中级宏观经济学ppt课件 (3).ppt

Chapter9 ARealIntertemporalModelwithInvestment 1 Introduction Objective Tobuildarealintertemporalmodeltoserveasabasisforanalyzinghowmacroeconomicshocksaffecttheeconomy Threeagentsinthiseconomy therepresentativeconsumertherepresentativefirmthegovernmentGovernmentbehaviorisidenticaltowhatitisinChapter8 2 TheRepresentativeConsumer worksandconsumesinbothcurrentandfutureperiod supplieslaborinthelabormarketsandpurchaseconsumptiongoodsinthegoodsmarket hashunitsoftimeineachperiod takesw w randTasgiven Currentbudgetconstraint whereSpdenotessavingsinthecurrentperiod 3 FuturebudgetconstraintInthesecondperiod theconsumerreceivestheprincipalandinterestonSp LifetimebudgetconstraintHeretheconsumer slifetimewealthdependsonhis herchoiceonlandl 4 RepresentativeConsumer sProblem MaxU 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 5 CurrentLaborSupply Currentlaborsupplycurveisarelationshipbetweencurrentlaborsupply N andcurrentrealwage w RecallfromCh 4thatachangeinwhasopposingsubstitutionandincomeeffectsontheoptimall Weassumethatsubstitutioneffectdominates Implication w l N Thus thecurrentlaborsupplycurveslopesupward 6 Factorsthatshiftthecurrentlaborsupplycurve 1 Realinterestratew w isthepriceofl l intermsofC C 1 r 1isthepriceofC intermsofC Sow 1 r isthepriceofl intermsofC Hence r thepriceofl relativetol substitutioneffect Assumesubstitutioneffectdominates thenr currentlaborsupplycurveshiftstotheright 2 LifetimewealthSincelisanormalgood we l Hence we currentlaborsupplycurveshiftstotheleft CurrentlaborsupplycurveisdenotedasNs r toindicatethatitisthelaborsupplyatagivenlevelofcurrentinterestrate 7 CurrentDemandforConsumptionGoods ThedemandcurveforcurrentconsumptionisarelationshipbetweencurrentaggregateincomeYandC LetCd r denotethiscurve indicatingthatitisthedemandatagivenlevelofr SlopeofCd r isthemarginalpropensitytoconsume Assumingthatsubstitutioneffectdominates thenr Cd r shiftstotheright we Cd r shiftstotheleft 8 TheRepresentativeFirm producesoutputinbothperiods investsinthecurrentperiodbyaccumulatingcapitalsoastoexpandfutureproductioncapacityandproducesmorefutureoutput demandslaborinthelabormarkets suppliesgoodsinthegoodsmarket anddemandsinvestmentgoodsinthecurrentgoodsmarket Assumethatconsumptiongoodsandinvestmentgoodsareidentical Moreover 1unitofCcanbeconvertedinto1unitofK viceversa Whenthefirminvests itusesupsomeoftheYitproduces thussomeofitsprofits inexchangeoffutureproductivecapacity K 9 TheformationoffuturecapitalisdescribedbywhereIdenotethequantityofcurrentinvestment andddenotetherateofdepreciation Attheendofthecurrentperiod afractionofthecapitalstock d wearsoutordepreciates Thosethatleftbehindplusthequantityofcurrentinvestmentwillbecomethequantityoffuturecapitalstock 10 RepresentativeFirm sProblem CurrentprofitsinunitsofthecurrentconsumptiongoodSinceweassumethatthecapitalstockisownedbytherepresentativefirm attheendofthefutureperiod thefirmwillconverttheremainingcapitalstock 1 d K backtoC andsellit Futureprofitsare 11 LetVdenotethepresentvalueofprofitsforthefirmExplicitly TheobjectiveofthefirmistochooseN N andItomaximizeV FOCs 12 DemandforLabor Thefirsttwoconditionsstatethatthefirmwillhirelaboruntilthemarginalproductoflaborequalstherealwageineachperiod Thedemandcurveforcurrentlabor Nd isidenticaltothemarginalproductoflaborschedule z orK Ndshiftstotheright 13 InvestmentDecision ThethirdFOCstatesthattherepresentativefirmwillinvestuntilthemarginalcostofinvestmentequalstoitsmarginalbenefit Recall Y wN I anadditionalunitofIreduces andsoV by1unit thusthemarginalcostofinvestment intermsofC is1 RecallandI by1unit K by1unit Y byMP Kunits by MP K 1 d unitsHence themarginalbenefitfrominvestment intermsofC is 14 OptimalInvestmentRuleMB I 1 MP K d r MP K disknownasthenetmarginalproductofcapital Inthismodel therearetwoassets bondsandcapital Therateofreturnonbondisr whichisalsotheopportunitycostofinvestinginK MP K d r investmoreincapital bonds 15 Thefirm soptimalinvestmentscheduleisthefirm snetmarginalproductofcapital Thisindicatestheoptimallevelofinvestmentateachparticularlevelofr Thescheduleisdownwardslopingbecausehigherr highertheopportunitycostsofinvesting sothefirmshouldreduceI 16 Factorstheshifttheoptimalinvestmentschedule 1 Futuretotalfactorproductivityz z MP K foreachlevelofK Ifthefirmexpectz toincrease itwillbewillingtoinvestmoreduringthecurrentperiodasthereturnoninvestmentisexpectedtohigher Hence z