1
Economic Fluctuations -- Short Run and Long Run
We have analyzed an economy where prices are flexible and total output is determined at the equilibrium
of the production factor market. As the price and nominal wage rate are flexible, the equilibrium is
realized at the full employment equilibrium. When the supply of production factors, K and L, are fixed at
̅ , 𝐿̅) and production technology is given, total output is determined by 𝑌̅=F(𝐾
̅ , 𝐿̅). The situation where
(𝐾
all prices are flexible will be called the long run, because prices will eventually adjust to the market’s
excess demand or excess although prices may not respond quickly in the short run. That is, we will call
the time period a short run if prices remain sticky and does not respond to excess demand/supply during
that period.
The major implication of price stickiness is that changes in aggregate demand can affect the aggregate
output. In other words, price stickiness implies that the aggregate supply is not perfectly inelastic with
respect to price, which was the case of the macro model we considered before.
We take the extreme case of perfectly elastic aggregate supply. The main objective is to analyze the
effects of various shocks (e.g. monetary and fiscal policies) on the aggregate demand (AD). This is useful
because the analyses are qualitatively similar even when the aggregate supply (AS) is not perfectly elastic.
Assumption: The short run AS is perfectly elastic, while the long run AS is perfectly inelastic.
This assumption implies that producers are willing and able to supply at a constant price any quantity that
buyers are willing and able to purchase. It implicitly assumes that there is no capacity constraints, no
changes in the average production costs for larger or smaller quantities, etc. Most importantly, the
equilibrium output is completely determined by the quantity demanded at the constant price.
The assumption of perfectly elastic short-run AS is equivalent to switching the roles of Y and P. In the
long run model, output is fixed at 𝑌̅ and P is determined by the system endogenously. In the short run
model, P is now fixed at 𝑃̅ and Y becomes an endogenous variable.
Equilibrium in a Closed Economy
The equilibrium conditions in each sector in the short run become
Real Sector:
̅
̅) + I(r) + G
Y = C(Y-T
Nominal Sector:
̅ /𝑃̅ = L(Y, r+𝜋e)
𝑀
̅ , 𝑃̅, 𝜋e, and the endogenous variables are Y, r, C and I. Since C
where exogenous variables are 𝐺̅ , 𝑇̅, 𝑀
and I are determined if Y and r are known, we can focus on finding the equilibrium values of Y and r that
satisfy the equilibrium conditions in both sectors. The figure below presents the set of Y and r for which
each sector is in equilibrium in this economy.
2
The IS curve represents the set of Y and r for which the real sector (goods and services market) is in
equilibrium, given exogenous variables 𝐺̅ and 𝑇̅.
The LM curve represents the set of Y and r for which the nominal sector (money market) is in equilibrium,
̅ , 𝑃̅ and 𝜋e.
given exogenous variables 𝑀
r
LM
•A
r
C • Y •B
r0
E0
IS
Y0
Y
The equilibrium in this economy is where both sectors are in equilibrium, i.e., point E0 with income Y0
and interest rate r0.
Properties of the IS Curve
(a) The IS curve is sloped downward in general, i.e., a negative relationship between Y and r.
̅.
̅ )-G
To see this, rewrite the equilibrium condition of the real sector as S=I(r), where S=Y-C(Y-T
Suppose that the goods and services market is at equilibrium for Y and r at point A in the figure above. If
r decreases by r (moving from A to C), I increases, while S stays the same because Y stays the same.
Therefore, I(r)>S at point C and the goods and services market is in excess demand. To restore the
equilibrium, S must increase. To increase S, Y must increase by Y (moving from C to B) given other
exogenous variables. Thus, to maintain the equilibrium, the effect of a decrease in r must be offset by the
effect of an increase in Y, which indicates a negative relationship.
r by r  I by I  I > S  S must  by I  Y must  by Y
(b) Slope of the IS curve - The IS curve is flatter, the greater the MPC and/or the higher the interest rate
elasticity of investment is.
3
Given a change in r (r), the slope of the IS curve depends on the magnitude of the change in Y (Y)
that is necessary to restore the equilibrium. If Y has to change a lot, the IS curve will be flatter, and vice
versa. There are two factors to consider:
the degree of the effect of r on I and
the degree of the effect of Y on S.
The first factor is determined by the interest rate elasticity of investment, and second factor by the MPC.
A higher interest rate elasticity of investment means a greater effect of r on I, and hence S must change
by a greater amount, which requires a change in Y by a greater amount for a given MPC. Recall that the
effect of a change in Y on S is smaller when MPC is greater. Therefore, for any given I, Y must change
by a greater amount when the MPC is greater.
(c) Effects of Changes in Exogenous Variables - An increase in G or a decrease in T shifts the IS curve
to the right (or upward).
̅ that an increase in G or a decrease in T reduces the national
̅)- G
It is easy to see from S=Y-C(Y-T
saving S. For any given Y, the interest rate must be higher to reduce I to the lower level of S. This holds
for any given Y, which implies an upward shift of the IS curve. Alternatively, for any given r, I(r) stays
the same and hence a decrease in S must be offset by an increase in Y to restore the equilibrium, i.e., the
IS curve shifts to the right. The magnitude of the shift depends on the interest rate elasticity of investment
and the MPC. The horizontal shift of the IS curve is greater when the MPC is greater, and the vertical
shift of the IS curve is greater when the interest rate elasticity of investment is lower.
Suppose that we wish to analyze the effect of an increase in G for two countries which are
identical except for the interest rate elasticity of investment. In this case, it is more convenient to measure
the shift of the IS curve horizontally because the horizontal shifts (from A to B on the l.h.s. figure below)
are the same for both countries. Conversely, if we wish to analyze the effect of an increase in G for two
countries which are identical except for the MPC, it is more convenient to measure the shift of the IS
curve vertically because the vertical shifts (from A to B on the r.h.s. figure below) are the same for both
countries.
4
r
Effect of an Increase in G
Different Interest Rate Elasticity of Investment (
)
r

