Aggregate Demand I: Building the IS-LM Modeljneri/Econ305/files/ch11- IS-LM_Aggre… · the IS-LM...
Transcript of Aggregate Demand I: Building the IS-LM Modeljneri/Econ305/files/ch11- IS-LM_Aggre… · the IS-LM...
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Aggregate Demand I: Building the IS-LM Model
Part 3
Chapter 11
A MORE COMPLEX THEORY OF SHORT-RUN EQUILIBRIUM IN THE GOODS MARKET THE IS CURVE
Planned Investment
• The Keynesian Cross model assumed that planned investment expenditure (I) is exogenous
• Recall that, in chapter 3, we had assumed that investment spending is inversely related to the real interest rate
• The IS Curve theory of the goods market brings back the investment function I = I(r)
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Investment and the real interest rate
• Assumption: investment spending is inversely related to the real interest rate
• I = I(r), such that r↑⇒ I↓
r
I
I (r )
Investment and the real interest rate
• Specifically, I = Io − Irr • Here Ir is the effect of r
on I and • Io represents all other
factors that also affect business investment spending such as business optimism, technological progress, etc.
• I1 > Io , increased business optimism increase in investment (I)
I
r
Io − Irr
I1 − Irr
Investment: example
• Suppose I = 12 – 2r is the investment function
• Then, if r = 5 percent,
…we get I = 12 – 2(5) = 2.
• Need to be careful with units: is 5 percent, 5 or .05?
• Hopefully, I remember to tell you.
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The IS Curve
• The goods market is in equilibrium when
Y = C + I + G
• The IS curve is a graph that shows all combinations of r and Y for which the goods market is in equilibrium
• Therefore, the basic equation underlying the IS curve is Y = C(Y – T) + I(r) + G
• Oops, we now have one equation and 2 unknowns!
Deriving the IS Curve: algebra
rC
IT
C
CGIC
CY
GrIITCCYC
GrIITCCYCY
GrIITCYCCY
GrIITYCCY
GrITYCY
y
r
y
y
oo
y
royoy
royoy
royyo
royo
11)(
1
1
)1(
)(
)()(
Spending multiplier
Tax multiplier
Interest rate effect
Deriving the IS Curve: algebra
rC
IT
C
CGIC
CY
y
r
y
y
oo
y
11
)(1
1
The basic equation underlying the IS curve is …
GrITYCY )()(
… for specific consumption and investment functions, the equation underlying the IS curve can also be expressed as:
The two equations are equivalent forms of the IS curve.
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Comparing the Equations of the Keynesian Cross and the IS Curve
rC
IT
C
CGIC
CY
y
r
y
y
oo
y
11
)(1
1
TC
CGIC
CY
y
y
oo
y
1
)(1
1
Keynesian Cross Model
IS Curve Model
Spending multiplier
Tax-cut multiplier
Interest rate effect
Spending multiplier
Tax multiplier
This is the only difference
The IS Curve
rC
IT
C
CGIC
CY
y
r
y
y
oo
y
11
)(1
1
Spending multiplier
Tax multiplier
Interest rate effect
Y2 Y1
r
Y
r1
IS
r2
ΔY
Δr
Any change in the real interest rate will cause an opposite change in real total GDP by a multiple determined by the size of the interest rate effect. This is why the IS curve is negatively sloped.
The IS Curve: effect of fiscal policy
rC
IT
C
CGIC
CY
y
r
y
y
oo
y
11
)(1
1
Spending multiplier
Tax multiplier
IS Interest rate effect
Y2 Y1
r
Y
r1
IS1 IS2 Y
Any increase in Co + Io + G causes the IS curve to shift right by the amount of the increase magnified by the spending multiplier
That is, if the real interest rate is unchanged, the Keynesian Cross model is the same as the IS curve model.
