s̅ + åR
4
⎪R = R + ≠Æ − ≠
⎪ 4
⎪Ø = Ø̅ ; ≠Æ = ccc
≠Æ
5
c
c
⎨ ≠ = ≠ + Bv; 0 < B < 1; ∞± ≠ = 0, B = 6
⎪t = t ̅
⎪
⎪u = R
⎩Ṙ = ≤7 (u − R)
u = C + I + G definition of aggregate expenditure with the extra component G.
Ø = Ø̅ ≥¥µ ≠Æ = ccc
≠Æ fixed, completely exogenous.
27
To solve the system isolate Y and find the solution.
Simplified (static) version of the income expenditure model with the state:
R =C+I+G
ccc − cT
I + c(1 − t)Y
C = Cc + cTr
∂
t = t̅
Ø = Ø̅
R = C + I + G Equilibrium condition
ccc − cT
I + c(1 − t)Y Consumption function
C = Cc + cTr
̅
t = t autonomous investments
Ø = Ø̅ autonomous public spending
In case of a boom: higher income, means higher taxes, thus higher fiscal revenues.
Fiscal revenues: depends positively to the level of income.
In case of recession, the fiscal revenues automatically decrease, during a boom they
automatically increase. They depend on the decision of the Government (≠c and T) and also on
what happens to the economy, generating a feedback effect from the level of the economic
activity to the budget of the state.
Fiscal pressure: percentage of households’ income taken by the government as form of taxes.
High fiscal pressure doesn’t mean a bad economy, because high fiscal pressure means more
expenditure for the community (ex Scandinavia 60%). It’s related to the degree of the productivity
of the public investments.
Income Expenditure model with the State
Expenditure Line: E = A + c (1-t) Y
Consumption function out of domestic income, not of disposable income:
C = s̅ + åR4
R4 = R + ≠Æ − ≠
C = s̅ + å [ Y + ccc
≠Æ −≠]
¢
C = s̅ + å [ Y + ccc
≠Æ − ≠]
c
≠ = ≠ + Bv
C = s̅ + å [ Y + ccc
≠Æ - ≠c – tY]
é
cccc - c∑
I + c (1-t) Y (Consumption function)
C = lc + n∑ù
28
c=
!(
!$3
n (∏ − π) =
!(
!$
c > c (1 − t)
%, 0 < c < 1: Marginal propensity to consume out of the disposable income.
%L4
!(
n(∏ − π) =
: Marginal propensity to consume out of income, after have paid taxes.
!$
c=
In fact it is lower than the marginal propensity to consume out of the disposable income because of
the taxes.
ccc − cT
I + c(1 − t)Y
C = Cc + cTr
R = C + t ̅ + Ø̅
ccc - cT
I +t ̅ + Ø̅
[1 – c (1-t)] Y = Cc + cTr
¢
Y* =
)
I]
cccc - c∑
I +∫c + ª
[lc + n∑ù
) – N ()AP)
I
Y* = mò
I = Cc + cTr
ccc - cT
I +t ̅ + Ø̅
A
>
> – R (>AS)
%L
m=
%AI
>
m = %T
.%L * %U.%L
m=
The multiplier with the state, as in a model without the state, is m > 1.
But the multiplier with the state is lower than the multiplier without the state because of the taxes.
Taxes depend positively to the level of domestic income, generates a reduction of the Keynesian
multiplier, which reduces the volatility of the GDP.
Increase in investments by 1 million, makes the aggregate demand, the aggregate supply, the
income increase all of them by 1 million.
But before consuming, households must pay the taxes, and this generates a dispersion in the
waves effect. Taxation reduces this wave effect, it’s negative if the shock is positive and it’s
positive if the shock is negative, like during a recession people pay less taxes so the disposable
income increases reducing the recession. Thus, the tax system is an automatic stabilizer
because in case of negative shock even if it reduces the amount of expansion in the GDP also
reduces the amount of recession.
Keynesian cross model:
29
u = C + t ̅ + Ø̅
I + c (1-t) Y
E=ò
E = Y Expenditure line is proportional to the level of income.
I + c (1-t) Y Consumption function line
E=ò
The intersection point L is the equilibrium level of output YL.
c < 0 ⟹ ΔA
I<0
ΔI̅ < 0 and ΔC
Suppose, because of a financial crisis, that the autonomous expenditures fall, then the expenditure
lines translate downwards, the economy converges from L to M, there is a recession or depression,
and there is an equilibrium of massive unemployment (M).
The Government has the power to push back YM to YL in the short run, shifting the line until it’s
I there are
reached the full employment, through 4 instrument; this is possible because inside A
transfers, taxes and public spendings.
4 types of budgetary or fiscal policy:
I > 0: spending more in goods and services increasing º̅, public spending. It’s the Keynes’
1. Δª
preferred instrument and has been used in Roosevelt Plan and Obama Plan, who used all the
instruments.
cccc > 0
2. Δ¨z
3. ΔÏ < 0
4. Δt < 0 Obama used it also to get more votes.
The first 3 instruments, or a mix of them, translate the line in a parallel way shifting the line upward
until the intersection point YM reaches the previous point YL.
Whereas the last one Δt < 0 is the slope of the expenditure line to increase, until the intersection
point goes back to L point.
Expansionary fiscal policy: involves increasing expenditures or decreasing taxation
(Roosevelt, Obama, Biden very strong in a few months, in EU with economy plan).
Austerity policy or Contractionary fiscal policy: involves decreasing expenditures or
increasing taxation.
Savings
Saving Function
30
Aggregate Savings: part of income not consumed
S=Y-C
Y =C + I in equilibrium
S = C + I - C ⟹ S = I in equilibrium
Alternative equilibrium: whenever there is equilibrium in the goods market there must be
equilibrium between savings and investments.
S = ΔBd and I = ΔBs ⟹ ΔBd = ΔBs
In this model savings coincide with the Bonds accumulation over time, thus savings is the demand
for bonds that are issued by firms. The equilibrium between S and I is exactly the equilibrium in the
Bonds market.
Find a saving and an investing function, and in the intersection between the 2 functions will get
the macroeconomic equilibrium.
The saving functions derives from the consumption function, since they are complementary:
Saving Function:
I = I̅ Investment function
S = Yd – C
S = Yd – Cc – cYd
S = – CI + (1 − c) Yd
¢
s = (1 − c)
S = – lI + sYd
S: savings.
s: marginal propensity to save, the complement to the marginal propensity to consume. It’s the
derivative of savings with respect to the level of income.
s = 1 - c: slope of the saving function.
- ¶c: negative intercept of the saving function.
∫c: Investment function is a constant, don’t depend to the level of income.
M: macroeconomic equilibrium,
It has less than one derivative.
In equilibrium the line S = I can be associated with Y = E, and since S = I ⟺ΔBD = ΔBS, by the
Walras’ law there is equilibrium also in the Bonds market.
Looking at the bonds market we have an equilibrium point and disequilibria points.
• If S > I ⟹ ΔBd > ΔBs ⟹ Y > E (on the right): if the savings are higher than the investments,
the demand for bonds is higher to the supply for bonds.
31
Using the Walras Law whenever there is an excess demand in the bonds market there must
be an excess supply in the goods market, and because of the effective demand principle
firms react by decreasing the quantity of goods produced.
•
If S < I ⟹ ΔBd < ΔBs ⟹ E > Y (on the left): the opposite.
Saving paradox
If households want to save: Δlc < 0 or Δs > 0.
Consequence: since S= -Cc + sY, they will obtain a reduction in Y < 0 because of the decrease in
I.
I and the multiplier m, because of R ∗ = mA
the autonomous expenditure ò
Solution: they will not succeed until the investments doesn’t change I = c∫.
In equilibrium S = t ,̅ thus a fixed and exogenous variable, and without any change in t ,̅ the savings
are pinned down by the investments.
56
This imply that
= 0; If people want to save more, increasing s the marginal propensity to save,
57
they can’t save the overall savings.
Because whenever S increases the multiplier decreases perfectly counterbalancing the
change.
Saving propensity increases as marginal propensity to consume decreases, and this starts a
negative wave.
Whenever s increases the saving function S becomes steeper, but the level of savings is peen
down by the level of investments, and it’s because after the shock there is a reduction in the level
of income because people want to save more, which reduce the level of the GDP, generated by
the reduction in the multiplier.
Conclusion: more people want to save, the more the economy is ruined because of the waves
effect.
Budgetary Policies
The solution of the income-expenditure model:
(
I=
Y ∗ = mA
ΩC + I + cTr − cT + Gæ
(:;((:=)
When there is the State, the equilibrium value Y* depends upon the values of the “budgetary
variables”: G, Tr, T and t.
Budgetary policy multipliers measure the variation in the level of output if 1 fiscal instrument
is modified.
(=
1.
2.
3.
4.
)
)AN()AP)
89 ∗
8:
89 ∗
8;"
89 ∗
8;
89 ∗
8<
= ø > 0 The spending multiplier partial derivative which result is equal to m.
= nø > 0
= – nø < 0
= – nø2 ) = – cm Y* < 0
32
Generally increase in expenditure is expansionary, increase in revenues in contractionary.
Use G as an expansinary fiscal policy instrument:
Increase G is more expansionary than increase Tr or decrease T or t, because the multiplier of
G is higher than the multiplier of taxes. Mathematically the variation in G translates all in new
demand (ΔG = ΔA), while other variations only partially because of c, which is 0 < c < 1(ΔTr =
ΔYd = cΔA).
Example: If I cut taxes of 1 million the disposable income increases by 1 million, but people partially
save, and thus will only partially consume; so people won’t spend all of that they have saved, in the
economy.
Keynesian policy is an expansionary fiscal policy driven by an increasing public spending
more than a reduced taxation, managing G.
Keynes says that this expansionary effect in the level of output holds even if G is totally
unproductive, because the workers will be paid for their useless work, they will consume,
generating the positive multiplier effect.
Deficit
Deficit
Deficit: costs related to the expansion of the fiscal policy.
In the model without the state the equilibrium in both Y = E and S = I holds.
In the model with the state Y = E always holds, but S = I not always.
State budget balance:
D = G + Tr - T
D = ¿ + ∑ù - ∑ - tY
D: public deficit, persistent deficit, should be financed by public bonds.
This means that what happens to the Deficit depends on:
• What happens to the 4 fiscal instruments, so the behavior of the government.
• What happens to Y (endogenous variable), so it not only depends to but also on the behavior
of GDP.
Public Deficit: Structural deficit + Cyclical deficit.
A. Structural Deficit: deficit that potentially would occur in the long run when the output, the GDP,
is at its potential level, in a situation of full employment of resources, and of labo. Respect to
the level of GDP:
• If the deficit is positive D > 0, we have a structural deficit.
• if the level is negative D < 0, we have a structural surplus.
It’s the deficit that will occur in the long run due to the fiscal policy parameter and It’s very
dangerous for the economy.
B. Cyclical deficit: the deficit that could occur in the short run due to fluctuations in the level of
output, GDP, like in case of recession or variation in fiscal revenues.
33
Expenditure function and the fiscal revenue function
G + Tr = G + Tr
T = T + tY
Assumed T = 0.
G +Tr horizontal line because everything is exogenous.
Thus, the structural deficit D=0.
a. Supposed a negative shock, a crisis, for example Δ I <0; the expenditure line translates
downwards.
The structural deficit D = 0, because it’s the structural deficit that will occur when the deficit
comes back in the long run automatically without any intervention; but in the short run the
cyclical deficit is positive because whenever there is a negative shock the output decreases
and the government gets less taxes, so less revenues, and this generates a cyclical deficit
that could generate a recession.
b. Suppose that government follows Keynesian prescription increasing G, ΔG > 0, and so the
expenditure line comes back to the previous point.
In the short run the cyclical deficit is positive. Less revenues generates a cyclical deficit, and
this can generate a recession, a way worse structural deficit generated by the intervention
policy.
Expansionary Fiscal Policies
When the public spending is increased Δ¿ > 0, it may happen 2 opposite effects:
1. Direct effect: it’s expansionary for the economy, the deficit increases one to one with the
expenditures. D = G + Tr - T – tY.
The direct effect prevails over the indirect effect.
∗
I; ∂Y = m.
2. Indirect effect: when G increases also Y increases because R ∗ = m A
∂G
But as secondary effect the deficit decreases. When economy expands, increasing the
expenditures, the revenue for the state automatically increases, which decreases the deficit.
VW
VL
= 1 − , VX
VX
VW
VX
VW
= 1 − ,m
S
= 1 − >AR(>AS)
VX
VW >AR(>AS)AS
= >AR(>AS)
VX
VW
(>AR)(>AS)
= >AR(>AS)
VX
>0
34
Conclusion: any expansionary fiscal policy, like driven by an increasing public expenditure,
makes the deficit and the fiscal debt increase.
Without the central bank, the seigniorage, or the possibility of printing money, the only way to
finance a deficit is to issue bonds I = ΔB.
In case of expansionary budgetary policy: GDP improves à increase tax base à increase fiscal
revenues.
Public Debt
Public Debt
The Budgetary constraints of the government says that the overall expenditures must be financed
in 2 ways:
- Taxes
- Issuance of public bonds.
Public debt (B): overall stock of bonds issued in the past by the state and not already repaid.
B: public debt
D: public deficit
Dt = ΔBt
Dt = Bt - Bt-1
Bt - Bt-1 = Gt + Trt - Tt
Trt = r Bt-1
Public Debt Dynamics:
Bt = Gt – Tt + (1+r) Bt-1
Ft= Gt - Tt
Bt = Ft + (1+r) Bt-1
This very important dynamic equation captures the time dynamic in public debt, here the value
of the variable depends not only on other variable, but also on the same variable lagged (dilatate)
of one period. it’s a first order differential equation.
There is a sort of inertia in the dynamic process.
It’s a dangerous equation because of the primary deficit: the public debt B tends to explode even
when F = 0. In order to prevent an increase in public debt, there must be a primary surplus: F = −
rB
Therefore, implementing a counter-cyclical deficit is risky.
Primary Balance (F): difference between public expenditures and tax revenues, net of interest
payment.
• F = 0 Primary Balance
• F < 0 Primary Surplus
• F > 0 Primary Deficit (Ft)
35
Suppose Ft=0 ∀t
Bt = (1+r) year Bt-1 This formula holds for any t, from 0 to infinity.
B1 = (1+r)1 B0
B2 = (1+r) B1 = (1+r)2 B0 = (1+r) (1+r) B0
(…)
Bn = (1+r) n B0
lim Bn = ∞
?→A
The debt automatically tends to grow exponentially over time, even if any country has
experienced that.
Debt crisis: when no investors want to pay the debt, is unpredictable depending on the
expectations of investors. In those cases it happens a default, a government bankrupt. (ex
Argentina, South America, Lebanon).
It’s a very costly crisis for a country because if the debts are not repaid none will lend money to the
country in at least for 10 years, being out of the economy market.
Bankrupt: debt is so high that no investor is willing to buy, this leads to crisis.
Power of compounding interests: interest payments accumulated exponentially over the time, it
generates a potential explosive dynamics in public debt.
Public Debt Sustainability
3 options to preserve the sustainability of the public debt, avoiding the explosion and therefore
a debt crisis:
1. Austerity policy
2. Inflation by the Government
3. Economic Growth
1. Austerity Policy
Bt = (1+r) Bt-1 + Ft ⟺ ΔBt = r Bt-1 + Ft
ΔBt = 0 At some point the debt is stabilized over time, avoiding the previous exponential
dynamics.
ΔBt = 0 ⟹ Ft = -r Bt-1 < 0
In order to prevent the explosion over time, the government must implement a surplus.
Surplus: means taxes should be higher than expenditures, and the surplus must be equal to
the interest payments in absolute values. So the higher is the stock of debts, and the higher
must be the primary surplus needed to stabilize the debt. The higher is the interest rate (ex
today) and the higher is the primary surplus needed.
Implement primary surplus means.
Primary Surplus = Taxes – Expenditures.
Implement primary surplus means increase taxes or decrease expenditures.
a. Tt > Gt ⟹ ΔTt > 0 or
b. Tt > Gt ⟹ ΔGt < 0
These 2 policies are part of the fiscal contraction policy, the opposite of the expansion fiscal
policy, the Keynesian policy.
In order for the Keynesian policy to be sustainable, the state must necessary and credibly be
committed to implement at some point the opposite of the expansion policy, the austerity policy,
to avoid the explosive dynamic of the public debt.
36
Austerity policy: decrease level of taxations and or increase taxation. The first option to
preserve the sustainability, stabilize the debt and to avoid the explosion (option preferred by
EU). This policy will bring the future generations to pay the debts.
Important distinction between the reaction implemented in the fiscal policy:
- In US: 2009 Obama plan extremely Keynesian, with implementation of deficit to GDP
ratio of 10%.
- In EU: was observed an austerity policy instead of a Keynesian one, the reason behind
this choice is the high debt level in many countries.
European policy makers are Neoclassical, not Keynesian.
- In Italy: 2011 Monti implemented austerity policies, increase taxes and decreased
expenditures, the expenditures were cut, it’s called spending review.
Apply austerity policy in the middle of a recession will amplify the recession, the right time for
the application is during a boom. Famous Keynes quote: ‘it’s not the slump, but the boom the
right period for the austerity’.
The austerity policy is costly for the society because it causes a recession. Because cutting
all the expenditures relevant to g, like on education for example, ending in a vicious cycle: use
austerity, which reduces g, and then you need more austerity.
2. Inflation by the Government
In our model there is no inflation, because we have the assumption fixed prices in the short
run in the income-expenditure model.
If prices can change it’s not relevant Bt, but the real debt (Bt/Pt): the debt divided by the price
level.
@#
+#
= (1 + ()
@#$%
+#
0' = 0'A> (1 + 3)
)=
D&
"&
=
+
A#
+#
+# B+#$%
Percentage increased in the price level.
+# BC
/EF D&$'
H
+ & Dynamics of real debt.
/EG "&$'
"&
The dynamics of public debt is no longer explosive as before at the condition that the inflation
rate is larger than the public deficit rate, nominal interest rate.
Because in case of a large inflation rate, the inflation rate decrease the real public debt,
avoiding the explosion.
The government enjoys the inflation, because it reduces the real value of the debt without
taxing people or implementing austerity. Ex Italian public debt right after IIWW didn’t exploded
because of the inflation.
The inflation is very costly for the society, it’s like a tax on money, in fact the inflation is also
called ‘hidden tax’, because reduces the real value of the money. This is the reason why the
main concern of many central banks is the price stability.
3. Economic Growth
It’s the percentage variation, in the real GDP. the variation is positive because it’s a growth,
thus increase.
37
The Public debt is evaluated not in nominal or real terms, but in terms of the size of the
economy, of what produces a nation.
@#
J+
#
=
+# I#
I#
RB = RB:( (1 + ¬)
I# BI#$%
@#
*=
D&
"& K&
I#$%
=
(/EF)
D&$'
(/EG)(/EL) "&$' K&$'
+
H&
"& K&
Now the dynamics of the debt to the GDP ratio depends on this coefficient g, which can be
lower than 1, even in case of inflation but not only in function of the inflation.
Now the dynamic inflation is friendly, doesn’t explode. Because of the so called growth
dividend. If the growth dividend is larger than the interest rate the debt GDP ratio doesn’t
explode (g > r).
It’s the best option because austerity and inflation are both costly for the society, this
equation will just decrease the GDP ratio, making the debt irrelevant. This is part of the
fundamentals of USA history.
Challenge for EU and Italy in this period is to implement the Keynesian policies as first condition,
the second condition is the adoption of Keynesian policies that make g increase.
The rate of growth (g) depends on 3 factors:
1. Fiscal capital: requires public or private investments.
2. Human capitals: requires education ex university.
3. Technology.
If it’s used g to counter the recession, and it’s used the right g elements, then it’s not only offset
the economic recession, but it’s also increasing the potential growth rate (g).
If g is higher than the interest rate means that the debt is sustainable
ΔBt: Variation of stocks of bonds in the time
Little t: meant as the time, the period took in consideration.
Ft: primary deficit
g: rate of growth of the Real GDP, thus of the long run economic growth
Integrations to the Income Expenditures Model
Balance Budget Theorem - Havelmo Theorem
Balance Budget Theorem is a particular class of budgetary policy, shows the effect of this
particular fiscal policy, in which an increment in public spending is totally financed in taxation,
without relying in public deficit or public debt accumulation.
This particular fiscal policy doesn’t generate any effect on the budget, maintaining the balance
budget unchanged.
ΔG = ΔT à ΔD = 0
38
The effects of a tax cut are negative, it must be financed by a reduction in public spending in order
to limit the damages à spending review: a policy in which taxes are cut and public spending is
reviewed.
S = Yd – C
Yd = Y + Tr – T
S = Y + Tr – T – C
Y=C+I+G
S = C + I + G + Tr – T – C
S = I + G + Tr – T
D = G + Tr – T
S=I+D
In a model with a state, the equilibrium condition can alternatively be expressed by the equality
between savings and the investments + the deficit (S=I+D).
It’s exactly the bonds market equilibrium because:
S=I+D
S = ΔBd
I + D = ΔBs
I = ΔBsF
D = ΔBsG
ΔBd = ΔBsF + ΔBsG = ΔBs
Implemented policy at the beginning
ΔG = ΔT à ΔD = 0
ΔS = Δt ̅ + ΔD
Δt ̅ = 0
ΔD = 0 because of the policy
ΔS = Δt ̅ + ΔD = 0
ΔS = 0
For the cases in which the public budget is totally financed by taxation, there is no variation in
aggregate savings, so no ΔS.
Next step: derive the saving function.
S = Yd – C = – s̅ + (1– c) Yd
ΔS = 0 ⟺ ΔYd = 0 because S is a function of Yd
⟺: if and only if
ΔYd = 0
ΔYd = ΔY + ΔTr – ΔT = 0
ΔTr = 0 by definition
ΔYd = ΔY + ΔTr – ΔT = 0
ΔYd = ΔY – ΔT = 0
ΔG = ΔT because of the assumption at the beginning
39
ΔYd = ΔY – ΔG = 0 ⟺ ΔY = ΔG (multiplier = 1)
ΔY = ΔG is the result of the Balance Budget Theorem.
A policy consists in increasing the government spending, financing the increment by increasing
taxations. It makes the GDP increase 1 for 1 with the level of taxation, so the multiplier is 1.
It’s expansionary on the level of output and therefore on the level of employment.
Intuition behind this result:
We have shown that the multiplier of public spending is higher than the multiplier of taxes.
If I increase both the multiplier the multiplier of spending prevails.
A part of the disposable income will be saved.
Ex increase G by 100, increase taxes by 100 à the GDP will increase by 100.
In this very simple model we got opposite results, not true that cutting taxes with a spending review
it’s expansionary, if ΔG < 0 à ΔY < 0, and so it’s contractionary because the multiplier of taxes is
slower.
This policy ΔG = ΔT is not implementable in reality because:
1. This generates an increasing that potentially leads the economy to the full employment level of
output.
2. Doesn’t generate problems of fiscal sustainability, because ΔT = 0.
This policy ΔG = ΔT > 0 is not implementable:
1. Essentially for political reasons, it’s unpopular for an electoral reason, you should justify the
implement taxation ΔT > 0.
2. Also for the economic reason by Arthur Laffer (a consultant of Ronald Regan during the 80s
in US).
The Laffer Curve
Arthur Laffer sustains that no one will work in function of the government, so with a taxation at
100% of the tax rate people won’t work at all, and the revenues for the government would be equal
to 0%.
T = tY
If ≠c = 0, the revenue to the Government is 0.
At a certain point the taxes will reach a maximum, estimated to be around 60%, beyond this point
people will reduce their working effort and will be disincentivized to work. It’s a problem of
elasticity. And there is an indirect negative effect in the labor supply.
If fiscal pressure is very high, you could generate a deficit, the revenues will not increase.
Partial Equilibrium Approach
40
Deepening the simplistic assumption I=t .̅
Partial Equilibrium Approach: can shed the light on the investment decisions.
Investment: is an intertemporal decision, because I expect that an actual investment will profit in
the future, giving back net revenues.
Initial assumption of perfect competition.
Assume that a given representing firm, will left to the decide a given investment project, whose
cost at time 0 is K0.
K0 R1, R2, …, RT expectations, expected futures net revenues, cash flows, profit, in different
periods of time.
Simplified version: K0 R1, where 0 is the present and 1 the future.
Net Present Value (NPV): It’s the future revenues, evaluated today, net of the cost of the
project Ko, which is the net present value. It’s the stream of future profit discounted of the interest
rate.
Assume that r is the interest rate prevailing, only one interest rate.
NPV =
•
•
•
C$
%&'
- K0 > 0 à R1 > (1+r) K0
Only if the NPV is positive, then it’s worth undertaking the investment project.
If the NPV is negative, then it is not worth undertake the investment project.
If the NPV is qual to zero, then it’s indifferent to undertake the investment project.
In the reality there are 2 different cases:
1. The entrepreneur has no money.
He has to borrow them from a bank, has to borrow K0 and then to repay the debt K0 the next
year.
Only if K0 > R1: R1 is expected to be higher of the cost of capital, then it’s worth to undertake
the project.
2. The entrepreneur has the money, thus K0, gives the same result.
Then (1+r) K0 is:
What the entrepreneur can get, investing in the financial market.
•
The opportunity cost of the investment project.
•
Only if R1 > R opportunity cost: R1 is higher than what I can get from the best alternative
investing in the capital market, then it’s worth undertaking the investment project.
Opportunity cost: in macroeconomic any choice has an opportunity cost, what I can get from
the best alternative (ex the husband’s happiness depends on the lover, not the wife -Oscar
Wilde).
NPV =
M'
/EF
+
M(
(/EF)(
+…+
M)
(/EF)*
- K0 > 0 Generalized Multiperiod
The variables that affect the profitability of an investment project:
1. The interest rate:
41
The decision for the investment on a project depends negatively on the interest rate, which
mathematically appears in the denominator.
The higher the interest rate, the higher the discount on future revenues, so the higher the cost
of capital, the lower the plausibility that the NPV is possible.
The interest rate cannot be negative, the central bank can at the maximum decrease it to zero.
Even if the interest rate is zero, if the expectations are negative, like loses in the future, the
investment won’t take place.
2. The expectations for future profits:
• The higher is the expected stream of profit, thus the more optimistic is the firm to get higher
future profit, the more likely the firm will invest.
• The lower is the expected stream of profit, thus the more pessimistic is the firm to get higher
future profit, the less likely the firm will invest.
Keynes prefers fiscal policy, and within it the spending policy, over monetary policy.
Internal Rate of Return (IRR)
Internal Rate of Return (IRR) variable, or Marginal Efficiency of Capital in general theory by
Keynes (ƒ ′z∆′): the particular discount rate that makes the present value of future revenues
equal to the cost of the project. That rate that once applied makes the discounted value exactly
equal to k0.
N%
= k0
CE O
R( = (1 + »)k0
M ' B PD
⟺ƒ>z
ƒ=
PD
» it’s an implicit profit rate that gives me the investment project.
Criterion: the firm must invest only if ƒ > z the profit rate is higher than the interest rate, than the
cost of the capital.
Even if the interest rate is zero, it isn’t sure that the entrepreneur would invest, because » could
anyway be negative, so for Keynes what crucially effect » are the expectations, which are
considered irrational à ƒ depends on the expectations.
N%
(CE Q)
+
N+
N,
= K0
+…+
+
(CEQ)
(CEQ),
Microfoundation suggested that investment decision by firms is:
• Negatively correlated with the interest rate, which is the cost of the capital, prevailing in the
capital market.
