IS LM Model new.pdf

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1. General Equilibrium of Product
and money market
(IS LM Model)
By: L.R. Lohani

2. Introduction
•TheIS-LMmodelwasdevelopedbyJ.R.Hicks
andA.Hansen.TheIS-LMmodelexplainshow
Productmarket(goodsmarketorRealmarket)
andMoneymarketattainequilibriuminan
economy.Thismodeldescribesthe
interdependencebetweenrealsectorand
monetarysector.Itisalsoknownasthe
Generalequilibriumtheory.

3. Concept of IS curve
•TheconceptofIScurveisdevelopedbyJ.R.
Hicksinordertoexplaintheproductmarket
equilibrium.InthewordIS,‘I’referstothe
Investmentand‘S’referstothesaving.
•IScurveisthelocusofvariouscombinations
ofrateofinterest(r)andlevelofincome(Y)
alongwhichthereisequalitybetweenIandS
(i.e.I=S)suchthatproductmarket
equilibrium.

4. Assumptions
1)Investment is an inverse function of ‘r’,
i.e. I= f(r), f’<0
2) Saving is positive function of ‘Y’,
i.e. S=f(Y), f’>0
3)The product market attains equilibrium when S=I
Mathematical Derivation
According to Keynes,
AD= C+I ..........(i)
AS= C+S...........(ii)
The economy enjoys equilibrium when AD=AS
i.e. C+I=C+S
I=S...........(iii)

5. As we know,
S= -a+ (1-b)Y ............(iv)
Where,
-a= autonomous dissaving
1-b= MPS (marginal propensity to save)
Y= level of income
Similarly,Investmentfunctionisthecombinationof
autonomousinvestmentandinducedinvestment
i.e.I=I
a-i.r..............(v)
Where, I
a= autonomous investment
i= marginal propensity to invest (MPI)
r= rate of interest

6. Product market enjoys equilibrium when,
S=I
-a+(1-b) Y = I
a-i.r
(1-b) Y = a+ I
a-i.r
................(vi)
Theequation(vi)showstheinverserelation
betweenrateofinterestandlevelofincome.
SlopeofIScurve,

8. •Inthefigure,panelAshowstheinverserelationship
betweeninterestrateandinvestment.PanelBshows
theequalitybetweenSandI.PanelCshowsthesaving
functionandpanelDgivestheIScurveorproduct
marketequilibrium.
•Letinitialinterestrateisr
0inpanelA.Atthisinterest
rateinvestmentisI
0.ThelevelofsavingshouldbeS
0
forequilibriumwhichisshowninthepanelB.thelevel
ofsavingS
0ispossiblewhenincomelevelisY
0whichis
showninpanelC.Thecombinationbetweenr
0andY
0
givespointe
0inpanelDwhichismarketclearing
situation.

9. •Ifinterestratelowersdowntother
1levelthe
levelofinvestmentincreasestoI
1(panelA).
ThelevelofsavingshouldbeS
1forgoods
marketequilibrium(panelB).Thisispossible
onlywhenincomelevelincreasestoY
1(panel
C).Thecombinationbetweenr
1andY
1gives
anothermarketclearingsituationdenotedby
e
1inpanelD.Whenthesepointse
0ande
1are
joined,thedownwardslopingIScurveis
derived.

10. Concept of LM curve
The concept of LM curve was developed by A.
Hansen in order to explain the money market
equilibrium. In the word LM, ‘L’ refers to the
liquidity preference (money demand) and ‘M’
refers to the money supply.
LM curve is the locus of various combinations of
rate of interest ‘r’ and level of income ‘Y’ along
which M
d=M
ssuch that money market is in
equilibrium

11. Assumptions
1)Supplyofmoneyisexogenouslydetermined.Ms=M......(i)
2)Moneyisdemandedfor3motivesi.e.TransactionMotive,
PrecautionaryMotiveandSpeculativeMotive(ByKeynes).
Md=Lt+Lp+Lsp
Md=K(Y)+L(r).........(ii)
Where, K(Y)= Sum of transaction and precautionary demand for money
L(r)= Speculative demand for money
Forsimplicity,weassumeastraightlinedemandfunctionforspeculative
demandformoney.
i.e.L(r)=L-l.i
Where, L and l are constant and iis interest rate
Nowequation(ii)becomes
Md=KY+(L-l.i).........(iii)

12. 3)Themoneymarketstandsequilibriumwhen,
Ms=Md
M=KY+(L-l.i)
KY=M-(L-l.i)
Y=1/K(M-L+l.i)………(iv)
Theaboveequationgivesthemoneymarket
equilibriumatdifferentlevelofincomeand
interestrate,whichiscalledLMfunction.

