S5M IS-LM Model

7/23/2019 S5M IS-LM Model

1/34

11/12/2015

1

Product(Goods)andFinancial(Money)

MarketEquilibrium:

The IS-LM Model

IS-LM Analysis

IS-LM analysis represents an interpretation of Keynes'

General Theory stemming from J.R. Hick's classic article

entitle "Keynes and the Classics.

Hicks argues that the essence of Keynes' theory is his

theory of liquidity preference. Individuals hold money(liquidity) for transactions, for speculative reasons, and for

emergencies.

IS-LM model was developed by Hicks and Hansen

incorporating Consumption Functions, Investment

Functions, Demand and Supply of Money function into

the national income and output determination model.


2/34

11/12/2015

2

IS-LM Analysis

IS-LM analysis allows us to solve for income(Y) and the interestrate(i) simultaneously.

It enables to analyse the impacts of Monetary and Fiscal Policy

changes on the economy.

A dichotomy between the goods market and the money markets

and equilibrium in both markets.

Fundamental inflexibilityassumptions:

W : Fixed

P : Fixed

i : Flexible

In all these cases W and P are assumed

to be constant

IS-LM analysis:

Two sector Model

Three Sector Model

Four Sector Model

Simple Model Keynesian IS-LM

Income Fixed Variable Variable

Interest Rates Fixed Fixed Variable

Price Fixed Fixed Fixed

Consumption AutonomousFunctions of

IncomeFunctions of

Income

Investment Autonomous AutonomousFunctions ofInterest Rate

Money Supply Not Included Not Included Autonomous.

Money

Demand Not Included

Functions of

Income andInterest Rate

Functions of

Income andInterest Rates

IS LMModel:Introducevariableinterestrate

ProductMarket

MoneyMarket


3/34

11/12/2015

3

IS-LM Analysis: Two Sector Model

1.TheGoodsMarketEquilibrium:

andtheISRelation

Equilibrium in the goods market exists when production,Y, is equal to the demand for goods, Z.

In the simple model the interest rate did not affect thedemand for goods. The equilibrium condition was givenby:

Product Market Eq(Keynes) :

Y= C+ I

or Y= C (Y) + I0(1)

Keynes assumes I as fixed as I0 i.e. autonomousInvestment


4/34

11/12/2015

4

InterestRate(i),Investment(I)andOutput(Y).

Hicks, now, we no longer assume investment is constant i.e. I0 We capture the effects of two factors affecting Investment:

The level of sales/income (+)

The interest rate (-)

So, I = f(Y,i)

Product Market Eqm(Hicks ):

Y = C(Y)+ I(i).(2)

Or S = I

Where C = Co+cY 0 Y = C0+cY+I0-hi

=> Y-C0+cY = I0-hi

=> S(Y) = I(i)..(3)

Taking into account the investment relation above, the equilibrium condition in the goodsmarket becomes:

Y=C0+cY+I0-hi.(4)

=>Y= 1 (C0+I0-hi) h>0(1-c)

The Determination of Output

Equilibrium in the

Goods Market

C0+cY+I0-hi

The demand for goods is an increasing function of output. Equilibriumrequires that the demand for goods be equal to output.

450

Y

Output, Y

D

emand,Z

A

Z


5/34

11/12/2015

5

Deriving the IS Curve

IS Curve: The IS curve shows the relationship betweenthe rate of interest(i) and national income (output, Y),with the product market equilibrium.

Anincreaseintheinterestratedecreasesthedemandforgoodsatanylevelofoutput

TheIScurveisthelocusofpointshowingequilibriumpointoftheproductmarketatdifferentlevelsofinterestrate,savings

and

income.

