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Mathematical Approach of the IS-LM Curve Model
We still maintain the assumption about the fixed price level: The price level P is assumed
to be fixed in the IS-LM model unless it is specified otherwise.
1. What Are We Trying to Do?
The IS-LM is the most broadly used frame of reference in macroeconomics theory.
In the IS-LM Curve Model, the interactions between the goods (output) market and the
financial market gives the equilibrium Y* and the equilibrium interest rate i*.
As this new Y* and i* satisfy the equilibrium conditions in the goods market as well as the
money market.
We would like to proceed in the following manner:
First, we will establish an inverse relationship between interest rates and investment in
the goods market. This eventually leads us to the IS curve or the various combinations
of i and Y, which satisfy the equilibrium condition in the goods market or make the
demand equal to the supply in the goods market.
Second, we will establish an inverse relationship between interest rates and (real)
money demand in the money market. This leads us to the LM curve or the various
combinations of i and Y, which satisfy the money market equilibrium or make the
demand equal to the supply in the money market.
Third, by equating the Ys or the i’s that we have obtained from the IS and the LM curves,
we will solve for the national income Y* or the interest rates i*, which satisfy the goods
and money market equilibrium conditions at the same time. Graphically, they are
obtained from the intersection of the IS and LM curves.
Fourth, we will examine various “comparative statics”, which is represented by the
multiplier. In this section, we examine the impact of exogenous changes in government
expenditures, money supply, monetary market conditions, etc.(these are only a few out
of many possible exogenous changes in the economy), on the equilibrium national
income Y* or the equilibrium interest rate i*.
2. IS curve
1) Components
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(1) Consumption Expenditure
Funtional Form of Consumption
C = C0 + c1 (Y-T)
For now, we assume that T = T0. However, later we should introduce a
more realistic assumption that T = T0 + t1 Y.
(2) Investment Expenditure
How does a high real interest rate dampen economic activities? Actually it works in two
ways; first it reduces the investment, and thus the AE, eventually reducing Y*. It also
reduces the real money demand. At this moment ignore the second impact.
The (real) interest rate constitutes a cost of obtaining (financial) capital for additions to
capital stock or investment. A higher interest rate means a higher cost, a lower
profitability and the lower rate of return on investment projects. Note well that the
investment is a decreasing function of real, not nominal, interest rates.
Some investment projects, which used to be marginally profitable or managed to make
both ends meet, are no longer profitable. So the desired investment will decrease as the
interest rate increases.
Functional Form of Investment
I = I0 – b i ,
I0 is the autonomous investment and b is the elasticity of investment with respect to
interest rates. b>0. Here b measures the responsiveness to changes in investment to
changes in the interest rate.
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The larger the value of b, the more responsive the investment with respect to changes in
interest rates. In other words, the larger the value of b, the more interest-rate elastic the
investment.
A numerical example would be I = 100 – 5 i: One percentage increases in investment will
bring about a 5% decrease in investment.
(3) Government Expenditure
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(4) Net Exports
X–M
As long as the prices are set to be constant (no changes in the relative price level or
competitiveness), and there is no change in Foreign exchange rates, they are
X = X0 or exogenous (as the domestic country has no control over its exports)
M = M0 - m 1 Y
*Question: Compare the consumption function and the import function. What is the
major difference? Why is M not a function of Y-T, but Y itself? – Why is T not deducted
from the Import Expenditure Function?
2) IS Curve: Goods Market Equilibrium
For simple illustration, for now, we assume that X-M =0 or that the
economy has no exports or imports. Later this should be relaxed.
The IS curve shows various combinations of national income and interest rates which
bring out the equilibrium, or the equality between demand and supply, in the goods
market.
Let’s plug the aforementioned modified investment function into the aggregate
expenditure function, and solve for Y* and i*.
(1) Algebraic Derivation
Recall there are three different cases of AE.
Case 1. All taxes are lump-sum or autonomous.
Under 3 unrealistic but simplying assumptions that T = T0, X-M =0 and all prices are
fixed.
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Suppose that we are dealing with the aggregate expenditures with only lump-sum taxes
and no exports or imports (This is Case 1 in the last chapter of the Keynesian Cross
Diamgram).
The AE will be
AE = C0 + c1 (Y – T0) + I0 – bi + G0
= c1 Y + (C0 - c1 T0 + I0 + G0 – b I0 )
At equilibrium,
Y= AE
Y = c1 Y + (C0 – c1 T0 + I0 + G0 – b i )
Y – c1 Y = C0 – c1 T0 + I0 + G0 – b i
Solve for Y* and i*: We can rewrite this equation as a functional relationship between Y *
and the interest rate i. That is, solving for Y* or i*, depending on what we need to know
about:
Y*=
1
( C 0 - c1 T 0 + I 0 - b i + G 0 )
1 - c1
or
i *=
1
1( C 0 - c1 T 0 + I 0 + G 0 ) - c1 Y
b
b
This is the algebraic expression of the relation between (i, Y) which represents
equilibrium in the final goods market.