Effect of an Increase in G
Different MPC
•D
•B
•C
r0
A•
•B
r0
A•
•C
•D

IS (high 
)

IS (low 
)
Y0
IS (high MPC)
IS (low MPC)
Y
Y0
Y
(d) Magnitudes of the Effects of Fiscal Policy Variables: G and T
When fiscal policy variables change by G and T, the horizontal shifts of the IS curve, measured by
Y for any given r, are
1
∆𝐺 → ∆𝑌 = 1−𝑀𝑃𝐶 ∆𝐺,
𝑀𝑃𝐶
∆𝑇 → ∆𝑌 = − 1−𝑀𝑃𝐶 ∆𝑇,
∆𝐺 = ∆𝑇 → ∆𝑌 = ∆𝐺 = ∆𝑇
The ratio Y/G = 1/(1-MPC) is called the government-purchases multiplier (G multiplier), which is
greater than 1 for any 0<MPC<1. The ratio Y/T = -MPC/(1-MPC) is called the tax multiplier. The
balanced budget multiplier, the ratio Y/G when T=G, is equal to 1 in this economy.
̅=I(r). Since I(r) is fixed for
̅)- G
These results can be seen from the equilibrium condition S=Y-C(Y-T
any given r (i.e., considering a horizontal shift: ∆I = 0), S must stay the same to maintain the equilibrium
when fiscal policy variables change. That is,
̅) − ∆G = ∆I = 0
∆S = ∆Y − MPC(∆Y − ∆T
It is straightforward to show the results above from this equilibrium condition.
This is also illustrated below. An increase in G shifts the S curve down by G, i.e., S decreases by G
for any given Y. The triangle ABC shows that the slope of the S curve 1-MPC=G/Y, which gives
Y=G/(1-MPC). Similarly, an increase in T shifts the S curve upward by MPC*T. The slope of the S
curve 1-MPC=MPC*T/Y, which gives Y=MPC*T/(1-MPC).
More conventional explanations for these results in terms of demand and supply in the real sector are
as follows. Assume that the supply of real output is perfectly elastic so that the equilibrium output is
determined solely by the demand C(Y-T)+I(r)+G. An increase in G by G initially increases the demand
and hence output by G. This increase in output increases income Y by the same amount, which increases
consumption demand by MPC×G, which increases output and income by MPC×G in the second round.
Note that the second round increase in income (MPC×G) is smaller than the first round increase G. The
5
second
round
increase
in
income
again
increases
the
consumption
demand
by
MPC×(MPC×G)=MPC2×G, and hence the output and income by MPC2×G in the third round. As this
process continues indefinitely, the total increase in income is
Y = G + MPC×G + MPC2×G + MPC3×G +  = (1+MPC+MPC2+)G = G/(1-MPC)
The process of income changes due to a change in T by T is the same as the case of an increase in G,
except that the first round change in demand is MPC×T, rather than G. When G and T change by the
same amount, the first round change in demand is (1-MPC)×T.
S, I
S, I
Effect of an Increase in G
Slope of S Curve = 1-MPC
S0
Effect of an Increase in T
Slope of S Curve = 1-MPC
S1
S1
S0
C•
I
A
•
G
Y
MPC *T

