MarketforGoodsintheClassicalModel

Q:Whatensuresthattheamountofconsumption ,investment
,andgovernmentpurchase
equalstheamountofoutput
produced
intheclassicalmodel?
A:Intheclassicalmodel,theinterest rate playsacrucialroleof
equilibratingaggregatesupplyandaggregatedemand.
Theclassicaleconomistsbelievethatahigher (lower)interestrate
encourages (discourages)savinganddiscourages (encourages)
consumption.

EquilibriumintheMarketforGoods

, where istherealinterestrate.

Investmentisanegative functionoftheinterest rate.

Figure 3A.1:InvestmentFunction

Theinvestmentfunctionslopes downward:whentheinterestrate
rises,fewerinvestmentprojectsareprofitable,andsothequantityof
investmentdemandedfalls.

EquilibriuminGoodsMarket
& : exogenousvariablessetbypolicymakers
,
,thelevelofoutputisfixed byinputs
Forsimplicity,
(orfactorsofproduction).
Equilibriumingoodsmarket:

Therealinterestrate istheonlyvariablenot alreadydetermined
sincetheinterestratemustadjusttoensurethattheaggregate
demandforgoodsequalstheaggregatesupply.

Attheequilibriuminterestrate,
.

TheSupplyandDemandforLoanableFunds
Q:Howdoestheinterestrategettothelevelthatbalancesthesupply
anddemandforgoods?
Toseehowtheinterestratebringsthemarketforloanablefundsinto
equilibrium,rewritenationalincomeidentityas:
where

Forfixedvaluesof , , , and , (national)saving isalsofixed.

Figure 3A.2:Saving,Investment,andtheInterestRate

TheSupplyandDemandforLoanableFunds
Thesavingfunctionisavertical linebecauseinthismodelsaving
doesnot dependontheinterest rate.
Theinterestrateadjuststobringsavingandinvestmentintobalance.
Saving:thesupply ofloanablefunds
Investment:thedemand forloanablefunds
Attheequilibriuminterestrate priceofloanablefunds,
thequantityofloanablefundssupplied=thequantityofloanable
fundsdemanded.

ChangesinSaving:TheEffectofFiscalPolicy
Letsseehowfiscalpolicyaffectstheeconomy.
Whenthegovernmentchangesitsspendingortheleveloftaxes,
itaffectstheaggregatedemandforgoodsandalterssaving,
investment,andtheequilibriuminterestrate.
Anincreaseingovernmentpurchases


becauseoutputisfixed bythefactorsofproduction,disposable
income
isunchanged,soconsumptionisunchanged as
well.

Figure 3A.3:ReductioninSaving

ChangesinSaving:TheEffectofFiscalPolicy
Increaseingovernmentpurchases
0 isnot accompaniedby
anincreaseintaxes
Thegovernmentfinancesadditionalspendingbyborrowing
thatis,byreducingpublic saving
Withprivatesavingunchanged,thisgovernmentborrowing
reduces (national)saving
Thesupplyofloanablefundsshiftsleftward
Theequilibriuminterestraterises
Investmentfalls
Thus,anincreaseingovernmentpurchasescausestheinterestrateto
rise from to andtheinvestmenttofall.

ChangesinSaving:TheEffectofFiscalPolicy
Adecreaseintaxes
Areductionintaxesof
0
Disposableincomerises by andconsumptionrisesby

Savingfalls bythesameamountasconsumptionrises,sinceY is
fixedandGremainsunchanged
Thesupplyofloanablefundsshiftstotheleft
Theequilibriuminterestraterises
Investmentfalls
Thus,areductionintaxesraises theinterestrateandcrowds out
investment.

ChangesinSaving:TheEffectofFiscalPolicy
Crowdingout
Thereduction ininvestmentthatresultswhenexpansionaryfiscal
policyraises theinterestrate

ChangesinInvestmentDemand
Wecanalsousethemodeltoinvestigatetheothersideofthemarket
thedemandforinvestment.
CausesofChangesinInvestment:
(i)Technologicalinnovation
(ii)Thegovernmentencouragesordiscouragesinvestmentthrough
thetaxlawssuchasinvestment tax credits.

ChangesinInvestmentDemand
Atanygiveninterestrate,thedemandforinvestmentgoods(andalso
forloanablefunds)ishigher
Theinvestmentfunctionshiftstotheright
Theequilibriuminterestraterises,buttheamountofinvestment
remainsunchanged becauseweassumedthatthesupplyofloanable
fundsorsavingisfixed

Figure 3A.4:AnIncreaseinDemandforInvestment

Becausetheamountofsavingisfixed,theincreaseininvestment
demandraises theinterestratewhileleavingtheequilibriumamount
ofinvestmentunchanged.

