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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.