Ch 11. Aggregate Demand II: Applying the IS‐LM Model
ECO 402
Context
• Chapter 9 introduced the model of aggregate demand and supply. • Chapter 10 developed the IS‐LM model, the basis of the aggregate demand curve.
Key Ideas
• How to use the IS‐LM model to analyze the effects of shocks, fiscal policy, and monetary policy
• How to derive the aggregate demand curve from the IS‐LM model
• Several theories about what caused the Great Depression
Equilibrium in the IS‐LM model
The IS curve represents equilibrium in the goods market.
r
LM
Y  C (Y  T )  I (r )  G
The LM curve represents money market equilibrium.
r1
IS
M P  L (r ,Y )
The intersection determines the unique combination of Y and r
that satisfies equilibrium in both markets.
Y1
Y
Policy analysis with the IS‐LM model
Y  C (Y  T )  I (r )  G
r
LM
M P  L (r ,Y )
We can use the IS‐LM model to analyze the effects of
r1
• fiscal policy: G and/or T
IS
• monetary policy: M
Y1
Y
An increase in government purchases
1. IS curve shifts right 1
by
G
1 MPC
causing output & income to rise. 2. This raises money demand, causing the interest rate to rise…
r
LM
2.
r2
r1
3. …which reduces investment, so the final increase in Y
1
G
is smaller than
1 MPC
IS2
1.
IS1
Y1 Y2
3.
Y
A tax cut
Consumers save (1MPC) of r
the tax cut, so the initial boost in spending is smaller for T than for an equal r2
G… 2.
r1
and the IS curve shifts by
1.
LM
1.
MPC
T
1 MPC
2. …so the effects on r
and Y are smaller for T
than for an equal G. IS2
IS1
Y1 Y2
2.
Y
Monetary policy: An increase in M
1. M > 0 shifts the LM curve down
(or to the right)
2. …causing the interest rate to fall 3. …which increases investment, causing output & income to rise. r
LM1
LM2
r1
r2
IS
Y1 Y2
Y
Interaction between monetary & fiscal policy
• Model: Monetary & fiscal policy variables (M, G, and T) are exogenous.
• Real world: Monetary policymakers may adjust M
in response to changes in fiscal policy, or vice versa.
• Such interaction may alter the impact of the original policy change. The Fed’s response to G > 0
• Suppose Congress increases G.
• Possible Fed responses:
1. hold M constant
2. hold r constant
3. hold Y constant
• In each case, the effects of the G
are different… Response 1: Hold M constant
If Congress raises G, the IS curve shifts right.
If Fed holds M constant, then LM curve doesn’t shift.
r
LM1
r2
r1
IS2
IS1
Results:
Y  Y 2  Y1
r  r2  r1
Y1 Y2
Y
Response 2: Hold r constant
If Congress raises G, the IS curve shifts right.
r
To keep r constant, Fed increases M
to shift LM curve right.
r2
r1
LM1
IS2
IS1
Results:
Y  Y 3  Y1
r  0
LM2
Y1 Y2 Y3
Y
Response 3: Hold Y constant
If Congress raises G, the IS curve shifts right.
To keep Y constant, Fed reduces M
to shift LM curve left.
LM2
LM1
r
r3
r2
r1
IS2
IS1
Results:
Y  0
r  r3  r1
Y1 Y2
Y
Estimates of fiscal policy multipliers
from the DRI macroeconometric model
Assumption about monetary policy
Estimated value of Y/G
Estimated value of Y/T
Fed holds money supply constant
0.60
0.26
Fed holds nominal interest rate constant
1.93
1.19
Shocks in the IS‐LM model
IS shocks: exogenous changes in the demand for goods & services. Examples: – stock market boom or crash
 change in households’ wealth
 C
– change in business or consumer confidence or expectations  I and/or C
Shocks in the IS‐LM model
LM shocks: exogenous changes in the demand for money. Examples:
– a wave of credit card fraud increases demand for money.
– more ATMs or the Internet reduce money demand.
Analyze shocks with the IS‐LM Model
Use the IS‐LM model to analyze the effects of
1. a boom in the stock market that makes consumers wealthier.
2. after a wave of credit card fraud, consumers using cash more frequently in transactions.
For each shock, a. use the IS‐LM diagram to show the effects of the shock on Y and r.
b. determine what happens to C, I, and the unemployment rate.