• Positively correlated with the state of firms expectations about future profits, which is
exogenously captured by the term t .̅
To simplify we shall employ a linear investment function in which:
I = t ̅ – br; b > 0
RS
=-b
RT
42
b: positive coefficient, measures the sensitivity of investments, respect to the interest rate, is
the derivative in absolute terms of the investment respect to the interest rate.
∫c: index that captures the state of firms expectations for future profits.
So, like for consumption with s̅ , if in the firms there is:
• A wave of optimism t ̅ increases.
• A wave of pessimism t ̅ decreases.
For Keynes those expectations are exogenous way. This is criticized by neoclassical economists.
IS Schedule
One limitation of the income-expenditure model: don’t have a satisfactory explanation of the
investment behavior by firms. Investment assumed to be completely exogenous à render the
investment endogenous.
Theory of investment development by another discipline, corporate finance. In order to do that, the
analysis of investment choices of firms is realized from a microeconomics perspective
Extend the income-expenditure model in the presence of the state, included in one important
dimension, microfounded an investment function in the income expenditure model and see
what happens.
How our income expenditure model modifies with respect to the adoption of an investment function
like this. The overall model with the state is exactly the same, with one difference, but with very
relevant implications:
u =C+I+G
⎧ C = s̅ + åR
4
⎪R = R + ≠Æ − ≠
4
⎪
⎪Ø = Ø̅ ; ≠Æ = ccc
≠Æ
5
c
c
⎨ ≠ = ≠ + Bv; 0 < B < 1; ∞± ≠ = 0, B = 6
⎪ m = ∫c – üù
⎪
⎪u = R
⎩Ṙ = ≤7 (u − R)
I – br] I’s called IS line or IS Schedule
à Y = m […
No longer a single equilibrium Y* as before because now the interest rate changes over time, it’s
an endogenous variable, now we have a locus of equilibrium point, a line of equilibrium in the
goods market, which is the IS line.
We need to have a theory for the determination of the interest rate, in order to determine the
GDP.
For sure GDP depends negatively on the interest rate, because the higher the interest rate, the
lower the investments, the lower the equilibrium level of output through the multiplier, because the
reduction in investments generates a negative multiplier.
This explain why the derivative of Y, respect to r, is – mb.
We get an equation in which we need to know how the interest rate (endogenous variable) is
determined. This locus of points (Y; r) that satisfy this equation is the equation called IS schedule,
which is defined as the set of combination between the level of output Y and of interest rate r
that guarantees the equilibrium in the goods market.
43
IS line or IS Schedule: the solution of the income expenditure model with endogenous
investments. It captures all the number of combinations between the 2 endogenous variables,
Y and r, that ensure the equilibrium in the goods market, the equilibrium between E and Y.
IS Schedule Graph (Goods Market):
IS is negatively sloped; -mb = slope.
#
Y
Intersection points: Point (mº̅; 0); Point (0; ).
$
Along all points of IS, E=Y. because it has been imposed. For a given interest rate ro the equilibrium
level of output is Y0, determined by IS.
This implies that outside IS, E≠Y:
To the right there is an excess supply, for E < Y.
To the left there is an excess demand, for E > Y.
For example when the interest rate is higher than the equilibrium level of output, so in all points to
the right there is an excess supply, there is a disequilibrium in the goods market.
In case of an excess supply the firms will reduce the quantity of goods produced. So there is a
tendency to go towards the IS line. So there is a tendency for output to increase.
Relevant information:
a. Comparative dynamics of IS: tells what happens in the disequilibrium points, when the
goods market is not in equilibrium, the arrows converge towards IS.
b. The position of IS can be controlled by the government and their fiscal policies.
I , makes the IS to translate
• Any expansionary fiscal policy that leads to an increasing …
upward.
Particular expansionary fiscal policy Δt < 0, it’s not a parallel movement, changes only the
slope.
• Any contractionary austerity policy, makes the IS go downward.
The Bonds Market
Price for Bonds
In order to explain the determinants in the GDP, we need for another relationship between Y and
r, we would get a 2 times 2 linear system, which would be easily solved for Y and r.
In order to get this other relationship, we have to make a number of preliminary considerations:
44
When we make the investments endogenous and depending on the interest rate, so when the
interest rates is a variable, can change over time, also the prices for bonds automatically must
be assumed as an endogenous variable (until this time we had assumed fixed prices for bonds).
To understand the aggregate relationship, especially from a qualitative perspective, between
interest rate and prices for bonds.
In the bonds market, when interest rates are a variable, also bond prices are a variable.
How Pb is determined:
Since macroeconomics wants to understand interactions across markets and agents, it’s not
considered heterogeneity among bonds, but just the simplest type of bond, we consider the same
bond issued by the government and or by firms.
Suppose in particular a zero-coupon bond (titolo senza cedola, a cedola nulla) the simplest bond
type, that gives me the right to receive a certain repayment after one year.
The Price for Bond must equal the present value of future payment, discounted by the interest
payment.
Suppose to buy a zero-coupon bond that must give me back a repayment of 100€ after 1 year. The
price for this bond should be lower than 100€ in order to make it profitable. In case of a rate of 5%,
the bond must have been paid 95€.
Rb =100€
Pb = 95€
r = 5%
UPb =
/EF
Pb: Price for buy a bond
Rb: repayment after one year from a zero-coupon bond.
c: coupon (cedola)
From this configuration, it emerges that:
• If the interest rate increases, then the price for bonds decreases.
• If the interest rate decrease, for a given repayment, then the price for bonds falls.
It implies that in the financial market there is a negative relationship between Pb and r.
Multiperiod level coupon bond:
V
V
VEUPb =
+
+…+
(
(/EF))
/EF (/EF)
T-maturity bond which gives me fixed payments c (cedola) and at the maturity it will give back a
repayment for the invested capital, behind the coupon.
The interest rate is determined by the bonds market.
Bonds market: (characterized by the 4 elements of the market)
When Pb is variable, we have a demand for prices for bonds which negatively depends on the price
for bonds and a supply which is negatively sloped, just like every market.
Price for bonds change every second, the equilibrium price makes the demand equal to the supply.
45
Agreeing with Keynes: prices for goods and wages are rigid in the short run because of contracts.
But we have to assume that in the bonds market the demand supply law prevails in every
instant in short and long run.
Whenever there is a disequilibrium, the bonds market always generates instantaneously the
equilibrium between the demand and the supply, so there is a tendency for the price to go back
in place in equilibrium.
In Bloomberg it’s shown the time evolution of Pb*.
If prices for bonds are determined by the demand supply law, also the interest rate is
determined, because they are related.
Curves theory about the determination of the interest rate:
In the bonds market the demand supply law generates an equilibrium price for bonds Pb*, that
via the inverse relationship with the interest rate corresponds to a certain equilibrium level for
the interest rate.
Say Law – Neoclassical Model
Say Law:
• Neoclassical model in contrast with the Keynesian income expenditure model.
• Leads the goods market to the equilibrium for any given Y. ‘Supply (Y) creates its own
demand (E)’. Every supply generates a demand automatically, it’s not a supplied generated
by a demand.
• This mechanism in the financial market will also generates full employment, without any
government intervention, by the Neoclassical view of self-correcting markets.
• ? It sustains that the interest rate is determined in the bonds market.
Say Law: E < Y ⟹ ΔBd > ΔBs ⟹ ΔPb > 0 ⟹ Δr < 0 ⟹ ΔI > 0 ⟹ ΔE > 0 ⟹ ΔY > 0 ⟹ E=Y
The simple essence of the reasoning: suppose a situation of excess supply in the goods market,
a situation that occurs during a crisis.
Step 1-2: By the Warlas’ Law: in case of excess supply in the goods market, then there is excess
demand in the bonds market.
Step 3-4: By the demand-supply law hold in the financial market: the price for bonds
instantaneously increases for the excess demand, and the interest rate will fall for the inverse
relationship with the prices for bonds.
Step 5: But when interest rate falls, firms investment will increase automatically without any
government intervention.
Step 6-7-8: the increase in I will generate an increase in the aggregate demand, and so the firms
will increase the supply, triggering the Keynesian multiplier, until E = Y, until we go back the full
equilibrium.
46
Say Law Confutation
We have to stimulate the equilibrium through fiscal policies, until we get E = Y (the essence of
the Keynesian prescription).
Say Law important limitation: don’t consider the Central Bank, and thus the money market.
Central Bank: institution that has the monopoly to print legal money, it’s an important player,
operator, that affect the market.
Open market operations: the most used instrument for introducing money in the system is buy
bonds in exchange for money, if I sell bonds I withdraw money from the system.
Implication: so the position of these 2 schedules depends on the central bank behavior. In the
same time in which we consider the bonds market, we must add the central bank as an operator
of our system, but as we introduce the central bank in the analysis, we have to consider a new
market, the money market.
But institutionally the central bank affects the bonds’ demand and supply. But now that we have
introduced the money market we have 3 markets, and the Say Law doesn’t hold, because
Walras’ Law now must regulate 3 markets.
Keynesian and Neoclassical mechanisms
The behavior of the macroeconomic system in the Neoclassical model is symmetric with respect
to that of the Keynesian model.
Keynesian Mechanism:
• Aggregate expenditure E adjusts to output Y.
• Investment I adjusts to saving S.
• The bonds market prevails over the goods market.
Neoclassical Mechanism:
• Output Y adjusts to aggregate expenditure E.
• Saving S adjusts to investment I,
• The goods market prevails over the bonds market
Keynesian confutations of this neoclassical model. The bonds market representation is too simple
because: there are also old bonds, not only the savers but also the speculators demand bonds, it’s
not considered the role of the money as an alternative to the bonds
The Money Market
Next step: introduce money, introduce a new agent (central bank) and a new market (money
market), that interacts with the bond market.
Money are defined in economics: as everything commonly accepted to make payments, and just
like the bonds are financial assets, with the only advantage to be liquid, and thus be able to make
immediate payments without the interest rate.
Legal money: a way in which we can comply with an obligation. Only issued by the central bank.
M = Cu + De
H = Cu + Re
47
Money Demand (L) by households and firms.
Money Supply (M) by the central bank, is the quantity of means of payments in
Total monetary aggregate:
- Currency (Cu): external, physical moneys (coins and bills).
- Deposits (De): not money, but considered as money because the underlying of bank
deposits are money because are the most commonly accepted as payments (banco mats
and credit cards) and the majority consists in bank deposits (not tangible, called internal
money or bank money). Deposits are not legal money because not everyone accepts banco
mats, and for this reason you can’t always extinguish an obligation with them.
Monetary base (H): the central bank prints H, not M, because in M there are also deposits. But
M is related to H.
Bank reserves (Re): banks are required to hold reserves, an part of these reserved are imposed
by the monetary system as required reserves, and part are called free reserves, which are freely
decided by the banks.
M and H are related to each other, this relationship is explained by 2 ratios:
1. Currency deposit ratio (gamma): Ñ =
(Z
[\
The percentage of deposit physically held by the owner in their pockets as a form of cash
related to the preferences. Preferred by households and firms.
Suppose I don’t trust the balance sheet of my bank, in case of suspected bankruptcy.
2. Reserve deposit ratio (delta): – =
]\
[\
The percentage of reserves kept by the banks, the other part is lend to households and firms
using people’s deposits.
H: Monetary base
Re: bank reserves, part of monetary base
Ñ: currency to deposit ratio
–: reserve deposit ratio
—m: monetary or deposit multiplier
Relationship between the money supply and the monetary base:
Cu = Ö De
Re = “ De
M = Cu + De ⟹ M = Ö De + De = (1 + Ö) De
H = Cu + Re ⟹ H = Ö De + “ De = (Ö + “) De
De =
^
<*_
)*7
H
7*`
)*7
Da
5m= 7 * ` ⟹ 5m= Db > 1
M=
H related to M via the overall coefficient.
48
Overall coefficient, monetary or deposit multiplier (5m):
• Measures how a variation in H generates multiple variations in M.
• Measures the derivative of M respect to H.
• Measure the increase in money supply M if the monetary base H increases by 1 euro.
• 5m > 1, It’s always positive because of the creation of deposits and the multiplier of deposits:
everyone (banks and people) keeps part of the money and in part lend, spend, or deposit it.
The credit function by the banks generates money.
Example: If the multiplier is 5, and I sped 1 euro, then the money supply is higher of 5 5euro, the
monetary multiplier is similar to the Keynesian multiplier.
GDP depends on M, which depends on H, Ñ and –.
The central bank can control the monetary base H, thus via the monetary multiplier 5m, can
exogenously control the money supply M.
Every month the central bank chooses H, so can indirectly control M.
The central bank is forced to print H whenever there is a reduction in the deposit multiplier 5m.
Central Bank can control H, the monetary base, and via the multiplier is able to control the money
supply.
The Great Depression has 2 explanations:
a. Keynesian explanation: is a fiscal policy mistake, due to implement a balance budget in
a time of recession.
b. Monetary explanation (Friedman): is a monetary policy mistake, due to a number of
bank failures, not saved by the governments, following in a collapse of credit market and
an increasing debt, and so less tendency to lend money.
Mathematically the increase of Ö and “ leads to a decrease of M.
Mistake: not have printed money H in a time of collapse of the monetary multiplier.
This mistake didn’t happen again during the Great Recession because of the increase in the
monetary base H, printing new money.
It’s not the physical money, but the money supply to affect the GDP, and so the inflation.
Print money in a time of reduction in the deposit multiplier will not create inflation, but avoid
deflation.
After the pandemic crisis the European central bank printed a lot of monetary base H.
An economic crisis can be determined by:
• Reduction in consumption and investment.
• Increase in the reserve-deposit ratio.
• Bank run phenomenon.
To avoid or defeat those problems it’s necessary to use both fiscal and monetary policies.
Bank run phenomenon (corsa agli sportelli): people are doubtful about the held of their bank, and
they run to the bank to withdraw money. It may happen in many types of financial crisis, in order to
don’t lose people’s deposits.
In order to avoid this phenomenon, central banks are obliged to lend to private banks, and also the
state can assure the deposit in the private banks.
Channel in which central bank can introduce money in monetary system:
49
1. Bond channel: through the open market operations, can buy private or public bonds in
exchange for money (ECB can’t buy public, because can’t finance governments, by the
Maastricht treaty).
2. Credit channel: print money and lend to credit companies, the banks. All modern central
banks are lenders of last resource towards private banks, it means that private banks can
always borrow money from central banks, forced to lend, this avoid the bank run
phenomenon.
3. Foreign channel: buy or selling foreign currencies. Ex if the European central banks buys
dollars, is introducing euros in the system.
Money Demand (L)
Money Demand (L): quantity of money that households and firms on average, in a given period,
decide to hold in their portfolio as cash, as liquid asset.
Money: financial asset that doesn’t pay an interest rate, is liquid and can be used to make payments
without occurring in any cost.
Bonds: pay interest rate, not liquid.
Description of the money market:
I
M=‘
”L = kY – hr k>0, h>0
L=M
It’s partial, only what happens inside the market.
3 motives, reasons, for demanding money:
1. Transaction motive: money is demanded to make payments.
Number of transactions in an economy are directly related to the level of (national) income.
2. Precautionary motive (precauzionale): simply to offset unexpected event, people make
increase the demand for money.
3. Speculative motive (Keynes): agents can demand money for speculative reasons.
Suppose a number of speculators in the economy, who buy an asset at low price in order to
sell it at a relatively high price, in order to refinance the capital gain. Any speculator has an
idea for the average (normal) price for bond on the base of wich buy or resell the assets.
a. Suppose that the prices for bonds are relatively high, this means that speculators expect
that the prices for bonds will decrease towards the normal price.
In order to get a capital gain, they sell the bonds, demanding money in order to do
not fail in capital loss.
This implies that when the prices for bonds are relatively high, the interest rate is
relatively low, then the money demand is relatively high.
b. Suppose that the prices for bonds are relatively low, this means that speculators expect
that the prices for bonds will increase.
In order to get a capital gain, they will demand bonds in exchange for money.
This implies that when the prices for bonds are relatively low, the interest rate is
relatively high, then the money demand is relatively low.
•
The money demand depends positively to the level of income, because it allows more
transactions.
50
•
•
The money demand depends positively to the level of output.
The money demand depends negatively to the interest rate.
Money demand function:
L (Y, r) = kY – hr
The interest rate is the opportunity cost of holding money, the best alternative is to buy the
assets, given from bonds.
M: money supply, multiplier of the monetary base
L: money demand
k and h: positive parameters that measures the partial derivatives of L with respct to Y, and r with
respect to r (?)
LM Schedule
The equilibrium condition for the money market:
I = ◊Q – ÿù
÷
/
P
I + K
(LM): r = - ÷
W
W
LM schedule: the relationship between the interest rate and the level of output that ensure the
equilibrium in the money market, between the money demand and the money supply.
This is the equation of a straight line, increasing, positive sloped, and with a negative intercept.
LM is relevant only for a positive interest rate, or equal to zero, but the interest rate cannot be
negative.
For a higher level of output Y we have an higher level of interest rate because higher Y implies
higher money demand, since money supply is fixed, the remaining part of the money demand
decreases, hence the interest rate is higher.
I
Money supply: M = ÷
Position of LM can be controlled by the central bank because the intercept depends to the money
supply. The money supply M is considered a monetary policy, it means that it is an exogenous
variable controlled by the central bank.
This implies that in the case the central bank wants to implement:
I < 0), then LM shifts upwards.
• A contractionary monetary policy (Δ÷
I > 0), then the intercept falls, LM shifts downwards.
• An expansionary monetary policy (Δ÷
51
Outside the LM
In all points belonging to the line LM there is the equilibrium between money demand and money
supply. But outside LM there are disequilibrium points.
r0: equilibrium level of interest rate.
Y0: equilibrium level of output.
What happens in case of disequilibrium in the money market:
•
Suppose excess money demand in the money market:
L > M ⟹ ΔBs > 0 ⟹ ΔPb < 0 ⟹ Δr > 0 ⟹ Æ̇ > 0
On the right side of the LM line the level of output is higher, then the money demand is higher
than the money supply (L > M).
The households and firms wish an higher demand for money respect to the money that circulates
in the economy. They can get those extra money by selling bonds in exchange for money.
So the supply for bonds increases, so the prices for bonds decreases, so the interest rate
increases (moves upwards).
Interest rate increases in order to reestablish the equilibrium, because the money demand
depends negatively to the interest rate.
•
Suppose excess money supply in the money market:
L < M ⟹ ΔBd > 0 ⟹ ΔPb > 0 ⟹ Δr < 0 ⟹ Æ̇ < 0
On the left side of the LM line the interest rate is higher, then the money supply is higher than
the money demand (L < M).
People demand less money than the money that circulates, so the demand for bonds increases
spending the extra money.
So the demand for bonds increases, so the prices for bonds increases, so the interest rate
decreases (tendency to fall downwards).
Interest rate decreases in order to reestablish the equilibrium.
Conclusion: The dynamics adjustment that take place in the points in which there is
disequilibrium, involves in dynamic change in the interest rate. So, in case of disequilibrium in
the money market we have a change in output and simpoultaneously a change in the interest rate.
This dynamic change outside the LM can be analytically represented by:
E'
ż = = ;z (L-M)
FG
52
ż : derivative of r over time
;z: coefficient that measures the velocity of the adjustments by the interest rate.
IS - LM Model
IS-LM Model
Combining all the information:
- IS schedule: in goods market, output dynamic adjustments.
- LM schedule: in money market, interest rate dynamic adjustments.
IS-LM Model: the most important model in macroeconomics, is an extension of the income
expenditure model by Keynes, to account also the role of the central bank in the economy.
IS-LM Model:
(IS) Y = m [?̅ − br]
⎧
⎪(LM) r = − > G
H + dI
c
⎨ J̇ = LJ (E − Y)
⎪
⎩ Ṁ = LM (L − M)
c
(E = Y)
(L = M)
The first 2 equations are equations in 2 endogenous variables Y and r.
Solving the system, we can compute the level of output and of interest rate that simultaneously
show the equilibrium in goods market, money market, and by the Walras’ Law also the bonds
market, because if 2 markets are in equilibrium, also the third market is in equilibrium.
In the IS-LM model, the equilibrium output Y is influenced by economic policy:
a. Fiscal policy: change in G, Tr, T and t, it shifts the IS line, It’s less effective than in the incomeexpenditure model because of the monetary-retroaction effect.
b. Monetary policy: change in M (through the instruments for controlling money supply); it shifts
the LM line, in this model money has real effect (is not neutral).
The effectiveness of the 2 polices depends on the slope:
• Steeper IS and Flatter LM, more effective the fiscal policy.
• Flatter IS and Steeper LM, more effective the monetary policy.
Business Cycle of Economy (for the Equilibrium)
Issues of the equilibrium stability:
The dynamically stability of the macroeconomic equilibrium can be affected by exogenous
changes in some variables.
IS - LM Model outside the equilibrium (Phase diagram):
53
M point: macroeconomic equilibrium, intersection point between the IS schedule E=Y and the
LM schedule L = M, since IS is negatively sloped and LM is positively sloped.
This intersection point M (r*; Y*) is the only combination that simultaneously ensures equilibrium
in any markets (goods, money, bonds) by the Walras’ Law.
This also implies that outside this point there is disequilibrium.
Outside the equilibrium there is a system of differential equations:
N
J̇ = LJ (E − Y)
Ṁ = LM (L − M)
We have 4 regions of disequilibrium:
1. Right Region:
• On the right of IS, there is E < Y, so by the effective demand principle there is a tendency for
the output to decrease over time (⇦ force).
• On the right of LM, there is L > M, so the interest rate tends to increase (⇧ force).
• So I have 2 ⇦⇧ forces that act simultaneously.
The economy will move in the middle of these 2 forces. The slope of the movement
depends on the coefficients ;€ and ;z.
2. Upward Region:
• On the right of IS, there is E < Y, so by the effective demand principle there is a tendency for
the output to decrease over time (⇦ force).
• On the left of LM, there is L < M, so the interest rate tends to decrease (⇩ force).
• So I have 2 ⇦⇩ forces that act simultaneously.
3. Left Region:
• On the left of IS, there is E > Y, so by the effective demand principle there is a tendency for
the output to increase over time (⇨ force).
• On the left of LM, there is L < M, so the interest rate tends to decrease (⇩ force).
• So I have 2 ⇩⇨ forces that act simultaneously.
4. Downward Region:
• On the left of IS, there is E > Y, so by the effective demand principle there is a tendency for
the output to increase over time (⇨ force).
• On the right of LM, there is L > M, so the interest rate tends to increase (⇧ force).
• So I have 2 ⇧⇨ forces that act simultaneously.
54
If the economy starts on the right, it changes the direction upwards, then on the left, then
downwards: it’s a business cycle, the trajectory changes direction every time it meets a curve,
until it converges to the equilibrium (Y=Y*, r=r*). There are fluctuations of the level of output, but
what matter to us is that the equilibrium is stable.
Degenerate Dynamics of the Economy
Remark: in the real world ;z is faster than ;€ (EÆ > Ev) because EÆ measures the velocity of
adjustment of the interest rate, and the bonds markets adjust instantaneously, whereas Ev is
slower because change the production requires time.
Because of the financial globalization it’s quite realistic that ;z tends to infinity.
In the limit case of EÆ that tends to infinity it’s possible the generated dynamics: immediately the
economy jump to LM and then it directly converges along the LM line, according to the other
coefficient Ev, towards the economic equilibrium M, without following the economic cycle.
Properties of the Equilibrium
Because the equilibrium is stable, we can focus on the properties of the equilibrium:
Solve the IS - LM model for the equilibrium, since now the economy converges endogenously
towards the macroeconomic equilibrium.
In order to find the equilibrium point, solve the system, before derive r from the LM, and after
substituting it in the IS solving for Y:
O
(IS) Y = m [?̅ − br]
H = kY − hr
(LM) G
Y=
>
e
I − fd
[ º̅ + ‘
> A C (>A')
c
c
[1 − å (1 − B) +
I]
fd
e
H
]
Y = º̅ − ‘
c
c
I + m2 ÷
I (equilibrium level of output)
Y* = m1 …
55
1
⎧ m1 =
1 − Y (1−') +
⎪
e
b0
ℎ
; 0 < m1 < m
⎨ m2 = m1 c
⎪ ̅
UUU ) + V ̅ + W̅
⎩? = (R̅ − STU + STM
Both m1 and m2 are positive. It means that we have those 2 partial derivatives:
%L∗
= m1 > 0
gh̅
%L∗
= m2 > 0
G
gi
This implies that in this model not only the expansionary fiscal policy that affect the autonomous
expenditures, so the fiscal variables, generates an increasing in the level of output, but also an
expansionary monetary policy is effective. So it’s possible to stimulate the economy by printing
more money, increasing the amount of money that circulates.
These are the effects of the fiscal policy and of the monetary policy.
m1: multiplier of the autonomous expenditure, lover than the regular multiplier because of the
presence if bk/h > 0.
m2: multiplier of the money supply.
Economic mechanisms
m1 is slower than the multiplier in income-expenditure model. It can even be lower than 1.
An expansionary budgetary policy can be less effective than it is in the income-expenditure
model.
Transmission mechanism of fiscal policy.
Transmission mechanism of monetary policy, why printing money is expansionary on the level of
output.
a. Fiscal Policy
YL: potential level of output
Suppose involuntary employment, in case of a crisis.
An expansionary fiscal policy (ΔØ̅ > 0) can restore the full employment.
56
Increasing public spending, IS shifts upwards in a parallel way, until we converge from M to the
point L.
If EÆ is lower than infinity the convergence is cyclical.
If EÆ is infinity the convergence is direct.
Fiscal policy: important instrument to push the level of output in the short run, directly in
correspond of the full employment. The conclusions that we have made so fare remains qualitative
unchanged.
The shift upwards of IS stimulates the level of output, but increases the equilibrium of the interest
rate, which doesn’t occur in the income-expenditure model.
As the interest rate increases, the private interest decreases, this important phenomenon is called
crowding out of investments.
Crowding out of investments (spiazzamento degli investimenti): an expansionary fiscal policy
that crowds out private investments because of the increase of the interest rate r. It’s the reason
why m1 > 0 but is slower in the income expenditure model because here we don’t have any crowding
up phenomenon. The reason for this effect is:
ΔØ̅ > 0 ⟹ ΔY > 0 ⟹ ΔL > 0
I ⟹ ΔBs > 0 ⟹ ΔPb < 0 ⟹ Δr > 0 ⟹ ΔI < 0
L>‘
Suppose a fiscal expansion policy, like an increasing public spending, that generates an
increasing aggregate demand, so firms produce more, triggering the standard Keynesian multiplier
effect.
In the income expenditure model things stop here,
But when also the money market interacts in the analysis, the increasing output, therefore the
increasing in the income generates an increase in the demand for money.
If money demand increases the money market falls in disequilibrium, leading to an excess demand
in the money market. And in this case people would sell bonds, reducing the price for bonds, and
increasing the interest rate. This crowds out the investment component of the aggregate demand.
Monetary retroaction effect: any fiscal expansion leads to a disequilibrium in the money
market, it, generates an excess demand that dealing with the money market, which interacting with
the bonds market generates changes in the interest rate, which increasing, crowds up the
investments.
Suppose to increase G as a variation in the autonomous expenditure, this affects the equilibrium
level of output. Then Y increases, IS shift upwards, the interest rates increases, and the investments
decreases.
%j
%?
> %k
= k;
=- ;
=-b
gL
gj
c g?
Remember Keynesian approach concentrates on the short run.
Crowding up of the investments may not be a problem in the short run, but it can be a problem
in the long run, for the economic growth rate g. Because all the theories for the long run suggest
that g depends on physical, human and technological capitals.
The reduction in investments implies a decumulation in the capital stock, which crowds out the
economic growth.
57
Conclusion: the governments should be careful with the systematic use of expansionary fiscal
policies because it could even stabilize the problem in the short run, but can create problems in
the long run, crowding out the economic growth in the long run.
