IS-LM ModelIS-LM ModelBy By

Hicks, Hansen, Lerner and JonesHicks, Hansen, Lerner and Jones

In Keynes’s simple model, the level of income is shown to be determined by the In Keynes’s simple model, the level of income is shown to be determined by the goods market equilibrium. goods market equilibrium.

In this simple model of equilibrium in the goods market, Keynes considered In this simple model of equilibrium in the goods market, Keynes considered investment to be determined by the rate of interest along with the MEC and was investment to be determined by the rate of interest along with the MEC and was shown to be independent of the level of national income. shown to be independent of the level of national income.

According to Keynes, the rate of interest is determined by money market According to Keynes, the rate of interest is determined by money market equilibrium, i.e., the intersection between demand for and supply of money. equilibrium, i.e., the intersection between demand for and supply of money.

In the Keynesian model changes in the rate of interest will affect the determination In the Keynesian model changes in the rate of interest will affect the determination of national income and output in the goods market through causing changes in the of national income and output in the goods market through causing changes in the level of investment. In this way changes in the money market equilibrium influence level of investment. In this way changes in the money market equilibrium influence the determination of national income and output in the goods market. But there is the determination of national income and output in the goods market. But there is only one flow in the Keynesian analysis. only one flow in the Keynesian analysis.

It has been argued that in the Keynesian model, whereas the changes in the rate of It has been argued that in the Keynesian model, whereas the changes in the rate of interest in the money market affect investment and therefore level of income and interest in the money market affect investment and therefore level of income and output in the goods market, there is seemingly no inverse influence of changes in output in the goods market, there is seemingly no inverse influence of changes in the goods market on the money market equilibrium.the goods market on the money market equilibrium.

Inverse influence shown by Hicks and others. According to them, the Inverse influence shown by Hicks and others. According to them, the level of income which depends on the investment and consumption level of income which depends on the investment and consumption demand determines the transaction demand for money which affects demand determines the transaction demand for money which affects the rate of interest. the rate of interest.

IS-LM model is a complete and integrated model based on the IS-LM model is a complete and integrated model based on the Keynesian framework wherein variables such as investment (I), Keynesian framework wherein variables such as investment (I), national income (Y), rate of interest (r), demand for (Mnational income (Y), rate of interest (r), demand for (Mdd) and supply ) and supply of money (Mof money (Mss) are inter-related and mutually interdependent and can ) are inter-related and mutually interdependent and can be represented by the two curves called IS and LM curves. be represented by the two curves called IS and LM curves.

This extended Keynesian model is therefore known as IS-LM curve This extended Keynesian model is therefore known as IS-LM curve model. In this model it is shown how level of national income and model. In this model it is shown how level of national income and rate of interest are jointly determined by the simultaneous rate of interest are jointly determined by the simultaneous equilibrium in the two interdependent goods and money market. equilibrium in the two interdependent goods and money market.

Derivation of the IS curveDerivation of the IS curve

In the Keynesian model of goods market equilibrium, now, rate of interest will be introduced as an important determinant of investment. With this introduction of rate of interest, the investment now becomes an endogenous variable in the model.

When the rate of interest falls, the level of investment increases and vice-versa. Thus changes in the rate of interest affect aggregate demand or aggregate expenditure by causing changes in investment demand. The increase in investment demand will bring about increase in aggregate demand which in turn will raise the equilibrium level of income. Thus IS curve relates different equilibrium levels of national income with various rates of interest.

The process isThe process is

So r is inversely related with Y

The IS curve or schedule is a curve which shows the relationship between the rate of interest and national income, the product market remaining in equilibrium, that is, S=I at different rates of interest.

I AD Y r

0

Planned Investment

I0 I1 I2

Rat

e O

f In

tere

st r0

r1

r3

X

Y

∆I ∆I

National Income

C+I2

C+I2

C+I3

Y0 Y1 Y30

Y

Agg

rega

te D

eman

d

X

A

B

C

X

Y

0 Y1 Y2 Y3

IS Curve

r0

r1

r3Rat

e of

In

tere

st

National Income

Why IS curve is downward slopping?Why IS curve is downward slopping?

A lower rate of interest is associated with a higher level of national income. And vice-A lower rate of interest is associated with a higher level of national income. And vice-versa. This makes IS curve to slope downwards. versa. This makes IS curve to slope downwards.