TheEffectsofanIncreaseintheInterestRateonOutput


Product Market Eq: Y= C(Y)+I(i)

=> Y=C0+cY+I0-hi

=> Y= (1/1-c) C0+I0-hi (5)

Y=f(i)(5a)

Example:

Let C(Y)=10+0.5Y

I(i)=200-2000i

So Y= C+I

=>Y=10+0.5Y+200-2000i

=>Y=420-4000 i

If i = 6%, then Y= 180


6/34

11/12/2015

6




7/34

11/12/2015

7

2.Financial(Money)Markets

Equilibrium:and

the

LMRelation

Money Market Equilibrium achieves when Demand for Money(Md) is equalto Supply of Money (Ms). The interest rate is determined by the equality ofthe supply of and the demand for money:

Keynes:

Supply of Money is fixed :

Demand for Money :

MT

d= Transaction and Precautionary Demand for Money

MdSp= Speculative Demand for Money

Ms = nominal money stock

Y = nominal income

i = nominal interest rate

)6.(..........sMMS

)(,,,

)7(..........

iLMandkYMWhere

MMM

d

SP

d

T

d

SP

d

T

d

RealMoney,RealIncome,andtheInterestRate

Money Market Equilibrium: when demand for money isequal to supply of money

The LM relation: In equilibrium, the real money supply is equal

to the real money demand, which depends on real income, Y,and the interest rate, i:

Recall: before, we had the same equation nominal terms (nominal incomeand nominal money supply). Dividing both sides by P (the price level)gives us the above equation in real terms.

)(, iLkYsMor

MsM d

P

iLkY

P

sM )(


8/34

11/12/2015

8

MoneyMarketEquilibrium

The Effects of an Increase in

Income on the Interest Rate

DerivationofLMCurve

LM curve shows the relationship between interest rate(i)and national income(Y) with Money Market Equilibrium.

LM curve is the locus of point showing equilibrium partsof the money market at different levels of interest rate,income and demand for money.

liLMLet

iLMandkYMWhere

MMM

dSP

d

SP

d

T

d

SP

d

T

d

,

)(,,,

)8().........(,

)(1

)(

:

ifYSo

liLsMk

Y

liLkYsM

iLkYsM

MsMEqulibrium d

l >0


9/34

11/12/2015

9

Example:

180%,6,

3000

)1500150150(5.0

1

15001505.0

1500150

5.0

150:

YiIf

iY

iY

iYliLkyMd

iliLMsp

YkYMt

sMLet

DerivationofLMCurve

DerivationofLMCurve


10/34

11/12/2015

10

DerivationofLMCurve

3.ProductandMoneyMarketEquilibrium

Simultaneously:ISLMModel

Product Market: Y=f(i)

Money Market : Y=f(i))(

1:Re

)(1

1:Re 00

liLsMk

YlationLM

hiICc

YlationIS

When the IS curve intersects

the LM curve, both goods and

financial markets are in

equilibrium.

Md>Ms

I>S

Ms>MdS>I


11/34

11/12/2015

11

Shift in the IS-LM curves and the Equilibrium

a. Shift in IS Curve ( due to Demand shocks, I )


a. Shift in IS Curve ( due to Demand shocks, I )

Shifting from IS1

to IS2

is due to shift in I.

what is the source of I?

Might be due to sale of bond to acquire fund

as result, bond price go down and interest

rate increase. So when IY, S MdT.


12/34

11/12/2015

12

b. Shift in LM Curve: due to (i) shift in MdT or Mdsp i.e. Md


b. Shift in LM Curve: (ii) due to shift in Money supply



13/34

11/12/2015

13

4.ShiftinISLMCurveandEquilibrium

Simultaneous Shift in IS and LM Curve

IS-LM Analysis: Three Sector Model


14/34

11/12/2015

14

FiscalPolicyandMonetaryPolicy: TheISLMModel

A. Fiscal Policy:Refers to the discretionary changes made in the governmentspending and taxes intended to achieve certain economic goals.

Fiscal Policy(spending and taxes)

Shifts IS curve

increase in spending or cut in taxes shifts IS curve to the right andvice versa

B. Monetary Policy: Refers to the discretionary use of the powers of themonetary authority to cane the demand for and supply of moneyin accordance with the need of the economy.

Monetary Policy (money supply)

Shifts LM curve

increase in money supply shifts LM curve to the right and vice versa

Fiscal Policy, the Interest Rate and the IS Curve

Fiscalcontraction:afiscalpolicythatreducesthebudgetdeficit.

ReducingGorincreasingT

Fiscal

expansion:increasingthebudgetdeficit.

IncreasingGordecreasingT

Taxes(T)andgovernmentexpenditures(G)affecttheIScurve,nottheLMcurve.