Crowding out the economic growth in the long run can happen only if Δg is totally unproductive.
If Δg is productive, like a public investment, the crowding out of private investment doesn’t
imply that there is a crowding out of the economic growth.
b. Monetary policy
The central bank alone, without the intervention of the government, is able to leave the economy
I >0).
in full employment YL, increasing the money supply (Δ‡
The LM line shifts downwards until potentially reaching the point L.
The monetary policy can stabilize the economy at the long run, at the potential level of output.
The Keynes Effect
Transmission mechanism on monetary policy: exactly the opposite because the interest rate
falls, crowding in the level of investments.
The expansionary monetary policy works by stimulating private investments.
The mechanism:
I > 0 ⟹ L < M ⟹ ΔBd > 0 ⟹ ΔPb > 0 ⟹ Δr < 0 ⟹ ΔI > 0 ⟹ ΔY > 0
Δ÷
The monetary expansion generates an excess supply in the money market, there is too much
liquidity, people will buy bonds, prices for bonds increases, and there is a reduction in the interest
rate, stimulating the investment component so that the level of output increases.
Because the increasing in investments triggers the Keynesian multiplier, so this mechanism
is called also Keynes effect.
Also the monetary policy is able to ensure the full employment, but it has some limits.
Role of fiscal policy
The IS-LM model used to understand the effects of monetary and budgetary policies.
•
Qualitatively speaking: the results are the same in the income expenditure model.
Expansionary budgetary policy always has a positive effect in the equilibrium level of output.
It implies that the fiscal policy is a powerful tool for stabilization purposes, as in the income
expenditure model.
58
•
Quantitively speaking: there is an important difference, that the multiplier of the autonomous
expenditures, called m1, is lower than m, the multiplier prevailing in the income expenditure
model.
Critical point: transmission mechanism of fiscal policy is altered, compared to the income
expenditure model, to what is called monetary retroaction effect.
So if we have a fiscal expansion (4 tools) the stimulus on the level of output that works through
the Keynesian multiplier generates an increase in money demand, so a disequilibrium in the
money market.
The money demand is higher than the money supply, so people will demand money by selling
bonds, supply for bonds increases, prices for bonds decreases, the interest rate increase, it
implies the crowding out effect of the private investments.
It depends whether public spending is productive or not, not important in short run, but it is
in the long run. Unproductive spending is expansionary because it triggers the Keynesian
multiplier effect.
Role of monetary policy
The monetary policy cam push the level of output to the full employment.
The transmission mechanism of monetary policy, it’s almost the opposite respect to the
transmission mechanism of fiscal policy.
Because an expansionary monetary policy, like an increase in money supply generated for example
by open market operations, the central bank buys bonds private or public in exchange for money,
so it’s introduced the monetary base to the system, the monetary base is multiplied, generating a
given money supply.
So an expansionary monetary policy generates an excess supply in the money market, so the
opposite mechanism is produced.
The excess supply means that there is too much liquidity, people will buy bonds, stimulates the
prices for bonds, the interest rate decreases, this stimulates private investments.
So since the fiscal policy crowds out private investments, the monetary policy crowds in
private investments. This second mechanism is called the Keynes effect.
Keynes prefer fiscal policy over monetary in order to stabilize the economy. Demonstration:
Suppose a relatively big recession, so distance between the full employment level of output and
the short run level of output is relatively big, like in the case of the Great Recession and the Great
Depression.
The monetary policy alone can reach Ymax but not YL:
59
I > 0) leading to a movement of LM to
The monetary policy can increase the money supply (ΔM
the right. But the interest rate falls, and at Ymax the interest rate is equal to zero, all the points to
the right of Ymax have a negative interest rate.
If the monetary policy prints more money, this won’t affect the equilibrium level of output because
the intersection with IS will occur only in correspondence of a negative interest rate, which can’t
be negative, so there never could be a monetary policy that allows a negative interest rate.
So Ymax is the maximum level of output that the central bank alone can reach.
‘Can’t push on a string’: the central bank can’t reduce the interest rate below zero.
When interest rate = 0:
• Money is superior to bonds, because even if both of them won’t profit, at least money is liquid
and can be used for transactions.
• The monetary policy cannot anymore stimulate the level of investments, so the investments
depends only on firms expectations.
If the marginal efficiency of capital, the internal rate of return, the expected profit is positive, then
the firm will invest.
If the expected profit are negative, like during recession, then the firms will not invest, even if
the interest rate is equal to zero.
This is the reason why Keynes prefers the fiscal policy over the monetary.
The fiscal policy immediately triggers the Keynesian multiplier
The monetary policy mechanism is limited. This problem is called liquidity trap problem.
Liquidity trap: when interest rate = 0, and people prefers money (liquidity) over bonds, so the
Keynes effect will no longer apply, the central bank will print more money, but people will keep
their money not spending them.
It can occur even with a positive interest rate, like when the prices for bonds are high and
speculators believes that the prices will decrease and thinks that it’s optimal to sell bonds and
receive money. If the central bank prints money, people will keep their money in order to avoid the
capital loss, and the Keynesian effect will not apply.
Summing up, in a situation of liquidity trap the monetary policy is ineffective, only the fiscal
policy is effective, this is the reason why Keynes prefers it over the monetary one.
z: minimum interest rate in which the liquidity trap occurs.
The Great Depression (1929-1933)
The emergence of an asset price bubble:
It’s a bubbling behavior driven only by the expectations and not by economic fundamentals. The
speculators will buy bonds, thinking that the assets price will increase in the future, they make
arbitral opportunities: capital gains without any cost, buying when price is low and sell when price
is high.
But at some point the bubble burst, there is an immediate plunge and the expectations are
reversed, the expectations are said to be self-fulfilling.
60
Everyone will sell the bonds because they expects that the prices will go down, and so will the
demand for assets.
Income expenditure model:
The Great Depression is a consequence of a series of shocks and problems:
H < 0)
Autonomous expenditure decreases (ΔX
The reduction in the wealth determines:
I<0
Δs̅ < 0 and Δt ̅ < 0 ⟹ Δ…
So the autonomous expenditure decreases and IS shifts downwards to IS’, since the position of
IS depends to the autonomous expenditure.
The new intersection point between IS’ and LM is M.
Like it is sustained by Friedman: great depression is not a mistake in the fiscal policy but a mistake
by the central bank. 2 central shocks amplified the recession:
Credit Crunch (monetary shock)
ΔÖ > 0 ⟹ Δ– < 0
Since the banks didn’t provide credit to households and firms, so it happened a credit crunch: if
the bank don’t provide credits, the profit rate by banks falls and if it becomes negative the banks
will fail.
At the time there were the free banking view, if the bank fail it means that it wasn’t capable to stay
in the market (liberal view). At the time the private banks couldn’t borrow from the central bank,
central bank weren’t the lenders of last resource.
In the financial market there is contagious effect: in case of bankruptcies and of a wave of
pessimism, then people will be doubtful about the bank and there will be a bank run phenomenon
that involves all the banks, this will imply in a series of bankrupts. But the banks will be short in
liquidity to provide, and since at the time the banks couldn’t borrow to the central bank there is a
crunch in the system.
Since Ñ increases, the deposit multiplier – decreases, so it happens the credit crunch, not
providing credit to the economy, so there is the collapse in the interbank market.
If the rese reserve deposit ratio “ decreases, then the deposit multiplier decreases.
ΔÖ > 0 and Δ“ < 0 ⟹ ΔM < 0
These 2 shocks generated ΔM < 0.
For Friedman and Bernanke, the mistake of the central bank was not printing money, not printing
the monetary base H at a time in the reduction of ·M < 0.
61
Since M = ·M H: when ·M < 0, it should be improved H, in order to let M go back in position.
So LM shifted to the left in LM’, and the new intersection point between IS’ and LM’ is M’.
Conclusion: when both IS and LM shift on the left in IS’ and LM’, then the Recession is big and
becomes a Depression.
New Deal by Roosevelt: adoption of Keynes ideas, the necessity for a fiscal policy in order to
recover the situation, in this case a big government plan 1933-1937.
Starting of the welfare state: the state that intervenes actively in the economy.
Great Recession (2008-2009)
In the Great Recession 2007 started with financial crisis was initially affected by exactly the same
financial shock, which at the end was very similar: bubble in asset prices generated by the
optimism. At the end of 90s there was the dotcom bubble, a huge increase in the stock prices in the
technological market. 2001 terroristic attack generated a reaction in the central bank, which
consistently decreased the interest rate, reduction in the mortgages rate.
At the time it wasn’t asked the collateral (ipoteca) when it was asked a mortgage for the house,
because in case of the lack of the mortgage payment the bank would have gained the house, if the
expectations continue to increase the bank would have obtain an house with an increased value,
so a capital gain.
But this mechanism reversed when the bubble burst, with a plunge in house prices and in assets
prices. This lead in the failure of banks, bankruptcies, because they obtained houses with a lower
price than the original, so a capital loss.
Great Depression and Great Recession happened exactly for:
• The same reasons:
o Burst Bubble.
o Plunge in the asset prices.
• The same shocks:
o Wealth of consumers decreases.
o Reduction in investments.
o Bank runs phenomena.
Because of the super Keynesian plan by Obama and Bernanke didn’t repeat both the same
monetary and fiscal policy mistakes. This is the reason why it’s called great Recession and not
Second great Depression, because IS moved to the left in IS’, but printing a lot of money to buy
assets the monetary mistake wasn’t repeated and with the Obama plan neither the fiscal policy
mistake was repeated.
So LM shifted to the right, until in 2 years the US came bake to YL.
The reactino to the Great Recession is a success of economic policy in US.
The Great Recession in US
The macroeconomic equilibrium after the shock in US:
62
Bernanke implemented an expansionary monetary policy leading the interest rate = 0.
Then the US, fallen in a liquidity trap, overcome it thanks to a fiscal policy.
So both fiscal and monetary policies were necessary.
The Great Recession in Europe
The macroeconomic equilibrium after the shock in Europe:
In Europe the banks were saved by the government, like in Italy it was saved Monte dei Paschi
di Siena. This implied an increase in the public debt for saving the banks.
This increase in the public debt led the fiscal variables largely outside of the 2 fiscal parameters
imposed by the Maastricht Treaty.
Maastricht Treaty 2 rule:
The deficit to GDP ratio should not be higher than 3% of the GDP.
There must be a tendency of the debt in the GDP ratio to converge to the 16% of the GDP.
In order to avoid the unsustainability of the fiscal policy, the Europe didn’t adopt a Keynesian type
I < 0, ΔÏ > 0, Δt > 0, ΔTr < 0.
policy, but an austerity policy: Δª
In Italy have been adopted all those 4 contractionary policies (spending review by Monti
government 2011-2013).
All these policy leads IS line to the left, and the recession amplifies, so we have a double deep
recession.
It is a mistake by Keynes: austerity policy should be applied during a boom, not a slump, because
during a recession it should be implement a deficit spending policy, and only after should be applied
an austerity policy to stabilize the public debt.
63
In Greece it verified a loss in GDP of 30%, it happened a self-defeating austerity: austerity so
pronounces that it’s counterproductive, because the debt to GDP ratio increases rather than
decrease.
At this point it could happen a possible euro crash. The president of the European Central Bank
Mario Draghi intervenes by implementing the same policy of Bernanke, by printing money during
the credit crunch in order to save the euro.
Mario Draghi policy:
I > 0 leading LM to the right in LM’.
ΔH > 0, Δ÷
But the problem is that Draghi couldn’t do more than this, the monetary policy alone isn’t enough, it
must be implemented, because the European countries have a persistent negative output gap.
The interest rate falls to 0, but the level of output was lower respect to the potential level of
output, until the pandemic crisis (not for the Germany that was able to reach YL).
In the pandemic crisis IS moved to the left, the monetary policy remained expansionary, and the
interest rate = 0 for 9 years (2012-2021).
Today there is a change in the fiscal policy, understood the mistake, it’s implemented both the
monetary and fiscal policy already implemented in the US.
With the Recovery Plan for the first time in Europe has been centralized a budgetary policy of
Keynesian type, leading IS to the right, until we came back at least to the GDP before the pandemic
crisis.
The Keynesian plan helped offsetting completely the pandemic crisis and it is a subcess of good
budgetary policies, even if we are far from YL.
Problem: now the economy will go in a boom, so we must apply the austerity policy in order to
preserve the sustainability.
64
Open Economy
Exchange rate
So far we have considered a closed economy with no international trade and no capital movements,
which are key aspects for the globalization.
There are different waves of globalization:
1° wave after industrial revolution, involves a cut in transport costs for technological innovation.
2° wave abatement of tariffs, by developing exports and imports across the countries.
3° wave, capitalistic wave, after 80s, financial globalization: very high capital movement across
country without any important costs, so with negligible costs.
The consequences of these characteristics for the design of monetary and fiscal policy.
There are variables which are critical for the monetary and fiscal policy transmission
mechanism, the most important variable is the exchange rate.
Exchange rate (e): the price of foreign currency in terms of domestic money; ‘e’ is the number
of unities of domestic money needed to buy one unity of foreign currency ex how many euros
needed to buy one dollar.
In flexible exchange rate regimes, like euro towards other currencies, the exchange rate is
determined by the market forces, by the law of demand and supply in the currency market.
The exchange rate is subject to many fluctuations: like depreciations and appreciations.
Open economy versions of IS-LM model -- Mundell-Fleming models
We can construct several many models essentially depending on 2 dimensions.
1. Exchange rate regime:
• Completely Flexible: determined by the market forces, by the law of demand and supply.
• Completely Fixed: because of an agreement or because of the constitution of a monetary
union like euro.
Completely flexible or completely fixed are the 2 polar cases, but there are many intermediate
kind of exchange rate regimes.
2. Degree of capital mobility:
• Absence of capital mobility.
• Perfect competition: the capital market is closed to a perfectly competitive market, there
are no capital controls or transaction costs (which are all characteristics of the globalization),
and also in case of capital control (ex. India strong).
There are 4 versions of open economy IS – LM model, they are called Mundell-Fleming models,
and they focus the attention on the goods market, the money market (like IS-LM model) and the
exchange rate market.
We will study the Keynesian approach with variable prices, that gives rise to the so-called
aggregate demand and aggregate supply !" − !$ model, called in this way because it recalls the
microeconomic framework of aggregate demand and aggregate supply in a market.
Since in microeconomics it happens in a partial equilibrium perspective in macroeconomics we
should employ a general equilibrium perspective, we have to account for endogenous inflation
in our analysis.
In 70s and 80s return of Neoclassical economics in Keynesian paradigm (that dominates between
30s and 60s), also because of the stagflation.
Stagflation: stagnation + inflation, there is a recession combined with inflationary prices. It
determined the decline of the Keynesian ideas and the return of the Neoclassical theories à birth
of the modern Neoclassical economics.
1
Robert Lucas won the Nobel prices for his critique to the old Keynesian approach, in addition to
the introduction of microeconomic approach in the macroeconomic system, so we obtained the
New Keynesian models.
International Transactions in the economy
So far, we have supposed that there were no transactions with the rest of the world.
An economic system is “open” when its residents make economic transactions with the rest of
the world.
• Residents: who carry out their main economic activity within the country (consumption,
production, labor, …).
• Rest of the world: those who carry out their main economic activity abroad.
There are 3 types of international transactions in the economy:
1. Transactions of goods and services: exports and imports.
2. Transactions of capitals:
• Real capitals: the so-called foreign direct investment (like when a non-resident opens a
foreign business in Italy).
• Financial capitals: (like transaction of bonds or corporation shares).
3. International transfers: implemented by the policy of the International Monetary Founds, an
institution created after to IIWW, devoted to ensuring the financial stability in the monetary
world.
Balance of payments
All those 3 kinds of transactions between the residents and the rest of the world are recorded in
the balance of payment:
• Revenues are recorded as a plus: everything that involves an entry of money or capital income
into the country ex export or if an investor opens a corporation in the country.
• Payments are recorded as a minus: everything that involves an exit of money.
This implies that balance of payments can be positive, negative or equal to zero. This last case of
balance of payment equal to zero, corresponds to a situation of external equilibrium. But
sometimes the external equilibrium can be in contrast with a situation of internal equilibrium, that
correspond to the full employment.
Balance of payment (&! ) has 2 components:
a. Current account (&" ): records transactions of goods and services, difference between
exports (revenues) and imports (payments) evaluated in terms of the same currency.
b. Capital account (&# ): records transaction of capitals, difference between revenues and
payments associated to the transactions of bonds.
We consider small open economy: an economy whose size is negligible versus the rest of the
world. For simplicity, we neglect transactions of real capitals and transfers, so we assume no
capital mobility, thus no &# .
&! = &" + &#
)$ = *+ – - *% .
# "'
!&
= +–
.
"
"
!&
= +– /.
"
% &(
/ =
&
2
The e (in terms of euros) is multiplied by *% . (in terms of dollars), so that we obtain the difference
between exports and imports in terms of the same currency.
X: exports of goods and services.
Z: imports of foreign goods and services, and at the same time the quantity of goods and services
exported from any other country except the domestic goods.
PX: nominal value of the exports.
Pf: foreign price level, denominated in terms of foreign currency, so in terms of dollars.
$: foreign currency, it’s the mean of payment used for transactions between residents and the rest
of the world (international money).
e: nominal exchange rate, number of unities of domestic money needed to buy 1 unity of foreign
currency, it’s the price of foreign currency (ex number of € needed to buy 1$).
v: real exchange rate, index of competitiveness in the country, it measures the number of unities
of domestic product needed to buy 1 unity of foreign product.
Nominal and Real appreciation and depreciation
•
•
78 > : Nominal depreciation:
It means that more euros are needed to buy one dollar, the value of foreign currency is higher,
the euro depreciate over time.
78 < : Nominal appreciation:
It means that less euros are needed to buy one dollar, the value of domestic currency is
higher, the euro appreciate over time.
•
7< > : Real depreciation:
It’s an increase in the prices of foreign goods or a decrease in domestic prices.
It implies a gain in competitiveness, it influences positively the exports, but negatively the
imports, the demand for foreign goods decreases.
It can be driven by a nominal depreciation.
•
7< < : Real appreciation:
It’s a decrease in the prices of foreign goods or an increase in domestic prices.
It implies a loss in competitiveness, it influences negatively the exports, but positively the
imports, the demand for foreign goods increases because it’s more expensive for nonresidents, it’s good for our wealth, but less good for domestic firms.
It can be drive by a nominal appreciation.
Simplifications
To write the agents’ budget constraints and derive the Walras’ law in an open economy, may be
useful, even if not essential, some simplifications:
1. Domestic and foreign goods and bonds prices are fixed and = 1 (* = *= = 1) we assume the
price rigidity for the @A − BC model, which is the Keynesian assumption in the short run, and it
follows that e = v, it’s the nominal rigidity assumption.
* = *% = 1 ⟹ - = /
2. There are no private banks, but only the Central Bank is considered.
How the Walras’ law modifies in the presence of the rest of the world with international
transactions (now only for goods and services and still not for the capital).
I consider households, firms, government and the rest of the world, I momentarily not consider
the private banks because they are not important for the Walras’ law.
It follows the simplifying assumption: E = F, there are no money deposits.
3. Only households demand money. It follows that ΔLF = 0 (and ΔLH = ΔL).
3
4. Transactions between residents and the rest of the world concern only goods and services
(no bonds). This is the “absence of capital mobility” hypothesis (it will be relaxed).
5. The size of the economy is small with respect to those of the rest of the world. This is the
“small country” hypothesis.
Agents’ budget constraint:
Households: K + L))* + LB = M + NO– N
7P because money is a stock, not a flow. Nothing changes except the demand for money.
Firms: @ = L)+,
Government: Q + NO = N + L)-,
*
*Central Bank: L)./
+ -L$./ = LC
It tells us how money (LC) are introduced by the Central Bank. There are formally 3 ways, but in
this case are valid just the last 2 ways:
1. Finance bank: there are no private banks by assumption.
*
2. Demand bonds (L)./
).
3. Buy foreign currency by issuing money (L$./ ), it’s called central bank intervention in the
currency market.
*Rest of the world: -. – + = -(L$* – L$, )
Also written as: + + -L$* = -. + -L$,
It follows that B0 = X − eZ = e(Δ$1 − Δ$2 )
The disequilibria in the balance of payments, so in exports and imports, correspond to the
disequilibria in the currency market.
• If imports are higher than exports a > b, then the demand for foreign currency is higher than the
supply 7$3 > 7$4 ⟹ so there is an excess demand in the currency market, it happens
whenever the balance of payments c5 is negative.
• If exports are higher than imports a < b, then the supply for foreign currency is higher than the
demand 7$3 < 7$4 ⟹ so there is an excess supply in the currency market, it happens
whenever the balance of payments c5 is positive.
Walras’ law for the open economy with 5 agents and 4 markets (goods, money, bonds, exchange
rate):
(d + e + f + b– 8a– g) + (7&3 − 7&4 ) + (7P − 7E) + 8[7$"6 + (7$3 – 7$4 )] = :
Also written as: (j – M) + (L)* − L) , ) + (LB – LC) + -[L$* – L$, ]
E = K + @ + Q + +– -.
Excess demand + intervention of central bank.
In some exchange rate regime, the central bank is forced to intervene, in others not.
Equilibrium of the exchange rate market works differently according to the exchange rate regimes.
Currency market or Exchange market: -[L$./ + (L$* – L$, )]
The central bank ensures the daily operation of the currency market, selling currencies to operators
when it is demanded, and buying currencies from operators when it is supplied.
7$"6 pertains to the central bank interventions, that is its net purchases of currency.
7$3 = 7$4 market is in equilibrium, the central bank’s purchases and sales balance each other ⟹
7$"6 = :.
4
But the central bank may decide autonomously (not in response to operators’ requests) to do an
intervention in the market:
• 7$"6 > : it accumulates currency in its own currency reserves.
• 7$"6 < : it draws currency out of reserves.
Exchange Rate Regimes
Classification of exchange rate Regimes
Every country is attached to a precise exchange rate regime. The International Monetary Fund
officially classifies all the exchange rate regimes into 3 categories:
1. Fixed or Hard-pegging Regimes
The exchange rate is irrevocably fixed, so the price of foreign currencies is given. In this ERR
the central bank systematically intervenes 7$"6 ≠ : to compensate the excess demand for
currency 7$"6 = −(7$3 – 7$4 ).
Fixed exchange rates require availability of currency reserves to finance interventions implying
currency sales.
There are 3 main subcategories:
a. Currency Union:
2 or more sovereign states decide to share the same currency, losing the monetary
sovereignty. The central bank of a country draws up a treaty with the central banks of other
countries in which it commits itself to keep the exchange rates fixed;
ex European monetary union is a particular form of hard-pegging regime in which - = 1, so
the exchange rate between 19 sovereign countries belonging to the Eurozone is 1.
The major advantage to join this system is in case of a problem of inflation, we can borrow
antiflationary credibility from an external institution, from the European Central Bank, that
strictly resemble to the Bundesbank, borrowing the credibility of Germany. In this way, especially
in Italy, was eliminated the tax effects of the inflation.
b. Dollarization:
A dollarize country is a country that by law employs foreign currency to make the payments
and domestic currency doesn’t circulate ex in Ecuador, El Salvador and Panama are
countries were only the dollar is accepted to make payments.
In this way the domestic central bank can’t print anymore the money, because in these countries
it printed too much money producing hyperinflation phenomenon and it’s convenient in order
to stabilize the expectations.
c. Currency Board:
It’s a unilateral pegging, the central bank of a country unilaterally (not because of an
agreement) decides to peg (link) its currency to another currency at a given price.
Moreover the central bank cannot finance private banks and cannot buy bonds, so open market
operation by bond channel and foreign channel are ruled out.
ex Argentina in 90s unilaterally decided the fixed exchange rate 1 pesos = 1$
ex Hong Kong, 7.8 HK$=1US$
An other case of fixed exchange rate may also happen after an agreement between different
countries, so it’s not an unilateral peg, and here e = 8n, which is the par value, it’s the price of
foreign currency.
2. Intermediate Regime
The central bank intervenes whenever it believes that it is appropriate. There is the bar value 8n,
but the exchange rate is allowed to fluctuate within a fluctuation band (banda di oscillazione), in
5
this way small fluctuations are allowed, since it’s not neither a hard-pegging regime nor a flexible
regime.
There are 2 important cases in the history:
• Bretton Woods System: after IIWW was decided the intermediate exchange rate regime in
which the dollar pegged to the gold and all other currency of the world were pegged to the dollar,
previous system every currency was pegged to the dollar and were decided the fluctuations
band values. This system ended in 1971, followed by a period of flexible exchange rate regime.
• European Monetary system: introduced in EU and entered into force in 1979, another
intermediate regime. The band is country specific, there is a band for each country ex band for
Italy is very large.
3. Flexible or Floating Regime
The exchange rate is determined by the market forces, it means that it’s determined by the law of
demand and supply, moreover there is no intervention by the central bank into the exchange
rate market (7$"6 = :) and 8 = o7 (7$3 – 7$4 ) in the currency market.
• If there is an excess demand for foreign currency 8 increases, so there is a depreciation.
• If there is an excess supply for foreign currency 8 decreases, so there is an appreciation.
ex China 10 years ago had a flexible exchange rate regime, but de facto the Chinese central bank
managed the exchange rate in order to make the Chinese economy competitive, so the intervention
was Δ$CB≠0, tending to avoid the appreciation of the currency that reduces the degree of
competitiveness, by buying continuously dollars in order to push up the price of the dollar, to
depreciate its Chinese currency and to sell its goods and services to America.
For this reason, China was classified by the International Monetary Fund not as a Flexible regime,
but as an hard-pegging regime, because its Central Bank systematically intervene to stabilize the
exchange rate.
The Currency Market
8*: equilibrium exchange rate where the demand is equal to the supply p(-) = A(-), so it’s
determined by the law of demand and supply.
The exchange rate changes the value every second, the exchange rate market is very efficient,
o7 : tends to infinity.
In the very short run, there is equilibrium when we have "(8) = $(8). This equation determines
the equilibrium exchange rate -*. Graphically, it is identified by the intersection point between the
demand curve and the supply curve.
• If the exchange rate is higher than the equilibrium (8 > 8∗ ), the demand for currency is lower
than the supply ($3 < $4 ), so that the exchange rate tends to fall.
6
If the exchange rate is lower than the equilibrium (8 < 8∗ ), the demand for currency is higher
than the supply ($3 > $4 ), so that the exchange rate tends to increase.
Thus, this equilibrium is stable.
•
Bipolar Tendency
Bipolar Tendency (or bipolar view by Stanley Fisher):
It’s the historical tendency to adopt one of the 2 polar cases, the Hard-pegging regimes or the
Flexible regime. Because historically all the intermediate exchange rate regimes collapse, in
particularly because they are subject to speculative attack, buying and selling the currency in the
hope that the central bank will evaluate it (-̅ > 0). Indeed Italy during the 80s changed many times
en because of speculative attacks.
So the Bretton Woods System collapsed in 1971 essentially because of the Vietnam war, that was
financed by seigniorage: printing money (dollars), pegged to the gold, which is not infinite. So there
wasn’t a clear meeting between the quantity of dollars and the quantity of gold that effectively the
America had, and the system collapsed.
But also the European monetary system collapsed for the speculative attacks in 1992 and 1993
against Italian, French and English domestic currencies.
The fiscal and monetary policies transmission mechanisms are completely different according to the
type of exchange rate regime, if it’s fixed or flexible.
4th preliminary consideration for building the model: what type of macroeconomic adjustment
must take place in a fixed and flexible exchange rate regimes when there is not external equilibrium.
When there is not an external equilibrium, what happens depends on the exchange rate regime,
that changes in case of excess demand or excess supply in the currency market.