CASE STUDY: The U.S. recession of 2001
• During 2001, – 2.1 million jobs lost, unemployment rose from 3.9% to 5.8%.
– GDP growth slowed to 0.8% (compared to 3.9% average annual growth during 1994‐
2000). CASE STUDY: The U.S. recession of 2001
Causes: 1) Stock market decline  C
Index (1942 = 100)
1500
1200
Standard & Poor’s 500
900
600
300
1995
1996
1997
1998
1999
2000
2001
2002
2003
CASE STUDY: The U.S. recession of 2001
Causes: 2) 9/11
– increased uncertainty
– fall in consumer & business confidence
– result: lower spending, IS curve shifted left
Causes: 3) Corporate accounting scandals
– Enron, WorldCom, etc. – reduced stock prices, discouraged investment
CASE STUDY: The U.S. recession of 2001
• Fiscal policy response: shifted IS curve right
– tax cuts in 2001 and 2003
– spending increases
• airline industry bailout
• NYC reconstruction • Afghanistan war
CASE STUDY: The U.S. recession of 2001
• Monetary policy response: shifted LM curve right
7
6
5
4
3
2
1
0
Three-month
T-Bill Rate
What is the Fed’s policy instrument?
• The news media commonly report the Fed’s policy changes as interest rate changes, as if the Fed has direct control over market interest rates. • In fact, the Fed targets the federal funds rate – the interest rate banks charge one another on overnight loans. • The Fed changes the money supply and shifts the LM curve to achieve its target. • Other short‐term rates typically move with the federal funds rate.
What is the Fed’s policy instrument?
Why does the Fed target interest rates instead of the money supply?
1) They are easier to measure than the money supply.
2) The Fed might believe that LM shocks are more prevalent than IS shocks. If so, then targeting the interest rate stabilizes income better than targeting the money supply. (See end‐of‐chapter Problem 7 on p.337.)
Problem 7‐7
The Fed is considering two alternative monetary policies:
– (I) Holding the money supply constant and letting the interest rate adjust, or
– (II) Adjusting the money supply to hold the interest rate constant.
In the IS‐LM model, which policy will better stabilize output under the following conditions?
a. All shocks to the economy arise from exogenous changes in the demand for goods and services.
b. All shocks to the economy arise from exogenous changes in the demand for money.
IS‐LM and aggregate demand
• So far, we’ve been using the IS‐LM model to analyze the short run, when the price level is assumed fixed. • However, a change in P would shift LM and therefore affect Y.
• The aggregate demand curve
(introduced in Chap. 9) captures this relationship between P and Y.
Deriving the AD curve
r
Intuition for slope of AD curve:
P  (M/P)
 LM shifts left
 r
 I
 Y
LM(P2)
LM(P1)
r2
r1
IS
P
Y2
Y1
Y
P2
P1
AD
Y2
Y1
Y
Monetary policy and the AD curve
The Fed can increase aggregate demand:
M  LM shifts right
r
LM(M1/P1)
LM(M2/P1)
r1
r2
IS
 r
 I
P
 Y at each value of P
P1
Y1
Y2
Y
AD2
Y1
Y2
AD1
Y
Fiscal policy and the AD curve
Expansionary fiscal policy (G and/or T) increases agg. demand:
r
LM
r2
r1
IS2
T  C
IS1
 IS shifts right
P
 Y at each value of P
P1
Y1
Y2
Y
AD2
Y1
Y2
AD1
Y
IS‐LM and AD‐AS in the short run & long run
Recall from Chapter 9: The force that moves the economy from the short run to the long run is the gradual adjustment of prices.
In the short‐run equilibrium, if
then over time, the price level will
Y Y
rise
Y Y
fall
Y Y
remain constant
The SR and LR effects of an IS shock
r
LRAS
A negative IS shock shifts IS and AD left, causing Y to fall.