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The IS Curve: effect of fiscal policy
rC
IT
C
CGIC
CY
y
r
y
y
oo
y
11
)(1
1
Spending multiplier
Tax multiplier
IS Interest rate effect
Y2 Y1
r
Y
r1
IS1 IS2 Y
Any decrease in taxes (T) causes the IS curve to shift right by the amount of the tax cut magnified by the tax-cut multiplier
What Shifts the IS Curve?
• The IS curve shifts right if there is:
– an increase in Co + Io + G, or
– a decrease in T.
• Also goes the other way!
Y2 Y1
Y2 Y1
Deriving the IS curve: graphs
r I
Y
PE
r
Y
PE =C +I (r1 )+G
PE =C +I (r2 )+G
r1
r2
PE =Y
IS
I PE
Y
Any change in the real interest rate will cause an opposite change in real total GDP by a multiple determined by the size of the interest rate effect.
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𝒀 Y1
𝒀 Y1
The natural rate of interest • Recall, the chapter 3
loanable funds model gave us a long-run theory of the real interest rate
• At the long-run interest rate, both
– Y = C + I + G (or, equivalently, S = I) and
– Y = 𝒀
• Note: r* in the diagram satisfies the requirement of long-run equilibrium.
• r* is the natural rate of interest. The interest rate consistent with full employment.
Y
PE
r
Y
PE = C + I(r1) + G
PE = C + I(𝒓 ) + G
r1
r*
PE = Y
IS
THE MONEY MARKET IN THE SHORT RUN: THE LM CURVE
The theory of short-run equilibrium in the money market
The Theory of Liquidity Preference
• Due to John Maynard Keynes.
• A simple theory in which the interest rate is determined by money supply and money demand.
• Two financial assets – Money and bonds.
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Money supply
The supply of real money balances is fixed:
s
M P M P
M/P real money
balances
i=r interest
rate
sM P
M P
M and P are
exogenous.
Money demand
Demand for real money balances:
M/P real money
balances
i = r interest
rate
sM P
M P
L (r )
( ) ( , )dM P L i Y
(𝑴/𝑷)𝒅 = 𝑳(𝒓 + 𝑬, 𝒀)
Assume E =0, => i = r
Equilibrium
The interest rate adjusts to equate the supply and demand for money:
M/P real money
balances
i=r interest
rate
sM P
M P
( )M P L r L (r )
r1
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Equilibrium The interest rate adjusts to equate the supply and demand for money.
Excess supply of money creates an excess demand for other assets – bonds in the Keynesian model.
Excess demand for money creates an excess supply of other assets – bonds in the Keynesian model.
M/P
real money
balances
i= r interest
rate
s
M P
M P
( )M P L r
L (r )
r1
r3
r2
Excess supply of money
Excess demand for money
How the Fed increases and decreases the interest rate
To decrease r, Fed
increases M, creating an
excess supply of money.
The demand for bonds
increase and interest
rates decrease.
M/P real money
balances
i=r interest
rate
1M
P
L (r )
r1
r2
2M
P
Prices are sticky (fixed?) in the short run
• Assumption: the money supply (M), which is controlled by the central bank, is exogenous
• Assumption: the overall price level (P) is fixed.
• Assumption: expected inflation (Eπ) zero
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Prices are sticky in the short run
• The long-run analysis of Chapter 5 assumed that P is endogenous.
– in the long run P changes proportionately with M.
• The short-run analysis in the IS-LM model assumes that P is exogenous: it is what it is, it is historically determined
– That is, the overall price level is “sticky”: what it was last week, it will be this week too
Prices are sticky in the short run
• This sticky-prices assumption is the crucial distinction between long-run and short-run macroeconomic analysis
• With the exception of this assumption, all assumptions made in short-run analysis are also assumed in long-run analysis
• So, the differences between long-run and short-run theories are caused by this sticky-prices assumption
CASE STUDY:
Monetary Tightening & Interest Rates
• Late 1970s: > 10%
• Oct 1979: Fed Chairman Paul Volcker announces that monetary policy would aim to reduce inflation
• From Aug 1979 to April 1980, Fed reduced M/P 8.0%
• Jan 1983: = 3.7%
How do you think this policy change
would affect nominal interest rates?
