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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.
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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
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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
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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
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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
Deriving the IS Curve
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
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Deriving the IS Curve
Deriving the IS Curve
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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 )(
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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
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Example:
180%,6,
3000
)1500150150(5.0
1
15001505.0
1500150
5.0
150:
YiIf
iY
iY
iYliLkyMd
iliLMsp
YkYMt
sMLet
DerivationofLMCurve
DerivationofLMCurve
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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
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Shift in the IS-LM curves and the Equilibrium
a. Shift in IS Curve ( due to Demand shocks, I )
Shift in the IS-LM curves and the Equilibrium
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.
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b. Shift in LM Curve: due to (i) shift in MdT or Mdsp i.e. Md
Shift in the IS-LM curves and the Equilibrium
b. Shift in LM Curve: (ii) due to shift in Money supply
Shift in the IS-LM curves and the Equilibrium
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4.ShiftinISLMCurveandEquilibrium
Simultaneous Shift in IS and LM Curve
IS-LM Analysis: Three Sector Model
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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.
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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.
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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
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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
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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
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Fiscal Policy and Shift in IS Curve
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
Fiscal Policy and Shift in IS Curve
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
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Fiscal Policy and Shift in IS Curve
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
Fiscal Policy and Shift in IS Curve
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
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Fiscal Policy and Shift in IS Curve
FiscalPolicyandShiftinISCurve
Measuring Shift in IS Curve
Y=(1/1-c)G
Or
Y=(1/1-c+ct)(Co-cT0+I0+G0-hi)
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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
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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
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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%.
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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
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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
The U.S. Recession of 2001
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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.
The U.S. Recession of 2001
The U.S. Recession of 2001
The U.S. Recession of 2001
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IS-LM Analysis: Four Sector Model
ISLMwithForeignSectors
OpenEconomy:
1.RealFlowofgoodsandservices
2.FinancialFlowofcapitalandforeignexchange.
Twotypes
of
transaction
1.AutonomousTransaction:i.e.XandMofconsumerandcapitalgoods.
2.InducedTransaction:Transactionsoccursintermsofmoneytopayforbalanceoftradeeitherdeficitofsurplus
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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
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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
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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
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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
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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
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German Unification and the German Monetary-
Fiscal Policy Mix
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