LM(P1)
IS2
Y
P
IS1
Y
LRAS
SRAS1
P1
Y
AD1
AD2
Y
The SR and LR effects of an IS shock
r
LRAS
LM(P1)
In the new short-run
equilibrium, Y  Y
IS2
Y
P
IS1
Y
LRAS
SRAS1
P1
Y
AD1
AD2
Y
The SR and LR effects of an IS shock
r
LRAS
LM(P1)
In the new short-run
equilibrium, Y  Y
IS2
Over time, P gradually
falls, causing
• SRAS to move down
• M/P to increase,
which causes LM
to move down
Y
P
IS1
Y
LRAS
SRAS1
P1
Y
AD1
AD2
Y
The SR and LR effects of an IS shock
r
LRAS
LM(P1)
LM(P2)
IS2
Over time, P gradually
falls, causing
• SRAS to move down
• M/P to increase,
which causes LM
to move down
Y
P
IS1
Y
LRAS
P1
SRAS1
P2
SRAS2
Y
AD1
AD2
Y
The SR and LR effects of an IS shock
r
This process continues
until economy reaches a
long-run equilibrium with
Y Y
LRAS
LM(P1)
LM(P2)
IS2
Y
P
IS1
Y
LRAS
P1
SRAS1
P2
SRAS2
Y
AD1
AD2
Y
Analyze SR & LR effects of M
a. Draw the IS‐LM and AD‐AS
r
LRAS LM(M /P )
1
1
diagrams as shown here. b. Suppose Fed increases M.
IS
Show the short‐run effects on your graphs. Y
c. Show what happens in the transition from the short run to the long run. d. How do the new long‐run equilibrium values of the endogenous variables compare to their initial values? P
Y
LRAS
P1
SRAS1
AD1
Y
Y
Problem 11‐2
Use the IS‐LM model to predict the effects of each of the following shocks on income, the interest rate, consumption, and investment. In each case, explain what the Fed should do to keep income at its initial level.
a. After the invention of a new high‐speed computer chip, many firms decide to upgrade their computer systems.
b. A wave of credit‐card fraud increases the frequency with which people make transactions in cash.
c. A best‐seller titled Retire Rich convinces the public to increase the percentage of their income devoted to saving.
Problem 11‐4
Explain why each of the following statements is true. Discuss the impact of monetary and fiscal policy in each of these special cases.
a. If investment does not depend on the interest rate, the IS curve is vertical.
b. If money demand does not depend on the interest rate, the LM is vertical.
c. If money demand does not depend on income, the LM is horizontal.
d. If money demand is extremely sensitive to the interest rate, the LM is horizontal.
The Great Depression
Unemployment (right scale)
220
30
25
200
20
180
15
160
10
Real GNP
(left scale)
140
120
1929
5
0
1931
1933
1935
1937
1939
percent of labor force
billions of 1958 dollars
240
What caused the Great Depression?
A. The Spending Hypothesis
B. The Money Hypothesis I
C. The Money Hypothesis II
THE SPENDING HYPOTHESIS: Shocks to the IS curve
• asserts that the Depression was largely due to an exogenous fall in the demand for goods & services –
a leftward shift of the IS curve.
• evidence: output and interest rates both fell, which is what a leftward IS shift would cause.
THE SPENDING HYPOTHESIS: Reasons for the IS shift
• Stock market crash  exogenous C
– Oct‐Dec 1929: S&P 500 fell 17%
– Oct 1929‐Dec 1933: S&P 500 fell 71%
• Drop in investment
– “correction” after overbuilding in the 1920s
– widespread bank failures made it harder to obtain financing for investment
• Contractionary fiscal policy
– Politicians raised tax rates and cut spending to combat increasing deficits.
THE MONEY HYPOTHESIS: A shock to the LM curve
• asserts that the Depression was largely due to huge fall in the money supply.
• evidence: M1 fell 25% during 1929‐33. • But, two problems with this hypothesis:
– P fell even more, so M/P actually rose slightly during 1929‐31. – nominal interest rates fell, which is the opposite of what a leftward LM shift would cause. THE MONEY HYPOTHESIS II: The effects of falling prices
• asserts that the severity of the Depression was due to a huge deflation:
P fell 25% during 1929‐33. • This deflation was probably caused by the fall in M, so perhaps money played an important role after all.
• In what ways does a deflation affect the economy?
THE MONEY HYPOTHESIS AGAIN: The effects of falling prices
A. The stabilizing effects of deflation:
• Real balance effect
P  (M/P)  LM shifts right  Y
• Pigou effect: P
 (M/P)  consumers’ wealth 
 C  IS shifts right  Y
THE MONEY HYPOTHESIS AGAIN: The effects of falling prices
B. The destabilizing effects of expected deflation:
 E
 r  for each value of i
 I  because I = I (r )
 planned expenditure & agg. demand 
 income & output 
 the nominal interest rate declines by less than the expected deflation. Thus the real interest rate increases.
