Chapter5

TheGoodsMarket

TheDeterminationofEquilibriumOutputContextChapter4introducedthemodelofaggregatedemandandaggregatesupply.

Longrunpricesflexibleoutputdeterminedbyfactorsofproduction&technologyunemploymentequalsitsnaturalrateShortrunpricesfixedoutputdeterminedbyaggregatedemandunemploymentisnegativelyrelatedtooutputWefocusontheshortrunandassumethepricelevelisfixed.4.1TwoSectorEconomyYd=Ydef:disposableeistotaleminustotaltaxes:Yd=Y–T4.1.1AENotation:C=planned

COMSUPTIONI=plannedinvestmentAE=C+I=plannedexpenditureY=realGDP=actualexpenditureDifferencebetweenactual&plannedexpenditure:unplannedinventoryinvestmentC=C(Yd),C=a+bYdAPC=averagepropensitytoconsume=C/YdMPC=△C/△Yd=bdef:ThemarginalpropensitytoconsumeistheincreaseinCcausedbyaone-unitincreaseindisposablee.TheConsumptionFunctionKeynes’sConjectures0<MPC<1APCfallsaseriseseisthemaindeterminantof

consumption.CY1bb=MPC=slopeoftheconsumptionfunctionc=a+bYdaCYslope=APCAserises,theAPCfalls(consumerssaveabiggerfractionoftheire).c=a+bYdCYOC=a+bYcaYE450SavingFunctions=Yd-c=Y-(a+bY)=-a+(1-b)YAPS=S/Yd

MPS=△S/△Yd=1-bAPS+APC=1MPS+MPC=1c、sYOC=a+bYaY0E450S=-a+(1-b)Y-afornow,

investmentisexogenous:I＝I0plannedexpenditure

AE＝C＋I＝(a+I0)+bY1，Equilibriumcondition:

Actualexpenditure=PlannedexpenditureY=AE

4.1.2DeterminationofEquilibriumeandOutput

AE-45oe,output,Y AE planned expenditure45oAE=YAggregateexpenditureswillbeequaltototaloutputforallpointsalongthe45°linefromtheorigin.The45°linemapsoutpotentialequilibriumlevelsofoutputfortheKeynesianmodel.AE=C+IYAEoY0AE=C45oIEAE=Y

2，J-W(Injection-Withdraw)

I=SInequilibrium,plannedinvestmentequalssaving.

AE=c+Iy=c+sI=sYJ,WW=SJ=II0Y0

3，F(xiàn)romFunction:AE=c+Ic=a+bYI=I0Y=AEAE=a+bY+I04.1.3TheinvestmentmultiplierTheincreaseinIcausesetoincreaseby5timesasmuch!Definition:theincreaseineresultingfroma$1increaseinI.Inthismodel,theImultiplierequalsExample:MPC=0.8Whythemultiplierisgreaterthan1Initially,theincreaseinIcausesanequalincreaseinY:Y=I.ButY C furtherY furtherC furtherYSothefinalimpactoneismuchbiggerthantheinitialI.e,Output Y≡Yd+T≡C+S+TPlannedExpenditure AE≡C＋I+G T=T0+tYG:governmentpurchasesisexogenous：G=G04.2ThreeSectorEconomy1,AE-45o

C+I+GYAEoY0C45oC+IAE=C+I+G=a+I0+G0+bYd=a+I0+G0+b(Y-T)=(a+I0+G0-bT0)+b(1-t)Y2，J－WAE=C+I+GY=C+S+TI+G=S+TyJ,WJ=I+GW=S+T(y)Y03,FromFunction：AE=C+I+GC=a+b(Y-T)T=T0

+tY

I=I0

G=G0Y=AEM=M0

+mY

X:exportisexogenousX=X04.3FourSectorEconomyAE=C+I+G+(X-M)C=a+b(Y-T)T=T0

+tY

I=I0,G=G0,X=X0

M=M0

+mYAE=YC+I+GyAEoY0C45oC+IC+I+G+(X-M)IntheKeynesiansystem,whentotaloutputislessthanplannedaggregateexpenditures,purchasesexceedoutputandinventoriesaredepleted.Firmsexpandtheiroutputtorebuildtheirinventoriestoregularlevels.Whenoutputismorethanplannedaggregateexpenditures,outputexceedspurchases,andinventoriesaccumulate.Firmsreduceoutputtoslowtheaccumulationoffurtherinventory.Whenplannedaggregateexpendituresequaltotaloutput,thereisKeynesianmacroeconomicequilibrium.4.4TheChangeofEquilibriume1,TheEffectsofaShiftinAggregateExpenditureShiftsarisingfromthefourcomponentsofAEConsumptionInvestmentGovernmentPurchasesNetExportsAnincreaseingovernmentpurchasesY

AEAE=Y

AE=C+I+G1AE1=Y1AE=C+I+G2AE2=Y2YAtY1,

thereisnowanunplanneddropininventory……sofirmsincreaseoutput,anderisestowardanewequilibriumGAnincreaseintaxesY

AEAE=Y

AE=C2

+I+GAE2=Y2AE=C1

+I+GAE1=Y1Y2,AtY1,thereisnowanunplanned

inventorybuildup…3,sofirmsreduceoutput,andefallstowardanewequilibriumC1,Initially,thetaxincreasereducesconsumption,andthereforeAE:APCfallsYAE45AE1AE2Y1Y2YAEWJ1Y10J2Y2I2,TheEffectsofaShiftinInjectionandWithdrawYAEJ0W1Y1W2TY2AE45ABAE（P1）AE（P2）Y2Y1Y2Y1YYPABP1P2AD4.5TheMultiplierDef:Themultiplieristheamountbywhichequilibriumoutputchangeswhenautonomousaggregatedemandincreaseby1unit.AE2yAEoy2AE145o△Iy1△yDerivationoftheMultiplier△y=△I+△Ib＋△Ib2+

△Ib3+△Ib4+…...b=0.8=MPC1+b+b2+b3+b4+……=TwoSectorEconomyAE=C+IC=a+bYI=I0Y＝AEAE=C+I+GC=a+b(y-T)T=T0+tY

I=I0,G=G0Y＝AEThreeSectorEconomyy=C+I+Gc=a+b(y-T)T=T0

+tYI=I0,G=G0Y=AETheTaxMultiplierFourSectorEconomyOutputisatitsequilibriumlevelwhentheaggregateexpenditureisequaltothelevelofoutput.Aggregateexpenditureconsistsofplannedspendingbyhouseholdonconsumption,byfirmsoninvestmentgoods,andbygovernmentonitspurchasesofgoodsandservicesandalsoincludesnetexports.When