Macroeconomic Adjustments
1. Fixed Exchange Rate Regime
r).
In a fixed exchange rate regime 8 = 8n ⟹ (< = <
If - cannot change since it’s fixed, the only way to which the currency market is in equilibrium is by
L$./ = −sL$* – L$, t.
Mathematically the intervention must cover the excess demand or the excess supply. So in a fixed
exchange rate regime, in order to ensure that the exchange rate is fixed, the central bank must
systematically intervene in the currency market. There are 3 cases:
1. &u < : Negative Balance of payment, in deficit ⟹ no external equilibrium.
+ < -̅ . ⟹ L$* > L$, ⟹ -̅ L$./ = 7E < :
Exports are lower than imports, then there is an excess demand for the foreign currency in the
currency market.
But the exchange rate is fixed, so it’s the central bank to provide the foreign currency, to withdraw
euros in exchange for dollars.
It implies that whenever the balance of payment is negative, the central bank loses its
currency reserves, providing the foreign currency to residents withdrawing (ritirare,
prelevare) the money from the system, so euros that circulates in the economy decrease.
There must be an intervention by the central bank (7E < :), the monetary policy in a fixed
exchange rate regime is no longer independent, because the exchange rate it’s not a variable.
2.
&u > : Positive Balance of payment, in surplus ⟹ no external equilibrium.
+ > -̅ . ⟹ L$* < L$, ⟹ -̅ L$./ = 7E > :
Exports are higher than imports, then there is an excess supply in the currency market.
7
The supply for foreign currency is higher than the demand, because foreign countries demand
domestic money for their exports, demanding euros in exchange for dollars.
The central bank prints (euro) the domestic money and accumulates foreign currency
reserves.
3. &u = : Balance of payment in equilibrium ⟹ external equilibrium.
+ = -̅ . ⟹ L$* = L$, ⟹ -̅ L$./ = 7E = :
Exports and imports are balanced.
Only when there is an external equilibrium, the intervention by the central bank is equal to
zero (7$"6 = :). It means that an equilibrium must satisfy also an external equilibrium (7E =
:), and there is absence of dynamics, there is neither creation or a destruction of money
supply.
Macroeconomic equilibrium, Balance of payment must be equal to zero &u = ::
• Goods market in equilibrium.
• Bonds market in equilibrium
• Money market in equilibrium
Because only in this situation 7E = :, in absence of dynamics.
Macroeconomic adjustment in a fixed exchange rate regime involves changes in the money
supply (E), which are necessary to keep the exchange rate fixed.
Whenever the exchange rate is fixed, the money supply C is not an exogenous but an endogenous
r , it’s unknown for the system, because it cannot be exogenously controlled by the
variable E ≠ E
central bank.
Indeed the position of PE schedule is endogenous, no longer exogenous, it is no longer controlled
by the central bank, but depends on &u, the balance of payments.
If the central bank has no currency reserves, there is an exchange rate crisis.
If the central bank has no dollars there are 2 possible options:
• The International Monetary Fund lends dollars to the central bank.
• It’s necessary to establish a new 8n.
2. Flexible Exchange Rate Regime
In a flexible exchange rate regime the exchange rate is determined by the law of demand and
supply, thus by this formula:
'#
= ve[L$9: + (L$; – L$< )]
'(
L$./ = 0
⟹ 8 = ow (x$3 – x$4 )
ow tends to infinity
By definition the intervention of the central bank is equal to zero (L$./ = 0), the determination of
the exchange rate is left to the market forces. Indeed by the Maastricht Treaty the exchange rate
isn’t an objective of the European Central Bank, the exchange rate of the euro is left to the market,
the primary purpose of the European Central Bank is the price stability.
If the intervention by the central bank is equal to zero, in the budget constraint of the central bank
only open market operations remain, thus the monetary policy, thus the central bank regains
r ), which is exogenous like in a closed economy
control over the money supply E (E = E
because of the lack of the intervention.
If the intervention is equal to zero, it means that if the balance of payment is in deficit or in surplus I
don’t intervene because the variable that adjust the system is the exchange rate.
Macroeconomic adjustments pass through the movements in the exchange rate.
8
1. &u < : Negative Balance of payment, in deficit ⟹ no external equilibrium.
+ < -̅ . ⟹ L$* > L$, ⟹ 78 > :
Whenever there is an external deficit in the balance of payments, there is an excess demand
in the currency market, price of foreign currency increases and there will be a depreciation of
the domestic currency (current situation: euro depreciation).
2. &u > : Positive Balance of payment, in surplus ⟹ no external equilibrium.
+ > -̅ . ⟹ L$* < L$, ⟹ 78 < :
Whenever the balance of payments is in surplus, there is an excess supply in the currency
market, price of foreign currency decreases and there will be an appreciation of the domestic
currency.
3. &u = : Balance of payment in equilibrium ⟹ external equilibrium.
+ = -̅ . ⟹ L$* = L$, ⟹ 78 = :
Only in this case the exchange rate doesn’t vary over time.
Consequences of exchange rate variations in macroeconomy
- = /
b = b (<; g= )
)*
)*
> 0 and
>0
)+
),>
a = a (<; g)
)./
< 0 and 0 > .0 < 1
)+
The movements in the nominal and in the real exchange rate, which affect the degree of
competitiveness of a country, will influence exports and imports.
Exports depends:
• Positively to the exchange rate <. If / increases it means that there is a depreciation of our
currency, so domestic goods costs less in terms of dollars, and this stimulates exports.
Today there is the depreciation of the euro, it’s goods for the European companies because they
become more competitive.
• Positively to the foreign level of output g= , the outputs in the rest of the world. Because if
GDP in US increases, it’s good for the Europe because it will also mean an increase in
consumption of European goods, so Europe will increase its exports.
Exported quantities are an increasing function of both the real exchange rate and the world
demand.
Imports depends:
• Negatively to the exchange rate <.
• Negatively to the foreign level of output g= , thus positively to the domestic output g.
Imported quantities are a decreasing function of the real exchange rate and an increasing
function of domestic product
Current Account
Definition of current account:
&" = b– <a
9
If < increases, there is a nominal depreciation ⟹ it’s a quantity effect. In addition, imports prices
increase.
Whenever there is a change in nominal or real exchange rate (in our economy there is no distinction,
since we have assumed price rigidity, equal to 1).
What happens to the current account &" when there is a depreciation (∆< < :) of the exchange
rate, there are 2 opposite effects:
a. Quantity effect (direct effect):
Increase in exports b and decrease in imports a, the depreciation makes the economy more
competitive, decreases the domestic prices in terms of foreign currency. It tends to improve
the current account. It’s good for domestic economy, improving the GDP.
b. Price effect (indirect opposite effect):
Cost of imports a increases, and it follows the tendency of reducing the current account
In order to define which effect prevails you have to compute the partial derivative of the current
account with respect to the exchange rate:
). = + (/, M+ ) – /. (/, M)
)!? .1
)= .0 – /
−.
)+
)+
)!?
)* 2 )- +
= ."
−
− 1#
)+
)+ - )+ )* 2
)- +
> 0 and
<0
)+ )+ )* 2 )- +
−
captures the quantity effect
)+ - )+ -
– 1 captures the price effect
&" = b (<, g= ) – <a (<, g)
Current account = exports – imports
Current account enters the aggregate demand, so:
• If positive: depreciation will stimulate net exports, and then it will stimulate the domestic
economy.
• If negative: depreciation will stimulate net imports, and then it will stimulate the foreign
economy.
The current account depends:
• Negatively on the domestic income, because higher the domestic income, higher the imports,
which tends to decrease &" .
• Positively on the exchange rate, because it implies depreciation, which improves the
competitiveness of a country.
Marshall - Lerner condition
34 5
Å@ = 35 4: elasticity of exports with respect to the exchange rate, the percentage variation in
the quantity demanded, the price should increase by 1%.
36 5
: elasticity of imports in the country with respect to the exchange rate, the percentage
6
ÅA = − 35
variation in the quantity imported when the exchange rate depreciates by 1%. It’s the degree of
sensibility of the imports with respect to the exchange rate.
10
Normally the elasticity is evaluated in absolute values, so it is a positive number. It recalls the
elasticity of the quantity produced with respect to the price of the goods.
%
BC
C
B&
&
'7 "
7
% = &'"
&
The first term is not yet an elasticity, but let’s assume to start with a situation of equilibrium in current
account:
Assume b = <a
2 +
)!?
)* +
)- +
= ⟹
= ."
−
−1#
- )+
)+ * )+ )!?
= ÉD + ÉE
)+
– 1 > 0 ⟺ (if and only if) ÉD + ÉE > 1
ÅÖ + ÅA > Ü (Marshall-Lerner condition)
Å ‘eta’: elasticity (Microeconomics).
Marshall - Lerner condition (considered in the medium run):
Then a depreciation in the real exchange rate x< > : always improves the current account if the
sum of the 2 elasticities of exports and imports with respect to the exchange rate is > 1.
Because the quantity effect prevails over the price effect (if the quantity effect is very
pronounced).
When / increases, â and ä stay constant, but the cost of imports increases, so that there is a
deterioration in the current account.
•
•
•
Elasticity = 0 means that exports and imports are not sensitive with respect to the exchange
rate, in this case there is only the price effect.
As the elasticity increases, the quantity effect increases. When elasticity reach the
threshold (soglia) where the sum > 1, the quantity effect prevails over the price effect.
Elasticity < 1 quantity effect is sufficiently low, so the revenues of the firm before increase and
then reached the maximum decrease.
In the flexible exchange rate regime we shall assume a linear function:
). = nn
)nn
. – äM + É/
ä>0
É>0
Å: a positive coefficient that applies if the Marshall Lerner condition is satisfied in flexible exchange
rate cases.
4 versions of the Mundell-Fleming Models
The role of fiscal and monetary policies crucially depends on:
• The exchange rate regime: in different regimes there are radical differences.
• The degree of capital mobility.
Assumption of absence of capital mobility (the first 2 models) isn’t realistic, because of the
globalization the financial markets are strongly integrated.
Any Mundell-Fleming Model can be described by a system of 3 equations, that change across
different models, and also the unknowns also change, depending on the 2 dimensions of exchange
rate regime and capital mobility.
1. Fixed ERR and No capital mobility
11
Small open economic assumption: what happens abroad affects what happens in the domestic
economy, but not vice versa, because the size of the economy is assumed to be negligible in terms
of the world economy.
&" = &#
r Fixed exchange rate
<=<
(e$)
ã (PE)
(&&)
ensures åççéè êëíìwî equilibrium
ensures êçówò êëíìwî equilibrium
ensures wôîwíóëö and õúííwóõò êëíìwî equilibrium
(ñ = g)
(P = E)
(&u = :)
•
e$: derive the @A in an open economy. Recall @A the solution of the income expenditure model in
the presence of endogenous investments.
Now inside the aggregate expenditures there are also exports and imports. b exogenous
because they are a function of /̅ , which is exogenous, and of M+ , which is exogenous for the
small open economic assumption.
•
r , no
PE: same of closed economy, but one important difference, now E is endogenous, not C
more exogenously controlled by the central bank.
•
&&: exports = imports, no need for central bank intervention. There is no capital mobility )F ,
then I have the equalities:
)$ = ). + )F
)F = 0 ⟹ )$ = ).
)$ = 0 ⟹ ). = 0
Solving the system, I obtain:
M = ù[û̅– üO]
1
† = 1−:(1−;) + 5I = ; 0 < m < 1
r = (K̅ + cNO
nnn − cNn) + @ ̅ + Q̅ + b
r−<
r
ra
!
°: marginal propensity to import out of income, the derivative of a with respect to the domestic
income, tells about the increase in income if the domestic income increases by 1€.
So qualitatively speaking nothing changes, but quantitively there are 2 main differences:
1. Keynesian Multiplier † is lower than in a closed economy, because of the dispersion effect
that decreases the size if the Keynesian multiplier.
If a component of the aggregate demand increases, like the investment component, then are
stimulated the aggregate demand, the aggregate supply and the income. But now people not
only have to pay taxes before consuming, but also the increase in income doesn’t translate fully
in the demand for the domestic goods, because according to the marginal propensity to import,
a part in the increasing income goes in the purchase of foreign goods ⟹ dispersion effect.
r autonomous expenditures definition changes, now exports and imports enter the
2. !
autonomous expenditures.
If there is an increase in exports + > 0, it translates in an increase in autonomous expenditures
in a fixed exchange rate regime (important for the exercises).
If there is an increase in imports . > 0 generates a decrease in autonomous expenditures.
1° version of Mundell-Fleming Model:
r – ¢£]
(e$) g = † [ !
ã(PE) E = §g − •£
r=<
r + °g)
(&&) b
r(a
12
There are 3 equation and 3 unknowns only endogenous.
The only endogenous variable is M, it means that it can be solved immediately, only looking at the
)) schedule.
We suppose exogenous exports + = +n and the linear relationship between the imports and the
domestic income . = .̅ + äM.
). = +– /.
). = 0
). = +n– /(.̅ + äM) = 0
Solution for the level of output:
g∗ = gJK =
> ?5
>
4
>6
5
>=
gJK : level of output that ensures that &u = :, so equality between exports and imports, it’s the
external equilibrium, doesn’t always ensures also the internal equilibrium, which correspond to the
full employment in the labor market.
It’s a reduced form, the endogenous variable of our interest depends only in parameters and
exogenous variables.
g∗ is neither affected by fiscal variable, nor by monetary variable.
So under a fixed exchange rate regime:
3@∗
3@∗
=
=:
>
3B
3C
This means that if the government tries to stimulate the economic activity, by increasing Q, or if the
central banks tries to print more money by financing banks or via open market operation, both fiscal
and monetary policy, that have a significant effect in closed economy, here with a fixed ERR and
no capital mobility have no effect, are neutral.
There are only 2 shocks that are able to increase the level of output:
• Increase in exports.
• Reduction in imports.
So the GDP is determined by external variables, and cannot be influenced by economic policies.
Capability of the central bank to influence the level of economic activity in a discretionary behavior
r for a fixed ERR.
is impossible because the central bank is committed to ensure the parity < = <
1° version of Mendel-Fleming model, graphical representation:
It’s convenient to draw before the BB line: locus of point exports = imports, only along the )) line
the balance of payments is in equilibrium.
Only in the intersection point E the 4 markets are in equilibrium.
13
There is only one level of output gJK compatible with the external equilibrium, this implies that the
line is vertical.
On the horizontal axis we have the domestic GDP.
• Imports depends positively on the domestic GDP.
• Exports depends on the foreign GDP.
So whenever the GDP is larger or smaller than the equilibrium, since respectively imports or
export are higher, then the balance of payment in disequilibrium
•
On the right side of the && line:
Balance of payments in deficit &! < :.
Imports are higher than exports ⟹ ∆¶ < : people want foreign currency, and central banks
gives them to them, losing currency reserves and withdrawing money to the economic circuit.
If for some reasons the equilibrium is to the right, the LM changes endogenously the position
because of ∆M < 0, shifting upwards in PE′.
•
On the left side of the && line:
Balance of payments in surplus &! > :.
Exports are higher than imports ⟹ ∆¶ > : nonresidents want our domestic currency, so they
change at the central banks gives foreign currency for domestic currency, and the central bank
accumulates foreign reserves, in exchange for domestic money, there are more money in the
economic circuit.
$ > &)
Fiscal policy (∆#
The government usually increases ∆Q̅ > 0 when MLM is lower than the potential level of output, to
the full employment, so there is a negative output gap. It’s not always sure that in MLM there is
domestic equilibrium, which is a situation of full employment in the labor market.
By the expansionary fiscal policy ∆Q̅ > 0:
•
e$ translate upwards to the right in @A N , like in a closed economy.
The P point corresponds to the closed economy equilibrium, but not to the open economic
equilibrium, since L is in &u < : the area of deficit balance of payment, because when income
increases, people also buy foreign goods, this is the reason why people need foreign currency
from the central bank.
•
As consequence the PE position doesn’t change exogenously but endogenously, translating
upwards to the left in BCN . So it’s reached a new equilibrium point E1 between &&, e$N , PEN .
g is not affected because of the increase in £, that crowds out the level of investment because:
M = C + I + G + ).
∆@ =– ∆Q̅
14
The fiscal expansion generates a decumulation of currency reserves, a decrease in money supply,
leading to a further increase in interest rate that completely crowds out the level of investment,
which also occur in closed economy, but it’s amplified in an open economy.
Monetary policy (∆' > &)
The central bank tries to print money and finance banks with the expansionary monetary policy
by increasing the money supply ∆E > ::
•
PE line translates downwards to the right in BC’ until the new equilibrium point P, which is
the closed economy equilibrium, where the M is higher and O is lower and this stimulates the
investments, thus the Keynesian effect.
•
The increase in investments in the short run makes the balance of payments falls into deficit
&u < : and again ∆¶ < :. In this case residents needs foreign currency in exchange for €, so
the money printed by the central bank comes back to the central bank. The equilibrium come
back to the initial level (money creation is destroyed by the foreign channel).
It happens the Keynesian effect:
For the reduction in the interest rate £, because there is too much liquidity E.
Then people buy bonds, reduction in interest rate, which stimulates the level of economic activity,
bringing the economy in an external deficit in the balance of payments, so that residents need money
for the imports and the central bank loses money.
So that the PE line translate back in the original position, and also the equilibrium goes back
from P to E.
Sterilization policy and Currency crisis
The movement in the exchange rate can be a policy that leads the system to the full employment,
like in B. (Remark) there is one way to reach P point.
Sterilization policy: stabilize BC schedule in the position PE’ is possible by printing
continuously money in a systematic way, neutralizing the endogenous movement to the left
because the balance of payments falls into deficit.
Problem: in P balance of payments stays systematically in deficit, and it’s not possible for a
country, because it would be necessary continuous interventions in the currency market, losing
continuously currency reserves.
But at some point, currency reserves will finish (I can continuously print domestic money, but I
cannot print foreign currencies), then the country will have to abandon a fixed exchange rates
regimes, because without currency reserves the intervention by the central bank is zero.
15
Currency crisis: may occur at this point, it’s a crisis of the fixed exchange rate regime, when
currency reserves end up, precisely it doesn’t happen when the currency reserves are equal to
zero but right before (by Paul Krugman). It happens before because if I know that the policy will be
staying in B, so implement a permanent deficit in difference of payment, the speculators anticipate
the end of the currency reserves, so there is a speculative attack as the central bank declares to
continuously print money. So this policy is inconsistent with the external equilibrium.
Conclusion: I can only temporally stay in P, not permanently. If I want to always remain in B it’s
necessary to change the regime, moving to a flexible exchange rate regime.
2. Flexible ERR and NO capital mobility
In a flexible exchange rate regime:
• The exchange rate depends on the excess demand in the currency market, which implies an
immediate depreciation in the exchange rate.
Exchange rate is determined by the Law of demand and supply, which applies
instantaneously in the market, so current account is always in equilibrium. It changes in order
to restore the instantaneous equilibrium.
If ov tends to infinity, the adjustment in exchange rate is almost instantaneous, so that the
current account is always in balance and the demand for foreign currency is always equal to
the supply.
r is exogenously controlled by the central bank since the intervention
• The money supply E
is zero by definition, it’s because there is no the external channel to introduce money, now only
by bonds or by financing credit companies.
<̇ = o<(∆$d – ∆$s) ⟹ &" = :
/̇ derivative of / over time
r ⟹ ∆$"6 = :
E=E
The euro is in a flexible exchange regime with all other currencies.
It’s the case of the European Central Bank, that by the Maastricht Treaty doesn’t try to influence
the value of the euro, and only cares about price stability.
2° version of the Mundell-Flaming Model:
r − ¢£]
(e$) g = †[!
r = §g − •£
ã(PE) E
nnnn
(&&) &" = &
" – °g + Å< = : ¨ó w≠ú¨ö¨Æí¨úê
Ø: measures the influence of the exchange rate on the current account.
•
•
IS schedule: exactly the same as the closed economy.
r because no intervention by the central bank, it’s exactly the same as the
BC schedule: E
closed economy.
We assume that now the Marshall-Lerner condition is satisfied ⟹
)!O
>0
)+
r + m2 M
r
Y* = m1 A
/∗ =
D, ∗ ? EEE
!O
F
The solution M ∗ is given by the closed economy solution, that also applies in a flexible exchange
rate regime, so by the first 2 equations. This implies that all the consequences for the design of
fiscal and monetary policy remain unchanged.
16
The exchange rate depends positively to the level of output.
Depreciation in the exchange rate is the channel that makes the policy effective, this channel is
not present in a fixed exchange rate regime because in the 1° model it’s exogenous.
G+ ∗
D G, ∗ D
=
= m >0
>
> F 1
GH
F GH
G, ∗
m1 = >
GH
In case of an expansionary fiscal policy, if the government increases the public spending,
increase in the level of output, it tends to deteriorate the current account, so there is an excess
demand in the currency market, it generates the depreciation, which restores the external
equilibrium.
G+ ∗
D
=
m2 > 0
>
GI
F
If there is an expansionary monetary policy it’s the same: output increases, income increases,
stimulating the imports and generating an excess demand in the currency market which leads to
a depreciation in the exchange rate.
In case of an expansionary monetary policy the investment increase, in this version of the model
everything works as in the closed economy, the )) determines only the exchange rate that makes
the external equilibrium compatible with the domestic equilibrium.
The && line is vertical because it’s endogenous, depends on the exchange rate, since it depends
on M and not on O.
• In case of deprecation, && shifts to the right.
• In case of appreciation, && shifts to the left.
The intersection between e$ and PE gives g, their position is exogenously controlled by the
fiscal and monetary policy. Then the )) residually determines the equilibrium exchange rate / ∗ .
In the version 1 it’s the opposite: )) exogenous and BC endogenous, and M was determined by the
)).
The full employment can be reached by fiscal and or monetary policy, in the graph are applied both.
The increase in the level of output leads to a shift of the && line on the right in ))’ because of the
depreciation.
In a flexible exchange rate regime, all the Keynesian conclusions remain unaffected, for this
reason Friedman prefers a flexible exchange rate regime over a fixed exchange rate regime. It’s
because in a fixed exchange rate regime the policy makers cannot influence in a discretionary way
the equilibrium level of output. Only if the exchange rate is determined by the market, the exchange
17
rate, as a sort of invisible hand, depreciates whenever there is an expansion balancing the current
account.
There are 2 limitations in this framework:
1. Here financial markets are not integrated, since we have assumed no capital mobility. It’s a
relevant problem since it doesn’t include the financial transactions of public bonds for example.
2. It doesn’t account the inflation, since it’s considered a model with nominal rigidity, the inflation
is exogenous.
Advantage: fixed exchange rate regime can be desirable for country that have experienced in the
past strong inflationary pressure or even hyperinflation phenomenon.
Fixed exchange rate regime eliminates the monetary policy discretion and the inflation tax. So there
is a trade-off (scambio) between stabilizing the level of output and stabilizing the level of inflation.
• Flexible exchange rate regime can stabilize the economy, but can generate the inflation.
• Fixed exchange rate regime can stabilize inflation, but can display involuntary unemployment.
So every country will choose an exchange rate regime based on their preferences.
The Perfect Capital Mobility
Perfect competition:
There is a large potential infinite number of buyers and sellers.
There are price takers, that are too small to influence the price of the good.
There is no imperfect information, everyone knows everything, all prices and qualities.
The goods are homogeneous, there is no qualitative differences among the goods.
There is free entry and free exits.
There are no transaction costs.
Perfect capital mobility in the capital market, assumed to be a perfectly competitive market,
defined by:
• Capitals can be moved across countries without any transaction costs, free movement of
capital.
• Price for any good should be equal, firms should sell the goods at the same price, if goods are
homogeneous, information is perfect, buyers and sellers are price takers.
• Goods are homogeneous so it’s the same for the financial market. Foreign bonds &= (whose
return is £= ) and domestic bonds & (whose return is £) are perfect substitutes, there is no
difference (perfect substitutes: linear indifference curve).
Since all the bonds have the same risk properties, then they have all the same interest rate.
£ = £= it’s exogenous, it’s determined by the rest of the world.
Interest rate and Balance of Payments
Bonds supplied by both government, to finance the deficit, and firms, to finance investments.
Suppose O > O+ and the market is perfectly competitive with no transaction cost, then our bonds
have a higher rate of return. It implies a capital inflow towards the country: nonresidents want to
buy our domestic because the bonds have a high rate of return. This phenomenon leads to a
potential infinite improvement in the capital account &# .
£ > £= ⟹ ∆&# > : ⟹ &! > :
∆Bd > 0 ⟹ ∆*ü > 0 ⟹ ∆O < 0
O = O+
Starting from a situation of positive differential in the interest rate £ > £F the capital inflow ∆&# >
: generates a reduction in the interest rate because stimulates prices for bonds.
Because of the assumption of perfect competition, all speculators and investors move the capital
towards the country, leading to a surplus in the balance of payments )$ > 0 for any )C, because
nonresidents buy our bonds and ∆)d increases.
18
Because of the increase in the demand, the price for bonds increases, then the interest rate will
decrease.
This capital inflow is effective, is operative until it’s restored the equality £ = £= , also called
absence of arbitral opportunity.
This absence of arbitrage activity allows the investors to make profits without any cost, and it happen
when £ > £F.
£ < £= ⟹ ∆&# < : ⟹ )$ < 0
∆)s > 0 ⟹ ∆*ü < 0 ⟹ ∆O > 0
O = O+ (Arbitrage mechanism)
The opposite occurs when O < O+ , then foreign bonds pay higher interest rate and there is a capital
outflow ∆&# < : towards the rest of the world.
Sell domestic bonds to buy foreign bonds, the balance of payments falls into deficit, prices decrease
and it’s increased the interest rate, until it’s restored the equality £ = £=
Only if £ = £= , then &! = :.
£ = £= is an equilibrium condition, it means that if it’s not satisfied, in the market for bonds there
will be endogenous competitive mechanism able to lead towards the equilibrium, so the equilibrium
is stable.
The condition O = O+ will be the && schedule, since it’s the condition that ensures that the balance
of payments is in balance. Balance of payments can be equal to zero if and only if there is the
equality between the interest rate and the foreign interest rate.
If this condition is not satisfied, then there will be a huge potentially infinite capital outflow or capital
inflow that leads in a surplus or in a deficit of the balance of payments.
!!! When O = O+ ⟹ )F ≠ 0, only ∆)F = 0.
Since )$ = 0 ⟹ )F = −).
Saving and current account
Saving definition:
A = M + NO − N − K
In open economies, the equilibrium output is:
g = d + e + f + &¥
$ = e + " + &¥
In open economies, households finance firms @, the State p, and the rest of the world )µ.
When )µ < 0, the rest of the world contributes to financing @ and p.
In open economy $ = e.
If and only if " = : and &¥ = :.
Saving takes the form of bonds purchase.
When )µ > 0, households lend to the rest of the world by buying foreign bonds.
&# = −&"
3. Fixed ERR and Perfect capital mobility
It’s a more realistic assumption because of the capital mobility.
3° version of the Mundell-Flaming Model:
r − ¢£]
(e$) g = †[!
ã(PE) E = §g − •£
(&&) £ = £=
19
)$ = ). + )F = 0
&! = : ⟹ &" = −&#
•
•
•
@A schedule: the usual one.
BC schedule: usual, E is endogenous variable because we are in a fixed exchange rate
regime.
)) schedule: the only one to change, condition of neither capital inflow, nor capital outflow are
operative.
Now ). can be different from 0 (&" ≠ :) in equilibrium and the balance of payments is equal to
zero (&! = :).
There are 2 sources of transaction: transaction of goods and services and transaction of bonds,
so there can be a surplus or a deficit in the external equilibrium.