The above two are identical. However, in economics, it is customary to put the
price or interest rate on the vertical axis, and the quantity on the horizontal axis
when drawing a graph or a diagram. So the second one is in line with the
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illustrative tradition. We can draw the IS curve by putting i on the vertical axis
and Y on the horizontal axis.

Note that the slope has a negative sign and thus the IS curve is downward sloping.
This means that in equilibrium, of the goods market, the interest rate and income
move in the opposite direction; if interest rate increases for some reason, in order
to stay at the same equilibrium in the goods market, national income should
decrease.
(2) Intuitive Explanation of the IS curve.
We can also give the following intuitive explanation about the negative slope of the IS
curve;
Let us start from one equilibrium: Y = YS = AE = C + I + G. Here let us change the
interest rate and examine the responsive changes in Y. If i and Y turn out to be moving in
the same direction, the slope of the IS curve will be positive, and vice versa.
Let us suppose that the interest rate decreases from i0 to i1. If investment is inversely
related to the interest rate, there will be an increase in investment and thus an increase in
the AE. This means that there will be an excess aggregate demand (now Y < AE’). How
can we re-establish the equality between AE and Y? The answer is by increasing Y. In
the equality of AE and YS, or the equilibrium of the goods market, when interest rates
goes down and national income goes up. The interest rate and national income should
move in the opposite direction.
We can express the above relationship with a curve in a graph with Y* on the horizontal
axis, and the interest rate i* on the vertical axis. This curve is called the IS curve because,
at equilibrium, AE = Y, which means C + I + G + G + X – M = C + S + T. As C in both
side cancels out, the equilibrium condition of the goods market can be expressed as I + G
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+X = S + T + M. The first letter of each side of the equality read ‘I’ and ‘S’. So along the
IS curve, I + G + X = S + T + M. So comes the word ‘IS curve’.
3. LM Curve for Money Market Equilibrium
LM cure shows the combinations of the interest rate and the income (i, Y) which
satisfies the equilibrium in the money market.
1) Components
(1) ‘Nominal’ versus ‘Real’ Money Supply/Demand
We should make distinction between Nominal Supply or Demand and Real Supply or
Demand. The first one is in monetary terms, and the second in quantity terms.
In microeconomic analysis of equilibrium, we define the demand and supply in real
terms, not in monetary or nominal terms. For instance, if we say that $20,000 worth of
hamburgers are demanded (or supplied), the statement is not clear enough. This $20,000
is nominal demand in monetary terms. What about the real demand or quantity? If the
price is $1 per hamburger, in real terms, 20,000 units of hamburgers are demanded. If the
price is $10, in real terms 2,000 hamburgers are demanded.
In the same vein, for the analysis of the money market equilibrium, the quantity of money
should be also defined in real terms, not in nominal or monetary terms. The nominal
quantity of money is the face value of the money, and the real quantity of money is the
face value divide by the price level;
Real quantity of money = Nominal quantity of money/Price level.
m = M/ P
The real quantity of money supply m is the nominal money supply divided by the price
level. For instance, nominal money supply is 2,000,000,00 dollars or $ 2 billion. The
price level is measured by a price index. Suppose that the price index is 100 (or 1.00)
right now. The real money supply m = 20,000,000,000/100 or 20/1.0 (units do not matter
as long as there is a consistency).
(2) Money Supply
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The nominal quantity of the money supply is determined by the monetary authority,
which usually is the central bank.
MS = M0
Money supply varies depending on the scopes of money: it may include only cashes (in
circulation) in a narrow scope, and may include cashes and all deposits in a broad
scope.such as M2. The different scopes of money supply will be discussed in full in the
separate chapter.
For instance, M0 = $20,000,000,000 or $20 billion.
The monetary authority does not have to determine the nominal money supply on the
basis of any variables in any given manner over time. Thus, we regard the nominal
money supply as an exogenous variable, and regard it as arbitrarily determined by the
monetary authority.
Mathematically, this means that the nominal money supply curve is vertical, being
independent of interest rates. As the money supply is independent of the interest rate,
when drawn in the interest rate and real quantity dimension, the money supply curve is
vertical, being the same regardless of the level of the interest rate.
At one point of time it is fixed. However, of course, over time it can be changed by the
monetary authority. In fact, the monetary authority sets the nominal money supply in
each period.
. For instance, depending on circumstances, the monetary authority may increase or