Figure 11‐8. Expected Deflation in the IS‐LM Model
THE MONEY HYPOTHESIS AGAIN: The effects of falling prices
C. The destabilizing effects of unexpected deflation:
debt‐deflation theory
P (if unexpected)  transfers purchasing power from borrowers to lenders
 borrowers spend less, lenders spend more
 if borrowers’ propensity to spend is larger than lenders’, then aggregate spending falls, the IS curve shifts left, and Y falls
Why another Depression is unlikely
• Policymakers (or their advisors) now know much more about macroeconomics:
– The Fed knows better than to let M fall so much, especially during a contraction.
– Fiscal policymakers know better than to raise taxes or cut spending during a contraction.
• Federal deposit insurance makes widespread bank failures very unlikely.
• Automatic stabilizers make fiscal policy expansionary during an economic downturn.
Problem 10.3
Let’ represent the tax system by writing tax revenue as where and t are parameters of the tax code. t is called the marginal tax rate.
a. How does this tax system change the way consumption responds to changes in GDP?
b. In the Keynesian cross, how does this tax system alter the government‐purchases multiplier?
c. In the IS‐LM model, how does this tax system alter the slope of the IS curve?
Problem 10.4
Consider the impact of an increase in thriftiness in the Keynesian cross. Suppose the consumption function is where is called autonomous consumption and c is the MPC.
a. What happens to equilibrium income when the society becomes more thrifty, as represented by a decline in ?
b. What happens to equilibrium saving?
c. Why do you suppose this result is called the paradox of thrift?
d. Does this paradox arise in the classical model of Ch 3? Why or why not?
Problem 11‐3
• Consider the economy of Hicksonia.
a. The consumption function is given by . The investment function is Government purchases and taxes are both 100. Obtain the IS curve.
ெ ௗ
௉
. The b. The money demand function is money supply M is 1000 and the price level P is 2. Obtain the IS curve.
c. Find the equilibrium interest rate and income .
d. Suppose that government purchases are raised from 100 to 150. Find the new equilibrium interest rate and income .
Problem 11‐3
e. Suppose instead that the money supply is raised from 1000 to 1200. How much does the IS curve shift? Find the new equilibrium interest rate and income .
f. With the initial values from monetary and fiscal policy, suppose that the price level rises from 2 to 4. What happens? Find the new equilibrium interest rate and income .
g. Derive and graph an equation for the aggregate demand curve. What happens to the curve in the above 3 cases (d), (e), and (f)?
CASE STUDY
The 2008‐09 Financial Crisis & Recession
• 2009: Real GDP fell, u‐rate rose to 10%
• Important factors in the crisis:
– early 2000s Federal Reserve interest rate policy – sub‐prime mortgage crisis
– bursting of house price bubble, rising foreclosure rates
– falling stock prices
– failing financial institutions
– declining consumer confidence, drop in spending on consumer durables and investment goods
Interest rates and house prices
9
8
170
interest rate (%)
7
6
150
5
130
4
110
3
90
2
70
1
0
2000
2001
2002
2003
2004
50
2005
House price index, 2000=100
Federal Funds rate
30-year mortgage rate
190
Case-Shiller 20-city composite house price index
Change in U.S. house price index and rate of new foreclosures, 1999‐2009
14%
1.4
10%
1.2
8%
1.0
6%
0.8
4%
2%
0.6
0%
0.4
-2%
0.2
-4%
-6%
1999
0.0
2001
2003
2005
2007
2009
New foreclosure starts
(% of total mortgages)
Percent change in house prices
(from 4 quarters earlier)
12%
US house price index
New foreclosures
House price change and new foreclosures, 2006:Q3 – 2009Q1
20%
18%
Nevada
Illinois
Florida
New foreclosures, % of all mortgages
16%
14%
Michigan
Ohio
California
Georgia
12%
10%
8%
Colorado
Arizona
Rhode Island
New Jersey
6%
S. Dakota
Hawaii
4%
Oregon
Alaska
2%
0%
-40%
Texas
-30%
-20%
-10%
Wyoming
N. Dakota
0%
Cumulative change in house price index
10%
20%
U.S. bank failures by year, 2000‐2009
Number of bank failures
140
120
100
80
60
40
20
0
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
100%
7/20/2009
120%
11/11/2008
140%
3/5/2008
(% change from 52 weeks earlier)
6/28/2007
10/20/2006
2/11/2006
6/5/2005
9/27/2004
1/20/2004
5/14/2003
9/5/2002
