aggregate demand ii is-lm model eva hromádková, 22.3 2010 macroeconomics eco 110/1, aau lecture 7

AGGREGATE DEMAND IIIS-LM MODEL

Eva Hromádková, 22.3 2010

Macroeconomics ECO 110/1, AAULecture 7

Overview of Lecture 7

IS-LM model of AD curve: Model for AD curve => analysis of

stabilization policies IS curve – goods market

Fiscal policy – expenditures and taxes LM curve – money market

Monetary policy – money supply Equilibrium – interest rates

2

IS-LM modelContext

3

We have already introduced the model of aggregate demand (QTM) 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

IS-LM modelContext II

4

Today we will develop IS-LM model, the theory that explains the aggregate demand curve

First, we focus on the short run and assume hat price level is fixed

Then, we allow price to be flexible, and derive AD curve

Finally, we analyze the effect of fiscal and monetary policy on the most important macroeconomic aggregates – output and unemployment

IS curveKeynesian cross

5

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

Notation: I = planned investmentE = C + I + G = planned expenditureY = real GDP = actual expenditure

Difference between actual & planned expenditure: unplanned inventory investment

IS curveElements of the Keynesian cross

6

Consumption function: C = MPC*(Y-T)

Govt. policy variables: G, T

Investment: I = I(r)

Planned expenditure: E = C(Y-T) + I(r) + G

Equilibrium: Y = E

IS curveGraphing planned expenditure

7

income, output, Y

E

planned

expenditure

E =C +I +G

Slope is MPC

IS curveGraphing the equilibrium condition

8

income, output, Y

E

planned

expenditure

E =Y

45º

IS curveEquilibrium value of income

9

E>Y: depleting inventories => produce more

E<Y: accumulating inventories=> produce less

income, output, Y

E

planned

expenditure

E =Y

E>Y

E<Y

IS curveFiscal policy

10

Fiscal stimulus: Increase in government expenditures Cut taxes Increase transfer payments

Fiscal restraint: Decrease in government expenditures Increased taxes Decreased transfer payments

IS curveIncrease in government purchases

11

Y

E

E =Y

E =C +I +G1

E1 = Y1

E =C +I +G2

E2 = Y2

Y

GLooks like Y>G

IS curveWhy is change in Y > change in G?

12

Def: Government purchases multiplier:

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

But Y C (Y-T) further Y further C further Y

So the government purchases multiplier will be greater than one.

YG

IS curveChange in G - Sum up changes in expenditure

13

Y G MPC G MPC MPC G

MPC MPC MPC G ...

1 2 3G MPC G MPC G MPC G ...

11

GMPC

So the multiplier is:

11 for 0 < MPC < 1

1YG MPC

This is a standard geometric series from algebra:

IS curveIncrease in taxes

14

Y

E

E =Y

E =C2 +I +G

E2 = Y2

E =C1 +I +G

E1 = Y1

Y

At Y1, there is now

an unplanned inventory buildup……so firms

reduce output, and income falls toward a new equilibrium

C = MPC T

IS curveChange in T - Sum up changes in expenditure

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Y C I G

MPC Y T

C

(1 MPC) MPCY T

equilibrium condition in changesI and G exogenous

Solving for Y :

MPC1 MPC

Y T

Final result:

IS curveTax multiplier

Question: how is this different from the government spending multiplier considered previously?

The tax multiplier:…is negative: An increase in taxes reduces consumer spending, which reduces equilibrium income.…is smaller than the govt spending multiplier: (in absolute value) Consumers save the fraction (1-MPC) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G.

16

IS curveHow to derive the IS curve I

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def: a graph of all combinations of r and Y that 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) + GThe IS curve is negatively sloped. Intuition:A fall in the interest rate motivates firms to increase 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.

Y2Y1

Y2Y1

IS curveHow to derive the IS curve II

r I

Y

E

r

Y

E =C +I (r1 )+G

E =C +I (r2 )+G

r1

r2

E =Y

IS

I E

Y

Y2Y1

Y2Y1

IS curveFiscal policy and IS curve – ex. of increase in G

At given value of

r, G E Y

Y

E

r

Y

E =C +I (r1 )+G1

E =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.

