is and lm model

8/2/2019 IS AND LM MODEL

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IS and LM Curve

Qazi Muhammad Adnan Hye


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IS-LM Model

IS Curve

LM CurveKeynesian cross

Government-purchases multiplier

Tax multiplier


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Long runprices flexible

output determined by factors of production &technology

unemployment equals its natural rate

Short runprices fixed

output determined by aggregate demand

unemployment negatively related to output


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This chapter develops the IS-LM model,the basis of the aggregate demand curve.

We focus on the short run and assume theprice level is fixed (so, SRAScurve is

horizontal).


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Price Level, P

Income, Output, Y

SRAS

ADY*Y*'

AD'AD''

Y*''

In the short run, when the price level is fixed,

shifts in the aggregate demand curve lead tochanges in national income, Y.

The IS-LM model =the leading interpretation of Keynes work.

The goal of the model: to show what determines nationalincome for any given price level.

The Keynesian model - shows what causes theaggregate demand curve to shift.


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1. The goods market and the IS curve

2. The money market and the LM curve

3. The short-run equilibrium


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The basic textbook Keynesian model: anelaboration and extension of the classicaltheory.


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The model of aggregate demand (AD) can be split into twoparts:- IS (investment and saving)model of the goodsmarket

- LM (liquidity and money) model of the moneymarket.


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The IS curve(which stands for

investment and saving) plots therelationship between the interest rate andthe level of incomethat arises in themarket for goods and services.

The LM curve(which stands for liquidityand money) plots the relationship

between the interest rate and the level ofincome that arises in the money market.

The variable that links the two parts of the IS-LM model: theinterest rate (it influences both investment and money

demand).


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In the General Theory of Money, Interest and Employment(1936), Keynes proposed: an economys total income was, inthe short run, determined largely by the desire to spend byhouseholds, firms and the government.

Thus, the problem during recessions and depressions,according to Keynes, was inadequate spending.

How to model this insight? - The Keynesian Cross


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Planned expenditure is the amounthouseholds, firms and government plan to

spend on goods and services.

Actual expenditure differs from plannedexpenditure when firms are forced to make

inventory- that is when firms unexpectedlyrise or lower their stock of inventories inresponse to unexpectedly low or high sales.


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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 = planned investment

PE = C + I + G = planned expenditure

Y = actual expenditure=GNP

Difference between actual & plannedexpenditure = unplanned inventoryinvestment


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Graphing planned expenditure

income, output,Y

PE

planned

expenditure

MPC1

GITYCE )(


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Graphing the equilibrium condition

income, output,Y

PE

planned

expenditurePE =Y

45


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The equilibrium value of income

income, output,Y

PE

planned

expenditurePE =Y

Equilibriumincome

GITYCE )(

A


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An increase in government purchases

Y

PE

PE1 =Y1 PE2 =Y2Y

AtY1,

there is now an

unplanned drop

in inventory

so firms

increase output,

and income rises

toward a new

equilibrium.

G

1)( GITYCE

GITYCE )(

A

B


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If government spending were to increase by $1, then you might expect

equilibrium output (Y) to also rise by $1.

But it doesnt! The multiplier shows that the change in demand for

output (Y) will be larger than the initial change in spending. Heres why:

When there is an increase in government spending (G), income rises by

G as well. The increase in income will raise consumption by MPC G, where MPC is the marginal propensity to consume. The increase in

consumption raises expenditure and income again. The second increase

in income of MPC G again raises consumption, this time by MPC

(MPC

G), which again raises income and so on.So, the multiplier process helps explain fluctuations in the demand for

output. For example, if something in the economy decreases investment

spending, then people whose incomes have decreased will spend less,

thereby driving equilibrium demand down even further.


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An increase in taxes

Y

PE

PE2 =Y2 PE1 =Y1Y

AtY1, 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 PE:

GITYCE )(1

ITYCE )(*

2


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The tax multiplieris negative:

A tax increase reduces C,which reduces income.

is greater than one(in absolute value):

A change in taxes has amultiplier effect on income.

is smaller than the govt spendingmultiplier:

Consumers save the fraction (1MPC) of atax cut,so the initial boost in spending from a tax cutissmaller than from an equal increase in G.