decrease the nominal money supply when there is an increase in the national
income. If the monetary authority wants to accommodate the booming or growing
(3) Real Money Demand
economy, it would increase the nominal money supply in the face of a rising
national income. The logic is that a larger economy has a larger volume of
(a) Uniqueness of Real Money Demand
economic transactions and needs a larger amount of medium of exchanges, i.e.,
money. On the other hand, if the monetary authority judges that the rising national
A few important things to remember about real money demand:
income may touch off inflation and thus decides to fight the inflation, it will
decrease the money supply in the face of a rising national income. This is called
‘ leaning-against-wind’ monetary policy. All in all, the monetary authority can
choose any of these policies. Mathematically, this means that there is no consistent
functional relationship between the national income and the nominal money supply.
In fact, nominal money supply has no consistent relationship with any economic
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First, note that the money market equilibrium should be defined in terms of real money
supply and demand;
Nominal money supply is equal to nominal money demand at all times, i.e., at and out of
equilibrium. The nominal quantity of money demanded by the society as a whole is
always equal to the nominal quantity of money supplied by the government; MS = MD at
all times. Suppose the government is handing out newly printed paper monies or notes on
the street. IS there anyone who would refuse them? Every dollar of money supply will
be gladly demanded.
Second, while an individual cannot control real money demand, the general public as
opposed to the monetary authority can control real money demand;
When an individual receives some new paper monies, her/his nominal (and real) balances
increase. S/he may succeed in decreasing the nominal money demanded or the real
money balanced back to the initial level by spending the excess money holdings.
However, because her/his expenditures will become someone else’s receipts, some other
members are getting the increased money supply. So from an individual’s view point the
nominal money demanded may be controllable, while it is not controllable from the entire
society’s viewpoint. What is true for individuals is not necessarily true for the society as
a whole. This is the ‘fallacy of composition’ commonly founded in macroeconomics.
As individuals are busy getting rid of the excess of money holding over the desired level
of demand (“I would like to have $200 in my pocket, but as government gives me a new
$100 bill, now I have the excess of money holding by $100. I would like to go back to
the desired level of money demanded, that is $200 by spending $100 away.”) The
increased money becomes a kind of ‘hot potato’. What does this mean in terms of the
real money demand? The real money demand, which is the nominal money demand ( =
the nominal money supply) divided by the price level, is going back to the initial level.
The increased speed o spending and expenditure will eventually push up the price level.
The general public are collectively changing the price level and thus controlling the real
money demand.
Suppose MS = M = MD = $200 billion and P = 1.00 initially in the equilibrium; the real
money demand is MD/P = 200/1 = 200 and should be equal to the real money supply at
the equilibrium. This real money demand is at the desired level at the equilibrium in light
of all the determinants of the demand including the income level and the interest rate.
Now the monetary authority increases the nominal money supply MS to $400 billion.
First, all the increased nominal money supply will be demanded. So the nominal money
demanded is equal to the new nominal money supply; MD’ = MS’ = M’ = $400 billion.
In the short-run, the price does not change, and thus the actual amount of the real money
holding will be m’ = m’’ = M’/P = $400/1.00 = 400. This is much larger than the desired
real money demand, that is, 200. As there are no change in the determinants of the real
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money demand, there should not be any change in the level of real money balances the
general public wish to hold. There is an excess of real cash balances over the desired real
money demand; ‘actual’ real money balances > ‘desired’ real money balances.
As individuals with excessive money balances try to recover the desired real money
balances by spending the excess money receipt, the price level is going up to P’. At this
new price level, the new ‘actual’ real money balances (M’/P’) become equal to the
desired level of real money balances.
Specifically, the price level will go up to the level of 2 (or the index number 200). The
actual real money demand will be 400/2 = 200, the same level as before any changes.
However, if P is fixed, there have to be permanent changes in real money demand, which
is only possible when there is a change in its determinants such as interest rates and real
income. The idea is that if there is an excess of liquidity, in the money market interest