•
B
I
B
• Y •
A
C
Y0
Y1
Y
Y1
Y0
Y
6
Properties of the LM Curve
(a) The LM curve is sloped upward in general, i.e., a positive relationship between Y and r.
Suppose that the money market is at equilibrium for Y0 and r0. What should happen to Y to keep the
money market in equilibrium, when the real interest rate increases? If r increases by r, the demand for
̅ /𝑃̅, there is an excess supply. The
real balances decreases. Since the supply of real balances is fixed at 𝑀
demand must increase to restore the equilibrium. And Y must increase to increase the demand for real
balances. Thus, to maintain the equilibrium, the effect of an increase in r must be offset by the effect of
an increase in Y, which indicates a positive relationship.
̅ /𝑃̅ > L  L must  by L  Y must  by Y
r by r  L by L  𝑀
(b) Slope of the LM curve - The LM curve is flatter, the higher the interest elasticity of money demand
and/or the lower the income elasticity of money demand.
Given a change in r (r), the slope of the LM curve depends on the magnitude of the change in Y (Y)
that is necessary to restore the equilibrium. If Y has to change a lot, the LM curve will be flatter, and vice
versa. There are two factors to consider:
the degree of the effect of r on L and
the degree of the effect of Y on L.
The first factor is determined by the interest elasticity of money demand, and second factor by the income
elasticity of money demand. A higher interest elasticity of L means a greater effect of r on L, and hence
Y must change by a greater amount for any given income elasticity of money demand. Similarly, for any
given change in L due to a change in r, Y must change by a greater amount if the income elasticity of
money demand is small.
(c) Effects of Changes in Exogenous Variables - An increase in Ms or a decrease in P or an increase in e
shifts the LM curve to the right (or downward).
An increase in money supply or a decrease in price increases the supply of real balances, which
creates an excess supply of real balances. The demand for real balances must increase to restore the
equilibrium, which requires either an increase in Y for a given r (rightward shift), or a decrease in r for a
given Y (downward shift). An increase in e increases the nominal interest rate, which causes a decrease
in the demand for real balances. To offset this, either Y must increase for a given r (rightward shift), or r
must decrease for a given Y (downward shift).
The magnitude of the shift depends on the interest rate and income elasticities of money demand.
When Ms increases or P decreases, the horizontal shift of the LM curve is greater when the income
elasticity of money demand is low, and the vertical shift is greater when the interest elasticity of money
7
demand is low. Reasons for these results are similar to the reasons in (b) above. Similarly, the horizontal
shift of the LM curve due to an increase in e is greater when the income elasticity of money demand is
low, while its vertical shift is exactly same as e.
Suppose that we wish to analyze the effect of an increase in Ms for two countries which are identical
except for the interest elasticity of demand for real balances. In this case, it is more convenient to measure
the shift of the LM curve horizontally because the horizontal shifts (from A to B on the l.h.s. figure below)
are the same for both countries. Conversely, if the two countries are identical except for the income
elasticity of demand for real balances, it is more convenient to measure the shift of the LM curve
vertically because the vertical shifts (from A to B on the r.h.s. figure below) are the same for both
countries.
r
Effect of an Increase in M s
Different Interest Rate Elasticity (
) of L
r
Effect of an Increase in M s
Different Income Elasticity (
) of L
LM (low 
)
r0