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Lets now relax the assumption that the level of planned

investment is fixed.- We write the level of planned investment as: I = I (r).

The investment function - downward-sloping (it shows theinverse relationship between investment and the interest rate)

The IS curve summarizes the relationship between the interestrate and the level of income. It is downward-sloping.

The IS curve combines:the interaction between I and r expressed by the investmentfunctionthe interaction between E and Y demonstrated by the

Keynesian cross.


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E

Income, Output, Y

Y=E

Planned Expenditure,E = C + I + G

r

Income, Output, Y

r

Investment, I

I(r) IS

An increase in theinterest rate (in graph a),

lowers plannedinvestment, which shiftsplanned expendituredownward (ingraph b) and lowers

income (in graph c).(a)

(b)

(c)


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E

Income, Output, Y

Y=E

Planned Expenditure,E = C + I + G

r

Income, Output, Y

IS1

An increase ingovernment purchases

or a decrease in taxes- IS curve shiftsoutward.

A decrease ingovernment purchasesor an increase in taxes- IS curve shifts inward.

IS2

An increase in government purchases

How fiscal policyshifts the IS curve?


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Summary

The IS curve shows the combinations of the interest rate andthe level of income that are consistent with equilibrium in themarket for goods and services.

The IS curve is drawn for a given fiscal policy.

Changes in fiscal policy that raise the demand for goods andservices shift the IS curve to the right.

Changes in fiscal policy that reduce the demand for goods andservices shift the IS curve to the left.


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r

M/PM/P

Supply

LM curve = the relationship between the interest rate and the

level of income that arises in the market for money balancesThe theory of liquidity preference- how the interest rate is determined in theshort run

The supply of real money balances - verticalThe demand for real money balances -downward sloping

Demand, L (r)

The supply and demand for real moneybalances determine the equilibriuminterest rate.


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Money Demand equals Real Money Balances

L(r) = M/P


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r

M/PM/P

Supply

Demand, L (r,Y)

Since the price level is fixed, a reduction in the money supplyreduces the supply of real balances. Notice the equilibriuminterest rate rose.

A Reduction in the

Money Supply: -M/P

Supply'


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(M/P)d = L (r,Y)

The quantity of real money balances demanded is negativelyrelated to the interest rate (because r is the opportunity cost of

holding money) and positively related to income (because oftransactions demand).


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r

M/PM/P

Supply

L (r,Y)'L (r,Y)

r1

r2

r

Y

LM

An increase in income raises money demand, whichincreases the interest rate; this is called an increase intransactions demand for money.The LM curve summarizes these changes in the money

market equilibrium.


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r

M/P

L (r,Y)

r

Y

LM

M/P

Supply

A contraction in the money supply raises the interest rate thatequilibrates the money market. Why? Because a higher interestrate is needed to convince people to hold a smaller quantity ofreal balances.As a result of the decrease in the money supply, the LM shiftsupward.

r1 r1

M/P

Supply'

LM'

r2 r2


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Summary

The LM curve shows the combinations of the interest rate andthe level of income that are consistent with equilibrium in themarket for real money balances.

The LM curve is drawn for a given supply of real moneybalances

Decreases in the supply of real money balances shift the LMcurve upward

Increases in the supply of real money balances shift the LMcurve downward


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r

Y

LM(P0)IS

r0

Y0

The IS curve/equation Y= C (Y-T) + I(r) + G

The LM curve/equation M/P = L(r, Y)The intersection of the IS and LM curves represents simultaneousequilibrium in the market for goods and services and in the marketfor real money balances for given values of government spending,

taxes, the money supply, and the price level.


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The Big Picture

KeynesianCross

Theory ofLiquidity

Preference

IScurve

LMcurve

IS-LMmodel

Agg.demand

curve

Agg.supplycurve

Model ofAgg.

Demandand Agg.Supply

Explanationof short-runfluctuations


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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 of r and Ythat equate planned expenditure withactual 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

rate4. LMcurve comes from liquidity preference theory when

money demand depends positively on income

shows all combinations of rand Y that equatedemand for real money balances with supply


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Chapter Summary

5.IS-LM model Intersection of ISand LMcurves shows the unique

point (Y, r) that satisfies equilibrium in both the

goods and money markets.

is and lm model

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