15/34

11/12/2015

15

FiscalPolicy,theInterestRateandtheISCurve

The Effects of an

Increase in Taxes

MonetaryPolicy,

InterestRateandLMCurve

Monetary contraction (tightening) refers

to a decrease in the money supply.

Monetary expansion refers to an

increase in the money supply.

Monetary policy affects only the LM curve,

not the IS curve.


16/34

11/12/2015

16

MonetaryPolicy,

Interest

Rate

and

LM

CurveThe Effects of a

Monetary Expansion

Product Market Equilibrium With Govt Sector:

The IS Curve

Assumption:

1. Govt. Exp. is determined exogenously and fixed

2. Tax means only income tax at flat rate (t) and tax

function is given by T=T0+tY

3. Govt. follows a balanced budget policy

ProductMarketEquilibrium: Y=C+I+G

Alternatively,

=>Y=C+S+G sinceS=I

=>Y=C+S+T

ifG=Tmeansgovtexp isfinancedthroughTax


17/34

11/12/2015

17

Derivation of the IS Curve

ProductMarketEquilibrium: Y=C+I+G

Where,C=C0+c(YT)

I=I0hi,h>0

G=G0

T=T0+tY,0Y=(1/10.75(10.20))*(1000.75*80+2002000i+100)

=>Y=8505000i

Alternatively:I+G=S+T

S=100+0.25(YT)

Now,I+G=S+T

=>2002000i+100=100+0.25(Y(80+0.20Y))+80+0.20Y

=>Y=8505000i

Ifi=6%,ThenY=550

Y=(1/1-c)G


18/34

11/12/2015

18

Derivation of the IS Curve: Graph

So+T

(T=0)

Fiscal Policy and Shift in IS Curve

a.Change(increaseordecrease)inGnoTax

LetGovtExpenditureisG=100andTisT=0,andinterestratei=6%,

thenwhatwillbeY?????

Y=(1/1c)G=>Y/G=(1/1c) theGovtmultiplier

Y=(1/10.75)*100=400SoequilibriumincomewillincreasesfromRs720toRs1120i.e.

720+400.andequilibriumpointwillshiftfromAtoB.SoIScurvewillbeISG=>16008000i=Y

Ifi=6%,Y=1120

a. Change(increaseordecrease)inGb. ChangeinTaxrate(t)c. ChangeinbothGandtd. DifferentcombinationsofchangeinGandt


19/34

11/12/2015

19


b.NowLetGovtImposeTax,DuetothistheISCurveShift

WeknowS+T=I+G

So,S=100+0.25(YT)

=>S+T=100+0.25(YT)+T=80+0.20Y

S+T=40+0.40Y

Now withtheintroductionoftaxfunctiontheshiftinIScurve

willbe

S0+T

left

wards

and

will

be

ISGT=>850

5000i=YIfi=6%,Y=550

SonetreductioninoutputwillbeY=170


1.Increase inG:duetothistheISCurveShiftrightward.

LetGovt.Expenditureincreasefrom100to200,andinterestrateis6%,withthisthe productmkt equilibriumwillbe,atY=800meansYincreasesfrom550to800

WeknowI+G=S+T

Since,S=100+0.25(YT),I=2002000iandT=80+0.20Y

=>2002000i+100=100+0.25(Y(80+0.20Y))+80+0.20YinitialISCurve

Now=>2002000(0.06)+200

= 100+0.25[Y(80+0.20Y)]+80+0.20Y

=>280=40+0.40Y

=>Y=800


20/34

11/12/2015

20


2.Decrease inTaxRate(t): duetothistheISCurveShiftrightward.

