中级宏观经济学ppt课件 (4).ppt

Chapter5AClosed EconomyOne PeriodMacroModel 1 TheModel Theeconomythatweconsiderisaclosedeconomy i e onethatdoesnottradewithothereconomies Besidesrepresentativeconsumerandrepresentativefirm thereisanadditionalagent thegovernment GovernmentTheonlyactionofthegovernmentistoimplementfiscalpolicy Fiscalpolicyreferstothegovernment schoicesoveritsexpenditures taxes transfersandborrowing 2 TheGovernment Supposethegovernmentwishestopurchaseagivenquantityofconsumptiongood G Sincethereisonlyoneperiod thegovernmentcannotborrowtofinanceG ThusGispaidbytaxingtherepresentativeconsumer Thegovernmentmustobservethebalancedbudgetconstraint G T 3 CompetitiveEquilibrium Competitivereferstothefactthatallconsumersandfirmsareprice takers Equilibriumreferstothestatewhentheactionsofallconsumersandfirmsareconsistent FormalDefinition AcompetitiveequilibriumisasetofendogenousquantitiesC Ns Nd TandY andanendogenousrealwagew suchthat giventheexogenousvariablesG z andK thefollowingaresatisfied 4 1 CandNssolvestheconsumer sproblem maxU C h Ns C NssubjecttoC wNs TandC 0 Ns 0 Inotherwords CandNsmustsatisfytheFOC U2 C h Ns wU1 C h Ns 0 2 Ndsolvesthefirm sproblemgivenz Kandw ThustheFOCissatisfied 5 3 Market clearingconditions Labormarketclearing Ns Nd N4 BalancedBudgetconstraint G T Wehave Goodsmarketclearing Y C GCombiningthetwoFOCs wehaveU2 C l zF2 K h l U1 C l 0 Since zF K h l wNdandG T fromthebudgetconstraintC zF K h l G Fromthese wecansolvefortheequilibriumCandl 6 GraphicalIllustrations Step1 Derivetheproductionpossibilitiesfrontier PPF whichdescribesthetechnologicalpossibilitiesfortheentireeconomy intermsoftheproductionofCandl Step2 PutthePPFtogetherwiththeconsumer sindifferencecurves sothatwecananalyzeacompetitiveequilibriuminasinglediagram 7 ProductionPossibilitiesFrontier Inequilibrium wehaveNd Ns N h l OutputisgivenbyY zF K h l whichisarelationshipbetweenoutputandleisure Y isthelevelwhenl 0 8 ProductionPossibilitiesFrontier Inequilibrium C Y G zF K h l GarelationshipbetweenCandl giventheexogenousvariablesz KandG ThisisthePPFwhichcapturesthetrade offbetweenleisureandconsumptiongiventheproductiontechnology OnlythepointsonDBareavailable whereC 0 9 ProductionPossibilitiesFrontier NegativeoftheslopeofthePPFiscalledthemarginalrateoftransformation MRTl Cwhichistherateatwhichonegoodcanbeconvertedintoanother MRTl C MPN SlopeofPPF Inequilibrium MPN w Thus wemusthaveMRTl C w ThishelpsusdeterminetheequilibriumvaluesC andl 10 CompetitiveEquilibrium Inequilibrium C andl arechosenbytherepresentativeconsumer NotethatADBisthebudgetconstraint BytheFOCoftheconsumer sproblemMRSl C w Hence inequilibriumMRTl C MRSl C w 11 Optimality Questions Isthecompetitiveequilibriumefficient Arethereanyotherwaystoobtainabetteroutcome AcompetitiveequilibriumisParetooptimalifthereisnowaytorearrangeproductionortoreallocategoodssothatsomeoneismadebetteroffandnooneismadeworseoff Sincethereisonlyoneconsumer wecanignorehowconsumptiongoodsareallocatedamongconsumers Rather wefocusonhowproductionisarranged 12 SocialPlanner sProblem ConsiderasocialplannerwhorunstherepresentativefirmandchoosesthequantitiesCandlsoastomaximizeconsumer sutility Graphically thesocialplannerchoosesaconsumptionbundlethatisonthePPFandisonthehighestpossibleindifferencecurvefortheconsumer 13 SocialPlanner sProblem