A
•
•
•
LM (high 
)

LM (high 
)
•
B
LM (low 
)
r0
 
A
•
•
C
•
D
C
•
D
Y0
Y
B
Y0
Y
Effects of Changes in Exogenous Variables on Equilibrium
(a) An increase in G or a decrease in T increases the equilibrium Y and r in the short-run, and hence
increases C and decreases I. The effects on Y and r are greater when the interest elasticity of investment is
smaller, and when the income elasticity of money demand is smaller
̅ or a decrease in price 𝑃̅ (i.e., an increase in real balances), or an
(b) An increase in money supply 𝑀
increase in the expected inflation rate e shifts the LM curve to the right, and consequently increases the
equilibrium Y and decreases the equilibrium r in the short-run. The effect on r is greater for an economy
with a lower interest elasticity of investment or a smaller income elasticity of money demand.
8
r
Effect of an Increase in G
Different Interest Rate Elasticity of Investment (
)
IS (low 
)

r1L
r1H
r0
r
Effect of an Increase in Ms
Different Interest Rate Elasticity of Investment (
)
IS (low 
)
LM
•
• E1H
E0
LM0

• E1L
•
r0
r1H
r1L

IS (high 
)
Y0 Y1H Y1L
LM1
Y
•
E0
•
• E1H
•E
1L
Y0 Y1L Y1H
IS (high 
)
Y
9
Dynamic Adjustments of Y and r in the Short-Run
Assumptions: It is the interest rate r that changes when there is an excess demand in the money market,
and it is the income Y that changes when there is an excess demand in goods and services market. The
directions of the changes in r and Y are illustrated below in each quadrant, where ESG and EDG indicate
the excess supply and excess demand in goods and services market, and similarly for the ESM and EDM
for the money market. A potential adjustment path of Y and r when G increases is illustrated on the r.h.s.
panel.
r
Directions of Changes in Y and r
ESG
ESM
•