Letthetaxratedecreasesfromt=0.20to0.15%,andinterestrateis6%,(withsimultaneousincreaseinG=100),withthisthe productmktequilibriumwillbeatY=888.88

WeknowI+G=S+T

Since,S=100+0.25(YT),I=2002000i

andT=80+0.20Y

2002000i+100=100+0.25(Y(80+0.20Y))+80+0.20YinitialIScurve

Now=>2002000(0.06)+200=100+0.25[Y(80+0.15Y)]+80+0.20Y

=>280=40+0.36Y

=>Y=888.8


3.DeficitFinancing: duetothistheISCurveShiftrightwards

Letthe initialinvestmentfunctionandtaxfunctionisasbelow

I=1002000iandT=0.20Y

Soequim: I+G=S+T

with S=100+0.25(YT),

=>1002000i+100=100+0.25(Y0.20Y))+0.20YinitialIScurve

=>Y=7505000i..(A)

NowifGovtfinancethespendingbyprintingadditionalcurrency(borrowingfromcentralbankorabroad) ofRs100billion,thenwhatwillhappentooutput????

I+G+G=S+T

=>200200i+100=100+0.4Y

=>Y=10005000i.(B)

At6%interestrate,YwillbeAB

Y=(10005000i)(Y=7505000i)

Y=(1005000*0.06)(7505000*0.06)

Y=250billion


21/34

11/12/2015

21


FiscalPolicyandShiftinISCurve

Measuring Shift in IS Curve

Y=(1/1-c)G

Or

Y=(1/1-c+ct)(Co-cT0+I0+G0-hi)


22/34

11/12/2015

22

Monetary Policy and Derivation of LM Curve

LM curve shows the relationship between interest rate(i) andnational income(Y) with Money Market Equilibrium.

LM curve is the locus of point showing equilibrium parts of themoney market at different levels of interest rate, income anddemand for money.

liLMLet

iLMandkYMWhere

MMM

d

SP

d

SP

d

T

d

SP

d

T

d

,

)(,,,

)(,

)(1

)(

:

ifYSO

liLsMk

Y

liLkYsM

iLkYsM

MsMEqulibrium d

0l

Monetary Policy and Shift in LM Curve

Example:

MoneyMarketEquilibrium:Ms=Md

Md=MdT+Md

Sp.(2)

LetMS=200billion

MdT=ky=0.5Y

Md

Sp=L0li=1002500i

ThenMs=Md MoneyMarketEquilibrium

=>200=0.5Y+1002500i

=>Y=200+5000iLMCurve

Fori=6%,Y=500


23/34

11/12/2015

23

MonetaryPolicyandShiftinLMCurve

1.ChangeinMoneySupplyandShiftintheLMCurve

LetMoneySupplyincreasesanother100billion,thentheshiftinLMwillbe

NowEq:Ms+Ms=Md

=>200+100=0.5Y+1002500i=>Y=400+5000i

Fori=6%,Y=700

LMcurveshiftrightwardandIncomeincreases

ShiftinLM:=Ms(1/k)=100(1/0.5)=200

LMCurveliLsMk

Y

liLkYsMEqulibrium

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

:

1. Changein

Money

Supply

shift

the

LM

Curve

2. ChangeinMoneyDemandShifttheLMCurve

Point c, if households decided to keep Mt unchanged then

eqm will fall from A to C, causing interest rate to fall and

Msp to increases,. It means they spend money to buy bond

and securities and hence interest rates falls

Equilibrium with Product and Money Market:

Three Sector Model

ProductMktEquilibriumC=100+0.75(YT)I=2002000i; G0=100

T=0.20Y=>Y=7505000i

MoneyMarketEquilibrium:

LetMS=200billion

Md

T

=ky=0.5Y

MdSp=L0li=1002500i

ThenMs=Md MoneyMarket

Equilibrium

=>200=0.5Y+1002500i

=>Y=200+5000i

BothMktwillbeinequilibrium

Ifi=5.5,equilibriumY=475


24/34

11/12/2015

24

A. Change in Fiscal Policy : IS-LM Curve

LetG=100,thisshifttheIScurvetoIS1andYincreasesfrom475to600LMremainingthesame,

interestrateincreaseto8%,calledascrowdingouteffect.

B. Change in Monetary Policy : IS-LM Curve

LetM=100,i.e.Money supplyincreasesto100, thisshifttheLMcurvetoLM1andY

increases from545to575,ISremainingthesame, interestratedecreasesto3.5%.


25/34

11/12/2015

25

C. Change in both Monetary and Fiscal Policy:

IS-LM Model

Using a Policy Mix

The Effects of Fiscal and Monetary

Policy.

