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1、Chapter9ARealIntertemporalModelwithInvestment1IntroductionObjective:Tobuildarealintertemporalmodeltoserveasabasisforanalyzinghowmacroeconomicshocksaffecttheeconomy.Threeagentsinthiseconomy:therepresentativeconsumertherepresentativefirmthegovernmentGo
2、vernmentbehaviorisidenticaltowhatitisinChapter8.2TheRepresentativeConsumerworksandconsumesinbothcurrentandfutureperiod.supplieslaborinthelabormarketsandpurchaseconsumptiongoodsinthegoodsmarket.hashunitsoftimeineachperiod.takesw,w’,randTasgiven.Curren
3、tbudgetconstraint:whereSpdenotessavingsinthecurrentperiod.3FuturebudgetconstraintInthesecondperiod,theconsumerreceivestheprincipalandinterestonSp.LifetimebudgetconstraintHeretheconsumer’slifetimewealthdependsonhis/herchoiceonlandl’.4RepresentativeCon
4、sumer’sProblemMaxU(C,C’,l,l’)C,C’,l,l’subjecttoMarginalconditionsthatmustbesatisfied:Fromthework-leisuredecisioninthecurrentperiod,MRSl,C=w.Fromthework-leisuredecisioninthefutureperiod,MRSl’,C’=w’.Fromtheconsumption-savingdecision,MRSC,C’=1+r.5Curren
5、tLaborSupplyCurrentlaborsupplycurveisarelationshipbetweencurrentlaborsupply(N)andcurrentrealwage(w).RecallfromCh.4thatachangeinwhasopposingsubstitutionandincomeeffectsontheoptimall.Weassumethatsubstitutioneffectdominates.Implication:wl,N.Thus,the
6、currentlaborsupplycurveslopesupward.6Factorsthatshiftthecurrentlaborsupplycurve:1)Realinterestratew(w’)isthepriceofl(l’)intermsofC(C’);(1+r)-1isthepriceofC’intermsofC.Sow’/(1+r)isthepriceofl’intermsofC.Hence,rthepriceofl’relativetol(substitutionef
7、fect)Assumesubstitutioneffectdominates,thenrcurrentlaborsupplycurveshiftstotheright.2)LifetimewealthSincelisanormalgood,wel.Hence,wecurrentlaborsupplycurveshiftstotheleft.CurrentlaborsupplycurveisdenotedasNs(r)toindicatethatitisthelaborsupplya
8、tagivenlevelofcurrentinterestrate.7CurrentDemandforConsumptionGoodsThedemandcurveforcurrentconsumptionisarelationshipbetweencurrentaggregateincomeYandC.LetCd(r)denotethiscurve,indicatingthatitisthedemandatagivenlevelofr.SlopeofCd(r)isthemarginalprope