14. •Inthefigure,Panel(A)showsthe
downwardslopingspeculativedemandfor
money(Lspcurve).Attherateofr
0,the
speculativedemandformoneyisL
sp0.With
thegivenmoneysupply,thetransaction
demandformoneywillbeL
t0,whichisshown
inpanelB.IfL
t0isthetransactiondemandfor
money,thelevelofincomewillbeY
0whichis
showninPanelC.Thecombinationofr
0and
Y
0clearsthemoneymarketshownbypointe
0
inpanelD.

15. •Inthesameway,ifrateofinterestlowerdowntor
1,
moremoneywillbespeculated.Theincreasein
speculativedemandformoneyimpliesdecreasein
moneyfortransactionpurposewithnochangein
moneysupply.Thedecreaseinmoneydemandfor
transactionimplieslowerincomelevelY
1.The
combinationr
1ofY
1andrepresentsanothermarket
clearingequilibriumshowne
1byinpanelD.When
thesetwopointse
0ande
1arejoined,theupward
slopingLMcurveisderived.
However,theslopeofLMcurvedependsonthe
natureofspeculativemoneydemandfunction.

16. General Equilibrium/ IS-LM
equilibrium
•Theparticularequilibriumpointofboth
market(productmarketandmoneymarket)
givesthegeneralequilibriumconditions.It
meansallpointsofIScurveandLMcurveare
notstable.Thecombinationbetweencertain
levelofincomeandaparticularrateof
interestcanclearbothmarket.

18. •Thefigureshowsthatthegeneralequilibrium
ofeconomytakesplaceatpointe.atthis
point,thecombinationbetweenr
eandY
e
makesbothmarketinsimultaneous
equilibrium.
•Any other combination other than r
eand Y
e
doesn’t make equilibrium of both markets i.e.
either product market or money market or
both markets.

20. •In the first figure, r is same as r
1at A and B. but Y
2>Y
1at
A, I<S.
So, to the right of IS curve I<S.
•Similarly, r is same as r
2at C and D, But Y
1<Y
2at C, I>S.
So, to the left of IS curve I>S.
•In the second figure, Y is same as Y
2 at A and D but r
1<r
2
at D, M
d>M
s
So, to the right of LM curve, M
d>M
s
•similarly , Y is same as Y
1 at B and C but r
2>r
1at B,
M
d<M
s
So, to the left of LM curve, M
d<M
s

22. Region GoodsMarket Money Market
I I<S Md<Ms
II I<S Md>Ms
III I>S Md>Ms
IV I>S Md<Ms

23. Due to these disequilibrium conditions in the
economy, the economy move along until it
reaches the stable equilibrium point e, as
shown in the figure.

24. Numerical Questions
1.a.Supposeconsumptionandinvestment
functionsaregivenas;C=200+0.8YandI=
200-2000i.Thenfindtheequilibriumlevelof
incomeatinterestrates10%,9%and7%.
b.DerivetheLMfunctionfromthefollowing
monetarysectormodel;M
T=0.5Y,M
SP=
110-1600iandM
S=200million.Give
economicinterpretationoftheLMcurve.

25. 2.Let consumption function (C) = 10 + 0.5Y ;
investment function (I) = 200-2000i; Money
supply (M
S) = Rs. 150 million M
T= 0.5 Y, M
SP=
150-1500i
a.Derive IS equation using S-I approach.
b.Derive LM equation.
c.Compute output and rate of interest at general
equilibrium.
d.What will be the new output and rate of interest
at general equilibrium when money supply
increases by 50 million?

26. 3.Let product market and money market models
given as follows C= 100+0.75Y
d, I= 120-0.5i, M
S
= 120, M
d= 0.2Y-500i, Lump sum tax (T) = 20
a.Compute equilibrium level of income and rate of
interest at general equilibrium.
b.What will be the effect on equilibrium level of
income and rate of interest when central bank
increases money supply by Rs 30 trillion?

27. 4.Suppose the product market model is given
as C= 100+0.8 Y, I = 110 –5i and the money
market model is found as M
S= 45, M
d= 0.5Y-
4i, where he symbols have their usual
meaning. Find:
a.IS and LM functions.
b.Determine equilibrium income (Y) and
interest rate (i).