Solution:
r − ¢£P ]
Y* = ê[∂
), ∗
=ù>0
)J̅
∗
),
=0
>
)L
Fiscal Policy
•
•
Region above: interest rate is higher than the foreign interest rate O > O+ , so there is a capital
inflow, so the balance of payments is positive ()$ > 0), and the central bank prints more money,
requested by the nonresidents (∆C > 0).
Region below: interest rate is lower than the foreign interest rate O < O+ ,, there is a capital
outflow so the balance of payments is negative ()$ < 0), and the central bank receives back
the money previously printed (∆C < 0).
r > ::
Suppose an expansionary fiscal policy 7f
• @A moves to the right in e$′.
The new point E1 is the closed economy equilibrium, not open economy equilibrium, because
there is a capital inflow that leads to a surplus in the balance of payments )$ > 0, so that the
central bank accumulates currency reserves and must print money ∆C > 0.
The level of interest rate is unchanged because of O = O+ , thus also the level of investment is
unchanged ∆@ = 0.
•
So the fiscal expansion makes also the BC shifts endogenously to the right in PE’.
In the new point P there is not the crowding out effect investments, the expansion is higher than
in a closed economy thanks to the capital inflow.
In this model fiscal policy is effective, it’s even more effective than in a closed economy because
there is no monetary retroaction effect, there is no crowding out effect in investments. It’s
20
because in equilibrium £ = £= , the interest rate is pinned down by the foreign interest rate, so cannot
increase in equilibrium because of the perfect capital mobility.
Fiscal policy is very important in a fixed exchange rate regime, also in the European monetary
union, because the nations have no monetary sovereignty, but conserve the fiscal sovereignty,
it’s up to each single country. So a discretionary fiscal policy is very important to reach the
domestic equilibrium.
Problem of EU: fiscal policy is constraint by very strict fiscal rules in Maastricht Treaty which
prevents what it’s shown in the graph above, and actually are subject to a revision.
A big problem for the short and long run stabilization of the economy is the policy. The European
members can receive money for the fiscal policy only if these are approved before by the EU.
Monetary Policy
If the central bank tries to print money ∆C > 0:
• The BC translates to the right in PE’. The intersection point E1 is not the open, but the closed
economy equilibrium.
The interest rate £ falls and there is a capital outflow, we sell our domestic bonds because
they pay a lower interest rate and buy foreign bonds. The capital outflow generates a deficit in
the balance of payments )∑ < 0 and a reduction in the money supply ∆C < 0.
•
The PE′ shifts back to the previous position. So the monetary policy is completely neutral,
investments remain unchanged (the destruction of money by the foreign channel is extremely
rapid).
Monetary policy is neutral because the solution is obtained only by substituting O = O+ into the @A
schedule. Only the fiscal policy is effective in a fixed exchange rate regime.
4. Flexible ERR and Perfect capital mobility
•
•
•
@A schedule: the relevant difference. Now I have to consider also &" , that depends on the
exchange rate, then I have a new equation coming from the current account function. Here the
exchange rate influences the current account, which is part of the aggregate demand, that
influences the supply.
So an increase in < (depreciation) generates an improvement in the current account &" ,
imports decrease and exports increase, this stimulates the Keynesian multiplier, having a
positive effect on the level of output.
So in this case the e$ schedule is endogenous because its position depends on <, on the
exchange rate, which is endogenous and determined by the law of demand and supply.
BC schedule: in a flexible exchange rate regime the money supply is exogenously controlled by
the central bank, which doesn’t intervene, so the E is exogenous.
)) schedule: remains the same.
4° version of the Mundell-Flaming Model:
21
r − ¢£ + Å∏]
(e$) g = †[!
r = §g − •£
ã(PE) E
(&&) £ = £=
Solution, mathematically obtained from the BC, substituting )) in BC:
M
N
r+
g* = E
O
£
N =
Monetary policy
Now M is influenced by the money supply. In a flexible exchange rate regime with perfect capital
mobility, monetary policy is effective, and fiscal policy not (opposite respect to the fixed
exchange rate regime).
•
•
Above && line: surplus of balance of payments ()$ > 0) because the interest rate is higher
(O > O+ ), but now the capital inflow is the demand for our money which leads to an appreciation
for the currency.
L/ < 0 because when there is capital inflow nonresidents sell their currency to buy our money,
so there is an excess supply in the currency market, that leads to a depreciation in the price of
foreign currencies.
Above && line: deficit of balance of payments ()$ < 0), there is a decrease in the interest rate
(O < O+ ) that generates a capital outflow, we buy foreign bonds, we buy foreign currency, their
price increase, our currency depreciates and the exchange rate depreciate L/ > 0.
In the case of an expansionary monetary policy 7E > ::
• PE translates to the right, M increases, this leads to a decrease in the interest rate in a closed
economy because of the Keynesian effect, so our bonds pay a law interest rate and there is a
capital outflow to buy foreign bonds, so residents demand foreign money.
The capital outflow leads to an excess demand in the currency market, thus a depreciation in
the exchange rate L/ > 0. The transmission mechanism passes through the depreciation in the
exchange rate, via the bonds market.
The currency depreciation is good for our economy because it makes our economy more
competitive, then exports increase and imports decrease.
Investments remain unchanged (the interest rate does not vary, only the exchange rate
increases).
•
If the Marshall-Lerner condition holds, ). increases (current account) triggering the multiplier,
which leads the e$ schedule to shift to the right, so that the central bank can reach the full
employment level of output.
The monetary policy in a closed economy is effective, it stimulates the investment, due to the
reduction in the investment rate.
22
The monetary policy transmission mechanism in an open economy works through a depreciation
in the exchange rate, which stimulates the component of the aggregate demand of the current
account, the net exports.
The nowadays euro Depreciation is good for us because it stimulates our exports, we become more
competitive. Problem of the structure of the Italian economy is based on the energy import, it implies
that in case of depreciation we pay more, so the marginal cost of firms increases and there is
inflation.
Fiscal policy
Transmission mechanism in case of an expansionary fiscal policy LQ̅ > 0:
• @A shifts to the right in e$’, so the interest rate tends to increase, reaching the closed economy
equilibrium C1, but it’s not an open economy equilibrium because as the interest rate increases.
It’s determined a capital inflow that generates a surplus in a balance of payments and an
appreciation of the currency, which decreases the current account, so there is a different
crowding out effect. While in a closed economy an expansionary fiscal policy crowds out the
investment, in an open economy any expansionary fiscal policy crowds out net exports (not
investments??) by the 100% ⟹ L). = −LQ̅ .
Fiscal policy is not effective. Any variation of the autonomous expenditure (̅ will be vanished by
a variation in the opposed direction of net exports triggered by the exchange rate
The Monetary policy could be used to stabilize the economy way more than the fiscal policy.
Twin deficit problem
r
7&" = −7f
r determines a deficit in:
It’s called twin deficit problem because 7f
• Domestic public deficit.
• Deficit in the current account (imports > exports) in an open economy with a flexible
exchange rate regime.
It’s the problem of the US since 80s, Reagan implemented a strong tax cut in order to try to stimulate
the level of economic activity and a at the same time generate an increase in production and income
in a way that generates revenues that decreases the deficit by Laffer. But this idea was wrong, the
deficit increases, generating an appreciation of the dollar towards other countries, which generates
a deficit in the current account, imports > exports. Since this period until now ). is strongly negative,
so in equilibrium the )F must be positive, and this disequilibrium in the current account in deficit
works only if the US has a capital inflow ()F positive), traditionally financed by China that has a
current account surplus. This form of equilibrium could collapse according to some economists.
The AD and AS schedules
23
with Perfect Competition
"# – Aggregate Demand
One important assumption: endogenous prices, they are variable.
It’s introduced a new variable: the price level (πQ ), strictly correlated to the inflation. In every
macroeconomic model, once * is a variable, understand the distinction between:
• Nominal variable.
• Real variable: the nominal variable divided by the price level, it gives the purchasing power
of money.
The decisions of economic agents depend on real variables, not on nominal variables. By the
rationality assumption: there is no money illusion, it means that people care about real
variables and not nominal variables. Indeed real consumption depends on the real disposable
income.
Old notation used until now indicate real variables. There is only one variable that remains
nominal: the money supply, which is the quantity of euro that circulates in the system.
How @A − BC model modifies in a closed economy when the price become a variable.
(@A) M = ù[û̅ − üO]
RRR
∫
P
(BC)
= ªM − ℎO
&
•
@A schedule: doesn’t change, so far no distinction between real and nominal interest rate. Here
we assume that the interest rate is both the real and the nominal interest rate.
There is an important distinction:
íwëö ¨óîwíwèî íëîw = óçê¨óëö ¨óîwíwèî íëîw – ¨óΩöëî¨çó íëîw.
But now we are not working on inflation, but only on price variations.
•
BC schedule: it changes in one dimension. The position of the schedule depends on the price
level. It’s the equality between the real money demand and the real money supply; the right side
is the demand for real money, also called demand for real money balances.
We have 3 variables M, C and * in 2 equations, so we can’t solve it and determine the equilibrium
level of output, so we have to develop a theory for the determination of the price level.
Solution of the income expenditure model:
RRRR
r + †T C
(!") g = †S !
Q
The real money supply affects the real GDP. In order to know the equilibrium level of output, I
must know how is determined the price. I have a schedule, a negative relationship between M and
*, it’s the equation of an hyperbole, in macroeconomics it’s called !" schedule, the aggregate
demand schedule, which is the solution of the e$ − PE model with variable price, and it’s named
in this way because it reminds the demand schedule of microeconomics which is negatively
sloped. There is one equilibrium level of output for each price level.
ûp is negatively sloped essentially for 2 reasons:
1. Keynesian effect.
2. Pigou Effect.
These 2 effects are the transmission channels that explain the impact on the real production
triggered by a variation in money supply or by a variation in the price level.
Keynesian effect
The initial price level is assumed to be πU , then I draw the position of @A and BC given for *V .
There is one BC for any price level.
24
When the price is *V , then the equilibrium level of output is MV and it corresponds to the
intersection point between @A and BC when * is equal to *V .
Suppose a decrease in the price level πS , then an increase in money supply
>
C
driving the
Q
Keynes effect, and there is an improvement in the purchasing power of money, the real money
supply increase, PE shifts to the right.
A decrease in the price level increases the money supply like an expansionary monetary policy.
It’s like if the central bank prints money, because if we print money and the price level is constant,
then our purchasing power improves; if the money is the same and the price falls, then our
purchasing power improves. So the purchasing power improves in case of:
• An increase in the numerator.
• A decrease of the denominator.
It captures the interaction between the money market and the bonds market.
If in this situation there is too much liquidity, people will buy bonds )* , increasing prices for
bonds *ü, decreasing the interest rate O, stimulating the investment @, (component of the
aggregate demand), triggering the Keynesian multiplier ⟹ this is the Keynesian effect.
Conclusion: lower the price level, the higher the level of output, because of the Keynes effect.
Problem of the mechanism: if the prices fall even further, then the BC shifts on the right until the
interest rate is zero, so the Keynes effect meets the zero-lower bound problem, but the interest
rate cannot be below the zero lower bound, it cannot be negative.
It implies that the Keynesian effect works until the reduction in the price level brings the interest
rate is zero, then there is the liquidity trap problem, and the output cannot increase more, it
reaches its maximum.
As the price falls, also the intersection points are moving gradually to the right and down,
assuming the movement of a curve, it is the ûp aggregate demand schedule.
This mechanism is called Keynesian effect, that is triggered by the reduction in the price level,
which generates a disequilibrium in the money market. Real money supply
real money demand B if prices fall L* < 0.
>
L
is higher than the
"
RRRR
C
7π < : or 7E > : ⟹ Q > P ⟹ L)* > 0 ⟹ L*ü > 0 ⟹ LO < 0 ⟹ L@ > 0 ⟹ Lj > 0 ⟹ LM > 0
Wealth effect or Pigou effect
The second effect explains why the aggregate demand !" should be always decreasing, by
Arthur Pigou, Keynes’ professor. What happens on the level of real wealth.
Wealth: sum of all the stock variables, and in reality also houses, not included in our case.
Wealth is different from the GDP.
Wealth =ø + ) + C
25
R+P
Real Wealth = ø +
&
¡: all the capital stock in means of production
&: all bonds
E: all money
) and C are in nominal terms, so the real wealth is over *. Indeed the real wealth, especially the
bond wealth and the money wealth, depends on the price level.
Wealth effect or Pigou effect: If the price level decreases, then the real wealth, the stock of
bonds and stock of money tend to increase, and consequently also the consumption increases.
Being consumption part of the aggregate expenditures j, then also the GDP increases.
7π < : ⟹ L
R+P
> 0 ⟹ 7d > : ⟹ Lj > 0 ⟹ LM > 0
&
If we include the real wealth in the Microfounded theory of consumption, it is shown that the
consumption not only depends on the expectations for the future level of income, but
depends positively on the stock of real wealth.
If the wealth effect is operative, even if we are in a liquidity trap and the price falls, the
consumption increases, the level of output increases, and it implies that the e$ moves to the
right.
For Pigou theory the liquidity trap is not a problem, if it’s coupled with deflation, because
deflation triggers an increase in the real wealth, thus also in the consumption.
If both the Keynesian effect and the Pigou effect are assumed to be operative, the aggregate
demand ∂¬ schedule always decrease for any price level, so it is always a decreasing line.
(ûp) M = ùW û̅ + ùX
RRR
P
&
),
= ù1 > 0
)J
),
SZ
=
>0
)L
"
"% – Aggregate Supply
We have to get the relationship between M and *, in order to obtain simultaneously the equilibrium
level of output and the equilibrium level of price. For this result is necessary to know what
determines the price level.
It must be studied firms’ behaviors, since they are price makers. Objective of firms: maximize
profits, not create work.
Then I can obtain the aggregate supply ûA schedule, which is a second set of combination
between prices and output along which firms choose prices for maximizing profits.
So to derive an aggregate supply !$ schedule are necessary:
• The market structure that prevails in the economy.
• The production function, for the level of technological procedures that transform inputs in
outputs.
Assume for simplicity that all the GDP is supplied by perfectly competitive firms. Keynes
wouldn’t like this assumption, but momentary it’s useful.
If firms are equal, I can normalize the number of firms √ to 1. Firms are price takers because
they are too small for influencing the price, the price of the output * is out of their control, the
firms’ choice variable is the quantity produced M,
In this model prices are endogenous, but the nominal wage is still assumed to be fixed by
contract.
26
Profit Maximization
To know the equilibrium level of output we have to know how the price level is determined. ⟹ it’s
necessary to analyze the problem of the representative firm operating in a perfectly competitive
market: choose M in order to maximize profits, * is given from the standpoint of the firm, since
firms are price takers.
Locus of point π − g along which firms are maximizing their profits.
max
≈ = NO − Nµ
r √ − K+
M = *M − ∆
∫
subject to M = »(√) = √ [ ; 0 < … < 1
£: total revenues.
¥: total costs, fixed costs + variable costs.
À: Number of works employed by the firms.
d= : fixed costs, it includes for ex the cost for capital.
Ã: elasticity of output with the respect to the labor input.
Profits are defined as total revenues – total costs.
Short run: (this case) not all costs are variables, some ones may be fixed.
Long run: all costs are variables.
The variable cost is the cost of labor.
This maximization is subject to the production function, the marginal productivity of the variable
input is decreasing.
Short run production function in a perfectly competitive market: is increasing and concave,
translates the input into output, for any quantity of input there is an output.
When one input is fixed the production function is constant in the short run, it cannot change.
In macroeconomics it is important the notion of the marginal (derivative) productivity of the input,
marginal implies the presence of derivative:
Marginal productivity of labor:
),
= Õ N (Œ)
)T
•
•
It measures the increase in the level of output if the firm hires one worker more.
It is the slope of the production function, and when the slope is increasing and concave it
decreases. So the marginal productivity is positive but the marginal increase is decreasing.
Common assumption in macroeconomics with a perfectly competitive market: when in the short
run one input is fixed and one input is variable, then the marginal productivity of the variable input
is decreasing but the quantity of the input increases, until the slope converges to zero. This
explains why the marginal cost is increasing.
It is a constraint-optimization problem, we can use Lagrangian function.
There is an objective function given by the definition of profits as the difference between total
revenues and total cost, and subject to the production function that links the output to the only
variable input in the short run, which is given by labor.
So the capital stock in the short run is given as microeconomic teaches us, so the capital stock
can be normalized to 1.
27
… is an elasticity, so it’s a percentage variation, a variation between 2 percentage rates.
… is lower than 1 because the production function is concave, if it was higher it would have been
convex.
…=
B\
\
B]
]
=
UV W
W
= αN^_W ` = …
UW V
W
Solution of the system:
!
√ = M"
!
r M " − K+
≈ = *M − ∆
max ≈ ⟹
RRRR
[
RRRR
'X
Y !#"
= 0 ⟹*− Z M " =0
',
$#%
π = \ g % profit maximization condition
E£ = E¥
CO = *
RRRR
Y
Cµ = Z M
!#"
"
E£: marginal revenues, increase in total revenues if I sell one good more.
E¥: marginal cost.
We solve the production function by √, substituting into the profit function, we get an equation in
which only M appears as the only variable.
We solve the problem in the system by converting the production function.
The firm maximize profits when the derivative of ≈, respect the derivative of M is equal to zero. The
profit function is a function only of M that is at its maximum when the derivative is zero.
The profit maximization condition according to which, in a perfectly competitive environment, the
marginal revenues is equal to the price (in a perfect competition) and to the marginal cost.
The marginal cost is increasing in M because we have assumed … < M, because we have
assumed that the production function is increasing and concave.
Standard Macroeconomic condition: marginal costs depend on the price of the input and
positively to the level of output.
Aggregate supply schedule (!$): profit maximization condition of microeconomics (E£ =
E¥) given by marginal revenues equal to marginal cost. (in the short run the marginal productivity
of labor is decreasing, given a capital stock).
"# − "% Model
The aggregate demand and aggregate supply !" − !$ model is the 3° Keynesian model and it’s
also called Keynesian-Neoclassical synthesis, since we can see the difference between the
Neoclassical and the Keynesian approach.
nn of short-run rigidity in the nominal wage:
The model is based on the essential hypothesis — = n—
RRRR
r + †T C
(!") g = †S !
Q
ã
RRRR
[ $#%
(!$) π = g %
\
(ûp) aggregate demand schedule
“
(AS) aggregate supply schedule
28
The system cannot be solved because it is not linear, and neither none of its equation, so we
should move to logarithms. There is no way to solve it explicitly.
Only if … = 0.5, then the marginal cost function is linear.
In all the other cases it is increasing, if * > 0 the firm is incentivized to produce more.
The ûp − ûA model enables us to compute: the level of employment, the level of real wage and
the level and the nature of unemployment.
r and monetary policy E
r:
The position of the !" schedule depends on both fiscal !
• Any kind of expansionary policy ∆! > : or ∆E > : will shift the !" to the right.
• Any kind of contractionary policy ∆! < : or ∆E < : will shift the !" to the left.
The position of the !$ schedule depends on 2 parameters: on the wage and on the elasticity Ã.
nnn < : or
• If the shocks reduce the marginal costs like in case of reduction in nominal wage ∆—
an increase in productivity ƈ > :, then the !$ schedule shifts to the right.
nnn > : or
• If the shocks increase the marginal costs like in case of increase in nominal wage ∆—
an decrease in productivity ƈ < :, then the !$ schedule shifts to the left.
Intersection point (g∗ ; π∗ ) is the macroeconomic equilibrium:
The ûp is decreasing and the ûA is increasing, so we only have 1 equilibrium point, 1 combination
* − M that ensures the equilibrium in all markets, and simultaneously ensures that the firms are
maximizing the profits ⟹ it’s the short run equilibrium.
Graphical representation of the !" − !$ model with perfect competition involves 4 graphs
which are related to each other. It’s the graphical representation of the short run solution:
29
1° graph: it represents the goods market. The intersection point between ûp and ûA between
the equilibrium level of output and the equilibrium level of price.
2° graph: we just represent the bisector line, M on both the vertical and horizontal axis, in a way
that we can translate M on the vertical axis of the 4° graph.
4° graph: it represents the production function, which is increasing and concave.
Using the production function, given M*, we get √* which is the optimal quantity of labor demanded
by firms.
3° graph: it represents the work of the labor market, because when prices are variable, even if
the nominal wage is fixed into contracts, it follows that the real wage is a variable (it is a real
cost for firms). Using the labor demand we get the equilibrium real wage
EEE
[
Q∗
.
Labor Demand
The labor demand can be defined as the mirror image of the profit maximization condition
because we can invert it by solving it for the real wage:
RRRR
Y
(AS) * = Z M
]
"
!#"
"
',
⟹
E[
EE
%#$
=Ãg %
Q
= 'T
Using the production function, I obtain exactly the marginal productivity of labor:
!
√ = M" ⟹
>
]
"
= …√`−1 ⟹
EEE
[
Q
= ‘N (À)
It comes out that the profit maximization condition which is price = marginal cost (π = E¥) can
be stated in an alternative way: when firms optimize profits, it comes out that the marginal
RRRR
[
productivity of labor must be equal to the real wage ’ Q = ÃÀb_S ÷.
30
So the firm will demand labor (√* optimal quantity of labor demanded by the firm) until the
marginal productivity of labor, so the contribution to the production of the last worker, is equal to
the real cost of labor, the real wage.
Marginal principle: until the marginal productivity of labor is higher than the real wage, it means
that the contribution to the production of the last worker is higher than the cost, which is the real
wage ⟹ it’s profitable to increase labor, until ’
RRRR
[
= ÃÀb_S ÷ the marginal productivity of labor is
Q
equal to the real wage.
This condition implicitly defines a labor demand function: gives for any real wage the optimal
quantity of labor demand of firms, since the » N (√) is decreasing, the labor demand function is
decreasing.
Along the curve, firms are maximizing profits, so using the production function we get √* and
using the labor demand we get the real wage
goods market (graph 1).
>
]
⟹ this is the short run solution obtained in the
"
To explicit the labor demand function, solve for √ the real wage equation, and I get the equation of
the labor demand À3 :
S
\ S−b
À = ◊[ ÿ
c
Q
It’s a schedule, a set of combinations, for any real wage it gives us the optimal quantity of labor
that makes the firm maximize the profits. It’s because I’ve obtained this equation from π = E¥.
There is one very crucial but missing information for the working of the model in dynamics terms:
the labor supply.
Labor Supply
It is possible to microfound the labor supply from the labor-leisure choice.
Real wage for workers is the opportunity cost of leisure. There are 2 opposite effects:
• Substitution effect: higher real wage, higher opportunity cost of leisure, then workers are more
incentivized to work instead of leisure. (Microeconomics)
• Income effect: if the real wage increase, I became richer then I will tend to desire more leisure,
because leisure is a normal good that increases with the income.
Microeconomics result: if in a typical representation of the labor market the substitution effect
prevails over the income effect, èúÆèî¨îúî¨çó > ¨óõçêw, then the labor demand À3 is
decreasing and the labor supply À4 is increasing, especially when the real wage is very high the
income effect at some point can prevail, so that the labor supply can become at some point
decreasing.
Labor Market
The changes in the macro-equilibrium depends on the wage —.
nnn.
• In the short run the nominal wage is fixed — = —
• In the long run the nominal wage is flexible, it’s variable according to the law of demand and
supply —̇ = oŸsÀ3 − À4 t. The potential level of output M is obtained in the labor market, not in
the goods market.
•
•
Short run equilibrium g∗ : intersection between !$ and !" in the goods market.
Long run equilibrium À∗ : intersection between À4 and À3 in the labor market.
31
The 2 equilibria g∗ and À∗ can be incompatible. It’s a typical Keynesian situation, all the markets
are in equilibrium (bonds, money, goods), except for the labor market. So there is an equilibrium
that displays the presence of unvoluntary unemployment, even a massive phenomenon.
⁄ = À= − À∗
⁄ = (À= − À4 ) + (À4 − À3 )
⁄ = ∏çöúóîëíò − úó∏çöúóîëíò
À= : labor forces, constant and exogenous, they are the part of the population that wish to work.
Overall unemployment (€) is the sum of the unvoluntary unemployment and the voluntary
unemployment:
• Unvoluntary unemployment s√ , − √ * t: who wants to work but is unable to find a job. It’s a
problem for the society and for the economic policies for Keynes, it’s a situation in which the
supply is higher the demand for a given wage
• Voluntary unemployment (√+ − √ , ): who is unsatisfied for his job, who want to be paid more,
it’s a matter of preferences. It’s not a problem for the society.
a. Without Policy intervention
In a similar situation of equilibrium with under unemployment, without the intervention of the policy
makers, government and central bank, the position of the ûp aggregate demand is constant, but it
can’t persistent over time.
The unvoluntary unemployment can’t persist in the long run because according to the
principles that defines a market in the economics in the long run, because the law of demand and
supply applies also in the labor market, also according by Keynes.
Excess supply in labor market, so there is a process of competition between the workers it
implies that some worker are willing to supply their labor at a lower wage in order to find a job,
leading to a reduction in the nominal wage until we arrive at the long run equilibrium level of
employment (ÀQ ), the intersection point between the 2 curves √p and √A.
32
So without any policy intervention, we have ∆— < :, which reduces the marginal costs for
firm, and makes the !$ to shift downwards in !$Q , meanwhile the !" remains stable.
We obtain the new point of equilibrium P and it takes a very long time, and it has a strong social
cost.
From B we get the long run level of output gQ , which is higher respect the short run equilibrium
level of output gQ > g∗ because of the involuntary unemployment.
Wage Devaluation
Wage devaluation: process in case of unvoluntary unemployment, without any policy
intervention, according by EU directives. This phenomenon is good for firms because the
marginal cost decreases (actually in Italy, decreasing wages).
Only in the long run the ûp − ûA model is determined by the law of demand and supply in the
labor market:
—̇ = oŸsÀ3 − À4 t
oŸ: measure the degree of flexibility of the nominal wages in the ûp − ûA model. It’s the velocity
of reduction of the wages (perfect rigidity) : < oŸ < ∞ (perfect flexibility).
One possible structural reform consists in increasing oŸ (applied in Italy), by making the labor
market more flexible, like in US, and thus more efficient, with the goal of let people find easily a
work. But it also implies that it’s very easy for firms to lay off people, abolishing the worker
protection policies previously existing in Italy.
The structural reform in question is the liberalization of the labor market during a situation of
unvoluntary unemployment triggers the wage devaluation.
Result: achieve the full employment (P) through the wage devaluation, at the cost of increasing
inequalities, that may cause the settlement and empowerment of populist political parties.
b. With Policy intervention
This process above without any policy intervention graphically works, the B is achieved, but it
takes a very long time, and it has a strong social cost. Rather than wait, it’s possible to move the
!" upwards in !"Q , obtaining the new equilibrium point P’, and reaching gQ but in a very short
time.
The ûp position can be modified, until it reaches the equilibrium, by using an expansionary fiscal
and monetary policy. And most important in short time and without any cost for the society.
Problem: in the solution that describes an expansionary economic policy, the price level is higher
in B’ respect in B. It’s not yet the inflation, but it could probably trigger the inflation.
2. AD-AS model with Imperfect competition
The implications will remain the same, but there is one important parameter more for discussing
economic policy in EU.
There are many market structures with imperfect competition: oligopoly, monopoly, monopolistic
competitions.
We are going to introduce imperfect competition from a microeconomic perspective.
Simplest assumption: all the GDP is supplied by a single firm that operates under monopoly.
Monopoly: one firm supply goods and is protected from the entrance in the market by other firms
by entry barriers.
So the problem for the firm is very similar to choose M to maximize the profits, but now * is not
given because the firm is not price taker, but price maker.
