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CHAPTER 10 Aggregate Demand I slide 1

Context

Chapter 9 introduced the model of aggregatedemand and aggregate supply.

Long run

prices flexible

output determined by factors of production &technology

unemployment equals its natural rate

Short run

prices fixed

output determined by aggregate demand

unemployment is negatively related to output


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Context

This chapter develops the IS-LMmodel,the theory that yields the aggregate demandcurve.

We focus on the short run and assume the

price level is fixed.

This chapter (and chapter 11) focus on theclosed-economy case. Chapter 12 presents

the open-economy case.


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The Keynesian Cross

A simple closed economy model in whichincome is determined by expenditure.(due to J.M. Keynes)

Notation:

I = plannedinvestment

E = C + I + G = planned expenditure

Y = real GDP = actual expenditure

Difference between actual & plannedexpenditure: unplanned inventory investment


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Elements of the Keynesian Cross

( )C C Y T

I I

,G G T T

( )E C Y T I G

Actual expenditure Planned expenditure

Y E

consumption function:

for now, plannedinvestment is exogenous:

planned expenditure:

Equilibrium condition:

govt policy variables:


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Graphing planned expenditure

income, output,Y

Eplannedexpenditure

E=C+I+G

MPC1


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Graphing the equilibrium condition

income, output,Y

Eplannedexpenditure

E=Y

45


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The equilibrium value of income

income, output,Y

Eplannedexpenditure

E=Y

E=C+I+G

Equilibrium

income


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An increase in government purchases

Y

E

E=C+I+G1

E1 = Y1

E=C+I+G2

E2 = Y2Y

At Y1,

there is now an

unplanned drop

in inventory

so firms

increase output,

and income

rises toward a

new equilibrium

G


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Solving for Y

Y C I G Y C I G

MPC Y G

C G

(1 MPC) Y G

1

1 MPCY G

equilibrium conditionin changes

because I exogenous

because C= MPC Y

Collect terms with Y

on the left side of theequals sign:

Finally, solve for Y:


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The government purchases multiplier

Example: If MPC = 0.8, then

Definition: the increase in income resultingfrom a $1 increase in G.

In this model, the govt purchasesmultiplier equals 1

1 MPC

Y

G

1 51 0.8

YG

An increase in Gcauses income to

increase by 5 times

as much!


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Why the multiplier is greater than 1

Initially, the increase in G causes an equalincrease in Y: Y= G.

But Y C

further Y further C

further Y

So the final impact on income is muchbigger than the initial G.


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An increase in taxes

Y

E

E=C2+I+G

E2 = Y2

E=C1+I+G

E1 = Y1Y

At Y1, there is now

an unplanned

inventory buildupso firms

reduce output,and income falls

toward a new

equilibrium

C= MPC T

Initially, the tax

increase reduces

consumption, and

therefore E:


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Solving for Y

Y C I G

MPC Y T

C

(1 MPC) MPCY T

eqm condition inchanges

I and G exogenous

Solving for Y:

MPC

1 MPCY T

Final result:


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The Tax Multiplier

def: the change in income resulting froma $1 increase in T:

MPC

1 MPC

Y

T

0 8 0 8 41 0 8 0 2

. .. .

YT

If MPC = 0.8, then the tax multiplier equals


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The Tax Multiplier

is negative:A tax hike reducesconsumer spending,which reduces income.

is greater than one(in absolute value):A change in taxes has amultiplier effect on income.

is smaller than the govt spending multiplier:Consumers save the fraction (1-MPC) of a tax cut,so the initial boost in spending from a tax cut issmaller than from an equal increase in G.


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Exercise:

Use a graph of the Keynesian Crossto show the impact of an increase in

planned investment on the equilibrium

level of income/output.


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The IScurve

def: a graph of all combinations ofr and Ythat result in goods market equilibrium,

i.e. actual expenditure (output)

= planned expenditure

The equation for the IS curve is:

( ) ( )Y C Y T I r G


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Y2Y1

Y2Y1

Deriving the IScurve

r I

Y

E

r

Y

E=C+I(r1)+GE=C+I(r2)+G

r1

r2

E=Y

IS

IE

Y


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Why the IScurve is negatively sloped

A fall in the interest rate motivates firms toincrease investment spending, which drives

up total planned spending (E).

To restore equilibrium in the goods market,output (a.k.a. actual expenditure, Y) must

increase.


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The IS curve and the Loanable Funds model

S, I

r

I(r )

r1

r2

r

YY1

r1

r2

(a) The L.F. model (b) The IS curve

Y2

S1S2

IS


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Fiscal Policy and the IScurve

We can use the IS-LMmodel to seehow fiscal policy (G and T) can affectaggregate demand and output.