Shift of IS

Shift of

LM

Movement of

Output

Movement

in Interest

Rate

Increase in taxes left none down down

Decrease in taxes right none up up

Increase in

spending

right none up up

Decrease in

spending

left none down down

Increase in money none down up down

Decrease in money none up down up


26/34

11/12/2015

26

The U.S. Recession of 2001

The U.S. Growth Rate, 1999:1 to 2002:4The Federal Funds Rate, 1999:1 to 2002:4

U.S. Federal Government Revenues and Spending (as

Ratios to GDP), 1999:1 to 2002:4



27/34

11/12/2015

27

What happened in 2001 was the following:

The decrease in investment demand led to a sharp

shift of the IS curve to the left, from IS to IS.

The increase in the money supply led to a downward

shift of the LM curve, from LM to LM.

The decrease in tax rates and the increase inspending both led to a shift of the IS curve to the

right, from IS to IS.





28/34

11/12/2015

28

IS-LM Analysis: Four Sector Model

ISLMwithForeignSectors

OpenEconomy:

1.RealFlowofgoodsandservices

2.FinancialFlowofcapitalandforeignexchange.

Twotypes

of

transaction

1.AutonomousTransaction:i.e.XandMofconsumerandcapitalgoods.

2.InducedTransaction:Transactionsoccursintermsofmoneytopayforbalanceoftradeeitherdeficitofsurplus


29/34

11/12/2015

29

Product Market Equilibrium and IS Curve with

Foreign Sectors

Equilibrium:Y=C+I+G+XM

or C+I+G+XM=C+S+T

LetX=X0andM=M0+mY

Where,C=Co+c(YT);S=C0+(1c)(YT);I=I0hi,h>0;G=G0;T=T0+tY,0Y=7404000iistheIScurve

Fori=0.06%,Y=500


30/34

11/12/2015

30

Product Market Equilibrium and IS Curve with

Foreign Sectors

Money Market Equilibrium and LM Curve with

Foreign Sectors

There is no change in the LM curve with foreign sector. Thesame LM curve which is derived for two sector is relevant here,

LM curve is the locus of point showing equilibrium parts of themoney market at different levels of interest rate, income anddemand for money.

liLMLet

iLMandkYMWhere

MMM

d

SP

d

SP

d

T

d

SP

d

T

d

,

)(,,,

)(,

)(1

)(

:

ifYSO

liLsMk

Y

liLkYsM

iLkYsM

MsMEqulibrium d


31/34

11/12/2015

31

Monetary Policy and Shift in LM Curve

Example:MoneyMarketEquilibrium:Ms=Md

Md=MdT+Md

Sp.(2)

LetMS=200billion

MdT=ky=0.5Y

MdSp=L0li=1002500i

ThenMs=Md MoneyMarketEquilibrium

=>200=0.5Y+1002500i

=>Y=200+5000iLMCurve

Fori=0.06%,Y=500

Equilibrium in both Product and Money market

with IS-LM Model

Example:

ISFunction:Y=7404000i IScurve

LMFunction:Y=200+5000iLMCurve

MarketEquilibrium:IS=LM

=>7404000i=200+5000i

=>540=9000i

=>i=0.06(6percent)

NowY=7404000(0.06)

=500


32/34

11/12/2015

32

Equilibrium in both Product and Money market

with IS-LM Model

References

1. Ch 16-18, Macroeconomic Theory and

Policy by D N Dwivedi

2. Ch 5 Macroeconomics by Blanchard

3. Ch 10-11 Macroeconomics by N Gregory

Mankiw


33/34

11/12/2015

33

Thank You All

Selected Macro Variables for West Germany, 1988-1991

1991 1992 1993 1994

GDP growth (%) 3.7 3.8 4.5 3.1

Investment growth (%) 5.9 8.5 10.5 6.7

Budget surplus (% of GDP)

(minus sign = deficit)

2.1 0.2

1.8

2.9

Interest rate (%) 4.3 7.1 8.5 9.2

German Unification and the German Monetary-

Fiscal Policy Mix


34/34

11/12/2015

German Unification and the German Monetary-

Fiscal Policy Mix

Documents

S5M IS-LM Model