Steepness of the IS curve depends onSteepness of the IS curve depends on

Elasticity of the investment demand curve

When the investment demand is more elastic to the changes in the rate of interestWhen the investment demand is more elastic to the changes in the rate of interest , , the the investment demand curve will be relatively flat i.e., more elastic and the IS curve will investment demand curve will be relatively flat i.e., more elastic and the IS curve will be relatively flat.be relatively flat.

The size of the multiplierThe higher the value of the multiplier, the higher will be the flatness of IS curve and The higher the value of the multiplier, the higher will be the flatness of IS curve and vice-versa.vice-versa.

Shifts in the IS curve

The level of autonomous expenditure determines the position of the IS curve and changes in the autonomous expenditure cause a shift in it.

Derivation of LM Curve from Money Market Equilibrium

The demand for money (Md) depends on the level of income and rate of interest. The money demand function can be expressed as

( , )dM L Y rWhere,

Y=Real Income

r= rate of interest

Thus, we can draw a family of many demand curves at various levels of income. Now the interaction of the various money demand curves corresponding to the different income levels with the supply curve of money fixed by monetary authority would give us LM curve.

The LM curve relates the level of income with the rate of interest which is determined by money market equilibrium corresponding to different levels of demand for money.

The LM curve tells us what the various rates of interest will be at different levels of income. The liquidity preference curve alone can’t tell us what will be the exact rate of interest.

Y0Y1 Y20

Y

X

r0

r1

r2

LM Curve

0 X

Y MS

Md0 (Y0)

Md1 (Y1)

Md2 (Y2)

r0

r1

r2

Ms

Graphical Derivation of LM Curve

Slope of LM CurveSlope of LM CurveThere are two factors on which the slope of the LM curve depends

The responsiveness of demand for money (i.e., liquidity preference) to the change in income

As the money increases, the demand curve for money shifts. Because with the increase in income demand for money would increase for being held for transaction motive [Md or L1=f (Y)]. This extra demand for money would disturb the money market equilibrium and for the equilibrium to be restored, the rate of interest would increase to the level where the given money supply curve intersects the new demand curve corresponding to the higher level of income.

Money supply is given and the transaction demand for money has increased. So to maintain the equality between money demand and money supply, the speculative demand for money would decline through increase in rate of interest.

The greater the extent to which demand for money for transaction motive increases with the increase in income, the greater the decline in supply of money available for speculative motive and so higher the rise in rate of interest and consequently steeper the LM curve.

The elasticity or responsiveness of demand for money to the changes in the rate of interest.

The lower the elasticity of liquidity preference for speculative motive with respect to the changes in rate of interest, the steeper will be the LM curve and in case of higher elasticity of the liquidity preference to the changes in the rate of interest, the LM curve will be flatter or less steeper.

Shifts of the LM Curve

LM curve is drawn keeping the stock of money supply fixed. So, when the money supply increases, given the money demand function, it will lower the rate of interest at a given level of income. This is because with income fixed, the rate of interest must fall so that the demand for money for speculative and transaction motive rises to become equal to the greater money supply.

This will cause the LM curve to shift outward to the right.

If the liquidity preference function for a given level of income shifts upwards,

this will lead to the rise in the rate of interest for a given level of income.

This will bring about a shift in the LM curve to the left.

Simultaneous EquilibriumSimultaneous Equilibrium

IS-LM curve model is based on(i)The investment demand function(ii)The consumption function(iii)The money demand function(iv)The quantity of money or money supply

So according to the IS-LM model both the real sectors, namely, saving and investment, productivity of capital and propensity to consume and save, and the monetary factors, that is, demand for money (liquidity preference) and the supply of money play a part in the joint determination of the rate of interest and the level of income.

Any change in these factors will cause a shift in IS and LM curve and will therefore change the equilibrium levels of interest and income.

With the help of IS-LM model, we will be able to explain in a better way the effects of changes in certain important economic variables such as desire to save, the supply of money, investment, demand for money on the rate of interest and the level of income.

Effects of Changes in Supply of MoneyEffects of Changes in Supply of Money

Level of Income0

Y

X

LM///

LM//LM/

Rat

e of

In

tere

st

r0

Given the Liquidity preference schedule, with the increase in supply of money, more money will be available for speculative motive at a given level of income which will cause the rate of interest to fall.

So LM curve will shift to the right.

With this upward shift in the LM curve in the new equilibrium position, rate of interest will be lower and level of income will be higher.

There will be no change in the IS curve.

In case of decrease in money supply, rate of interest will be higher and income level will be lower.