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Monetary Tightening & Interest Rates, cont.
i < 0 Why? i > 0 Why?
8/1979: i = 10.4%
1/1983: i = 8.2%
8/1979: i = 10.4%
4/1980: i = 15.8%
flexible sticky
Quantity theory,
Fisher effect
(Classical)
Liquidity preference
(Keynesian)
prediction
actual
outcome
The effects of a monetary tightening
on nominal interest rates
prices
model
long run short run
The LM curve Put Y back into the money demand function:
( , )M P L r Y
The LM curve is a graph of all combinations of
r and Y that equate the supply and demand for
real money balances.
Equating money supply to money demand (M/P
to Md), the equation for the LM curve is:
d
M P L r Y ( , )
Deriving the LM curve
M/P
r
1M
P
L (r , Y1 )
r1
r2
r
Y Y1
r1
L (r , Y2 )
r2
Y2
LM
(a) The market for
real money balances (b) The LM curve
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Understanding the LM curve’s slope
• The LM curve is positively sloped.
• Intuition:
• An increase in income raises money demand.
• Since the money supply (supply of real balances) is
fixed, there is now excess demand in the money
market at the initial interest rate.
• Sell bonds, the interest rate increases to restore
equilibrium in the money market.
How M shifts the LM curve
M/P
r
1M
P
L (r , Y1 ) r1
r2
r
Y Y1
r1
r2
LM1
(a) The market for
real money balances (b) The LM curve
2M
P
LM2
NOW YOU TRY:
Shifting the LM curve
• Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions.
• Use the liquidity preference model to show how these events shift the LM curve.
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SHORT-RUN EQUILIBRIUM IN THE IS-LM MODEL
Both the goods market and the money market need to be in equilibrium
The short-run equilibrium
The short-run equilibrium is the
combination of r and Y that
simultaneously satisfies the
equilibrium conditions in the
goods & money markets:
( ) ( )Y C Y T I r G
Y
i=r
( , )M P L r YIS
LM
Equilibrium
interest
rate
Equilibrium
level of
income
Remember: E = 0:
𝒀 = 𝑪(𝒀 − 𝑻 ) + 𝑰(i - E)+𝑮
M/𝑷 = L(i,Y),
Short-run equilibrium
Note that the short-run equilibrium GDP does not have to be equal to the long-run
equilibrium GDP (𝑌 , also called potential GDP and natural GDP)
Thus, like the Keynesian Cross model, the IS-LM model can explain recessions and booms. Y
r
IS
LM
Equilibrium
interest
rate
Equilibrium
level of
income
But, the Keynesian Cross model could determine only equilibrium GDP. The IS-LM model determines the equilibrium interest rate as well.
𝒀
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The IS-LM Model: summary • Short-run equilibrium in the goods market is represented
by a downward-sloping IS curve linking Y and r. • Short-run equilibrium in the money market is
represented by an upward-sloping LM curve linking Y and r.
• The intersection of the IS and LM curves determine the short-run equilibrium values of Y and r.
• The IS curve shifts right if there is: – an increase in Co + Io + G, or – a decrease in T.
• The LM curve shifts right if: – M/P increases (M or P ) – If constant term in money demand equation increases
• Later we show the impact of a change in Eπ
Y
r
IS
LM
The Big Picture
Keynesian Cross
Theory of Liquidity Preference
IS curve
LM curve
IS-LM model
Agg. demand
curve
Agg. supply curve
Model of Agg.
Demand and Agg. Supply
Explanation of short-run fluctuations
Preview of Chapter 12
In Chapter 12, we will – use the IS-LM model to analyze the impact of
policies and shocks.
– learn how the aggregate demand curve comes from IS-LM.
– use the IS-LM and AD-AS models together to analyze the short-run and long-run effects of shocks.
– use our models to learn about the Great Depression.