Lets start by using the Keynesian Crossto see how fiscal policy shifts the IScurve


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Y2Y1

Y2Y1

Shifting the IScurve: G

At any value ofr,G E Y

Y

E

r

Y

E=C+I(r1)+G1E=C+I(r1)+G2

r1

E=Y

IS1

The horizontal

distance of the

IS shift equals

IS2

so the IS curve

shifts to the right.

1

1 MPCY G

Y


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Exercise: Shifting the IS curve

Use the diagram of the Keynesian Crossor Loanable Funds model to show how

an increase in taxes shifts the IS curve.


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The Theory of Liquidity Preference

due to John Maynard Keynes.

A simple theory in which the interest rateis determined by money supply and

money demand.


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Money Supply

The supply ofreal money

balances

is fixed:

s

M P M P

M/Preal money

balances

rinterest

rate

sM P

M P


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Money Demand

Demand forreal money

balances:

M/Preal money

balances

rinterest

rate

sM P

M P

( )d

M P L r

L(r)


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Equilibrium

The interestrate adjusts

to equate the

supply and

demand formoney:

M/Preal money

balances

rinterest

rate

sM P

M P

( )M P L r L(r)

r1


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How the Fed raises the interest rate

To increase r,

Fed reduces M

M/Preal money

balances

rinterest

rate

1M

P

L(r)

r1

r2

2M

P


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CASE STUDY

Volckers Monetary Tightening

Late 1970s:

> 10% Oct 1979: Fed Chairman Paul Volcker

announced that monetary policy

would aim to reduce inflation.

Aug 1979-April 1980:

Fed reduces M/P 8.0%

Jan 1983: = 3.7%

How do you think this policy changewould affect interest rates?


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Volckers Monetary Tightening, cont.

i < 0i > 0

1/1983: i= 8.2%8/1979: i= 10.4%

4/1980: i= 15.8%

flexiblesticky

Quantity Theory,

Fisher Effect(Classical)

Liquidity Preference

(Keynesian)

prediction

actualoutcome

The effects of a monetary tightening

on nominal interest rates

prices

model

long runshort run


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The LM curve

Now lets put Y back into the money demandfunction:

( , )M P L r Y

The LMcurve is a graph of all combinations of

r and Y that equate the supply and demand

for real money balances.

The equation for the LM curve is:

d

M P L r Y ( , )


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Deriving the LM curve

M/P

r

1M

P

L(r,Y1)

r1

r2

r

YY1

r1

L(r,Y2)

r2

Y2

LM

(a) The market forreal money balances(b) The LM curve


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Why the LMcurve is upward-sloping

An increase in income raises moneydemand.

Since the supply of real balances is fixed,

there is now excess demand in the money

market at the initial interest rate.

The interest rate must rise to restore

equilibrium in the money market.


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How M shifts the LM curve

M/P

r

1M

P

L

(r

,

Y1

)

r1

r2

r

YY1

r1

r2LM1

(a) The market forreal money balances(b) The LM curve

2M

P

LM2


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Exercise: Shifting the LM curve

Suppose a wave of credit card fraudcauses consumers to use cash more

frequently in transactions.

Use the Liquidity Preference modelto show how these events shift the

LMcurve.


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The short-run equilibrium

The short-run equilibrium isthe combination ofr and Y

that simultaneously satisfies

the equilibrium conditions in

the goods & money markets:

( ) ( )Y C Y T I r G

Y

r

( , )M P L r Y

IS

LM

Equilibrium

interest

rate

Equilibrium

level of

income


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The Big Picture

KeynesianCross

Theory of

Liquidity

Preference

IScurve

LM

curve

IS-LM

model

Agg.

demand

curve

Agg.

supply

curve

Model of

Agg.

Demandand Agg.

Supply

Explanation

of short-run

fluctuations


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Chapter summary

1. Keynesian Cross

basic model of income determination

takes fiscal policy & investment as exogenous

fiscal policy has a multiplier effect on income.

2. IScurve

comes from Keynesian Cross when planned

investment depends negatively on interest rate

shows all combinations ofr and Ythat equate planned expenditure with

actual expenditure on goods & services


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Chapter summary

3. Theory of Liquidity Preference

basic model of interest rate determination

takes money supply & price level as exogenous

an increase in the money supply lowers the

interest rate

4. LMcurve

comes from Liquidity Preference Theory when

money demand depends positively on income shows all combinations ofr andY that equate

demand for real money balances with supply


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Chapter summary

5. IS-LMmodel

Intersection ofISand LMcurves shows the

unique point (Y, r) that satisfies equilibrium

in both the goods and money markets.


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CHAPTER 10 A D d I

Preview of Chapter 11

In Chapter 11, we will use the IS-LMmodel to analyze the impact

of policies and shocks

learn how the aggregate demand curve

comes from IS-LM

use the IS-LMandAD-ASmodels togetherto analyze the short-run and long-run

effects of shocks use our models to learn about

the Great Depression