IS-LMKHJBHJ

8/12/2019 IS-LMKHJBHJ

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The IS-LM Model

During the current period of a cyclical slowdown in economic activity, economists

debate on effectiveness of macroeconomic policies.

e studied goals and instruments of fiscal policy and their impact on macroeconomicvariables in the real sector. !n the other hand, we studied goals and instruments of monetary

policy and their effectiveness in the regulation of the financial sector. In real life these two

sectors are not isolated. "ow we have to analy#e the impact of both fiscal and monetary

policy on macroeconomic activity.

Since the central economic problems at the moment are related rather to income and

unemployment than to the price level, we will concentrate on changes in macroeconomic

e$uilibrium under the assumption of constant prices.The analytical tool widely used in this analysis is the IS-LM model, developed by the

%ritish economist Sir &ohn 'ic(s and the )merican economist )lvin 'ansen.

The IS-LM model brings together the impact of fiscal and monetary policies on both

the real sector and the financial sector.

In addition to the assumption of

constant price level

we will assume only two types of financial assets* money and bonds +interest bearing assets ,

and

a closed economy +we will ignore foreign e change fluctuations and

international capital movements

Later we will rela some of these assumptions.

. The LM curve

a the e$uilibrium in the money mar(et as a function of income and definition of the

LM curve

In order to put together the monetary and the real sector, we have to define the

e$uilibrium in the monetary sector as a function of a income, which is a real sector

variable.


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The e$uilibrium in the monetary sector is set when MS / MD. 0nder a given level of

income +1 money supply and money demand determine the e$uilibrium interest rate

+i , presented on the graph below +2ig. .

i

M/ P

MS

MDi 1

2ig. . 3$uilibrium in the money mar(et.

The increase in income from 1 to 1 4 raised the demand for real money balances and

the money demand curve shifts to the right, as shown on 2ig. 4 +left panel . Thus, if income

rises, the equilibrium interest rate increases, other things held constant. e can build a

relationship between income and the e$uilibrium interest rate, as shown on 2ig. 4 +right

panel . The point of macroeconomic e$uilibrium 3 under income 1 is presented on the right

panel as a function of income. It shows what the interest rate should be, in order to have

e$uilibrium in the money mar(et. hen income rises to 1 4 the e$uilibrium in the moneymar(et at point 3 4 is achieved at a higher interest rate i4 .!n the left panel this e$uilibrium

point shows what the interest rate should be under income 1 4 in order to have e$uilibrium in

the money mar(et. hen we put together the e$uilibrium points on the money mar(et we

derive the LM curve . It presents the relationship between the level of income and the

e$uilibrium interest rate, as shown on 2ig. 4 +left panel .


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i

M/P

MS

MD1

i 1

i

YY1

i 1

Y2

MD2

i 2

LM

E1

i 2

E2

E1

E2

2ig. 4. Deriving the LM curve

The LM curve shows what the interest rate should be at every level of income, so that

we have e$uilibrium in the money mar(et.

b analy#ing the LM curve

The first point of the analysis of the LM curve is its slope . hen is the LM curve

shallow and when is it steep5

If money demand is highly elastic as regard income, a relatively small increase

in income in percentage terms, would lead to a relatively large increase in the money

demand in percentage terms. The e$uilibrium interest rate will increase significantly

and as a result the LM curve will be very steep, as shown on 2ig. 6.

If money demand is inelastic as regard income, a relatively large increase in

income in percentage terms, would lead to a relatively small increase in the money

demand in percentage terms. The e$uilibrium interest rate will increase 7ust a little and

as a result the LM curve will be very shallow, as shown on 2ig. 8.


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i

M/P

MS

MD1

i 1

i

YY1

i 1

Y2

MD2

i 2

LM

E1

i 2

E2

E1

E2

2ig. 6. 'ighly elastic money demand as regard income and a steep LM curve.

i

M/P

MS

MD1

i 1

i

YY1

i 1

Y2

MD 2

i 2

LM

E1

i 2

E2

E1

E2

2ig. 8. 'ighly inelastic money demand as regard income and a shallow LM curve

The second factor determining the slope of LM depends on the slope of the MD curve.

If the money demand is elastic as regard interest rate, the money demand curve is very

shallow and this will contribute to a greater slope of the LM curve. If money demand


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is inelastic as regard interest rate, the MD curve is steep and this will contribute to a

steeper LM curve.

Thus, the slope of the LM curve depends on

the elasticity of money demand as regard income and

the elasticity of money demand as regard interest rate.