To simplify this model, we simplify the production function, assuming a linear production function,
where + is an exogenous parameter, which is both the marginal and average productivity of labor.
33
In a linear production function the marginal and the average productivity of labor b are
equal:
nnÀ − d=
†›Öfi = πg − n—
“
fl‡ü·-µ‚ ‚„ g = bÀ; + > 0
+=
UV
V
=
U1 W
4
[
=
Imperfect competition
M^=
Q
[
b= Q
Perfect competition
It’s a quite realistic assumption, usually monopolistic firm has a spare production capacity
(capacità produttiva inutilizzata) to face the demand, so the firm can increase the capital stock
more easily than an atomistic firm. (Atomistic competition: market structure with numerous firms,
price takers, perfect competition.)
This implies that the marginal productivity of labor can be assumed to be constant.
It follows the same procedure as before, we solve for √ the production function and then we
substitute into the profit function:
V
√=1
≈ = *M −
RRRR
Y
1
M − K+
'X
_Q
=0⟹π+g
−
',
_@
'X
= 0 ⟹ CO − Cµ =
',
EEE
[
=:
4
0
_Q
E£ = π + g _@
RRRR
[
E¥ = 4
We get a profit function in which only M appears.
Now the monopolistic firm faces all the demand, which is decreasing, so if the firm wants to
increase the production, then it must decrease the price.
Indeed the * in the profit function is a decreasing function of M, *(M). * is endogenous, no longer
exogenous, because now the firm is price taker (CHECK mi sa che prof si è spaglaito). Hence the
derivative is the derivative of a product with the respect to M, because * depends negatively on M.
The marginal revenue under imperfect competition:
U&
M UV < 0;
'"
< 0;
',
',
<0
'"
π ≠ E£ ⟹ π > E£
Since the demand schedule !" is decreasing the values are negative.
Now the marginal revenue is not equal to the price * ≠ CO (result of microeconomics)
Consequently the marginal revenue under monopoly, or generally under imperfect competition
is lower than the price * > CO , because it’s the sum between the price and a negative quantity.
We can rearrange the terms as follows:
_Q @
RRRR
[
π ‰Ü + _@ Q = 4
'" ,
<0
', "
34
!"
" Ê = Á_@ QÁ
Å = Ê !#
_Q @
#
Å>:
_Q @
: inverse of the elasticity of the quantity produced with the respect to price.
_@ Q
Å: elasticity the percentage variation in the quantity produced if the price increases by 1%.
The elasticity É > 0 is a positive number, but
'" ,
< 0.
', "
If Å tends to infinity, then we are in a case of perfect competition, π = E£.
So the more competitive is the market, the higher is the elasticity because there are many
competitors, the more the marginal revenue is close to the price.
RRRR
Y
1
RRRR
`−1
Y
*‰ ` Â = 1
RRRR
` Y
* = `−1 1
1
`
* ‰1 − Â =
(!$) π = (Ü + °)
M
° = a−M
(ûA) * = (1 + ä)
RRRR
[
4
RRRR
Y
1
Q−Cb
* = (1 + ä)Cµ ⟹ ° =
Cb
π > E¥
°: mark up (ricarico) degree of monopoly.
° is the degree of difference with the respect to the marginal cost.
Tells how the monopoly is distant from the benchmark perfectly competition environment.
It’s a variable and a percentage rate ex if ä = 20% it means that in imperfect competition the
prices are 20% higher than the marginal cost.
It measures the competition deficit, which depends negatively on the elasticity of the firm
1
‰ä = `−1Â: the lower the elasticity, the steeper is the demand schedule and the higher is the mark
up.
So the less competitive is a market, the higher is the mark up. The optimal mark up maximize its
profits.
There is a second interpretation for ä, it measures the degree of monopoly (by microeconomics),
but also measures the distributive shares of the total GDP that goes to workers as opposed to
firms, it’s a sort of measure for the degree of inequality that characterize the economy.
Now the aggregate supply !$ is horizontal because we have assumed a linear production
function, characterized by horizontal marginal costs.
The simplifying conditions that make the ûA schedule horizontal:
o Rigid wages in the short run.
o Imperfect competition in products’ market.
o Constant marginal productivity (independent of the quantity produced).
o Constant (independent of the quantity sold) mark-up (that is, constant demand elasticity).
RRRR
Y
Since (ûA) * = (1 + ä) 1 :
35
•
•
If ° increases the !$ shifts upwards ⟹ equilibrium output g∗ and employments À∗ fall.
If ° decreases the !$ shifts downwards ⟹ equilibrium output g∗ and employments À∗ increase.
So ° is the measure of the extra profits by firms in percentage rate.
Under monopoly there are persistent extra profits because there is no free entry.
In the case of free entry, new firms will enter the market ant it would become a contestable market
(mercato contendibile), in which there can be even one firm, but it is free entry, it implies that all
the extra profits will converge to 0 in the long run.
Now we get a new !" − !$ model with 2 differences:
1. E¥ ¥ÍÎÏ›ØÏ Marginal costs are constant, related to the fact that we have assumed a linear
production technology.
2. π > E¥ Price is higher than the marginal cost, which is a deadweight loss for the society. It
introduces a Pareto inefficiency, because the optimal production is lower under monopoly.
Pareto efficiency: when it’s not possible to improve the position of an agent without worsening
the position of another agent, all resources are employed at best.
If there is no full employment, there is inefficiency.
If there is full employment:
• If the market is perfectly competitive, there is Pareto efficiency.
• If there is imperfect competition, even in the long-run equilibrium (with full employment), there is
Pareto inefficiency.
&−P:
ä = P:
Cµ =
>
]
*
YW
Yc
…d = &V = V &
c
W
RRRR
[
4
Y
(AS) * = 1 (1 + ä) ⟹ =
Q
M^=
1 1
M
…d = 1+c 1 ⟹ Ãe = M+=
Ãf = Ü − Ãe = 1 −
1
=
⟹ Ãf =
1+c
M+=
b: marginal productivity of labor.
@
: average productivity of labor.
d
When economy consists largely on imperfect competitive market, there is a sort of distributive
conflict between firms and workers. Indeed the higher extra profit, the lower real wage.
If the prices are higher than the marginal cost * > Cµ, the real wage is lower than the marginal
productivity of labor.
•
•
Ãw: distributive share in favor of workers as the ratio between the wage income over the
nominal GDP, so it’s the share of the nominal GDP that goes to workers. It depends negatively
by z, the price mark up.
Ãf : distributive share in favor of firms. It depends positively by ä, the price mark up.
Graphical representation of the model relies on 4 graphs:
36
The variables of the 4 graphs are exactly the same as the previous panel.
1° graph: now ûA is horizontal because the marginal productivity of labor is exogenous, is
constant, not decreasing. It implies that Cµ of the firms are constant over time.
(ûp) decreasing.
(ûA) π =
RRRR
[
(Ü + °) constant.
4
2° graph: bisector line.
3° graph: production function: M = +√
4° graph: the labor market.
Labor supply (√ , ) is positively sloped.
Labor demand (√ * ) is horizontal
[
4
=
.
Q
M^=
The goods market sets up the equilibrium level of output M ∗ in the short run (C).
Using the production function we get À∗ , which is the short run level of employment, which can
be distant from ÀQ which is the long run level of employment.
The line between √ ∗ and √g is the involuntary unemployment.
Just like in the previous lesson in the short run there can be a situation of equilibrium that
displays the presence of involuntary unemployment, which implies a disequilibrium in the
labor market À3 < À4 .
Without any government intervention or any monetary policy intervention the excess supply, by
the law of demand and supply, must imply a decrease in the nominal wage, called wage
devaluation while the real wage stays constant.
The reduction in the nominal wage makes the !$ translate endogenously in the position !$Q ,
leading to the potential level of output Mg .
37
gQ : is the long run potential level of output that is reached once the decrease in the nominal wage
leads the labor market in equilibrium.
The wage devaluation process makes the ûA decrease, once in the long run the contracts are
revised, indeed in the long run ∆ is endogenous and depends on the law of demand and supply.
But for Keynes this process can take a very long time and can also imply important social cost for
workers.
In order to save time and social costs, it’s possible to move the !" in the position !"Q .
reaching the full employment in the short run. It explains the role of the economic policy for
Keynes, that consists in bringing the system to the full employment without waiting the wage
devaluation process.
Notice that in this case there is no increase in the price (like there was in the previous panel)
because ûA is horizontal, ant this follows from the linear production technology.
Except for the difference that the !$ and À3 are horizontal lines, the structure and the implication
of the model is exactly as the previous one.
There is another remarkable distinction with the previous model, useful for explaining the
existence of inflation, that’s the fact that It is obvious that gQ and ÀQ are not Pareto efficient.
In microeconomics the benchmark, the first best for maximizing the social welfare is precisely the
perfect competition environment, and this surplus is maximized in a perfect competitive market in
which * = C.
So the first best in this environment occurs when ° = :. At this point we can precisely identify the
Pareto efficient level of employment or the Pareto efficient level of output.
In a hypothetical perfectly competitive market the real wage would be equal to the marginal
productivity of labor. Using !$ we can indicate the Pareto efficiency level of employment as
À! , it’s the level of employment that would prevail if t ° = :, so there is no a deadweight loss for
society and the surplus for agents is maximized.
Using g = bÀ the production function we get g! > gQ .
g! : Pareto efficient level of output which corresponds to the Pareto efficient level of employment.
With imperfect competition the potential level of output gQ is Pareto inefficient because ° >
:, since ä is positive, there are extra profits and therefore deadweight loss for the society.
It’s simply because under imperfect competition the level of production is always lower than
the level of production under perfect competition. In graphical terms we can identify precisely the
Pareto efficient level of employment and the Pareto efficient level of output.
If there is imperfect competition there must be an incentive, called also a temptation, for the
policy maker to bring the level of output even further than gQ .
It’s enough to set ä = 0 in the labor market to make the real wage equal to +, the marginal
productivity of labor, which is higher than
*
2^e
.
So the Pareto efficiency also held in macroeconomics when each input has a remuneration equal
to the marginal contribution to production. So in this case the real wage is exactly equal to what
the marginal worker produces.
Using the labor supply À4 we get À! which is a hypothetical level of employment in
correspondence of which there is Pareto efficiency, because it’s the level of employment that
would prevail under perfect competition. Consequently, I can also obtain g! .
38
Perfectly competitive market at its first best: the market in which the price is at lowest level
and the quantity produce is at the highest level possible, so the production is maximized.
Therefore, bend the price at the lowest level means that the surplus for consumers is at the
highest level.
Can the policy maker reach M$ without any cost: temptation of policy maker to go beyond Mg bc it is
Pareto inefficient?
Logarithm and its properties
For simplification, many macroeconomic models are express in logarithmic terms because many
macroeconomics models are expressed by nonlinear equations, for this reason it’s not possible to
find an algebraic solution. On the other hand the model expressed in logarithm enables us to
linearize the model, the nonlinear equations.
Natural logarithm M = Ì„Ó+ ; - h = +
It’s increasing and concave
The small case will indicate the logarithm for any generic variable: â = Ì„Ó+ ; ù = Ì„ÓC; Ô =
Ì„ÓM...
Proprieties of the logarithm:
a. Ì„Ó+M = Ì„Ó+ + Ì„ÓM
1
b. Ì„Ó = Ì„Ó+ − Ì„ÓM
V
c. Ì„Ó+ [ = …Ì„Ó+
Uf
U hijV
d. Suppose we have: Ô = …â; … = Ug = U hij1 =
;i
i
;j
j
which is an elasticity.
So once we linearize, the coefficient has an economic interpretation, the coefficient is the
elasticity of the level of output with the respect to the public spending.
In a linear equation expressed in logarithm terms, the coefficients are elasticities, even if
elasticity is 1, the coefficient is 1.
t ≈ b

e. öçåsÜ + b
If +Ú is not very high, like 10%, then logs1 + +Út approximates exactly to +Ú.
 (‘x tilde’): percentage rate, percentage variation in the variable X.
b
f.
+Ú ≈ Ì„Ó+ − Ì„Ó+_W ≈ ∆â
 ≈ Ö − Ö_S ≈ ∆Ö
b
The variation of a log is approximately equal to the percentage variation in X.
+Ú is approximately equal to ∆â (logarithmic variation).
Example:
Suppose +Ú is the inflation rate.
1−1−1
1
+Ú =
=
−1
1−1
1−1
b_S : level of X in the previous period.
39
1
1 + +Ú =
1−1
 : gross percentage variation.
Ü+b
1
)
1−1
log(1 + +Ú) = log(
t ≈ b
 (property e)
öçåsÜ + b
1
⟹ +Ú = log(1
−1
1
)
Ì„Ó V = Ì„Ó+ − Ì„ÓM (property b)
⟹ +Ú = Ì„Ó+ − Ì„Ó+_W = â − â_W = ∆â (property f)
Ì„Ó+ = â
Ì„Ó+_W = â_W
Example 2:
If we have a relationship in logs which says that the price level is equal to a coefficient times the
money supply:
∑ = …ù ⟹ *Ú = ∆∑ = …∆ù; (property f)
∆∑: approximately the inflation rate.
*+ − *- model with imperfect competition
!" − !$ model with imperfect competition:
RRRR
r + †T C
⎧(!") g = †S !
Q
⎪
RRRR
[
(!$) π = (Ü + °)
4
⎨
(˜íçéúõî¨çó Ωúóõî¨çó)
g = bÀ
⎪
[
(¨óõíwëè¨óå öëÆçí èú˜˜öò Ωúóõî¨çó)
Àk = ( Q )l
⎩
¯: elasticity of labor supply with the respect to the real wage.
If ˘ > 0 the function is increasing and convex.
!" − !$ model with imperfect competition in terms of logarithms:
RRR
⎧ (ûp) M = ùW û̅ + ùX P
&
⎪
(ûA) ∑ = ṙ − â + ä
⎨
Ô =â+˚
⎪
⎩
˚ m = ˘ (˙ − ∑)
Computation of !" in logarithm terms:
P
(ûp) M = ùW û̅ + ùX
&
P
RRR
P
For simplicity I íwêç∏w î˝w Æëí, & instead of &
k
P
ùX & = M − ùW û ⟹ * = V−k2 l C
1
Multiply both sides by M
k V
2
*M = V−k
C
1l
Bring M in the denominator
40
k2
ÿC
V−k1 oi
*M = ◊
J
can be assumed to be constant
,
πg = ˛E
˛=
Q@
C
˛=
mT
@−mS p
q
˛: money velocity.
Q@
˛ = C : ratio between the nominal GDP and the quantity of money that circulates in the economy.
˛: new variable called money velocity for money circulation, synthetizes the average number of
times in a year that 1€ is used for making transactions.
The nominal GDP synthetizes the number of transactions that are made in an economy, it’s the
value of all the transactions, all goods and services sold in a year.
Suppose that the nominal GDP is 5 times the money supply, the stock of money that circulates in
the economy. It means that on average in a year 1€ (meant as the same coin) is used 5 times to
make payments, since all transactions requires money.
The money velocity ˛ is a function that depends positively on autonomous expenditures !.
Suppose an increase in public spending: û̅ increases, M decreases, so ˇ increases.
Indeed it’s confirmed that an increase in public spending generates an increase in the GDP, given
money supply.
So the GDP can increase without an increase in money supply, via increasing the money
velocity ˛, which is a fiscal variable that can be used in an expansionary way.
Simplified version of the ûp schedule from the resolution of the @A − BC model using the definition
of money velocity:
(ûp) M =
&n
⟹Ô=ù
r −∑+/
P
!" − !$ model of Keynesian type with imperfect competition in logarithmic terms:
⎧(!")
⎪( )
!$
⎨
⎪
⎩
r −u+<
!=†
r −Ö+°
u=Ÿ
!=Ö+Ø
Øk = ¯(Ÿ − u)
All the equations are linear and the coefficients are partial elasticities.
There are 2 solutions of this model:
1. Long run solution: obtained from the equilibrium in the labor market.
ØQ = Ø3 = Øk = ˘(˙ − ∑)
∑ =˙−â+ä ⟹˙−∑ =â−ä
˚g = ˘(˙ − ∑)
ØQ = ¯(Ö − °)
!Q = Ö + ØQ = (Ü + ¯)Ö − ¯°
M$ = (1 + ˘)â
M$ > Mg
41
In the Keynesian model only in the long there is equilibrium in the labor market.
By the equality between labor demand and labor supply Ø3 = Øk I get the long run level of
employment, the potential level of employment ØQ .
Using the production function we get the long run level of output, the potential level of
output. I know that M$ > Mg , the potential level of output Mg is lower than the Pareto efficient
level of output M$ , which is obtained by setting ä = 0.
2. Short run solution: solution of the system obtained by substituting u in the !" and !$.
r− Ÿ
r +Ö−°+<
g∗ = †
Substitute ∑ in the logarithmic version of the ûp equation we get immediately the solution.
With an expansionary monetary policy or with an expansionary fiscal policy, which increases
the money velocity, we can influence positively the level of output.
Inflation
The inflation rate in EU and US around 10%, the highest since 40 years.
70-80s period of very high inflation, also characterized by very high inflation differentials, in Italy it
was much higher respects other countries.
Hyperinflation happened in Latin American countries during the 80s and actually present in
Venezuela.
Supply-side policies
Previously we have studied demand-side Keynesian type policies.
Keynesian type policies enable the system to reach the full employment level of output, even in the
short run by means of expansionary fiscal or monetary policy.
But there is another strategy that can be studied by the ûp − ûA model, and it is precisely the
strategy of the EU between the aftermath (conseguenze) of the Great Recession 2008, until the
Pandemic Crises 2020.
EU strategy was different from the strategy implemented by US.
Given ûA and ûp, suppose that g ∗ is an equilibrium in which there is involuntary unemployment,
which is the situation of the EU after the Great Recession, so there is an output gap with respect to
gQ , which is the potential level of output.
•
•
US strategy: based on shifting the !" upward by using both fiscal and monetary policies,
implemented by Obama, Trump and Biden administration.
EU strategy: based on shifting the !$ downwards in ûA’, to move the equilibrium from C to B.
Supply-side policies: policies that determines a shift in the !$ and not in the !".
In the European context those policies are called structural reforms.
The position of the aggregate supply ûA depends on 3 supply-side policies:
42
nnn < :
1. ∆—
Modify the labor market in a way to decrease the nominal wage, so the wage devaluation
process, making the labor market more flexible.
The marginal cost by firms decrease and therefore we can potentially reach the full
employment level of output.
Particular type of wage devaluation that involves the fiscal wage, which reflects the difference
between the wage that the firm pays and the wage that the workers obtain, this difference is
given by taxes and social contributions by workers.
The marginal cost for firms depends on the wage that the firm pays, which is higher because of
the fiscal wage with respect to the net wage that workers obtain.
So a particular type of supply-side policy involves a cut in taxes for firms or social contribution,
which implies an !$ downwards movement, bringing up a positive effect on the level of output.
2. ∆b > :
Increase the productivity of labor, in order to reduce the marginal costs, which are the ratio
of nominal wages over productivity.
Increase in productivity means increasing public investments, from infrastructures to digital
economies.
It’s not easy the productivity increase, it may depend even on cultural elements, on the social
capability, which is the capability of the economic system to import new technologies, and it’s
not easy especially for countries where there is a lot of corruption, because it would implies
abating the links between the administrators, politicians and domestic firms, it may tourn out to
be very inefficient.
3. ∆ ° < :
Decrease the firms markup (rendita), which is a rent, the extra profits rate.
The elimination of the entry barriers makes the market more competitive due to the entry of
new firms, and it follows an increase of the degree of competition, thus a decrease in the
extra profits, therefore a downwards shift of ûA, stimulating the level of economic activity.
Unfortunately EU has focused too much on reforming the labor market through the wage
devaluation, and very little on increasing the productivity and decreasing the mark up. Especially
the competition policies were not strongly implemented in the countries. But it must be pointed up
that the enhancing of the degree of competition is the principle number one for the constitution of
the EU, in order to integrate the economies and maintain the peace.
Competition policies: enhance the degree of competition and are expansionary.
A decrease in ä, makes ∆ increase, so is beneficial for workers:
[
Q
=
4
M^=
With recovering plan EU is going to implement the last 2 policies:
• ∆b > :: investments in digital economies, educations, infrastructures.
• ∆ ° < :: EU is now imposing a liberalized market ex in Italy liberalization of bathhouses
(stabilimenti balneari)
However, there is an important limitation for these 3 supply-side policies compared to the demandside polices: supply-side policies aren’t suitable for the short run, but are policies for the long run;
increasing the productivity, the social capabilities, foster the competition takes time. For this reason
those polices are subject to the Keynes’ critique, who preferred to increase the ûp using fiscal and
monetary policy.
The EU is accompanying supply-side policies with demand-side policies ex increasing transfers and
using an expansionary monetary policy.
43
2 Inflations Theories:
Inflation: continues tendency of the prices to increase over time, it’s not a una tantum event.
 = Q−Q−S = ∆u
π
Q−S
A. Cost-Inflation theory:
∑ =˙−â+ä
L∑ = L˙ − Lâ + Lä
Lä = 0 ⟹ L∑ = L˙ − Lâ
The central role is carried out by the ûA schedule. If I express the ûA in terms of Δ it must be that
the inflation rate depends strictly on the difference between the rate of growth of wages 7Ÿ and
of productivity 7Ö, assumed Lä = 0.
It’s not true that the inflation will become persistent if wages increase a lot. Because by the equation,
if the wages increase as the marginal productivity of labor, there is no inflation.
So the wages can increase as long they are accompanied by an increase in productivity, without
triggering the inflation
Cost-Inflation theory emphasize the supply side of the economy.
The increase in ûA and ûp is driven by an initial shock in !$.
There the initial position in ûpV and ûAV , their intersection point corresponds to the full employment
level of output.
•
Suppose an initial shock, the increase in markup ∆° > :, that if continuous may lead to a
distributional conflict in the economy between workers and corporations, indeed ä depends
negatively to the distributional shares for workers and positively to the distributional shares for
firms. Distributional conflict was evident in 60s-70s, not today.
An increase ä can be driven by an increase in the energy prices, in the price of raw materials ex
oil price, so the marginal costs Cµ increase and firms increase the markup in order to not suffer
any reduction in the extra profits.
So an initial shock ca be driven by a distributional conflict or by an increase in energy costs
(current situation).
If ä increases the !$ line shifts upwards in !$S , consequently the intersection point shifts
upwards from Mg to MW , so we are witnessing a recession and prices increase (current
situation).
If the model stop here, there would be a una tantum increase and a recession, but it’s still not
inflation, because it’s not a continuous increase in the price, this shock is not enough to justify
the rise of inflation.
44
•
Since we have a recession and involuntary unemployment, suppose that the objective of the
government and of the central bank is to stabilize the level of output, by shifting the !" in
!"S to stabilize the level of output. This position can be reached through ∆E > : or ∆< > :,
because they contain fiscal variables.
Again it’s not inflation yet, there is a una tantum increase in the price equal to Lä.
•
After the shock Ɗ > 0, the increase in the price mark up decreases the real wage.
˙−∑ =â−ä
∆(˙ − ∑) = − ∆ä
Therefore is plausible that workers will react, by asking an increase in the nominal wage, in
order to try to stabilize the real wage. If the nominal wage increases, then the !$ moves
upward a second time in ûAW .
•
There is a distributional conflict between workers and firms, the increase in nominal wages is
an increase in the marginal costs for the firms, so the prices increase again. The policy
makers stabilize the economy again, so the process continues.
As the E¥ increases, also the prices increase which decreases the real wage: vicious circle
starts called the wage price spiral. During this phenomenon the !$ always shifts upwards
because it’s driven by the increase in nominal wage in order to try to stabilize the real wage, this
leads the firms to increase the prices, that decreases the real wage and the process continues.
The wage price spiral leads directly to the inflation, which becomes persistent
It is happening nowadays in the US. In Europe not yet, there is another mechanism that is triggering
the inflation rate. The wage price spiral won’t stop until, and only if, is established an agreement
about the distributional conflict that stop this process, or if the policy maker accept the
recession and doesn’t move the ûp.
Summing up:
Initial shock, ä increases or decrease in productivity, this decreases the real wage, workers ask an
increase in nominal wage in order to stabilize the real wage, for firms an increase in nominal wage
is an increase in the marginal costs, so prices increases and consequently the real wage decreases
again, and workers are incentivized to ask for a third nominal wage increase ⟹ it’s the vicious circle
of the wage price spiral.
It’s exactly what happened during the 70s in Italy, with 2 shocks in 1973 and 1979, the wage price
spiral was triggered by an increase in oil prices, and led directly to the inflation.
During the 70s firms were willing to approve an increase in the wage because they expected a
depreciation in the lira in order to stabilize the completeness.
There is a second reason why the wage spiral can be trigged, it’s related to the demand inflation
theory.
B. Demand-Inflation theory:
∑ =ù−Ô+/
∆∑ = ∆ù − ∆Ô + ∆/
∆Ô = 0 "˚# ∆/ = 0 (in the long run)
⟹ ∆∑ = ∆ù
It’s obtained from the ûp, solved for ∑. This theory highlights the fact that inflation is also related
to printing money, to the possibility for central bank to increase persistently fiat money, the money
without any intrinsic value. According to this theory the inflation rate is equal to the rate of growth
of money supply Ơ, because the elasticity is 1.
Demand-Inflation theory emphasizes the demand side of the economy.
The increase in ûA and ûp is driven by an initial shock in !".
45
•
gQ is Pareto inefficient because there is imperfect competition, prices are higher than
marginal costs, and in an imperfect competition market the prices are higher than in the
benchmark case of perfect competition.
Pareto efficient level of output g∗ is higher than Mg (M ∗ > Mg ) and it corresponds to a situation
of perfect competition.
The target level of the policy markers it’s to go beyond Mg , reaching g∗ , so they shift the !"
to !"S , by increasing the money supply † or the money velocity <.
•
But there is a problem, in order to achieve g∗ it’s necessary more labor (Ø∗ > ØQ ) ⟹ there is
an excess demand in the labor market , it’s called overheating situation, in which is very
difficult for firms to find workers (nowadays in US, where the level of output is even higher than
the potential level of output, the level of unemployment rate is very low, but firms can’t find
workers).
But according to the law of demand and supply, if in a market there is excess demand, a
competition between firms will start: some firms are willing to offer a higher wage in order to get
labor and hire workers. So an increase in the wage generates an increase in !$, that reaches
ûAW , that brings back the output to gQ .
•
A una tantum increase in money supply cannot bring the level of output persistently to g∗ ,
because in g∗ the labor market is not in equilibrium (M ∗ is the equilibrium in the long run).
But the central bank would continuously print money Ơ > :, stabilizing the rate of growth
of money, shifting again the !" in ûpX .
This generates again a disequilibrium in the labor market, so that the !$ will shift another
time in ûAX , and so on.
As result we have inflation: there is the same wage price spiral, a continuous increase in prices
starts to apply, now triggered by the excess demand in the labor market, which is in
disequilibrium.
The initial shock is in ûp because the long run level of output is Pareto inefficient, then the
government and the central bank attempt to push the level of output above, but above the labor
market is not in equilibrium, so the firms will demand labor and offer higher wage, this will bring the
ûA up, but since the goal of the policy maker is achieve M ∗ also ûp is brought upwards again. ⟹
we obtain inflation.
It’s discussed that this is the actual situation in US, as a consequence of a too generous fiscal plan
by Biden.
In this case the inflation is the cost that the policy maker must bear to reach the Pareto efficient
level of output, this is also a great explanation for the definition of inflation. Inflation follows from
the temptation of the policy maker to implement expansionary monetary and fiscal policy, to bring M
beyond Mg .