EDG
ESM


•
• E0

•
r
A Path of Dynamic Adjustment
LM
LM

•E
 
1

• EDM

E0 •
ESG
EDG
EDM
IS
IS0
Y
Consider the following linear structure of the economy:
C = a + b(Y-T), I = c - dr,
L(Y, r+e) = eY - f(r+e)
We can trace the adjustment of Y and r to a change in G as follows.
G  EDG  Y by Y1=G/b  EDM  r by r1 = eY1/f  I by I1=dr1
 ESG  Y by Y2=I1/b  ESM  r by r1 = eY2/f  I by I2=dr2  
IS1
Y
10
Aggregate Demand
We have shown that a decrease in price P increases the equilibrium income Y. This negative relationship
is called the aggregate demand (AD). Notice that this definition of demand is not the same as the usual
definition of quantity demanded in microeconomics. An interpretation of this aggregate demand function
is as follows: A higher price requires more dollars for each transaction. Since money supply is fixed, the
quantity of transactions and thus the quantity of goods and services Y must fall.
P
P0
AD
Y0
Y
Effects of changes in exogenous variables on AD - An increase in exogenous variables Ms, e, G and a
decrease in T shifts the AD curve to the right. The magnitudes of the shift depends on the various factors
that determine the shifts and slopes of the IS and LM curves.
This can also be seen from the following. Suppose we solve the real sector equilibrium in terms of interest
rate r and write it in terms of national savings
̅ I(r)=S= Y - C(Y-T
̅ r = r(S)
̅) + I(r) + G
̅) - G
Y = C(Y-T
Real Sector:
where r and S are negatively related. Substituting this solution into the nominal sector equilibrium
condition, we can write
Nominal Sector:
̅ /𝑃̅ = L(Y, r+𝜋e) = L(Y, r(S)+𝜋e)
𝑀
or
̅
𝑀
𝑃̅ = 𝐿(𝑌,𝑟(𝑆)+𝜋𝑒 )
The negative relationship between P and Y can be seen as follows. An increase in Y affects the money
demand L in two ways: the direct effect through the first term which is positive, and the indirect effect
through its effect on S and then r and then L. The indirect effect on L is also positive. Therefore, P falls as
Y rises.
11
To see the effect of a change in exogenous variables on the AD curve, it is clear that an increase in money
supply will increase P and shifts AD upward. An increase in e reduces L and hence shifts AD upward.
An increase in G or a decrease in T reduces S which increases r and thereby reduces L, which means an
upward shift of AD.
Suppose that we wish to analyze the effect of an increase in M s for two countries which are identical
except for the interest elasticity of demand for real balances. In this case, it is more convenient to measure
the shift of the LM curve horizontally because the horizontal shifts (from A to B on the l.h.s. figure below)
are the same for both countries. Conversely, if the two countries are identical except for the income
The first factor is determined by the interest elasticity of money demand, and second factor by the income
Short-Run and Long-Run Adjustments of Economy to a Demand Shock
̅, P0 and r0 (see figures
Suppose that the economy is at the short-run and long-run equilibrium Y0=Y
below). An increase in money supply shifts the LM curve from LM0 to LM1 and shifts the AD from AD0
to AD1. In the short-run, price stays at P0, income rises to Y1s and interest rate falls to r1s. Consumption C
rises and investment I rises. This decreases the unemployment rate below the natural rate of
unemployment, putting upward pressures on the nominal wage rate and prices. As price rises over time,
the SRAS curve shifts upward and the LM curve shifts to the left. Income falls along the AD 1 curve and
interest rate rises along the IS curve. This adjustment process continues until the SRAS curve reaches
̅ and r1=r0.
SRAS and the LM curve shifts back to LM0. A new long-run equilibrium is reached at P1, Y
Therefore, there is no change in Y, r, C and I in the long-run. Only price rises from P0 to P1.
An increase in G shifts the IS curve from IS0 to IS1 and shifts the AD from AD0 to AD1. In the short-run,
price stays at P0, income rises to Y1s and interest rate rises to r1s. Consumption C rises and investment I
̅, there is an upward pressures on the nominal wage rate and prices. As
falls. Since Y1s is greater than Y
price rises over time, the SRAS curve shifts upward and the LM curve shifts to the left. Income falls
along the AD1 curve and interest rate rises further along the IS1 curve. This adjustment process continues
until the SRAS curve reaches SRAS and the LM curve shifts back to LM1. A new long-run equilibrium
is reached at P1, ̅
Y and r1. Therefore, there is no change in Y and C in the long-run, but I falls by G. Price
rises from P0 to P1.
12
P
SR and LR Adjustments to Demand Shock
P
LRAS
LRAS
LRE1=SRE

•
P1
Long-Run and Short-Run
Equilibrium
•
SRAS0

P0
SRAS

SRE 1

•    •
P0
SRAS0
LRE0=SRE0
   AD
AD0
Y

Y
r
1
AD0

Y
r
Effects of an Increase in G
Y
Y1s
Effects of an Increase in Ms
LM 
r1
LRE1=SRE
•
LM 0