11 MPC

Y G

Y

LM curveHow to build the LM curve

20

The theory of liquidity preference:

Developed by John Maynard Keynes.

A simple theory in which the interest rate

is determined by money supply and money demand.

LM curveMoney supply

M/P

real money balances

r

interestrate

sM P

M P

The supply of real money balances is fixed.

LM curveMoney demand

22

M/P

real money balances

r

interestrate sM P

M P

L

(r,Y )

The demand for real money balances is negatively dependent on interest rate.

LM curveEquilibrium

23

M/P

real money balances

r

interestrate

sM P

M P

L (r,Y ) r1

The interest rate adjusts to equate the supply and demand for money

LM curveMonetary policy

24

LM curveMonetary policy – How can CB affect the interest rate?

25

M/P

real money balances

r

interestrate

1M

P

L

(r ,Y)

r1

r2

2M

P

To reduce r, central bank reduces M.In reality, this is hardly he case. More used technique = change of discount rate.

LM curveHow to derive LM curve?

26

The LM curve 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:

The LM curve is positively sloped. Intuition: An increase in income raises money

demand. 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.

( , )M P L r Y

LM curveHow to derive LM curve II

M/P

r

1M

P

L (r , Y1 ) r1

r2

r

YY1

r1

r2

LM1

(a) The market for real money balances

(b) The LM curve

2M

P

LM2

IS-LM modelEquilibrium

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

r

( , )M P L r Y

IS

LM

Equilibriuminterestrate

Equilibriumlevel ofincome

causing output & income to rise.

IS1

IS-LM modelFiscal policy: An increase in government purchases

1. IS curve shifts right

Y

rLM

r1

Y1

1by

1 MPCG

IS2

Y2

r2

1.2. This raises money

demand, causing the interest rate to rise…

2.

3. …which reduces investment, so the final increase in Y

1is smaller than

1 MPCG

3.

IS1

1.

IS-LM modelFiscal policy: A tax cut

Y

r

LM

r1

Y1

IS2

Y2

r2

Because consumers save (1MPC) of the tax cut, the initial boost in spending is smaller for T than for an equal G…

and the IS curve shifts by MPC

1 MPCT

1.

2.

2.

…so the effects on r and Y are smaller for a T than for an equal G.

2.

2. …causing the interest rate to fall

IS

IS-LM modelMonetary Policy: an increase in M

1. M > 0 shifts the LM curve down(or to the right)

Y

r LM1

r1

Y1 Y2

r2

LM2

3. …which increases investment, causing output & income to rise.

IS-LM modelShocks I

32

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 banking reduce

money demand

IS-LM modelShocks II

33

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

Aggregate demandHow to get from IS-LM to AD

34

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 the LM curve and therefore affect Y.

The aggregate demand curve (introduced in chap. 9 ) captures this relationship between P and Y

Y1Y2

Aggregate demandHow to get from IS-LM to AD II

Y

r

Y

P

IS

LM(P1)

LM(P2)

AD

P1

P2

Y2 Y1

r2

r1

Intuition for slope of AD curve:

P (M/P )

LM shifts left

r

I

Y

Aggregate demandEffect of monetary policy

Y

P

IS

LM(M2/P1)

LM(M1/P1)

AD1

P1

Y1

Y1

Y2

Y2

r1

r2

The Fed can increase aggregate demand:

M LM shifts right

AD2

Y

r

r

I

Y at each value of P

Y2

Y2

r2

Y1

Y1

r1

Aggregate demandEffect of fiscal policy

Y

r

Y

P

IS1

LM

AD1

P1

Expansionary fiscal policy (G and/or T ) increases agg. demand:

T C

IS shifts right

Y at each value of P AD2

IS2

Aggregate demandWhen is fiscal policy more effective?