46
Benefits and costs of inflation
•
Benefit: Inflation is convenient, it has the advantage to push the level of output beyond Mg and
towards g∗ . It requires printing money continuously ∆ù > 0 or increasing public spending
continuously, and leading to an overheating economy.
•
Cost: reach the Pareto efficient level of output M ∗ , requires an extremely high level of inflation
rate. There are 3 type of costs for the inflation:
1. Since the inflation decreases the real value of debt and credit, it causes a redistribution of
the real wealth between debtor and creditors, in favor of debtor, and in disadvantage of
creditors. This is the reason why Germany wants to fight inflation since they are creditors.
2. Inflation is an hidden tax, it decreases the real value of money and of wealth, generating an
advantage for the State, indeed it was one of the options for the sustainability of a fiscal
policy. If the inflation is higher than the interest rate, the dynamics of the real debt are no
longer explosive. It is the reason why Italy did not default.
3. The hyperinflation takes place when inflation is very high if I demand money I’m losing
purchasing money, so I try to anticipate the purchases, but acting in this way the demand
increase so the price increases and the inflation increase even more (self-fulfilling inflation).
In this case also the money velocity increases, it is convenient to buy goods because the
money is losing its real value, it’s the mechanism of the German hyperinflation. Until nobody
will demand money as it lose its purchasing power, becoming just a piece of paper, it’s not
related to gold. At this point the monetary economy is destroyed.
For this reason no policy maker brings the level of output to the Pareto efficient level
M ∗ , because the inflation rate can increase and translate into an hyperinflation
phenomenon.
Optimal inflation rate
The optimal inflation rate corresponds to the point in which the marginal benefits of inflation
equals the marginal cost ⟹ in the point in which the marginal revenues of inflation are equal to the
marginal cost E£ = E¥.
In Macroeconomics we have many co-movements:
1. Okun Law: as the GDP grows, the unemployment rate falls.
2. Philips curve: an empirical observation about a negative relationship between the rate of
growth of nominal wages and the unemployment rate.
It’s the scatterplot below, the points can be interpolated by a regression function, which is the
equations that minimizes the distance between the points and the equation.
This is a stylized fact, that requires a compatible theory, and it is the law of demand and supply
in the labor market.
The intersection point $Q is the unemployment rate in correspondence of which the wage growth
is zero, and by the law of demand and supply it’s zero when the labor market is in equilibrium,
when Ø = ØQ .
The $Q can be rationalized as the equilibrium level of unemployment in which ˚ m = ˚r . So $Q is
only given by the voluntary unemployment, there is no involuntary unemployment, because
here there is equilibrium the equilibrium point ˚ m = ˚r = ˚g .
For a Keynesian economist $Q is not efficient because there is imperfect competition, and there
is a temptation of the government to go below $Q , but this implies that I must pay a higher inflation
rate ⟹ this is the demand inflation theory.
47
Demand inflation theory: if I want to go below ‡g , then I have to pay a positive inflation. The lower
is the unemployment rate, the higher is the inflation that I have to pay.
Inflation is the economic cost for bringing the economy beyond the long run level or to bring the
unemployment below the long run level.
In a recession, which is graphically represented by the points below the ˚ axis, there is involuntary
unemployment and the wages fall, there is wage devaluation.
Philips curve in terms of inflation rate
Assume a linear Philips curve:
% = ∆Ÿ = &($Q − $)m
—
&: slope of the Philips curve.
!$ u = Ÿ − Ö + °
ûA ∆∑ = ∆˙ − ∆â + ∆ä
∆â = ∆ä = 0 ⟹ ∆u = ∆Ÿ
If we suppose that there is no growth in productivity Ɖ and in the markup Ɗ, then it remains Ʒ =
∆˙, so I know that ∆∑ and ∆˙ are strictly related.
I get a Philips curve in terms of inflation rate, not only in terms of wages growth, on the vertical
axis there is ∆u at the place ∆Ÿ
Philips curve: a set of possibilities of the economic policies to reach one of the points along the
line, the preferred one, by managing the money supply and the public spending. It resembles a
microeconomic constraint because it gives a trade-off between inflation and unemployment (like
a microeconomic trade-off), If I want lower unemployment I have to pay with a higher inflation.
trade-off: choice of one variable over another.
To know the optimal point, the optimal trade-off between inflation and unemployment, we have
to define preferences (microeconomics).
 = ∆u = &($Q − $)
π
Inflation and unemployment are not 2 goods, they are opposite: the higher the inflation, the lower
the utility, the higher the unemployment, the higher the loss for society. This is the reason why we
don’t write a utility function but a loss function.
48
And instead of a constraint maximization problem, we have a constraint minimization, we need to
minimize a loss function.
 T + (Ü − ')$T
ê¨ó
P = 'π
ã {*Ú, ‡}
0<+<1
fl‡ü·-µ‚ ‚„
*Ú = *(‡g − ‡ )
' (,›†¢-›): relative weight that the policymaker attaches to inflation stabilization as opposed of
unemployment stabilization. It’s a critical parameter, the higher +, the more the policy is intransigent
in fighting inflation (high level of + in Germany, low in Italy).
The loss function is increasing and convex. It is a quadratic loss function: the loss increases
more than proportionally with respect to the increase in price because we are getting close to an
hyperinflation phenomenon, where the costs increase more than proportionally, for this reason *Ú
is elevated to the power of 2.
Solution for the minimization of the loss:
∗ = :
π
$∗ = :
It’s an ideal solution, it’s analytically convenient but not realistic, the unemployment rate cannot be
zero.
=π
 ∗ )T + (Ü − ')($ = $∗ )T , the distance with
In the case of the loss function written as P = '(π
respect to the target is penalized; the higher the distance, higher the loss, higher the marginal loss.
The utility function, increasing and concave.
The loss function, increasing and convex, gives rise to indifference curves.
B3 > B2 > B1: the more the indifference curve is is close to the origin, the lower is the loss (*Ú
and ‡ are cost for the firms).
49
The optimal inflation or optimal trade-off (ñ) is the tangency point between the Philips curve
and the point in which we have the lowest loss, the lowest indifference curve of the loss function,
in any other point there is a higher loss. It’s the point in which the marginal rate of substitution
between inflation and unemployment equals the slope of the Philips curve.
The policy makers try to choose the point of the Philipps curve that corresponds to the lowest
indifference curve. It gives me the equilibrium intersection point with the optimal inflation rate and
unemployment rate which realistically are not zero.
The Philips curve is consistent with the macroeconomic theory because of the application of the
law of demand and supply in the medium run in the labor market. The equilibrium of the
unemployment rate (‡g ) is consistent with the equilibrium between labor demand and labor supply.
Left side (below ‡g ): when unemployment rate is lower than the long run unemployment rate there
is an excess demand in the labor market ⟹ overheating situation leads to an increase in wages
and therefore an increase in prices because of the related increase in the marginal cost.
Right side (above ‡g ): when unemployment rate is higher than the long run unemployment rate
there is an excess supply in the labor market ⟹ tendency of wages and therefore of prices to
decrease over time.
There is a tendency of policy makers, according the Keynesian theory, to accept an higher
inflation rate respect to the target rate, in order to decrease the unemployment rate, because ‡g
is Pareto inefficient and markets are characterized by imperfect competition, so that prices are
higher than marginal cost, real wages are lower than the marginal productivity of labor, so there is
a temptation to go below $Q .
Inflation differential across countries (1970-1998)
Not all countries have the same preferences, they depends on the policy maker, history, and so on.
So in each country there will be different indifference curves and different points of equilibrium.
Those are the inflation differentials across countries, that depends on different values of '.
Italy is historically characterized by more accommodating authorities, which means that authorities
are willing to accept a higher increasing inflation in order to reduce the unemployment rate by
1%. The marginal rate of substitution for more accommodating authorities is relatively high, so the
indifference curve is more vertical and the equilibrium point j is characterized by a relatively high
inflation rate and a relatively low unemployment rate.
Germany is not willing to accept a higher increasing inflation in order to reduce the unemployment
rate. The equilibrium point j is characterized by a lower inflation differential and a relatively high
unemployment rate.
The inflation differentials historically depends on different preferences of each country.
This model explains the inflation differentials but not the behavior of the unemployment rate.
50
There is a problem with this model: the optimal inflation rate of Italy is higher than the Germany’s
one, but it doesn’t imply that the unemployment rate is lower in Italy respect to the Germany.
Italy 1970-1998 was characterized by a systematically higher inflation rate and unemployment rate
with respect to Germany.
In this model 2 important aspects are missing:
1. By Keynesian theory.
2. By Neoclassical theory.
1° explanation (Keynesian):
 = ∆˙ = *(‡g − ‡) ⟹ Philipps curve, from law of demand and supply in the labor market.
∆

P = ∆p = ∆w − ∆x + ∆z ⟹ AS schedule in terms of differential, explicit inflation rate.
*Ú = *(‡g − ‡) − ∆â + ∆ä ⟹ Philipps curve ∆Ö ≠ :; ∆° ≠ : ⟹ without the assumption ∆â = ∆ä = 0
The position of the Philipps curve may be different across countries because Ɖ and Ɗ are
different across countries, since ∆â ≠ 0 and ∆z ≠ 0.
Before, about the optimal inflation rate, we have assumed that Italy and Germany face the same
Philipps curve, but it’s not the case because the position of the Philipps curve depends on ∆ô and
∆°, which are exogenous ⟹ for the Keynesians the position of the Philipps curve is exogenous.
The position of the Philipps curve is higher when ∆° < : and ∆Ö > :, the lower the rate of
productivity.
Italy golden age 1950-70, the rate of growth productivity Ɖ was even higher respect any other
country. Thanks to the Marshall Plan: increase of public investments by US in Europe to help
European countries after the IIWW. But starting from 70s the productivity doesn’t grow anymore in
Italy and nowadays it’s negative in Italy.
Looking at the data in that period 1970-1998 Ɖ in Germany was systematically higher with respect
to Italy. Meanwhile in Italy in 1970-1998 the Ɖ was systematically lower with respect to Germany.
Essentially Ɖ is relatively slow in Italy because the economic structure of the Italian economy
consists of small firms, that don’t invest in innovation.
Economic structure of Italy is full of rents (rendite di posizione), there is a strong monopolistic power
and lack of competition in a number of jobs, this implies that Ɗ is higher In Italy respect to the
Germany.
Differentials in the rate of growth of productivity ∆Ö, in the rate of growth of the markup ∆°, generates
essentially this situation:
The position of the Phillips curve is country specific, because the intercept depends on ∆ô and
∆1.
The inflation and the unemployment differentials don’t depend only on the different preferences,
but also on different position of the Phillips curve. The model is consistent with the reality, in
51
Italy both the inflation and the unemployment rate is higher respect to the Germany. The reason is
the deteriorated trade-off between inflation and unemployment because of the low productivity
growth and very high level of markup.
The Keynesians type Phillips curve was the synesis of macroeconomics until the end of 1960s.
In this Keynesian view there was an active role for fiscal and monetary policy. Policy makers
attempted to simulate the economy at a level beyond the potential level of output, and any
country would have chosen the optimal trade-off according to their preferences.
In the 70s began a sort of revival of the Neoclassical theories. Some critiques by Neoclassical
economists have been accepted even by Keynesian economists, giving rise to the New Keynesian
school.
2° explanation (Neoclassical)
Neoclassical economists demonstrate that in the reality the position of the Phillips curve is no
longer exogenous, as it was for the Keynesians where we had a given constraint, a given Phillips
curve by knowing Ɖ, Ɗ, *.
For Neoclassicals the position of the Phillips curve endogenous, depends on agents decisions,
especially it critically depends on inflation expectations.
Neoclassical Economics
At a general level there are 3 types of Neoclassical schools, but there are 2 aspects in common
for each neoclassical school:
1. Prices and wages are flexible in the short run, not rigid. Price flexibility like in microeconomics,
indeed the Neoclassical theories are grounded on the microeconomic foundations, especially
given by the law of demand and supply applied in all the markets. This implies that the labor
market is always in equilibrium and all the unemployment observed is voluntary unemployment.
2. Perfect competition because they believe that markets distortions are negligible, not
important or essential aspects of reality. Neoclassicals are aware that there isn’t perfect
competition in many markets, but the methodology of economics consists in working through
model, which are the simplified representation of the reality, and any model has an unrealistic
assumption and should not be judged on the realism of the hypothesis, but should be judge on
its capability to predict the reality, because any model, even the most complicated, is not
realistic.
On the other hand, imperfect competition is an essential feature for Keynesians. But
Neoclassicals will be able to set up macroeconomics models that with those 2 assumption prices
and wages flexibility and perfect competition are able to resemble the reality quite well. For these
reasons there is a revival of the Neoclassical economics, and they critique the Keynesian
approach about the fact that the Phillips curve can be exploited by the economic policy to reach
the desired point.
3 types of Neoclassical schools:
1. Pure Neoclassical Model or Real Business Cycle School, whose leaders are Finn Kydland
and Prescott who won the Nobel prize for this theory.
2. Monetarist School, whose is the Nobel prize Milton Friedman.
3. New Classical Macroeconomic School (the most important) whose leader is the Nobel prize
Robert Lucas.
All these schools elaborated an aggregate demand and aggregate supply !" − !$ model.
We already know the ûp − ûA model in Keynesian version with perfect competition and Keynesian
version with imperfect competition. There is no much disagreement about the demand side of the
economy, both Keynesians and Neoclassicals agree that the demand side of the economy can
be described by this equation, which is the solution of the @A − BC model for Keynesian economists
52
and is the logarithmic version of the quantity equation that involves the definition of the money
velocity for Neoclassicals.
(!") ! = †
r −u+<
The source of disagreement is especially about the supply side of the economy.
All the following models are in logarithmic terms.
A. Pure Neoclassical Model - Kydland and Prescott
By assumption there is: perfect competition in the markets, perfect price and wage flexibility.
The equilibrium of the economy is not reached in the goods market but in the labor market
because wages are flexible.
Pure Neoclassical Model: benchmark model of Neoclassical type.
Ô=ù
r −∑+/
aggregate demand
⎧
M = +√ [!
production function
⎪ Ô = …V + …W ˚; (…W < 1)
˚* = vV − vW (˙ − ∑)
labor demand
⎨ ˚ , = ˘ + ˘ (˙ − ∑)
labor supply
V
W
⎪
3
4
⎩Ø = Ø
equilibrium in labor market
ÃS : elasticity of output with respect to labor input, technological parameter in the production function.
¯S : elasticity, slope of the labor supply with respect to the real wage.
•
•
•
The central bank controls the money supply exogenously ù
r and the fiscal policy controls the
money velocity /.
The production function Ô = …V + …W ˚ is the production technology, the linear version of a
production function with the decreasing marginal productivity of labor, because …W < 1.
The labor demand ˚* = vV − vW (˙ − ∑) is decreasing in the real wage. It’s the logarithmic linear
version of the optimal profit maximization condition according to which, under perfect
RRRR
[
competition, the real wage is equal to the marginal productivity of labor ◊ Q = ‘N (À)ÿ.
•
If the marginal productivity of labor is decreasing, we get a downward sloping demand for labor.
As in the ûp − ûA model Keynesian version with perfect competition, the labor demand was
decreasing.
Ø3 = Ø4 no Keynesian economist could accept this Neoclassical equation about the
equilibrium on the labor market. It can be stated in the short run because of the assumption of
price and wages flexibility. The law of demand and supply prevails to ensure the equilibrium in
the labor market.
A Keynesian economist may agree on the first 4 equation, but for sure will never agree on the
last equation Ø3 = Ø4 , it’s the key difference between Keynesians and Neoclassicals.
For the Pure Neoclassical Model, the labor market equilibrium determines the level of employment
in equilibrium. To solve the system, we equalize the labor demand and supply function by ˚* = ˚ , ,
and solve directly the system for the equilibrium level of the real wage. Solution of the system:
Assumption …V = 0 and ˘V = 0
˚* = ˚ , ⟹ = vV − vW (˙ − ∑)= ˘W (˙ − ∑)
o
(˙ − ∑)∗ = (˙ − ∑)g = o +0p
1
1
o p
0 1
˚∗ = ˚g = o +
1 p1
Z o p
Ô ∗ = Ôg = …W ˚∗ = o1 +0p 1
ã
1
1
∑∗ = ù
r − Ô∗ + /
53
From the solution of the system we get 2 important results:
)q ∗
)q ∗
=
=0
)S
>
)+
)r∗
)r∗
=
=1
)S
>
)+
Monetary and Fiscal Neutrality: the economic policy is not effective. An increase in the money
supply is not able to stimulate the level of the economic activity.
If an expansionary monetary policy is implemented, we don’t have any effect on the level of the
economic activity, but there is a positive effect on the level of prices. Thus we have an increase in
the price gain with no effect on the economic activity ⟹ money is neutral.
The economic intuition behind this result is that in the short run the equilibrium level of
employment, therefore the equilibrium level of output, is determined not in the goods market but
in the labor market by the law of demand and supply.
So we get Ô ∗ which depends only on technological parameters, like …W , and only on preferences,
like ˘W .
!" schedule is decreasing.
!$ schedule is vertical, in correspondence M ∗ or Mg , it doesn’t depend on P.
The fluctuations in the GDP, the business cycle can occur only if there is a change in these
parameters. ⟹ it’s the real business cycle conclusion.
The position of the ûp and the ûA lines implies that the real business cycle can only be driven by
movements in !$, so it depends on shocks on technological, productivity and preferences
parameters, on the parameters of the solution …V , vV , vW , ˘W .
We have fluctuations in the ûA, that moves on the right and on the left, and as the parameters
change over time, we have fluctuations in the level of output, Ô fluctuates around Mg , and it can
be explained only by the movements in ûA, not ûp.
It does not depend on monetary or fiscal policy, the government and the central bank are neutral,
not effective. In case of an expansionary monetary or fiscal policy (∆C > 0 or ∆/ > 0) there is a shift
upwards by the !" schedule in ûp’, with no gain in output, but with an increase in the price.
The price level increases proportionally with the slope of the ûp, because the elasticity of prices
with respect to the money supply is 1.
So first of all the business cycle is an equilibrium phenomenon because it’s a general
equilibrium in all the markets.
The most important implication is that the central bank shouldn’t try to influence the level of the
economic activity, because if the central bank tries to push the level of output beyond the Mg , it
54
doesn’t reach its outcome, so the money is neutral, but money is not neutral, if the central bank
prints more money the output doesn’t change, only the prices do change.
Conclusion:
• The government: should only focus on maintaining a sustainable public debt, with all public
accounts in order, taxes equal to expenditures. As it is in Europe.
• The central bank: should focus only on price stability, indeed it’s the only aim of the
European Central bank. The European institutions have strongly been influenced by this model,
the EU institutions are Neoclassical.
This model doesn’t take into account:
• The co-movement between output and aggregate demand, in particular for the "non-neutrality"
of money.
• The presence of the Phillips curve.
• Displays (wrongly) countercyclical prices, since it does not have an increasing ûA
Important limitation of this model, admitted also by the Neoclassicals: this model explains the
business cycle, but doesn’t explain all the reality, doesn’t explain a very common empirical
phenomenon.
• When GDP increases because the ûA shifts to the right, the prices decrease.
• When GDP decreases because the ûA shifts to the left, the prices increase.
So in this case prices are countercyclical (anticiclici), it means that the variable in question
depends negatively to the level of output, so is negatively related to the GDP; in the opposite
case, the variable is procyclical.
And this evidence is a problem, because in the real world it’s exactly the opposite case: prices are
strongly procyclical, not countercyclical as it came out in this model.
The only way to predict procyclical prices is by adopting not a vertical ûA but a positively sloped
!$, just like the Keynesian ûA in perfect competition.
Challenge of the school: derive an ûp − ûA model with generating a positively sloped ûA but
applying the Neoclassical assumption ˚* = ˚ , , and not any kind of Keynesian assumption.
It’s not easy because when ˚* = ˚ , , the equilibrium level of output depends on the equilibrium in
the labor market.
B. Monetarist Model - Friedman
Friedman answers this limitation, corrects the Pure Neoclassical model in order to generate a
positively sloped !$, based on wrong values in the expectations, but maintaining the
Neoclassical assumption Ø3 = Ø4 .
Friedman applies 2 corrections to the Pure Neoclassical model, which also corresponds to the
assumptions of the Monetarist model:
1. Firms and workers agree the nominal wage, not the real wage (it implies that the labor market
determines the nominal wage), so the agreement fixed in a contract is related to the nominal
wage, and it’s consistent with a real world.
2. Firms observe prices, are price takers, they make decisions about it, but workers, as
consumers, are not able to observe all possible prices of goods and services.
The assumption of rationality is satisfied, they make decisions on the real variables, on the
basis of the expectations of the price level, so there is a sort of misperception, imperfect
information.
When the workers agree on the nominal wage, they want to stabilize the real wage, which is an
expected real wage on the basis of the expectations on the price level.
The Monetarist model:
55
Ô=ù
r −∑+/
aggregate demand
⎧Ô = … ˚
production
function
W
⎪
*
˚ = vV − vW (˙ − ∑)
labor demand
⎨Ø4 = ¯ (Ÿ − u7 )
labor supply
S
⎪ *
,
equilibrium in labor market
⎩˚ = ˚
u7 : price expectations, the ‘e’ stands for the expectations
All the equations remains the same, the only source of the distinction is about the labor supply
equation, now there are the price expectations, u is endogenous, not exogenous. People care
always on the real variable, on the real wage but on the base of an expected price level.
Since ˚* = ˚ , ⟹ ˚* = ˚ , = ˚, Ø is directly the equilibrium.
To solve the system I solve the labor supply substituting ˙ into the labor demand, and then solve
for ˚.
1
˙ = p ˚ + ∑t
1
1
˚ = vV − vW ’p ˚ + ∑t − ∑÷
1
o
˚ = ’1 + p 1 ÷ = vV + vW (∑ − ∑t )
1
o p
o p
0 1
1 1
˚=o +
+o +
(∑ − ∑t )
1 p1
1 p1
˚ = ˚g + v(∑ − ∑t )
o0 p1
o1 + p1
o1 p1
v=o +
1 p1
˚g =
ØQ : the solution for the equilibrium level of unemployment in the Pure Neoclassical model.
So in the Pure Neoclassical model u = u7 , there is no imperfect information. This means that
the Pure Neoclassical model is a particular case of perfect information of the Monetarist model,
thus the ûA is vertical only in this case, which it may happen when workers verify all the prices, but
it’s pretty much not believable.
Ô = Ôg + …W v(∑ − ∑t )
… = …W v
(!$) ! = !Q + Ã(u − u7 )
!Q : solution of the Pure Neoclassical model, long run level of output, where long run means a
situation of perfect information, because we assume that in the long run the workers perfectly
observe the price level, it’s a situation in which there is not surprise.
I’ve obtained the Monetarist ûA, with a positive relationship between g and u. Obtaining a
positively sloped !$ schedule.
If ∑ ≠ ∑t the expectation is wrong and ûA increases.
If ∑ > ∑t the real price level is higher than the expected price level, there is a sur-price, the real
wage decreases, is lower than the expected real wage, then firms demand more labor and they
produce more, and produce more is optimal for firms. This is the reason why ûA is upward sloping.
M depends positively on ∑, given u7 , which is endogenous, so the model is missing from the
definition on how ∑ is formed, how expectations are formed.
2 implications from Monetarist Model:
1. Augmented Phillips curve:
56
From the ûA or from the solution for the equilibrium level of unemployment we can derive a Phillips
curve which is directly comparable with the Phillips curve of the Keynesian economists. The Phillips
curve of the Monetarist economists contains an extra term, the inflation expectation, and for
this reason it’s called augmented Phillips curve. The inflation expectation didn’t appear in the old
Keynesian theory.
It means that the position of the Phillips curve is not stable, so the Phillips curve cannot be
rationalized as a stable relationship, as a sort of microeconomic constraint that gives us the set of
possible choices for the police makers, who can choose one point along the Phillips curve.
Ôu = Ôg + (∑u − ∑ut )
t )
∑u − ∑ut = (∑u − ∑u_W ) − (∑ut − ∑u_W
= *u − *Úut
7
%v − π
 v it’s the surprise inflation, the effective inflation rate is higher than the expected inflation
π
rate.
˚u = ˚g + v(*u − *Úut )
1
*u = (˚u − ˚g ) + *Úut
o
‡u = ˚+ − ˚u
‡g = ˚+ − ˚g
˚u − ˚g = ‡g − ‡u
1
*u = (‡g − ‡u ) + *Úut Neoclassical Phillips curve obtained from the Monetarist model.
o
1
ε=o
$Q : natural unemployment rate.
Solve it for the inflation rate, then we introduce the unemployment rate ‡u , and by substitution ˚+
disappears.
There is an important distinction, in the Keynesian Phillips curve the last term doesn’t appear, it’s a
negatively sloped stable relationship.
But in the Neoclassical Phillips curve the position critically depends on inflation expectations.
Even if we are in the long run equilibrium level of unemployment ‡u = ‡g , if workers expect an
increasing inflation, then they will ask higher wages, and so the inflation rate increases.
1° critique to the Keynesian approach:
 7v = :, without any kind of inflation
The Keynesian Phillips curve (graph) holds if and only if π
expectation.
 7v > : then
But as people expect higher inflation rate, in case of a positive expected inflation rate π
they internalize it into wages and as a consequence the Phillips curve translates upwards. ⟹
The position of the Phillips curve is not exogenous, it’s not a stable constraint, it depends critically
on the expectations, and for the Neoclassicals the expectations are endogenous.
It’s predicted by the Monetarist model and it’s the 1° critique to the Keynesian approach, which
holds only in absence of inflation expectations.
57
Meanwhile the Keynesian Phillips curve comes from a rigid labor market, sticky labor market
(vischioso), in which wages are revised slowly because they are incorporated in the contract.
Here the Phillips curve are based on the imperfect information, there are no wage rigidities, the
mechanism is different for the trade-off, which come from the misperception of the workers.
This critique and the alternative version of the augmented Phillips curve will be accepted even by
the Keynesian economists ⟹ they become New Keynesian economists.
2. How expectations are formed – Theory
Solve ûp − ûA model, theory about how the expectation is formed.
From the 2 solutions of the Monetarist model (we can skip the first solution and study only the
second one):
a. 1° solution assumes the following supply schedule !$, in which the expectations rely on the
price level.
Ôu = ù
r u − ∑u + /
“
Ôu = Ôg + …(∑u − ∑ut )
b. The second solution is more general. Solve the model directly in terms of inflation rate and it
studies the monetary implication. To solve the model we express ûp in terms of rate of
variation, of change:
Ôu = ù
r u − ∑u + /
“
Ôu = Ôg + …(∑u − ∑ut )
v − π
 7v )
(uv − u7v ) = (π
“
Ô=ù
r u − ∑u − /
Ôu = Ôg + …(*u − *Úut )
Ôu_W = ù
r u_W − ∑u_W + /
Ôu − Ôu_W = (ù
ru − ù
r u_W ) − (∑u − ∑u_W )
%v
 −π
(!") !v − !v_S = E

C = Δù
r =ù
ru − ù
r u_W
*u = ∑u − ∑u_W
 : rate of growth of the money supply, it’s constant for any t.
E
 , and for simplicity, we assume
We assume that the central bank is able to exogenously control C
that it applies a rule for the rate of growth of the money supply.
Since I subtract Ôu − Ôu_W , then / disappears, / − / = 0.
 − *u .
1° step: Rewrite the !" in terms of variation ⟹ Ôu − Ôu_W = C
2° step: To solve the model we need to define how the expectations are formed.
The expectations for the Neoclassical economists are endogenous, while for Keynes are
exogenous.
Adaptive Expectation Hypothesis
Adaptive Expectation Hypothesis proposed by Friedman states that:
 7v is a weighted average between past expectations and past
The expected inflation rate π
realization of the inflation rate, so the observed inflation rate in the past.