Changes in Desire to Save or Propensity to SaveChanges in Desire to Save or Propensity to Save

IS//

IS

IS/

Level of Income

Rat

e of

In

tere

st

LM

0

r0

X

YWhen people’s desire to save falls, i.e., when MPC rises, AD curve will shift upwards and so level of income will rise at each rate of interest. As a result, IS curve will shift outward to the right.

LM curve will remain unchanged. So both rate of interest and income will rise.

In case of rise in desire to save, both rate of interest and income will come down.

Changes in Autonomous investment and Government Changes in Autonomous investment and Government ExpenditureExpenditure

If there are increase in autonomous investment and Govt. expenditure, IS curve will shift outward to the right. LM curve will remain unchanged. So both the rate of interest and level of income will rise.

If there is decrease in the above two variables, IS curve will shift in the left. LM curve will remain unchanged. So both rate of interest and level of income will rise.

Changes in the Demand for MoneyChanges in the Demand for Money

If the liquidity preference or demand for money of the people rises, the LM curve will shift to the left. So equilibrium rate of interest will rise and the level of national income will fall.

If the demand for money or the liquidity preference of the people falls, the LM curve will shift to the right, So equilibrium rate of interest will fall and equilibrium level of national income will rise.

Derivation of Multiplier for Govt. Expenditure changes in case of Derivation of Multiplier for Govt. Expenditure changes in case of IS-LM modelIS-LM model

In order to determine the multiplier impact arising out of an autonomous rise in Govt. Expenditure, we consider both money market and product market simultaneously.

For this we take total differential of both the equilibrium conditions of money market and product market.

The equilibrium condition for the product market is given by

And the equilibrium condition for the money market is given by

[ ] ( ) ...........( )Y C Y tY I r G A

0

( ) ( )...............( )M

K Y L r BP

Taking total differential of (A), we getTaking total differential of (A), we get

Taking total differential of (B), we getTaking total differential of (B), we get

/ / / /( ) ( ) ..............( )dY C dY t dY I r dr dG A

/ /

//

/

0 ( ) ( )

( )...................( )

( )

K Y dY L r dr

K Ydr dY B

L r

Now putting the value of Now putting the value of dr dr in equation (Ain equation (A//), we get), we get

// / /

/

// / / /

/

// / / /

/

// / /

/

( )( ) ( )[ ]

( )

( )( )

( )

( )[1 ( )]

( )

1

( )1 (1 ) ( )

( )

K YdY C dY t dY I r dY dG

L r

K YdY C dY C t dY I r dY dG

L r

K YdY C C t I r dG

L r

dY

K YdGC t I r

L r

This the value of multiplier in case of IS-LM modelThis the value of multiplier in case of IS-LM model

The multiplier in the simplified framework isThe multiplier in the simplified framework is

So, in case of IS-LM model, the multiplier value is observed to be So, in case of IS-LM model, the multiplier value is observed to be less than that of simplified framework.less than that of simplified framework.

It happens because in case of IS-LM model, money market is It happens because in case of IS-LM model, money market is explicitly considered, and here investment is a function of r, i.e., explicitly considered, and here investment is a function of r, i.e., I=I(r) where II=I(r) where I//(r)<0. (r)<0.

The logic can be given in the next slide.The logic can be given in the next slide.

/

1

1

dY

dG c

Where c/=Marginal Propensity to Consume

Multiplier EffectY

K/(Y)>0K(Y)

For the Balance of Money market

L(r)

L/(r)<0rI/(r)<0

IMultiplier Effect

Y

G

So Income rises initially but it again comes down due to the money market operations. So net increase in Y will be less than the simplified framework. So, Y is more than it was before the rise in G but not as much as it was in the simplified framework.

Here Govt. expenditure Crowds Out the private investment. It is called Crowding Out effect.

Y0

r

Y0 Y1 Y2

IS

IS/r0

r1

Due to increase in G, the IS curve will shift upwards to IS/. So Y is supposed to rise up to Y2. But due to increase in r, Y will rise up to Y1. So, desired effect will not be achieved.

So, Y1>Y0<Y2

Concept of Balanced Budget Multiplier in case of Simplified Concept of Balanced Budget Multiplier in case of Simplified frameworkframework

The budget is said to be balanced when govt. expenditure (G) is equal to the tax yield. If initially G=T and then dG=dT., then in any period budget is said to be balanced. The multiplier effect of equal change in G and T is known as the balanced budget multiplier.

There are some assumptions

Price level is fixed

Aggregate real consumption expenditure is a function of aggregate disposable real income.

So, C=f (Yd).

Private investment is assumed to be autonomous

All taxes are lump-sum and independent of the level of income.

Govt. expenditure is also autonomous.