Increase in M
LM 0
LM 1
s
• SRE 1
r1s
r0


Increase
in P
r1=r0
•

• LRE =SRE

LRE =SRE
1
0
LRE0=SRE0

Increase in G IS1
r1s

0


• SRE 1
Increase in P
IS0

Y
Y1s
IS0
Y

Y
Y1s
Y
13
Short-Run and Long-Run Adjustments of Economy to a Supply Shock
Suppose that the economy is at the short-run and long-run equilibrium ̅
Y and P0. An adverse supply shock
(an increase in short-run price) shifts SRAS up from SRAS0 to SRAS1 and shifts the LM curve from LM0
to LM1.
(a) Increase in short-run supply price and no monetary intervention
If the government (Fed) does not intervene with a stabilization policy to offset the effect of the supply
shock, the short-run equilibrium moves from SRE0 to SRE1 (see figures below), causing a stagflation (a
combination of rising price and falling income). Interest rate rises to r1s and investment falls in the shortrun. At the short-run equilibrium SRE1, the unemployment rate is above the natural rate of unemployment,
putting downward pressures on the nominal wage rate and prices. As price falls, the SRAS curve shifts
downward and the LM curve shifts to the right from LM1. Income rises along the AD0 curve and interest
rate falls along the IS0 curve. This adjustment process continues until the SRAS curve falls back to
SRAS0 and the LM curve moves back to LM0. The new long-run equilibrium is same as the initial longrun equilibrium. Therefore, there is no change in the long-run.
P
r
LRAS
LM 1
SRE 1
P1s

•
•

P0
SRAS1
r1s
SRAS0
r0
SRE 1
•
LM 0
• LRE0=SRE0
LRE0=SRE0
AD0
Y1s

Y
IS0
Y
Y1s

Y
Y
14
(b) Increase in supply price and accommodating monetary intervention
The government can avoid the stagflation by increasing Ms to offset the short-run effect of the adverse
supply shock. This shifts AD0 to AD1 and LM1 to LM0 (see the figure below). This policy stabilizes the
income in the short-run, but the price level will be higher in the long-run as well as in the short-run. All
real variables Y, r, C and I will stay unchanged under this stabilization policy.
P
r
LRAS
LM 1

(Increase in Ms)
LRE1

P1
•
SRAS1
r1s
P0
•

SRAS0
r0
SRE 1
•
LM 0
• LRE0=SRE0
LRE0=SRE0
AD0
Y1s

Y
AD1
Y
IS0
Y1s

Y
Y
15
Interaction between Monetary and Fiscal Policy
We have shown the short-run effects of the changes in fiscal policy variables G and T. Suppose that the
monetary authority attempts to offset the adverse effects of fiscal policy changes. The targets of monetary
policy may either (a) to keep the interest rate stable, or (b) to keep the national income stable, in the shortrun. For example, consider an increase in tax to reduce the federal budget deficit. An increase in T shifts
the IS curve from IS0 to IS1 (see the figure below). If the Fed does not change the money supply to offset
the effect of a change in T, the short-run equilibrium Y and r fall from Y0 and r0 to Y1s and r1s,
respectively.
(a) If the Fed aims to keep the interest rate constant, it needs to reduce the money supply, shifting the LM
curve upward from LM0 to LM1a. The result is the unchanged r, but Y falls even further to Y1a.
(b) If the Fed aims to keep the national income constant, it needs to increase the money supply, shifting
̅, but equilibrium r falls
the LM curve downward from LM0 to LM1b. The result is the unchanged Y at Y
further to r1b.
r
Monetary Stabilization Policy
LM a