rate should fall and this should in turn boost investment and national income. This is the
case in hand.
(b) Functional Form of Real Money Demand
The real money demand is given a functional form such as
md = L ( i, Y ).
The above equation defines the real money demand as a decreasing function of interest
rates and a increasing function of national income. What determines the desired level
(quantity) of real money demand? Just as the desired quantity of hamburgers is
determined by the consumers’ income and the price of hamburger, the real demand for
money is determined by the income level of the economy, that is the national income, and
the price of the money, that is, the interest rate.
Let us examine the second point in the above statement: the price of money is the interest
rate. In other words, the opportunity cost of holding money balances is the interest rate.
Money is one of many assets, which include bonds, stock, equities and real assets.
Money and other assets are substitutes. The major difference between money and other
assets is that money does not bring in any positive pecuniary returns. Actually it is very
often subject to the erosion of real value due to inflation, and other assets do have
pecuniary returns. However money, or cash balances in a precise term, renders a unique
non-pecuniary service, which is known as ‘liquidity’. Money is the most generally
accepted medium of exchange and most ‘liquid’. So when you decide to hold assets in the
form of cash balances instead of any other, you are showing your preference for liquidity
over pecuniary returns. This is the reason why the money demand is called’ liquidity
preference’, and the money demand function ‘liquidity preference function.’
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The interest rate represents the foregone pecuniary return or the economic sacrifice you
have to take when you are choosing cash balances over other assets, as your mode of
holding assets; in other words, the interest rate is the opportunity cost of holding cash
balances. When the interest rate goes up, the cost of holding cash balances increases and
naturally you would like to hold less assets in the form of cash balances and more interest
bearing assets. This means that the demand for money is inversely related to the interest
rate.
Now we have another major factor to be considered, which affect the real money
demand; the income level. When real income increases, in most cases, the demand for
money increases in real terms, too. To name one reason, when real income increases,
there occur more transactions, and then more cash balances should be held to back up the
increased transactions.
We can give the liquidity preference function the following specific functional form;
md = kY – h i + u,
where K is the elasticity of real money demand with respect to the national income; h is
the elasticity of real money demand with respect to interest rates; and u is the random
component of real money demand.
The liquidity preference curve is negatively sloped when drawn with the interest rate on
the vertical axis and the amount of real money on the horizontal axis. The variables Y
and u are the shift parameters of the real money demand curve.
Also, we can draw a set of liquid preference curves for different levels of income; the
higher the level of national income, the larger the demand for real money balances. You
may remember, from the class of introductory economics, that an increase in income
shifts the demand curve to the right.
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2) LM Curve as the Money Market Equilibrium
As emphasized, the money market equilibrium should be defined in real terms; the
money market is in equilibrium when real money supply is equal to real money demand
ex-ante. If the demand is larger than the supply, the price will go up. With an increased
price some people will give up their demand. The price, which adjusts to equate the
supply and demand, is nothing but the interest rate. The money market interest is set at
such a level as to make the supply equal to demand ex-ante.
(1) Algebraic Solution
LM Curve: Money market equilibrium condition ms = md yields the following
equations. And then you can solve for Y* or i*.
In line with the illustrative tradition of economics (what was it?; do you recall?; if
not go back to the IS curve illustration as shown above), rearranging the equation with ‘i’
on the left hand side and ‘Y’ on the right hand side, we get a LM Curve.
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M0
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= kY - h i + u
P0
h i= i=
M0
+k Y +u
P0
M0
1
k
(+ u )+ Y
h
h
P0
We can draw a LM curve with the interest rate on the vertical axis and the national
income on the horizontal axis. The LM curve is upward-sloping, or in other words, it as a
positive slope.
Of course, as we have discussed in the case of IS, the above LM can be expressed in
terms of Y as well:
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M0
P0
= kY - h i + u 0
kY =
Y=
Eco320 Note #1
M0
P0
M0
+ hi  u 0
1
h
(
 u0 ) + i
k P0
k
If you draw a curve from this, you will have an inverse curve of the above LM curve.
(2) Intuitive Explanation
Why is the LM curve upward-sloping LM?