If the money demand is elastic as regard income and inelastic as regard interest

rate, the LM curve is steep.

If money demand is inelastic as regard income and elastic as regard interest

rate, the LM curve is shallow. Such an LM curve is usually observed during

recessions.

If the money mar(et is in dise$uilibrium, at a given level of income the interest

rate is either lower, or greater than the e$uilibrium interest rate. Let9s ta(e the case

when the level of the interest rate is below the e$uilibrium, as shown on 2ig. :. )t

point ) at a lower interest rate the opportunity cost of holding money is lower. The

public will prefer more li$uidity. MD ; MS. 'ow can the public have more li$uidity5

They will start selling their interest bearing assets +bonds . The e cess supply of bonds

will drive their price down and the interest rate will increase until it gets to its

e$uilibrium point )9 on the LM curve.

i

Y

LM Ai 1

y1

A


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2ig. :. MD;MS and a move to e$uilibrium interest rate.

If the LM curve is very steep, the achievement of the e$uilibrium interest rate

assumes a significant reduction in the prices of financial assets and a respective

significant increase in the interest rate. If the LM curve is shallow, small activities in

the bonds mar(et lead to e$uilibrium in the money mar(et.

The second point of the analysis of the LM curve is its location. Thus, we have

to analy#e factors, determining the shifts in the LM curve .

espectively, point 3 shifts to point 3 4, at the same level of income +right

panel . The LM curve shifts to the right.

i

M/P

MS 1

MD

MS 2

i 1

i 2

i

Y

LM 1

i 1

Y

i 2

LM 2

E 1

E2

E1

E2

2ig. =. Increase in money supply and a shift in the LM curve to the right

If MS falls, the LM curve shifts leftwards.

)utonomous changes in money demand

)utonomous increase in money demand means that it rises not because of the

increase in income, in the interest rate or in the price level, but because of a change in


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an e ogenous variable. 2or e ample, if holding bonds becomes more ris(y, the public

prefers li$uidity as a less ris(y asset and money demand rises. )t the same level of

income the e$uilibrium interest rate increases +2ig. ? left panel and respectively, the

LM curve shifts leftwards +2ig. ? right panel .

i

M/P

MS

MD1

MD2i 1

i 2

i

Y

LM1

i 1

Y

i 2

LM2

E1

E2

E1

E2

2ig. ?. )n increase in autonomous money demand and a leftward shift in LM

If autonomous money demand falls, LM shifts rightwards.

4. The IS curve

a the e$uilibrium in the real sector as a function of the interest rate and the IS

curve

In the analysis of the LM curve we studied the impact of income as a real sector

variable on the e$uilibrium in the monetary sector. "ow we will shift our attention to

the impact of the interest rate as a monetary sector variable on the e$uilibrium in the

real sector.

0nder the assumption of a constant price level the e$uilibrium in the real sector

is best presented on the )3-1 diagram. !n 2ig. @. )3 / 1 under a given price level.


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8: A

1A

A E

AE

Y1

AE1

2ig. @ )3 B 1 diagram

)3 / < C I C C E B M. Investment spending depends on the interest rate. If

the interest rate falls, investment spending rises. Since investment spending is a

component of )3, aggregate e penditures increase with the reduction in the interest

rate. )s a result, the e$uilibrium income rises from 1 to 1 4, as shown on the upper

panel of 2ig. F. Thus, we found a relationship between the interest rate and the

e$uilibrium income. e can develop in on a graphical model as shown on the lower

panel of 2ig. @. )t the higher interest rate i the e$uilibrium income +)3 C 1 is 1 . )t

a lower interest rate i4, the e$uilibrium income rises to 1 4 . hen we put together all

e$uilibrium points 3 as a function of the interest rate we derive the IS curve , as shown

on 2ig. @.

The IS curve shows what should be the e$uilibrium income at every level of

the interest rate.


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AE

Y

AE1

Y1

AE2

Y2i

Y

i 1

Y

i 2

Y

I S

E1

E2

E1

E2

2ig. @. Deriving the IS curve

c analy#ing the IS curve

The slope of the IS curve depends on the elasticity of investment demand as regard

the interest rate.

If the investment demand is highly elastic as regard the interest rate, small changes

in the interest rate in percentage terms cause large changes in investment in percentage

terms. >espectively, )3 changes significantly and the IS curve is shallow, as shown

on 2ig. F.

If the investment demand is highly inelastic as regard the interest rate, significant

changes in the interest rate in percentage terms cause small changes in investment

demand in percentage terms and respectively in the )3. )s a result, the IS curve is

steep, as shown on 2ig. A.


