IS-LM MODEL

Eva Hromádková, 12.4 2010

0VS452 + 5EN253Lecture 8 – part II

Overview of Lecture 8 – part IIIS-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

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IS-LM modelContext

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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

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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

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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

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

Govt. policy variables:G, T

Investment:I = I(r)

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

IS curveGraphing planned expenditure

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income, output, Y

E

planned

expenditureE =C +I +G

Slope is MPC

IS curveGraphing the equilibrium condition

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income, output, Y

E

planned

expenditure

E =Y

45º

IS curveEquilibrium value of income

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E>Y: depleting inventories => produce moreE<Y: accumulating inventories=> produce less

income, output, Y

E

planned

expenditure

E =Y

E>Y

E<Y

IS curveFiscal policy

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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

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Y

E

E =Y

E =C +I +G1

E1 = Y1

E =C +I +G2

E2 = Y2Y

GLooks like Y>G

IS curveWhy is change in Y > change in G?

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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

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Y G MPC G MPC MPC GMPC MPC MPC G ...

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

11 G

MPC

So the multiplier is: 1 1 for 0 < MPC < 11

YG MPC

This is a standard geometric series from algebra:

IS curveIncrease in taxes

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Y

E

E =Y

E =C2 +I +G

E2 = Y2

E =C1 +I +G

E1 = Y1Y

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 MPCY 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.

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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 expenditureThe 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 – example 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 MPCY G

Y

LM curveHow to build the LM curve

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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

rinterest

rate sM P

M P

The supply of real money balances is fixed.

LM curveMoney demand

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M/P real money

balances

rinterest

rate sM P

M P

L

(r,Y )

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

LM curveEquilibrium

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M/P real money

balances

rinterest

rate sM P

M P

L (r,Y ) r1

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

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

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M/P real money

balances

rinterest

rate

1MP

L

(r ,Y)

r1

r2

2MP

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?

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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

1MP

L (r , Y1 ) r1

r2

r

YY1

r1

r2

LM1

(a) The market for real money balances

(b) The LM curve

2MP

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

slide 28

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 MPC G

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 MPC G

3.

slide 29

IS1

1.

IS-LM modelFiscal policy: A tax cut

Y

rLM

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 MPC T

1.

2.

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

2.

slide 30

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.