The economy is an advanced capitalist economy suffering from the deficiency of aggregate demand and there is sufficient amount of unemployment in the economy.

Now the equilibrium in the simplified framework is given byNow the equilibrium in the simplified framework is given by

Now suppose changes in income is a function of changes in taxes, changes in Now suppose changes in income is a function of changes in taxes, changes in autonomous expenditure and govt. expenditure.autonomous expenditure and govt. expenditure.

Now taking total differential of equation (i), we getNow taking total differential of equation (i), we get

( ) .........( )Y C Y T I G i

/

/ /

/ /

/

/

( )

(1 )

.....................( )1

dY C dY dT dI dG

dY C dY dI dG C dT

dY C dI dG C dT

dI dG C dTdY ii

C

Now, if dI=0 and govt. finances its increased expenditure by imposing an equal amount of direct tax on the individuals, i.e., dG=dT

Now putting dI=0, dG=dt in equation (ii), we getNow putting dI=0, dG=dt in equation (ii), we get

So the value of balanced budget multiplier is 1. So the value of balanced budget multiplier is 1.

So if the govt. expenditure rises, then the equilibrium level of income will rise by the So if the govt. expenditure rises, then the equilibrium level of income will rise by the same amount.same amount.

Now the mechanism behind this particular value can be interpreted if we consider the Now the mechanism behind this particular value can be interpreted if we consider the dynamics lying at this stage.dynamics lying at this stage.

The increment in G by the amount dG unleashes a chain of increase in y in the The increment in G by the amount dG unleashes a chain of increase in y in the following fashion.following fashion.

/ /

/ /

(1 )

1 (1 )

1

dG C dG dG CdY dG

C C

dY

dG

2 3/ / / ........( )dY dG C dG C dG C dG iii

At the same time we see that increase in G is financed out of an At the same time we see that increase in G is financed out of an equivalent increase in T. This means disposable income of the equivalent increase in T. This means disposable income of the people falls. As a result, in the initial period consumption people falls. As a result, in the initial period consumption expenditure falls by an amount . So ultimately fall in income expenditure falls by an amount . So ultimately fall in income isis

So balancing equation (iii) and (iv), net increase in income is by So balancing equation (iii) and (iv), net increase in income is by amount amount dY=dG.dY=dG.

/C dG

2 3/ / / ...........( )dY C dG C dG C dG iv

Balanced Budget Multiplier in case of IS-LM model

The equilibrium condition for the product market is

The equilibrium in the money market is given by

Taking total differential of (A) and (B), we get

( ) ( ) .........( )Y C Y T I r G A

0

( ) ( ).............( )M

K Y L r BP

/ / /

/ / /

/

/

( ) ( ) ........( )

0 ( ) ( ) .....................( )

( )

( )

dY C dY dT I r dG A

and

L r dr K Y dY B

K Ydr dY

L r

Putting the value of Putting the value of dr dr in equation (Ain equation (A//), we get), we get/

/ //

// / /

/

// / /

/

/ /

/ // / / /

/ /

/

// /

/

( )( ) ( )[ ]

( )

( )( )

( )

( )[1 ( ) ]

( )

( ) ( )1 ( ) 1 ( )

( ) ( )

11

( )1 ( )

( )

K YdY C dY dT I r dG

L r

K YdY C dY C dT I r dY dG

L r

K YdY C I r C dT dG

L r

dG C dT dG C dGdY

K Y K YC I r C I r

L r L r

dY C

K YdGC I r

L r

By putting dG=dt

Since, K/(Y)>o, L/(r)<0

I/(r)<0

So value of Multiplier differs from simplified framework

Elasticity of the LM curve and Relative effectiveness of Monetary Policy and Fiscal Policy

Monetarists think that only money matters and fiscal policy is quite ineffective as greater govt. expenditure will crowd out private investment. On the other hand, early Keynesians believed that money does not matter and it is active fiscal policy that if effective in controlling economic fluctuations.

The source of controversy is the assumption that Keynesians and Monetarists make about the elasticity of the LM curve.

Keynesian Range

Horizontal or perfectly interest-elastic part of LM curve.

Classical Range

Interest-inelastic part of the LM curve.

Intermediate Range

Interest-elastic part (0<e<1) of the LM Curve.

The Critique of The IS-LM Model

It is based on the assumption that the interest is flexible. If interest is quite inflexible, then the appropriate adjustments will not take place.

It is based upon the assumption that investment is interest-elastic. If investment is interest inelastic, the IS-LM model will break down.

It is too simplified and the change in price is not considered.