Fiscal policy is effective (Y will rise much) when:

LM flatter

As the rise in G raises Y,

the increase in money demand does not raise r much:

so investment is not crowded out as much.

LM’

Y2’

2’

Y2

IS2

2

LM

Y1

IS1r

1

Aggregate demandWhen is monetary policy more effective?

Monetary policy is effective (Y will rise much) when:

IS flatter

As a rise in M lowers the interest rate (r),

investment rises more in response to the fall in r,

so output rises more.Y2

LM2

2

Y1

LM1

r

1

Y2’

2’

IS

IS’

IS-LM and AD-AS modelcombination of short & long run

Y Y

Y Y

Y Y

rise

fall

remain constant

In the short-run equilibrium, if

then over time, the price level

will

IS-LM and AD-AS modelshort & long run effect of IS shock I

A negative IS shock shifts IS and AD left, causing Y to fall.

Y

r

Y

PLRAS

Y

LRAS

Y

IS1

SRAS1P1

LM(P1)

IS2

AD2

AD1

IS-LM and AD-AS modelshort & long run effect of IS shock II

Y

r

Y

P LRAS

Y

LRAS

Y

IS1

SRAS1P1

LM(P1)

IS2

AD2

AD1

In the new short-run equilibrium, Y Y

IS-LM and AD-AS modelshort & long run effect of IS shock II

Y

r

Y

P LRAS

Y

LRAS

Y

IS1

SRAS1P1

LM(P1)

IS2

AD2

AD1

In the new short-run equilibrium, Y Y

Over time, P gradually falls, which causes• SRAS to move

down• M/P to increase,

which causes LM to move down

AD2

IS-LM and AD-AS modelshort & long run effect of IS shock III

Y

r

Y

P LRAS

Y

LRAS

Y

IS1

SRAS1P1

LM(P1)

IS2

AD1

Over time, P gradually falls, which causes• SRAS to move

down• M/P to increase,

which causes LM to move down

SRAS2P2

LM(P2)

AD2

SRAS2P2

LM(P2)

IS-LM and AD-AS modelshort & long run effect of IS shock IV

Y

r

Y

P LRAS

Y

LRAS

Y

IS1

SRAS1P1

LM(P1)

IS2

AD1

This process continues until economy reaches a long-run equilibrium with

Y Y

The Great DepressionCASE STUDY

120

140

160

180

200

220

240

1929 1931 1933 1935 1937 1939

bill

ion

s o

f 19

58

do

llars

0

5

10

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25

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pe

rce

nt o

f la

bo

r fo

rce

120

140

160

180

200

220

240

1929 1931 1933 1935 1937 1939

bill

ion

s o

f 19

58

do

llars

0

5

10

15

20

25

30

pe

rce

nt o

f la

bo

r fo

rce

Unemployment (right scale)

Real GNP(left scale)


Real side of economy: Output: falling Consumption: falling Investment: falling much Gov. purchases: fall (with a delay)


Nominal side: Nominal interest rate: falling Money supply (nominal): falling Price level: falling

(deflation)


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

1. Stock market crash exogenous C Oct-Dec 1929: S&P 500 fell 17% Oct 1929-Dec 1933: S&P 500 fell 71%

2. Drop in investment “correction” after overbuilding in the

1920s widespread bank failures made it harder

to obtain financing for investment3. Contractionary fiscal policy

in the face of falling tax revenues and increasing deficits, politicians raised tax rates and cut spending

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:1. P fell even more, so M/P actually rose

slightly during 1929-31. 2. nominal interest rates fell, which is the

opposite of what would result from a leftward LM shift.

The Money Hypothesis: Revision

There was a big deflation: P fell 25% 1929-33.

A sudden fall in expected inflation means the ex-ante real interest rate rises for any given nominal rate (i)

ex ante real interest rate = i – e

This could have discouraged the investment expenditure and helped cause the depression.

Since the deflation likely was caused by fall in M, monetary policy may have played a role here.

aggregate demand ii is-lm model eva hromádková, 22.3 2010 macroeconomics eco 110/1, aau lecture 7

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