Let us start with an equilibrium, ms = md.

When the interest rate increases there will be a decrease in the real quantity of
money demanded, (a new md < an old md = ms).
How can we recover the equality between the real money demand and the real
money supply? The real money supply cannot change unless the government
changes the nominal money supply MS or M to a higher level, or the price level
changes. So the real money demand should rebound back to the initial level in
order to re-establish the equality. One way of doing it is to increase Y*. When
the national income increases, the real money demand will increase. This
increase in real money demand offsets the previous decrease in real money
demand. So we can observe that the interest rate and the national income move in
the same direction.

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4. (Expanded) Equilibrium National Income and Interest Rate in the ISLM Framework
Now we would like to get Y* and i* which encompass both goods and money markets.
The intersection of the IS and LM Curves give the equilibrium national income and the
interest rate that satisfy the market clearing condition in both goods markets and money
markets; ex-ante all the goods produced are demanded, and real money supply is equal
to the real money demand.
1) Graphic Solution
2) Algebraic Solution
Steps
1. Get the IS and LM curve
2. Equate the
IS and LM curve
Case 1 with Three Simplifying
Assumptions:
All taxes are lump-sum or autonomous
3. Solve
Y* Prices are fixed
T = T0, Closed Economy
NX=for
0, and
4. Substitute the solution of the Y* for the variable Y and the
LM equation to get the value for i*;
5. Differentiate the above equations for multipliers.
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The strategy here is to bring up the IS and the LM, and solve for Y* and i* that satisfy
both IS and LM. So we go:
 Step 1: Recall the IS Curve: Goods market equilibrium condition AE = Y yields
1
( C 0 - c1 T 0 + I 0 - b i + G0 ),
1 - c1
or
Y=
1
1 - c1
i = ( C 0 - c1 T 0 + I 0 + G 0 ) Y
b
b

Step 2: Recall theLM Curve: Money market equilibrium condition ms = md yields
M0
P0
= ky - h i + u 0
h i= i=
M0
P0
M0
+ k Y + u0
1
k
(+ u0 ) + Y
h
h
P0
or
Y=
1 M0
h
(
 u0 ) + i
k
k
P0
where K is the elasticity of real money demand with respect to the national income; h is
the elasticity of real money demand with respect to interest rates; and u is the random
component of real money demand.
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Step 3: Equate the above two equations for i or Y: The Simultaneous Equilibrium
of Goods and Money Markets yields:
In practice, we may go either ways. First, when we equate Y of the IS and Y of
the LM as shown above:
1
( C 0 - c1 T 0 + I 0 - b i + G0 )  1 M
h
0
1 - c1
(
 u0 ) +
i
k
k
P0
Alternatively, we may equate i of the above IS and i of the above LM:
1
1( C0 - c1 T 0 + I 0 + G0 ) - c1 Y = 1 M 0
k
(+ u0 ) + Y
b
b
h
h
P0
The first equation will yield to the equilibrium Interest Rate. And the second will
yield to the equilibrium National Income. We have to get both. For now, we
focus on Y*:
*
Y =
M
h
b
( C 0 - c1 T 0 + I 0 + G 0 ) +
( 0 - u0 )
h(1 - c1 ) + kb
h(1  c1 ) + kb P0
Rewriting the above we get,
*
Y =
1
kb
1 - c1 +
h
( C 0 - c1 T 0 + I 0 + G 0 ) +
b
h
kb
1 - c1 +
h
(
M0
P0
- u0 )
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* Can you solve for i* by yourself?
3) Comparative Statics of IS-LM: Multipliers:
i) Impacts of Exogenous Changes in Variables on Y* (or i*)
We may remember that in the simple Keynesian model of income determination (the
Cross-Diagram with Y = YS and AE) the multipliers were obtained by differentiating the
equilibrium national income equation.
Now, in the IS-LM curve model, another set of the multipliers can be obtained by
differentiating the first equation, which describes the equilibrium national income in the
goods and money market, with respect to the Autonomous components of AE ( C, T, I, G
and M). The result of differentiation is the coefficient of each variable in the above
equation.
Y
=
C 0
*
1
1 - c1 +
kb
h
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Y
=
I 0
*
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1
1 - c1 +
Y
=
 G0
*
kb
h
1
1 - c1 +
kb
h

The first two multipliers have something to do with business cycles as the C0 and
I0 show cyclical movements over time beyond the control by government.