Decrease in Ms LM
0
r0
•
LM b
•
r1s
r1b
• LRE0=SRE0

Increase in M
•
IS0
s
IS1
Y1a
Y1s

Y
Y
16
The Great Depression - What caused it?
The IS-LM analysis shows that income decreases if the IS curve shifts to the left, or if the LM curve shifts
upward. Note the difference between these two changes: In the case of the IS shift, Y and r both fall,
while in the case of the LM shift, Y falls, but r rises.
The Spending Hypothesis: Shocks to the IS Curve
This hypothesis asserts that contractionary shift of the IS curve (decrease in spending) caused the Great
Depression. This explanation matches the fall in both Y and r during the depression. What caused the
contractionary shift of the IS curve? Stock market crash of 1929, decline in residential building, bank
failures, contractionary fiscal policy
The Money Hypothesis: A Shock to the LM curve
This hypothesis asserts that a contractionary monetary policy (nominal money supply fell from 1929 to
1933) caused the depression. Two problems with this explanation: (i) interest rate fell, (ii) real money
balances rose between 1929 and 1931.
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Wealth Effects in Consumption
Real Sector:
̅,
̅, W) + I(r) + G
Y = C(Y-T
Nominal Sector:
̅ /𝑃̅ = L(Y, r+𝜋e)
𝑀
̅ + 𝐵̅)/𝑃
W=(𝑀
̅ , 𝐵̅, 𝑃̅, 𝜋e, and the endogenous variables are Y, r,
In this economy, the exogenous variables are 𝐺̅ , 𝑇̅, 𝑀
C and I. The IS curve is sloped downward as before (verify this). An increase in the real wealth W shifts
the IS curve to the right. The LM curve is the same as above. We wish to analyze the short-run and longrun adjustments of the economy to a demand shock and a supply shock.
Effects of an increase in Ms
An increase in money supply shifts the LM curve from LM0 to LM1s, shifts the IS curve from IS0 to
IS1s, and hence AD shifts from AD0 to AD1. In the short-run, price stays at P0 and income rises to Y1s.
However, the effect on interest rate is ambiguous: it depends on which curve shifts more to the right. To
analyze this, let Cw be the marginal change in consumption as wealth changes by one unit, and Ly be the
marginal change in money demand as income changes by one unit. An increase in money supply by M
changes wealth by ∆W=∆M/P, and hence changes consumption by ∆C=Cw(∆W)=Cw(∆M/P). This
exogenous increase in consumption plays a role similar to an increase in other exogenous variables such
as G, and hence it has a multiplier effect on Y. The multiplier effect is
∆𝑌 =
∆𝐶
1−𝑀𝑃𝐶
=
𝐶𝑤 ∆𝑊
1−𝑀𝑃𝐶
=
𝐶𝑤 ∆𝑀/𝑃
1−𝑀𝑃𝐶
and this is the size of the horizontal shift of the IS curve.
For the shift of LM curve, the change in supply is ∆M/P and change in demand due to a change in Y
is equal to Ly∆Y. Therefore the size of the horizontal shift of the LM curve is
1 ∆𝑀
𝑦 𝑃
∆𝑌 = 𝐿
Now we can conclude that the change in r has the following signs
∆𝑟 = 𝑟1𝑠 − 𝑟0 ⋛ 0 𝑖𝑓𝑓
𝐶𝑤 ∆𝑀⁄𝑃
1−𝑀𝑃𝐶
⋛
1 ∆𝑀
𝐿𝑦 𝑃
⇒ 𝑖𝑓𝑓
𝐶𝑤
1−𝑀𝑃𝐶
⋛
1
𝐿𝑦
Thus, the interest rate will rise in the short-run if the marginal effect of wealth on consumption and/or
MPC is large, or if the marginal effect of income on money demand is large.
The graph shows the case of falling interest rate to r 1s. Consumption C rises to C1s and investment I
rises to I1s. This decreases the unemployment rate below the natural rate of unemployment, putting
upward pressures on the nominal wage rate and prices. As price rises to P1 over time, the SRAS curve
̅. This increase in P shifts both the IS
shifts upward to SRAS1, and the equilibrium output falls back to Y
18
̅ so that
and LM curves to the left. The new curves, denoted by IS1 and LM1, will cross each other at Y = Y
the new SR equilibrium income is equal to the LR equilibrium income ̅
Y. What is the new long-run
equilibrium interest rate r? This depends on the positions of the new curves IS1 and LM1.
The new long-run equilibrium r1 is lower than the initial long-run equilibrium r0. We may prove this
by contradictions.
(i) Suppose r1=r0. This can happen only if LM1s have shifted to LM0 (i.e., LM1=LM0). This means that
P is proportional to Ms and there is no change in the supply of real balances M/P in the long-run.
̅ 1+ B
̅0)/P1 is smaller than the initial wealth
If M/P were unchanged, the new wealth level W1=( M
̅ 0+ B
̅ 0)/P0, and hence C1 is smaller than the initial equilibrium C0. Therefore, the
level W0=( M
goods and services market cannot be in equilibrium because I(r1)=I(r0) due to r1=r0. That is, the
IS1 cannot cross LM1 at r0.
(ii) Suppose r1>r0. This can happen only if the LM1 lies at the left of LM0. This means that P is
proportionally greater than Ms and there is a decrease in M/P in the long-run. If M/P were lower,
the new wealth level W1 is smaller than W0, and hence C1 is smaller than the initial equilibrium C0.
Therefore, the goods and services market cannot be in equilibrium because I(r 1) is less than I(r0)
in this case due to r1>r0. That is, the IS1 cannot cross LM1 at r1 higher than r0.
(iii) This leaves only other alternative r1<r0. This will happen if the LM1 lies at the right of LM0. This
means that P is proportionally less than Ms and there is an increase in M/P in the long-run. The
price must rise sufficiently high to make the new wealth level W 1 is smaller than W0. Otherwise,
the IS1 will be at the right of IS0 and the equilibrium Y will be greater than Y bar. This situation is
illustrated below.
Compared to the initial LR equilibrium, the new LR equilibrium P and M/P is higher, r and C are lower
and I is greater, while Y stays the same at Y bar. Can r1 be lower than r1s?
P
SR and LR Adjustments to a Demand Shock
r
Effects of an Increase in Ms
LRAS
LRE1=SRE1