12/28/2001
4/21/2001
8/13/2000
12/6/1999
Major U.S. stock indexes DJIA
S&P 500
NASDAQ
80%
60%
40%
20%
0%
-20%
-40%
-60%
-80%
Consumer sentiment and growth in consumer durables and investment spending
110
15%
10%
100
5%
90
0%
80
-5%
-10%
70
-15%
Durables
-20%
Investment
60
UM Consumer Sentiment Index
-25%
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
50
Consumer Sentiment Index, 1966=100
% change from four quarters earlier
20%
Real GDP growth and Unemployment
10
10%
Real GDP growth rate (left scale)
Unemployment rate (right scale)
8
6%
7
6
4%
5
2%
4
3
0%
2
-2%
1
-4%
1995
0
1997
1999
2001
2003
2005
2007
2009
% of labor force
% change from 4 quaters earlier
8%
9
Chapter Summary
1. IS‐LM model
– a theory of aggregate demand
– IS curve: goods market equilibrium
– LM curve: money market equilibrium – exogenous: M, G, T
– Predetermined: P exogenous in short run, Y in long run – endogenous: r, Y endogenous in short run – endogenous (in the long run): P
Chapter Summary
2. AD curve
– shows relation between P and the IS‐LM
model’s equilibrium Y. – negative slope because P  (M/P )  r  I  Y
– expansionary fiscal policy shifts IS curve right, raises income, and shifts AD curve right.
– expansionary monetary policy shifts LM curve right, raises income, and shifts AD curve right.
– IS or LM shocks shift the AD curve.
Problem 11‐1 (self‐study)
• According to the IS‐LM model, what happens in the short run to the interest rate, income, consumption, and investment under the following circumstances?
a. The central bank increase the money supply
b. The government increases government purchases
c. The government increases taxes
d. The government increases government purchases and taxes by equal amounts
Problem 11‐2
• Use the IS‐LM model to predict the effects of each of the following shocks on income, the interest rate, consumption, and investment. In each case, explain what the Fed should do keep income at its initial level.
a. After the invention of a new high‐speed computer chip, many firms decide to upgrade their computer systems.
b. A wave of credit‐card fraud increase s the frequency with which people make transactions in cash.
c. A best‐seller titled Retire Rich convinces the public to increase the percentage of their income devoted to saving.
Problem 11‐3
• Consider the economy of Hicksonia. The following data are collected:
C = 200+0.75(Y‐T)
I = 200 – 25r
G = T = 100
(M/P)d = Y – 100r
M = 1,000
P = 2
Problem 11‐3
a.
b.
c.
d.
Derive the IS schedule in the form of Y = ____.
Derive the LM schedule in the form of Y = ____.
Find the equilibrium interest rate r and income Y.
Suppose that the money supply is raised from 1,000 to 1,200. How much does the LM curve shift in the horizontal direction? Obtain the new equilibrium interest rate r and income Y.
e. With the initial value for M, suppose that the price level rise from 2 to 4. What happens? Obtain the new equilibrium interest rate r and income Y.
f. Derive and graph an equation for the aggregate demand curve. What happens to this AD curve if money supply changes as in (d)?
Problem 11‐4
• True / False? Explain.
a. If investment does not depend on the interest rate, the IS curve is horizontal.
b. If the money demand does not depend on the interest rate, the LM curve is vertical.
c. If the money demand does not depend on income, the LM curve is vertical.
d. If the money demand is extremely sensitive to the interest rate, the LM curve is vertical.
Problem 11‐6
• Use the IS‐LM diagram to describe the short‐run and long‐run effects of the following changes on national income, the interest rate, the price level, consumption, investment, and real money balance.
a. An increase in the money supply
b. An increase in government purchase
c. An increase in taxes
Answer using the format in the following slide.
Problem 11‐6
Short Run Effects Y
r
P
C
I
M/P
a
b
c
Long
a
b
c
Run Effects Y
r
P
C
I
M/P
Problem 11‐0 (review)
Discuss each of the following terms or statements. 1. The Pigou effect
2. The debt‐deflation theory
3. A decrease in expected inflation (e.g., from 0% to ‐3%) can make a recession worse. Explain using an IS‐LM diagram.
4. In a liquidity trap, conventional monetary policy is powerless to expand the economy. Discuss three possibilities the monetary authority can still maintain effectiveness in times of recession.