Modification:
Consumptiondependsontheinterest rate;
consumptionisanegative functionoftheinterestrate,whichmeans
savingisapositive functionoftheinterestrate,sothesaving
schedulewouldbeupward slopingratherthanvertical.

Figure 3A.5:AnIncreaseinInvestmentDemandWhenSaving
DependsontheInterestRate

AnIncreaseinInvestmentDemandWhenSaving
DependsontheInterestRate
Anincreaseininvestmentdemand
Boththeequilibriuminterestrateandtheequilibriumquantityof
investmentrise
Thus,theincrease intheinterestratecauseshouseholdstoconsume
less andsavemore.Thedecreaseinconsumptionfreesfundsfor
investment.

Example (3A.1):GoodsMarketinClassicalModel
Considerthefollowingmodeloftheeconomy(inbillionsof$):
3600 2000
0.10
1200 4000
1200 and
100
a)Byhowmuchdoes changeforeachpercentagepointincreasein
therealinterestrare ?
(Ans.)

4000

Investmentfallsby4000.

Example (3A.1):GoodsMarketinClassicalModel
b)Writeoutthesavingsfunctionforthiseconomy.Byhowmuchdoes
increasewhen increasesbyoneunit?
(Ans.)
3600 2000
0.10
1200

4800 2000
0.9

0.9

Example (3A.1):GoodsMarketinClassicalModel
c)When
6000
,findtherealinterestratethatclearsthe
marketforgoods.
(Ans.)
Equilibriumcondition:
4800 2000
0.9
1200 4000
0.9
6000 6000 .
6000,0.9 6000 6000 6000
When
6000

600

0.1

10%

Example (3A.1):GoodsMarketinClassicalModel
d)Governmentpurchasesriseto1440,holdingothervariablesconstant.
Howdoesthischangethesavingequation?Showthechangegraphically.
Whathappenstothemarketclearingrealinterestrate?
(Ans.)
3600 2000
0.10
1440
WhenG =1440,

5040 2000
0.9 .
Equilibriumcondition:
5040 2000
0.9
1200 4000
0.9
6240 6000
At
6000,0.9 6000 6240 6000
6000

840

0.14.

Consumption
InLecturenote#3,weassumedthatconsumptiondependedonlyon
currentdisposable income,butitistoosimpletoprovideacomplete
explanationofconsumerbehavior.Inthisnoteweexaminethe
consumptionfunctioningreaterdetailanddevelopamorethorough
explanationofwhatdeterminesaggregateconsumptionbyshowing
diverseapproachestoexplainingconsumption.

IrvingFisherandIntertemporalChoice
Keynessconsumptionfunctionrelatescurrentconsumptionto
currentincome.However,whenpeopledecidehowmuchtoconsume
andhowmuchtosave,theyconsiderboththepresent andthe
future.Themoreconsumptiontheyenjoytoday,thelesstheywillbe
abletoenjoytomorrow.Makingthistradeoff enableshouseholdsto
lookaheadtotheincometheyexpecttoreceiveinthefutureandto
theconsumptionofgoodsandservicestheyhopetobeableto
afford.

TheIntertemporalBudgetConstraint
TheeconomistIrvingFisherdevelopedthemodelwithwhich
economistsanalyzehowrational,forwardlookingconsumersmake
intertemporalchoices thatis,choicesinvolvingdifferent periodsof
time.
Q:Whydopeopleconsumeless thantheydesire?
A:Becausetheirconsumptionisconstrainedbytheirincome.
Toputanotherway,consumersfacealimitonhowmuchtheycan
spend,calledabudget constraint.

TheIntertemporalBudgetConstraint
Def.(3B.1):Intertemporalbudgetconstraint
Thelinethatmeasuresthetotalresourcesavailablefor
consumptiontodayandinthefuture
Theconstraintconsumersfacewhendecidinghowmuchto
consumetodayversushowmuchtosaveforthefuture
DevelopmentofFishersModel:
Assumptions:(i)Aconsumerlivesfortwoperiods;periodone
representstheconsumersyouth,andperiodtworepresentsthe
consumersoldage.
(ii)Allvariablesarereal thatis,adjustedforinflation.

TheIntertemporalBudgetConstraint
(iii)Theinterestrateforborrowingisthesame astheinterestratefor
saving.
:Aconsumersincomeinperiod1
:Aconsumersconsumptioninperiod1
:Aconsumersincomeinperiod2
:Aconsumersconsumptioninperiod2
Q:Howdoestheconsumersincomeinthetwoperiodsconstrain
consumptioninthetwoperiods?

TheIntertemporalBudgetConstraint
Inthefirstperiod, 3 . 1 :
,where canrepresent
eithersavingorborrowing.
Aconsumerissaving,and ispositive.

Aconsumerisborrowing,and isless thanzero.