Comparison Representativeconsumerfacesalinearorkinkedbudgetconstraint SocialplannerfacesaconcavePPF TheParetooptimumisatBwheretheequalityholdsMRTl C MRSl C MPN 14 SocialPlanner sProblem Thesocialplannersolvesthefollowingconstrainedmaximizationproblem MaxU C l C lsubjecttoC zF K h l GLagrangianL U C l zF K h l G C 15 First order Necessary conditions Combiningthefirsttwoconditions whichstatesthattheParetooptimumisthepointwheretheindifferencecurveistangenttothePPF Notethatwehavealsoderivedthesameconditionforacompetitiveequilibrium 16 TwoWelfareTheorems ThefirstfundamentaltheoremofwelfareeconomicsUndercertainconditions acompetitiveequilibriumisParetooptimal Indivisiblehand anunrestricted freemarketeconomycanproducesociallyoptimaloutcome ThesecondfundamentaltheoremofwelfareeconomicsUndercertainconditions aParetooptimumisacompetitiveequilibrium Remark Paretooptimalityignoresthedistributionissueamongindividualsandisthusanarrowconceptofsocialoptimality 17 SourcesofSocialInefficiencies AcompetitiveequilibriummaynotbeParetooptimaldueto ExternalitiesAnexternalityisanyactivityforwhichanindividualfirmorconsumerdoesnottakeaccountofallassociatedcostsandbenefits Externalitiescanbenegative e g pollution orpositive e g knowledgespillover Therootcauseofanexternalityisthatitistoocostly ifnotimpossible tosetupamarkettotradeforthebenefitsandcostsassociatedwiththeexternalities marketfailure 18 DistortingTaxesSupposeGisfinancedbyaproportionalwageincometaxatratet ratherthanbyalump sumtaxT Thewageincomeisnoww 1 t h l Sotheeffectivewageisw 1 t TheconsumeroptimizesbysettingMRSl C w 1 t whilethefirmstillsetsMPN w Thus inequilibrium MRSl C MRTl C w TheconditionforParetooptimumdoesnothold hencethefirstwelfaretheoremfails 19 MarketPowerFirmsmaynotactasprice takers Ifafirmislargerelativetothemarket itcanuseitsmonopolypowertoreduceoutput raisepricesandincreaseprofits Thisleadtounderproductionrelativetothesociallyoptimallevel 20 ComparativeStatics GraphicalIllustrations Consideran inGfromG1toG2whichshiftsthePPFfromPPF1toPPF2 ThisshiftleavestheslopeofthePPFconstantforeachl ThenewParetooptimumisatB SinceG T G mustbefollowedbyT ofthesameamount Thus G leadstoanegativeincomeeffectonCandl 21 GraphicalIllustrations G C Privateconsumptioniscrowdedoutbygovernmentpurchases ThedecreaseinCissmallerthantheincreaseinG l N Y andw 22 ComparativeStatics MathematicalDerivations TodeterminetheeffectsofchangesinGandzonequilibriumC l Yandw Fromthesocialplanner sproblem weobtainthesystemzF K h l G C 0 U2 C l zF2 K h l U1 C l 0 Totallydifferentiatingthesegives 23 Inmatrixform DeterminantoftheborderedHessianisQuasiconcavityofUandF 0 A 24 EffectsofaChangeinG UsingCramer srule wegetConsumptionandleisurearenormalgoods U22 zF2U120 Thus 25 Sincew zF2 K h l wehaveSinceY C G wehaveConclusion G C l w andY Businesscyclefacts Ch3 employmentprocyclical consumption realwagecontercyclical Thus governmentspendingisnottheprimarycauseofbusinesscycles 26 EffectsofaChangeinTFP z productionfunctionshiftsup NotonlymoreYcanbeproducedgivenN buttheMPN i e theslopeoftheproductionfunctionalsoincreasesforeachN Inthesecondfigure weseethatthenewPPFisADwhichissteeperthantheoriginalone AB ThenewParetooptimumisatHwhereC andY 27 GraphicalIllustrations PPF1correspondstoz1 whilePPF2correspondstoz2 ConstructaPPF3sothatitisjusttang