optimalinvestmentscheduleshiftstotheright 2 CurrentCapitalStockKK K foreachlevelofI MP K foreachlevelofK diminishingMPK Hence K optimalinvestmentscheduleshiftstotheleft 17 CurrentLaborMarket Giventherealinterestrate theequilibriumrealwageisw theequilibriumquantityofemploymentisN Fromtheproductionfunction thecorrespondingquantityofaggregateoutputsuppliedisY 18 OutputSupplyCurve Next wewanttoderiveanoutputsupplycurveYs whichdescribeshowmuchoutputwillbesuppliedbyfirmsforeachpossiblelevelforr r Nscurveshiftstotheright w N Y Hence Ysisupwardsloping Ysconsistsofallcombinations Y r forwhichthecurrentlabormarketisinequilibrium 19 FactorsthatshiftYs 1 LifetimewealthSupposeG orG duetothebalancedbudgetrestrictionthepresentvalueoftaxesmust Thisleadstowe we demandforl incomeeffect Nscurveshiftstotheright Y foreachgivenr Yscurveshiftstotheright 20 2 Totalfactorproductivityz productionfunctionshiftsup MPN foreachlevelofN Ndcurveshiftstotheright Y forgivenlevelofr outputsupplycurveshiftstotheright 3 CurrentCapitalanincreaseinKhavethesameeffectasanincreaseinz 21 DemandforCurrentConsumptionGood AggregatedemandforcurrentconsumptiongoodisgivenbyRecallthatCd r dependsoncurrentincome whichisacomponentoflifetimewealth TheequilibriumdemandY1isthequantityofaggregateincomethatgeneratesatotaldemandjustequalstoitself 22 OutputDemandCurve Itisanegativerelationshipbetweencurrentaggregateoutputandtherealinterestrate r Cd r andId r demandcurveforcurrentconsumptiongoodsshiftsdown Y Hence theoutputdemandcurveYdisdownwardsloping EverypointonYddenotesapair Y r inwhichthegoodsmarketisinequilibrium 23 FactorsthatshiftYd 1 GovernmentSpendingG Demandcurveforcurrentgoodshiftsup Y atgivenr Ydshiftstotheright 2 PresentValueofTaxesPVoftaxes we Cd r atgivenr Ydshiftstotheright 24 3 FutureincomeY Y we Cd r atgivenr Ydshiftstotheright 4 Futuretotalfactorproductivityz z MP K foreachlevelofK Id r Ydshiftstotheright 5 CurrentCapitalStockKK K foreachlevelofI MP K foreachlevelofK diminishingMPK Id r Ydshiftstotheright 25 CompetitiveEquilibrium Acompetitiveequilibriumconsistsofastateofaffairswheresupplyequalsdemandinthecurrentlabormarketandthecurrentgoodsmarket Fromthesewecandeterminetheequilibriumvaluesw r N andY Marketsinthefutureisneglectedtomakeourmodelsimpletoworkwith 26 TemporaryIncreaseinG SupposeG whileG isunchanged Beforethechange theeconomyisinequilibriumwithw1 r1 N1andY1 G PVoftaxes we demandforl incomeeffect Nscurveshiftstotheright YsshiftstotherightMeanwhile we Cd r atgivenrSinceMPC 1 onnetwemusthaveHence Ydshiftstotheright 27 ThetemporaryG shouldleadtoonlyasmalldecreaseinwe sotheshiftinYsshouldbesmallrelativetotherightshiftinYd Hence r andId Inthecurrentlabormarket r Nscurveshiftsfurthertotheright fromNs2 r1 toNs2 r2 Result w N andY 28 Conclusions Temporaryincreaseingovernmentspendingleadstoahigheraggregateoutput butthiscomesatacost Bothcurrentconsumptionandinvestmentdecreasesasaresult i e theyarecrowdedoutbycurrentgovernmentspending Fortherepresentativeconsumer he sheconsumesless takeslessleisureandfacesalowerrealwage Investmentspendingdecreasesimpliesfuturecapitalstockwillbecomelowerandthustheeconomy sfutureproductivecapacitywillbecomelower 29 PermanentIncreaseinG SupposenowbothGandG increasesby G Effects PVoftaxes we demandforlandCd r atgivenr1 demandforl Nscurveshiftstotheright fromN1s r1 toN2s r1 Ysshiftstotheright 2 Cd r butG Whatisthenetimpactonthecurrentdemandforgoods 30 PermanentIncreaseinG AccordingtoMiltonFriedman spermanentincomehypothesis therewouldbenochangeinthecurrentdemandforgoods Reason Tofinancethepermanentincreaseinspending thegovernmenthastoincreasetaxesby G Theconsumer spermanentincomewoulddeclineby G AccordingtoFriedman themarginalpropensitytoconsumeoutofpermanentincomeis1 Hence Cd r G Conclusion Ydisunaffectedatgivenlevelofr 31 PermanentIncreaseinG Ysshiftstotheright r andY Inthecurrentgoodsmarket r Id r andCd r Inthecurrentlabormarket r Nscurveshiftstotheleft fromN2s r1 toN2s r2 N 0sinceweknowthatY Results r w N andY 32 Remarks Thepermanentincreasedoesnothavethesamecrowding outeffectsasthetemporaryincrease Bothinvestmentandconsumptionrisesduetothedecreaseinrealinterestrate Whichtypeofincreaseingovernmentspendingwillincreasecurrentaggregateoutputmore TemporaryincreasehasalargeroutputdemandeffectPermanentincreasehasalargeroutputsupplyeffectTheanswerdependsontherelativestrengthsofthetwoeffects 33 EquilibriumEffectsofK SupposeKdecre