28. Shifts in IS and LM functions:
change in general equilibrium

29. Shifts in the IS curve
AccordingtoKeynes,IScurveshiftstotheright
duetofollowingreasons.
When,
•C, I, G, or NX increases
•Saving decreases
•Tax decreases
And vice versa.

30. IS
1
IS
2
IS
3
LM
Income
Rate of interest
Y
0Y
1Y
2
R
0
R
1
R
2
E
0
E
1
E
2

31. Shifts in the LM curve
•TheLMcurve,theequilibriumpointsinthe
moneymarket,shiftsfortworeasons:changesin
moneydemandandchangesinthemoney
supply.
•Ifthemoneysupplyincreases,ceterisparibus,the
interestrateislowerateachlevelofYorinother
words,theLMcurveshiftsrightandviceversa.
•Similarly,whenmoneydemandincreasewiththe
constantsupplyofmoney.

32. Contd.
•Forexample:whencentralbankfollowsan
expansionarymonetarypolicy,itwould
increaseliquidityinthemarketduetowhich
increasesforbothi.e.transactionand
speculativepurpose.ThisshiftstheLMcurve
totheright.Similarly,whencentralbank
adoptscontractionarymonetarypolicy,the
LMcurveshiftsleftward.

33. Y
0Y
1Y
2
R
2
R
1
R
0
Income
IS
LM
1
LM
0
LM
2
E
2
E
0
E
1
Rate of interest

34. Simultaneous shifts in the IS and LM
functions
•Basedonaboveexplanations,itcanbeconcluded
thatwhenIScurveshiftstotherightdueto
increaseininvestmentordecreaseinsaving,both
therateofinterestandlevelofincometendsto
riseandviceversagiventheLMcurve.
•Ontheotherhand,whenLMcurveshiftstothe
rightduetoanincreaseinmoneysupplyor
decreaseindemandformoney,rateofinterest
tendstofallandlevelofincometendstorise
giventheIScurve.

37. Derivation of IS curve with fiscal policy
1. IS model with lump sum tax
Assumptions
•Thegovernmentexpenditureandlumpsumtaxboth
determinedbyexogenousfactorssotheyareconstant.
•Thegovernmentadoptbalancebudget(G=T)
ProductmarketwillbeequilibriumwhenAD=AS
i.e.C+I+G=C+S+T…………..(i)
WhereC=a+bY
d,I=I
a-hi,T=T
a,G=G
aandS=-a+(1-b)(Y-T)
ThenequationIbecomes

38. 2.IS model with tax function
Thismodelcanbederivedonthebasisof
followingassumptions.
i.Thegovernmentexpenditureisdetermined
autonomouslyandremainsconstant.
ii.Taxesmeanonlyincometaxataflatrate
iii.taxfunctionisgivenasT=T
a+t.Y
Thentheincomefunctionbecomes

39. Numerical
1.The following data are given for an economy
Consumption (C) = 40+0.75Y
d,
Investment (I) = 140-10i
Government Expenditure (G) = 100
Lump Sum Tax (T)= 80
Money demand (M
d) = 0.2Y-5i
Money Supply (M
S) = 85
where the symbols have their usual meaning
a.Find out the equilibrium income and interest rate
b.Suppose the government increases its expenditure on
education and health services by Rs 65 crores, what
would be its effect on equilibrium income and interest
rate?

40. 2.Consider the following features of Nepalese Economy
C= 1009+0.8Y
d, I= 200-1080i, G= Rs. 100 billions, T= 50+0.2Y, M
s=
250 billions, M
d= 100+0.5Y -2500i
a.Determine equilibrium equation for the product market.
b.Derive IS and LM functions.
c.Find the shift in the IS schedule if deficit financed (ΔG= 72
billion) and comment your results.
d.Find the shift in the IS schedule if tax rate is increased by 5%
and comment your results.
e.Find the shift in the IS schedule if ΔG= 72 billion and tax by 5%
and comment your results.
f.Find the shift in the LM schedule if ΔM
s= Rs. 50 billion and
comment your results.
g.Find the equation for the general equilibrium, equilibrium
income and rate of interest at t=0.20, G =Rs 100 billions and
M
s= Rs 250 billions.
h.Find the equilibrium income and rate of interest at Δt =0.05, ΔG
= Rs. 72 billion and ΔM
s = Rs 50 billion and comment your
results.