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AE

Y

AE1

Y1

AE2

Y2i

Y

i 1

Y1

i 2

Y2

I S

E1

E2E1

E2

2ig. F. 3lastic investment demand as a shallow IS curve

AE

Y

AE 1

Y1

AE 2

Y2

i

Y

i 1

Y1

i 2

Y2

I S

E1

E 2

E1

E2

2ig. A. Inelastic investment demand and a steep IS


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The economy is in dise$uilibrium when )3 are larger or smaller than income

for a given interest rate. If, for instance income is at a lower level for a given interest

rate +at point ) on 2ig. , investment demand is motivated by this the low interest

rate and )3 ; 1. )s you remember, in this case inventories fall, production rises,

unemployment falls and income increases. This process of increase in income will ta(e

place until it grows to its e$uilibrium point )9.

i

Y

IS

AA

2ig. . )3 ; 1 and a move to e$uilibrium income

If the economy is at a dise$uilibrium above the IS curve, )3 G 1. Inventories

increase, production falls, unemployment rises and income falls until it achieves its

e$uilibrium point on the IS curve.

Thus, the IS curve shows what should be the level of income at every level of

the interest rate so that )3 / 1.

2actors, determining the location of the IS curve*

In7ections

In7ections are assumed to be autonomous, which means that they do not depend

on the interest rate, or income. These could be government spending, autonomous investment

and e ports.


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If for instance government spending rises at the same level of the interest rate, )3

increases and the e$uilibrium income increases. The e$uilibrium point ) shifts to point )9. )s

a result, the IS curve shifts to the right as shown on 2ig. 4.

AE

Y

AE1

Y1

AE2

Y2i

Y

i 1

Y1

i 2

Y2

I S

A A

A

A

2ig. 4. )n increase in in7ections and a shift in the IS curve to the right.

If in7ections fall the IS curve shifts leftwards.

lea(ages

Lea(ages are assumed to be autonomous as regard interest rate. These are autonomous

savings, ta es and imports. If lea(ages increase, e$uilibrium income falls and the IS curve

shifts to the left.

If lea(ages fall the IS curve shifts rightwards.

6. Macroeconomic e$uilibrium in the real sector and in the monetary sector

The LM curve shows what should be the e$uilibrium interest rate at every level of

income. In other words, it shows the e$uilibrium in the monetary sector as a function

of income.

The IS curve shows what should be the e$uilibrium income at every level of

the interest rate. In other words, it shows the e$uilibrium in the real sector as a

function of the interest rate.


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Macroeconomic e$uilibrium is achieved when there is an e$uilibrium in the monetary

sector and at the same interest rate there is an e$uilibrium in the real sector.

raphically it is presented by the intersection of the IS and the LM curve. 2ig. 6

i

Y

ISLM

i e

Ye

2ig. 6. Macroeconomic e$uilibrium in the real and in the monetary sector B the IS-

LM e$uilibrium

The IS-LM e$uilibrium could be easily destroyed by any changes in the real or in the

monetary sector.

. This destroys the e$uilibrium in the monetary sector. )t

the higher income level 1 4 i is lower than the e$uilibrium i. MD ; MS. The public starts

selling bonds, because they prefer more li$uidity. H of bonds falls and the interest rate rises.

'owever, the increase in the interest rate affects the real sector, as well. )t the higher interest

rate investment falls and as a result income falls. This is why the move is along the new IS

curve instead of being straight upwards to point J. The new e$uilibrium is achieved at 3 4.

Thus, the increase of in7ections raises the e$uilibrium income, but it raises the

e$uilibrium interest rate as well.


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i

Y

IS1 LMIS 2

Y2

i 1

Y1

2

1

K

R

2ig. 8. The impact of an increase in in7ections on the IS-LM e$uilibrium

e can draw a conclusion that e pansionary fiscal policy leads to an increase in

e$uilibrium income but to a rise in the e$uilibrium interest rate, as well.

>estrictive fiscal policy +a leftward shift in the IS curve would reduce both

e$uilibrium income and e$uilibrium interest rate.


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i

Y

ISLM 1

E1

LM2

Y1

2

T P

2ig. :. The impact of the increase in money supply on the IS-LM e$uilibrium

3 pansionary monetary policy reduces the interest rate and at the same time

raises the e$uilibrium income.

Monetary restriction + a leftward shift in the LM curve raises the e$uilibrium

interest rate and reduces the e$uilibrium income.

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