The Short-Run: IS/LM

Prof. Lutz Hendricks

Econ520

February 23, 2017

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Issues

I In the growth models we studied aggregate demand wasirrelevant.

I We always assumed there is enough demand to employ allfactors / sell all output.

I Why is this appropriate for long-run analysis?

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The Short and the Long Run

Short run: supply is elastic

I only demand mattersI IS/LM model

Long run: output is on its trend growth path

I only supply mattersI capital stock adjusts

growth models

Medium run: supply depends on prices

I demand and supply matterI price setting mechanisms push output towards trendI AS/AD modelI the transition from short to long run

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Why Isn’t There One Model?

In state of the art research, there actually is one model.It has the price adjustment frictions that give rise tounemployment, business cycles, ...It has capital accumulation that matter for long-run output(growth)

It has an explicity transition path between short run and long runequilibrium

I over time, prices adjust and demand becomes less and lessimportant

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Objectives

In this section, we are concerned with the short-run IS-LM model

You will learn:

1. how to set up and interpret the IS-LM model2. what its limitations are3. how to solve for the equilibrium4. how to analyze the effects of shocks and policies

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IS-LM Model

Key assumptions:

I Output is determined by aggregate demandI There is no supply sideI Prices are fixedI Closed economy

Think: economy in recession, with lots of unemployed resources.

We relax all of these assumptions later.

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IS-LM Model

Two markets

I Goods (IS). Money (LM)I In the background there is also a bond market

Two endogenous variables

I Output (Y). Interest rate (i)

Two policy variables

I Government spending (G). Money supply (M)

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The Goods Market: IS Curve

Aggregate Demand

Start from an identity

Z = C + I + G + X− IM

Z is aggregate demand / expenditure.For now: closed economy with X− IM = 0.Add behavioral assumptions to give it content.

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Consumption function

C = C(YD) = c0 + c1YD (1)

YD = Y−T: disposable income (after taxes and transfers)c0: “autonomous consumption” (intercept)c1: marginal propensity to consume (slope)s = 1− c1: marginal propensity to save

Consumption might also depend on wealth, interest rates, expectedincomes, etc.

I these are stuffed into c0

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Investment function

I = I(Y, i) = I + b1Y−b2i (2)

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Government

I Exogenous G and T.I G is government consumptionI T is tax revenue net of transfer payments

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Goods Market Clearing

Assumption: supply is perfectly elastic.

Y = C + I + G (3)= [c0 + I + G− c1T]︸ ︷︷ ︸

Z

+ (c1 + b1)Y−b2i (4)

Z: autonomous spending / demandSolve to get the IS curve:

Y =Z−b2i

1− c1−b1(5)

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Goods Market Clearing

Y

A

45°

ZZ

Demand

Income, Y

Dem

and

Z, P

rodu

ctio

n Y

Y

Equilibrium Point:Y ! Z

Slope ! c1

AutonomousSpending

Slope ! 1Production

What happens when theinterest rate i rises?

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IS Curve

IS! (for T! > T )

IS (for taxes T )

Inte

rest

, i

Y!

Output, YY

i

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Intuition: IS Curve

Why is IS downward sloping?

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Shifting the IS CurveOnly autonomous demand Z shifts ISExample: G ↑

I Excess demand → Need higher i to reduce II New IS curve shifted up

What else shifts IS?

Clearly distinguish moving along the curve vs. shifting thecurve!

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The Fiscal Multiplier

Y =Z−b2i

1− c1−b1(6)

I Increasing government spending by $1 =⇒ increasing Y by1/(1− c1−b1).

I This holds the interest rate constant (which will not be true inequilibrium)

I Intuition:

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The Fiscal Multiplier

Y

A

BC

DE

ZZ

ZZ!!

Income, Y

Dem

and

Z, P

rodu

ctio

n Y

Y

Y!

Y!

A!

45°

$1 billion

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Saving Equals InvestmentWe can also think about goods market clearing as equating savingwith investment.Private saving:

S = YD−C = Y−T−C (7)

Public saving:SP = T−G (8)

Total saving equals investment:

I = Y−T−C + T−G (9)

This yields goods market clearing

Y = C + I + G (10)

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The Money / Bond Market: LM Curve

LM Curve

The LM curve equates supply and demand of “money.”What is “money”?

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Money Demand

How to divide wealth between “money” and bonds?

I Money: liquidity benefitI Bonds: interest benefit

Division depends on

I transactions volume (nominal income)I interest rate

Money demand can then be written as

Md = $Y×L(i) (11)

$Y is nominal income (in dollars)

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Money Demand

M

Md

(for nominal income $Y )

Md!! (for $Y! > $Y )

Money, M

Inte

rest

rat

e, i i

M !

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Money Supply

Real world: money = [currency] + [checkable deposits]

Currency: controlled by CBCheckable deposits: created by banks

For now: assume that CB controls money supply

M = Ms (12)

Money market clearing:

Ms = $YL(i) (13)

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Money Market Clearing

M

Money DemandMd

Money SupplyMs

Money, M

A

Inte

rest

rat

e, i

i

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Money Demand Increases

M

A

A!!

Md

Ms

Md!($Y ! > $Y)

Money, M

Inte

rest

rat

e, i i !

i

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Money Supply Increases

M!!

A!

A

Md

Ms!Ms

Money, M

Inte

rest

rat

e, i i

M

i!

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Open Market Operations

I The markets for money and bonds are linked.I To increase the money supply, the CB buy bonds and pays

with currency.I The price of bonds rises =⇒ the bond yield i falls.I A complication: the CB has no direct control over the supply

of bonds / the bond interest rate.I open market operations do not always work

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Reading

I Blanchard / Johnson, Macroeconomics, ch. 3-4

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