The third one is called the ‘Fiscal Policy Multiplier’. It measures the ratio of the
change in the goods and money market equilibrium national income to a change
in government expenditure. Note that this new multiplier or the fiscal policy
multiplier in the IS-LM framework is smaller than the government expenditure
multiplier in the Cross-Diagram setting. Both measure ∆Y* due to ∆G. However,
the fiscal policy multiplier takes account of the resultant change in interest rate
and the consequent crowding out effect while the government expenditure
multiplier does not; The thus difference between the government expenditure
multiplier and the fiscal policy multiplier is the crowing-out effect which results
from an increase in interest rates and its suppression of private investment.
Because of the secondary feedback in the money market, the magnitude of fiscal
policy multiplier is smaller and thus ∆G has a smaller impact on Y*.
Y
=
T 0
*

 c1
1 - c1 +
kb
h
The above multiplier measures the change in income to a change in a lump-sum
taxes responsible for it.
b
h
Y *

M
kb

1 - c1 +
p
h

The above multiplier is called the ‘Monetary Policy Multiplier’. It measures the
ratio of the increase in income to an increase in money supply –recall that the
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price level or P is constant, and thus any changes in M/P or real money supply
come from changes in M or money supply.
ii) Impacts on Interest Rates: Solve for the equilibrium interest rate, and examine its
coefficient
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Appendix1: Complicating the Tax Function
So far we have assumed a very simple model where all taxes are lump sum and there are
no exports or imports. Now, let’s extend our model to more complex cases of aggregate
expenditures as we have seen before.
1. Now we may assume that there are Autonomous and Proportional Taxes. T = T0 +
t1Y, and there are no imports or exports.

IS Curve: Goods market equilibrium condition AE = Y yields
Y =
i=

1
( C 0 - c1 T 0 + I 0 - b i + G 0 )
1 - c1 (1 - t 1 )
1
1 - c1 (1 - t 1 )
( C 0 - c1 T 0 + I 0 + G 0 ) Y
b
c1 (1 - t 1 )
LM Curve: Money market equilibrium condition ms = md yields
M0
P0
= ky - h i + u 0
h i= i=
M0
P0
M0
+ k y + u0
1
k
(+ u0 ) + y
h
h
P0
Alternatively,
Y 

1
M
h
(
 u )+
i
k
k
P0
Simultaneous Equilibrium of Goods and Money Markets
By equating the IS and LM curves, we solve for Y* (we can solve for i* as well;
how?) as follows:
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M
h
b
( C 0 - c1 T 0 + I 0 + G0 ) +
( 0 - u0)
h(1 - c1 (1 - t1 )) + kb
h(1 - c1 (1 - t1 )) + kb P0
*
Y =
or,
1
*
Y =
kb
1 - c1 (1 - t1 ) +
h

( C 0 - c1 T 0 + I 0 + G0 ) +
b
h
(
M0
kb P0
1 - c1 (1 - t1 ) +
h
- u0)
Note: compared with the equilibrium national income equation without the
LM curve (in the previous handout), there is an additional term kb/h in the
multiplier for the autonomous expenditures.
Assignment Question 1:
Once again let’s take one more step forward to the realistic model where there are
proportional taxes, and Imports are proportional to national income.
NX = X - M;
M = M0 + m1 Y;
X = X0,
where M0 denotes the Autonomous imports and m1 denotes the Marginal Propensity to
Import.
To recap, Assumptions are : T = To + m1 Y; NX =X0 - (M0 + m1 Y); Prices are
fixed.
Advanced Macroeconomics
23
Eco320 Note #1
1) Solve for Y*; and Solve for i*.
2) Analyse the multiplier of Y*.
3) If there is a change in foreign imports by 1%, what will be impact on the domestic
interest rate? Give the numerical magnitude of the impact for the given values of
the coefficients such as the marginal propensity to consume =0.8, mpi =0.3,
mtr=0.3, elasticity of investment with respect to interest rate = (-) 0.2, and
elasticity of money demand with respect to (national income) = 0.5 , the elasticity
of money demand with respect to interest rate is equal to (-)0.2.
- The answer for the last question is 2.016% (down).