•
P1
SRE 1s
P0
•


•
Increase in M s

SRAS0
r0
r1
r1s
LRE0=SRE0

AD1

Y
AD0
Y1s
LM 0 LM 1

SRAS1
Y



Increase
in M
LM 1s
s
•
•
• SRE 1s




Increase
in P Increase in P

Y
IS1
Y1s
IS0
IS1s
Y
19
̅ +𝐵̅=0,
Effects of an Open Market Purchase: 𝑀
̅ > 0
𝑀
An open market purchase increases Ms and decreases bond holdings 𝐵̅ by the same amount. This
shifts the LM curve to LM1s, but IS stays the same because there is no change in W. In the short-run, price
stays at P0, income rises to Y1s and interest rate falls to r1s. Consumption C rises to C1s and investment I
rises to I1s. This decreases the unemployment rate below the natural rate of unemployment, putting an
upward pressure on the nominal wage rate and prices. As price rises to P1 over time, the SRAS curve
̅. This increase in P shifts both IS and
shifts upward to SRAS1, and the equilibrium output falls back to Y
̅. Compared to the initial LR equilibrium, the new
LM curves to IS1 and LM1, which cross each other at Y
LR equilibrium P is higher and r is lower, and hence, I is higher, W is lower, C is lower, and M/P is
higher, while Y stays the same at ̅
Y.
Effects of an increase in G
An increase in G shifts the IS curve from IS0 to IS1s, and hence AD shifts from AD0 to AD1. In the
short-run, price stays at P0, income rises to Y1s and interest rate rises to r1s. Consumption C rises to C1s
and investment I falls to I1s. This decreases the unemployment rate below the natural rate of
unemployment, putting an upward pressure on the nominal wage rate and prices. As price rises to P1 over
̅. This increase in
time, the SRAS curve shifts upward to SRAS1, and the equilibrium output falls back to Y
̅. Compared to the initial
P shifts both IS and LM curves to IS1 and LM1, which cross each other at Y=Y
LR equilibrium, the new LR equilibrium P and r are higher, and M/P, C and I are smaller, while Y stays
the same at ̅
Y.
r
r
Effects of an Increase in G
Effects of an Open Market Purchase
LM 0
LM 1



 Increase
in
P
r1
r1s
r0
LM 0 LM 1
Increase in P
•



Increase
in M
LM 1s
s


• SRE 1s
Increase in P
•


Increase in G
IS1s
r0
•
r1
r1s
•


Increase in P
• SRE 1s
IS1
IS0

Y
Y1s
Y

Y
IS1
Y1s
IS0
Y