The expectations are backward looking, on the basis of what I have observed in the past and
expected in the past.
This hypothesis says that the people learn from past mistakes because the provision is
proportional to the past mistake. There is a sort of error correction mechanism in Statistics.
It’s valid for any variable in which there is ‘e’.
Adaptive Expectations:
t
*Úut = 3*Úu_W (1 − 3)*Úu_W
58
t
t
*Úut − *Úu_W
= 3(*Úu_W − *Úu_W
)
t
t
*Úu − *Úu_W Revision (change) in the expectations in 2 years.
t
*Úu_W − *Úu_W
Past Mistake = effective inflation rate − previous expectation.
There are 2 polar cases:
• 4 = :: there is no learning, so the expectations are equal to the previous expectations. In
this case the expectations are said to be myopic.
• 4 = Ü: in this case *Úu_W is cancelled, so the expected inflation is equal to the previous
inflation rate. So in this case the expectation is purely backward looking. I set the inflation
rate on the base of what I’ve observed in the past. In this case the expectations are said to
be static. I solve the system by setting 3 = 1.
 − *u
(ûp) Ôu − Ôu_W = C
∫
1
(ûA) *u − *Úu_W = (Ôu − Ôg )
Z
4 = Ü ⟹ Ôu = Ôg + …(*u − *Úu_W )
The ûA is solved in terms of inflation rate. I apply the static expectation hypothesis 3 = 1.
Then I solve for *u and I obtain a dynamic system, 2 times 2 system, mathematically it’s a first
order difference equation system because Ôu depends on Ôu_W and on *u ; and *u depends on
*Úu_W and Ôu . So both Ôu and *u are backward looking, there is a dynamics, both the 2 equations
interacts each other.
To obtain the graphical solution of a system of 2 difference equations are necessary 2 steps:
1° step derive the demarcation lines, simply the equation represented graphically:
%v = E

1. Ôu = Ôu_W ⟹ π
2. *u = *Úu_W ⟹ !v = !Q
The demarcation lines correspond to a steady state: also meant as the long run, is a situation
of no dynamics, all variables are constant over time, they are equal to the variables in the
previous period.
In the steady state the unemployment rate ‡g is directly proportional to the level of equilibrium
inflation *∗ , so if one increase, also the other one increases.
Property of the Monetarist model (explain the Friedman rule):
in the steady state the inflation is univocally determined by the rate of growth of the money
 , along the 1° demarcation line !v = !v_S .
supply E
Friedman rule: to control the inflation in the long run we set the rate of growth for money
 always equal to 2% in every period, so if my objective is a 2% inflation, I must allow
supply E
the money supply to increase exactly by 2%.
This means that the demarcation line divides the plan in 2 regions Ôu > Ôu_W and Ôu < Ôu_W . So
we have 2 possibilities: either Ôu can increase or decrease.
2° step draw the dynamics:
59
%v = E
 , determined by !v = !v_S , divides the plan in
This means that the 1° demarcation line π
2 regions Ôu > Ôu_W and Ôu < Ôu_W . So we have 2 possibilities:
•
 <
In the region above: the rate of growth of the money supply is lower than the inflation rate E
%v ⟹ !v < !v_S it implies that the level of output decreases over time.
π
Ô moves over time ⟹ horizontal arrow towards the left.
•
 >
In the region below: the rate of growth of the money supply is higher than the inflation rate E
%
πv ⟹ !v > !v_S it implies that the level of output increases over time.
Ô moves over time ⟹ horizontal arrow towards the right.
%v = π
 v_S .
The 2° demarcation line !v = !Q is vertical, along the line π
The inflation is stable only when Ôu is at a long run level Ôg .
Also in this case the demarcation line divides the plan in 2 regions in which the inflation is not
stable, it’s stable only along the demarcation line.
•
In the region on the right: Ôu > Ôg ⟹*u > *Úu_W .
The inflation is in increasing over time ⟹ vertical arrow goes upwards.
•
In the region on the left: Ôu < Ôg ⟹ *u < *Úu_W .
The inflation is in decreasing over time ⟹ vertical arrow goes downwards.
3° step join the results, overlapping the 2 graphs.
60
%v = E
 and !v = !Q is the long run
The intersection between the 2 demarcation lines π
equilibrium P, the steady state of the economy. In the long run the inflation is pinned down by
the rate of growth of the money supply and the output is equal to Ôg , the Pure Neoclassical
model, because in the long run people learn.
Suppose to start in û with the economy outside the equilibrium, then the model follows this
circular behave:
• Output increases inflation increases ⇧⇨
• Output decreases inflation increases ⇦⇧
• Output decreases inflation decreases ⇦⇩
• Output increases inflation decreases ⇩⇨
The equilibrium is dynamically stable, the economics converge towards the equilibrium, there
is a cycle convergence, this model explains and is consistent with the business cycle.
Now that we know that the model is stable we can perform a comparative statics analysis,
comparing 2 different steady states if some parameters change.
Also the comparative dynamics analysis, how the system reaches the new equilibrium if
some parameters or exogenous variables change.
.
The variable that we want to change is the rate of growth of the money supply C
The economy is in a steady state and a shock occurs: suppose that at the time 0 the central
V to C
W (C
W > C
V ) because of an
bank increases permanently the money supply from C
expansionary monetary policy (the same result would appear also with the fiscal policy, by
applying a dynamics for /).
As a result the horizontal demarcation line changes its position going upwards, and the
economy converges from P to the new equilibrium PS , which is the new steady state
comparative statics, comparing 2 different equilibria.
61
The economy reaches the new steady state through the business cycle, because once the
old demarcation line shifts upwards, then it disappears, so that a dynamic starts.
At the beginning the prices are procyclical: because of the monetary expansion the output
increases and the inflation rate increases, so the real wage decreases and the firms starts to
produce more. Then it happens the opposite, there is a stagflation period (prices increases
even more and the output starts to decrease).
The reason behind it’s the learning process: at the beginning monetary policy is effective on
the level of output because it generates a surprise since people expect the previous inflation,
so there is a change in the real variables, that depends on the imperfect information; but at some
point the agents observe the situation and understand that they were wrong, so they set an
higher inflation expectations, until the effect on the output becomes negative, since people
expects a very high inflation rate ⟹ The trend will reverse itself.
Conclusion of this model: an expansionary policy is temporarily effective on the level of
output, but only in the short run. In the long run the output will come back on Ôg , so money
is not neutral in the short run (like for Keynesians) because of the imperfect information, but
money is neutral only in the long run. Consequently an expansionary policy has a
permanent effect on the inflation rate.
This policy is not desirable for 2 reasons: (CHECK se giuste)
1. Ôg is Pareto efficient, so there is no need to go beyond.
2. Even the assumption of perfect competition is inefficient.
So an expansionary policy generates a necessary fluctuation, and in the long run the output
comes back to Ôg , but the inflation rate is higher. So the policy is Pareto Welfare decreasing,
because apart from the fluctuations.
For Friedman, as for the 2 Neoclassical models, money is not neutral, and he demonstrates
that an activistic monetary policy generates a welfare deterioration, since it let increase the
inflation, and not the output, in the long run.
Once we achieve PS is very costly to come back to P.
If the economy starts in BW and the central bank tries to disinflate the economy (like nowadays)
by decreasing the rate of growth of the money supply, which is welfare improving because we
have disinflation, but the disinflation can be costly for the society because of the dynamics.
Indeed at the beginning there is a decrease in the level of output, so an increase in the
unemployment rate.
The disinflationary periods, like in Italy during 80s and also the Maastricht Treaty condition, were
very costly because Italy had to implement a very strong contractionary monetary policy that
generates the dynamics above, so the output decreases and the unemployment rate increases.
So the Neoclassical conclusions are quite the same of the Pure Neoclassical model: the central
bank should not be activistic but should be passive, should set the rate of growth from money
supply equal to a k% rule, where k% is the target inflation rate; any business cycle is
unnecessary and brings permanent effects on the inflation rate.
C. New Classical Macroeconomics - Lucas
The leader of the New Classical Macroeconomics school is Robert Lucas.
The difference with respect to the Monetarist school is the critique to the Adaptive Expectations
Hypothesis, because of the people irrationality, because they base their tomorrow decisions
on the today situations, people don’t use all the information available.
Lucas proposes the Rational Expectations Hypothesis.
Lucas uses a model very similar to Friedman, he introduces:
62
•
•
A stochastic model: It means that random variables can affect the outcome of the economy
ex Covid is an example of random variables.
He treats πv as the realization of a random variable and a shock in the !$, which is also the
realization of a random variable.
Rational Expectations Hypothesis: is a non-distorted expectation, a systematically correct
expectation. People are assumed to know 3 elements:
1. All the past history of the variable, all the time series of the variable (like for the Adaptive
Expectations Hypothesis).
2. The distribution of the shocks of the random variables, what is the mean, variance,
covariance, correlation.
3. The equation of the model, how the economy works, which is resumed in the system of 2
equation, this point is meant as the fact that people rely on who knows the equation and its
function.
New Classical Macroeconomics model:
(ûp) Ôu = ù
r u − ∑u + /u
“
(ûA) Ôu = Ôg + …(∑u − ∑ut ) + *u
s
Ö7v = ñ(tv )
v
Example:
Ôut = Ôg + …(∑ut − ∑ut ) + *ut
*ut = 0 ; …(∑ut − ∑ut )
Ôut = Ôg
Ö7v : rational expectation of a given variable.
ñ: variable mathematical operator, useful to compute the mathematical expectation.
9v : information available at time ‚.
&7v : expected epsilon *.
The Rational Expectation is a conditional expectation: the rational expectation of a given variable
âut is the mathematical expectation conditional upon the information available at time Ï Ωu .
For example If I have to forecast the GDP I don’t use Ôu_W but I use the first equation of the system
or the second one, which is even better.
Ôut = Ôg because the expectation of a constant is the constant.
Ôut = Ôg + Ã(u7v − u7v ) the expected price level - the expectation of an expectation, which is the
expectation itself.
Ôut = Ôg + …(∑ut − ∑ut ) + &7v the expected epsilon *, if * has a 0 mean and constant variance, then the
mathematical expectation is zero. Then I obtain Ôut = Ôg .
The expected realization is the mean, in this case they are both 0, If the mean was 4, then also the
expectation would have been 4.
To solve a model with rational expectation, to compute any expectation, it’s necessary to use the
equations of the model with the rule computed for the mathematical expectations.
Example: the mathematical expectation of a sum between 2 variables it’s the sum of the 2
expectations.
Solution of the Lucas model:
(ûp) Ôu = ù
r u − ∑u + /u ;
/u (0, <wX )
;
(ûA) Ôu = Ôg + …(∑u − ∑ut ) + *u ; *u (0, <xX )
The Lucas model ûp corresponds:
• For a Keynesian economist to the resolution of the @A − BC model with variable prices.
• For a Neoclassical economist to the logarithmic version of the quantity equation.
63
It’s a stochastic model, so <v is treated as a demand shock, is the realization of a random variable
with a given distribution. For example with zero mean and variance <wX constant over time. In any
period ‚ there is a shock, which is the realization of a normal variable and the shocks are nor
correlated to each other. So the realization of a shock in the period Ï doesn’t affect the
distribution in the period ÏS , it means that the 2 shocks <v and &v are not correlated.
These shocks are white noise, it gives rise to the time series below, with variance constant over
time and mean equal to zero, which implies that the number of positive shocks is roughly equal
to the number of negative shocks.
Contrary to Friedman, Lucas used the notion of Rational Expectations: mathematical expectation,
which is the mean of the distribution. So the mathematical expectation ∑ut conditional upon the
information available at time ‚.
The information set ev includes the time series of all the variable, the distributions of the
shocks (the mean, the variance and the fact that the shocks are not correlated) and agents are also
assumed to know the relationship between the variables, so they know this model, or rely on that
people who know this model. But the information set ev doesn’t include the realization of the
shock ex Covid was unexpected.
∑ut = j(∑u |@u )
Solve the model with rational expectations. We must express the 2 endogenous variables of our
interest Ôu and ∑u as a function of exogenous variables (like the exogenous shocks) and the
parameters.
To influence the level of economic activity there must be an inflation surprise. We must derivate
an expression for this surprise and substitute it into the ûA.
Ôut = Ôg + …(∑u − ∑ut ) + *u
Ôut = Ôg + 0 + 0
!7v = !Q
Expected level of output can be obtained by the ûA, since Ôg is given and known by the agents, the
expectations of a constant is the constant itself.
The expectation of the expectation is the expectation itself (∑ut )t = ∑ut .
The expectation of * = 0.
The best prediction that agents can make about the GDP, is that f"π = !Q .
We have to derivate an expression for the surprise inflation uv − u7v , and for this purpose we use
the ûp, and applying the Rational Expectation Hypothesis to the ûp equation I obtain:
(ûp) ∑u = ù
r u − Ôu + /u
t
t
∑u = ù
r u − Ôg
∑u − ∑ut = (ù
ru − ù
r ut ) − (Ôu − Ôg ) + /u
Ôu = Ôg + …(ù
ru − ù
r ut ) − …(Ôu − Ôg ) + … /u + *u
r 7v : expected money supply, what people expect about the behavior of the central bank.
†
rv −†
r 7v : monetary surprise, the unexpected money supply.
†
It’s yet not the final solution, but it’s the semi-reduced form, to get the solution we need to compute
the expectations about the policy behavior. Then what happens to the GDP depends on the
shocks and on the expectation about the policy behavior. It’s what we can call the monetary
surprise: difference between the effective money supply effectively decided in time ‚ by the
central bank and the expected money supply.
By solving the semi-reduced form for Ôu I obtain:
Z
Z
Z
Ôu = Ôg + 1+Z (ù
ru − ù
r ut ) + 1+Z /u + 1+Z *u
64
Ôu depends on the unexpected component of the policy ù
ru − ù
r ut and the shocks /u and *u .
We assume that the central bank follows a policy rule, the central bank announces to the public, the
agents, that it will follow a certain policy rule, which is an equation describing the behavior of the
central bank.
To simplify we assume a very simple policy rule:
ù
ru = ù
r W + >u
ù
r ut = ù
rW
ù
ru − ù
r ut = >u
\
\
!∗v = !Q + M+\ (?v − <v ) + M+\ &v
)qy∗
=0
)S
>z
r S : constant.
†
?v : policy shock.
Suppose that ù
r u decided by the central bank is equal to a constant ù
r W (systematic component of
the policy rule) + a monetary policy shock >u (random component of the policy rule) which has zero
mean and is the realization of a random variable. The monetary policy shock is a sort of surprise
that agents cannot predict in advance, in economics it’s called economic policy shock: a change
in money supply that cannot be predicted, it’s the realization of a random variable with a 0 mean.
The money supply is the sum of a systematic component known by the agents and a shock. It
follows that the expected money supply, so the rational expectations ù
r ut is just equal to ù
r W . So that
t
the monetary surprise (ù
ru − ù
r u ) is equal to the shock >u .
I simplify the short equations and I get the final solution, which is in a reduced form because it’s a
function only of endogenous variables, the realization of the shocks and the parameters.
It gives rise to the economic policy ineffectiveness proposition: states that only the unexpected
component of economic policy (in this case monetary policy) can influence the level of output,
so the GDP, because only the unexpected components cannot be forecasted in advance.
The economic policy ineffectiveness proposition is very important because if the policy makers
systematically tries to influence the economic activity, producing for example inflation, doesn’t
produce any effect when it’s internalized in the information set since it is internalized in the wages
in a way that the real variable is not effective.
Lucas’ critique:
)qy∗
The systematic component is completely neutral
= 0. In practice suppose that the central
)S
>z
bank announces that it will implement a systematic expansionary monetary policy ù
r W > 0, that will
generates an increased inflation and increase wages, and that it is completely neutral because it’s
internalized in the information set of the agents, it’s incorporated in their wages, but in a way that
real variables are not affected, only the nominal variable are influenced by it.
Only the random component of the policy cannot be predicted, then has real effects, but it can be
used few times, if it’s used more times it becomes systematic because agents observe it’s behavior.
Lucas’ conclusion is the Neoclassical conclusion: the central bank should only focus on the
price stability, not trying to influence systematically the level of output, because it won’t produce
any effect, only the inflation which is costly for the society.
D. New Keynesian economics – Lucas’ critique
Apart of this proposition which is very specific for this model, the Lucas’ critique is very influential,
especially for a methodological point of view. The Keynesians recognized that their model misses
the presence of expectations, so from this critique it begins in 80s-90s the New Keynesian
65
literature. They introduce the rational expectations in the macroeconomic model, but they
maintain Keynesian assumptions, of rigid wages in the short run.
Result: the ineffectiveness proposition is less general than what we think.
New Keynesian model (simplified version):
r u − ∑u + /u
Ôu = ù
Ôu = …W ˚u
production function
@
˚u = vV − vW (˙u − ∑u )
labor demand
˙u = A + ∑ut
wage rule
<v : is a shock.
B (omega): constant, expected real wage that workers want to stabilize.
It maintains the rational expectations, but differ from the Lucas model for 2 aspects:
1. Wage rigidity, specifically the wages are decided at the beginning of the period ‚, and cannot
be revised for 1 year, we are considering 1 year fixed contracts.
It implies that the wages re decided prior the realization of the shock and cannot be indexed to
the shock. At the moment of the contract the agreement is based on the expected price level
over the year.
2. (Dalle slide, prof aveva lasciato in bianco) Agreement between firms and workers on the real
wage.
The labor demand depends negatively on the real wage.
˙u is fixed over the period according to the rule ˙u = ˙ + ∑ut . Which implies that people are rational
and they want to stabilize the expected real wage B omega. They decide the wage by taking
into account and internalizing any increase in the expected price level.
˚u = vV − vW A + vW (∑u − ∑ut )
Ôu = …W (vV − vW A) + …W vW (∑u − ∑ut )]
Ôu = Ôg + …(∑u − ∑ut )]
Ôg = …W (vV − vW A)
… = …W vW
By substituting ˙u in the labor demand, and also in this case I obtain an explicit surprise inflation.
Then I substitute it into the production function and I get the aggregate supply ûA.
This equation is algebraically equal to the Lucas’ one, but with 2 important differences:
1. There are nominal wage contracts.
Ôg can be inefficient, depends on A, on the agreements, and the agreements between workers
and firms doesn’t necessarily leads to the full employment.
If A is very high there can be an excess supply, so Ôg can be inefficient and display the presence
of voluntary unemployment.
There are wages contracts, so ∑u − ∑ut decided at the beginning of period ‚ and cannot be revised
over the period.
2. While workers decide nominal wages at the beginning of period and cannot internalize the
shocks into wages, on the contrary the central bank has an information advantage, it
observes the realization of the shock and can react to it ex Pandemic crisis. Meeting of central
bankers occurs once a month, whereas the wages can be changed only once a year.
\
\
!∗v = !Q + M+\ (?v − <v ) + M+\ &v
The procedure for the solution of the model is exactly the same, but with a modification because
of the information advantage: the non-systematic component of the monetary policy can be
decided after the observation of the shock, in order to stabilize the level of output.
Example during covid:
/u < 0
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*u < 0
?v can be decided after observing the shock.
I have to impose Ôu = Ôg and solve it for >u , then I get the policy rule.
M
If I want to stabilize !v = !Q It’s possible if and only if ?v = −<v − &v
\
So if the shock is negative I have to increase the money supply.
So with those 2 realistic assumption of nominal wage contracts and central bank’s information
advantage, the economic policy is still effective, but only the non-systematic policy is
effective, because the systematic component is still not effective.
Optimal inflation rate
There is a remaining issue, the policy maker can stabilize the level of output at Ôg but we know that
there is a temptation of the policy makers to go beyond the Ôg . This model investigates it.
Robert Barro and Robert Gordon propose a model that reconsiders the optimal trade-off within
inflation and unemployment rate.
The optimal inflation and the optimal unemployment rate is in j, in which ‡∗ is below ‡g , then Ô ∗ is
above Ôg . For Keynesians we can bring the level of the unemployment rate and therefore the level
of output close to the Pareto efficient level.
But the Lucas critique and Friedman critique made explicit the fact that the position of the
Philipps curve depends on the inflation expectations, which are endogenous.
This Philipps curve holds only if u
C7 = :, only if there are no inflation expectations.
 v = &($Q − $v ) + π
 7v
π
The Augmented Philipps curve, First derived by Friedman and then adopted even by Keynesians,
it is not only the Neoclassical Philipps curve, but also the New Keynesian one, because also in the
New Keynesian model the supply side is identical, it gives rise to an identical aggregate supply ûA,
therefore to an identical Philipps curve.
Strategic interactions between agents of the economy.
Policy problem: sort of strategic interaction because the outcomes of the macroeconomy not only
depends on the policy implemented by the central bank and the governments, but also on how
people expect that this policy will be. So it will merge a problem of credibility of reputation of fiscal
and monetary policy. The outcomes depend both on the policy and on the expected policy.
The working of the Barro-Gordon model is the following:
New Keynesian assumptions: rational expectations, 1 year wage contract decided at the
beginning of the ‚, for now there are no shocks or disturbances. The monetary and fiscal policies
are decided over the year after the agreement about the wage between workers and firms.
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It’s a non-simultaneous game, decisions are not simultaneous: I have to decide what’s the
expectations, and therefore my wage, knowing that the central bank will decide after me, also the
central bank takes into account that will decide after the agreement in the contracts.
The central bank announces at the beginning of the year a given policy, we assume that the target
levels, the first best, for inflation and unemployment rate are normalized to zero.
$%∗ = 0
(∗ = 0
Now suppose that the central bank announces *Ú = 0, equal to the target. At this point people have
2 options:
• Believe in the announcement and incorporate it in the contract.
• Cheat the announcement.
If people believe to the announcement they will set their expectations to 0 and the position of
the Phillips curve is the usual one ⟹ u
C7 = :. But the announcement is not respected because once
people have made the contract not internalizing the inflation, then the optimal choice is the one
below, so for the people there is a incentive to cheat correlated to the believe in the
announcement, because they are aware that the same announcement will be cheated on itself
 = : is not credible.
⟹ *ÚW cannot be an equilibrium because the announcement π
This credibility problem discovered by Kydland and Prescott is very important and it’s the time
inconsistency problem: incentive ex post, to cheat the announcement, to not respect it, so the
policy is not time consistent, the announcement is never respected.
Time consistent policy: policy incompatible with the incentive to cheat, to not respect the
announcement, so an announced policy that is respectable.
It graphically corresponds to the tangency point between the augmented Phillips curve and the
indifference curve of the loss function in correspondence of the natural rate of unemployment.
There can be credible announcements about a high inflation rate and credible announcements
about a low inflation rate. They depend on the parameter + of the loss function and on the central
bank’s reputation.
The announcement *Ú = 0 is not credible because it’s time inconsistent, because if I decide my
expectations according to your announcement, I already know that you will cheat on me.
Conclusion: I will decide my expectations only if you announce an inflation rate that is time
consistent, that has an incitive to the respect of the announcement.
The equilibrium of the model
The reasoning is the same also in the case in which the central bank announces the inflation rate
*Ú = *ÚW .
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 S the position of the Phillips curve will shift upwards, then in
If I believe to the announcement π
this case I will move to the left, because I will tend to cheat the announcement, I will set a higher
inflation rate.
The only equilibrium ñ is the tangency point in which I don’t have the incentive to go to the left.
=π
 { I won’t have an incentive to cheat
So only in the case of the announcement of an inflation π
and I will set my expectations according to the announcement.
Outcome: the policy maker is not able to go below $Q because people anticipate the temptation
to go below ‡g and they will set the expectations according to it.
If the inflation is relatively high and the unemployment rate stays at ‡g , the marginal cost of the
inflation increases more than proportional, until at some point is not convenient to cheat, and I’ve
reached j.
This outcome of the model is an application of the concept of the Nash equilibrium: equilibrium in
game theory in which each agents implements the best strategy, given the strategy of the other.
This is a very undesirable outcome because the inflation rate is higher than the target, so ñ is
Pareto inefficient. It’s called the cost of discretion. Monetary policies are discretionary, there isn’t
a commitment, you can choose the policy preferred for any period.
The point ñ also depends on the parameter ', the weight attached to the inflation stabilization.
• The more accommodating I am (low +), the higher is the incentive to cheat and the higher is the
inflation rate ⟹ high j (Italy).
• The more intransigent I am (high), the lower is the incentive to cheat and the lower is the
inflation rate ⟹ low j (Germany).
To solve the problem:
1. Delegate the monetary policy to a very tough, intransigent independent central banker with
' = Ü. When + = 1 the solution is ‡g , there aren’t indifference curves, you only care about the
inflation, by setting the inflation rate equal to 0.
The equilibrium point in ‡g is Pareto superior to the point j, because ‡ = ‡g and *Ú = 0.
2. Commitment: constraint that ties the hands to the central banks, for example a commitment
could be introducing in the constitution a rule that states that every year the inflation rate must
be equal to a tot, and if you don’t respect this rule you don’t respect the constitution, it’s a
binding commitment. This is why the main objective of many central banks is the maintenance
of the price stability.
The Shocks
Commitment and delegation are not fully used. There is a sort of minimum degree of flexibility,
for example in the Maastricht treaty it’s stated that in the medium run should be reached the 2% of
inflation, in the medium run and not in all the periods.
The reason for the degree of flexibility is because in the reality there is another reason that justify
the movements in the Phillips curve, and it’s that the Phillips curve is subject to shocks.
Solve the Phillips curve by ‡u :
M 
7
$v = $Q − (π
v − πv ) + Åv
u
Åv : stochastic disturbance, it’s the realization of the shock.
Assume as a shock the Pandemic crisis, but it could also be the war, increase in energy costs and
so on, we live in a stochastic world. The position of the Phillips curve can move because of the
realization of the shocks.
We start from the Nash equilibrium, the equilibrium without the shocks, the time consistent policy,
the outcome of the game. Suppose that for a shock the Phillips curve translates to the right:
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Graphically the segment Åv it’s the realization of the shock.
": point with a discretionary policy. With the discretion I have a systematic inflation bias.
d: point with a commitment. With the commitment I solve the inflation bias, I have an inflation rate
equal to zero because it’s written in the constitution.
Without shocks commitment is always better than discretion because it stabilizes the
expectations. But in case of a shock Éu the commitment is not always better than discretion,
because under commitment I have to set the inflation rate equal to zero and I cannot react to
negative shocks.
If under commitment the inflation rate is equal to zero s*Úu − *Úut t = 0, then the unemployment rate
increases from ‡g to ‡′. It’s because if in case of a shock ‡u increases one for one, if the shock is
10 the unemployment rate increases by 10. I cannot react to the shock.
Under discretion I can react in case of shock, with the new indifference curve I achieve p′. I can
see graphically that in the discretion case the increase in the unemployment rate is lower than in
the commitment, because under commitment I cannot react, but if I have some flexibility, like under
discretion, I can react to the shocks.
So I can use the monetary policy in an expansionary way to try to dumpen the effects on the
unemployment rate.
This is the reason why no central banks in the world is ultra conservative, ultra intransigent, no
binding commitment is adopted, because it can be more costly than the discretion if exogenous
shocks hit the economy.
So having a positive inflation rate in the equilibrium allows to react to exogenous shocks in a
flexible way, so have some inflation may be welfare improving because it allows the policy
makers to react to the shocks. This is the reason why also in a very conservative central bank like
the European Central Bank, in the Maastricht treaty it’s written that the inflation rate should be equal
to 2% in the medium run, not every year. It allows the European Central Bank to react to the shocks,
a binding rule like a commitment wouldn’t have allowed it. Very strict rules are not desirable, they
are desirable without shocks, but not in a stochastic environment in which we live.
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