宏观经济学英文教学课件：lecture13 Neoclassical Model

0Lecture13NeoclassicalModel1EconomicModelsRealeconomyistoocomplicatedtounderstandBuiltyourown,simpleeconomyIngredientsPeopleGoodsandtechnologiesInstitutionsMicrofoundationsUsemodelsthatexplicitlyincorporatehouseholdandfirmdecisionproblemsAllowstocapturehowdecisionsadjustwheneconomicenvironmentofpolicieschange2UsingModelsToolstopredictoutcomes:OptimizationMarketClearingCheckwhethermodelmatchesdata:Yes:LikelythatmodelworldcaptureskeyfeaturesoftherealworldNo:Buildnewmodel3ASimpleMarketEconomyOneconsumer,onefirmConsumerandfirmtradeinmarketsMarketsforconsumptionCandlaborN4MarketPricesPrices:PriceofconsumptionnormalizedtoonePriceforNisrealwagew5TheHousehold’sProblemintheMarketEconomyUtilityfunctionU(C,l)C:Consumption(coconuts)l:LeisureBudgetconstraintConsumptionexpenditureequalsincomefromcapitalandlabor

pisgiven,capitalincomeNisgivenbytimeconstraint:N=h-l6TheConsumer’sPreferencesUtilityfunctionU(C,l)Assumptions:Moreisbetterthanless:,Diversityisgood:FallingMRSConsumptionandleisurearenormalgoods7IndifferenceCurves8PropertiesofIndifferenceCurvesDownwardsloping:FollowsfrompositivemarginalutilitiesConvex:Followsfromfallingmarginalrateofsubstitution9IndifferenceCurves10MarginalRateofSubstitutionMRS:theminimum#ofCoconutsconsumeriswillingtogiveupforanotherunitofleisureEqualtominusslopeofindifferencecurveMathematically:11TheBudgetConstraint12TheOptimizationProblemMaximizeutilitysubjecttothebudgetconstraintbychoosinglandCs.t.13GraphicalRepresentationDrawindifferencecurvesasbeforeDrawbudgetconstraintasafunctionofleisureOptimalchoiceispointinthebudgetsetthatliesonthehighestindifferencecurve14GraphicalOptimization15Outcome16SlopeofindifferencecurveequalsslopeofbudgetconstraintSlopeofbudgetconstraint:wagewResult:wage=MRSThisisaverygeneralresult:theMRSbetweenanytwogoodsisgivenbytherelativeprice!MathematicalOptimizationSubstituteconstraintsintoU(C,l)First-orderconditionwithrespecttol:Result(onceagain):wage=MRS17Example

wageequals10coconutsperhourTime:24hoursProfitandtax:p=30andT=30

18ExampleMaximizationproblem:Solution:,19PredictingtheReactiontoChangesintheEconomySeparateincomeandsubstitutioneffectsPureincomeeffect:consumemoreofevery(normal)goodPuresubstitutioneffect:consumemoreofthegoodthatgetscheaperInpractice,oftenbotheffectsarepresent20APureIncomeEffect21AnIncreaseintheWage22TheFirm’sProblemintheMarketEconomyProductionfunctionNumberofcoconutsproducedwithcapitalandlaborinputAssumptions::bothinputsrequired:positivemarginalproducts:decreasingmarginalproducts23Graphof24TheMarginalProductofLabor25EffectofanIncreaseinProductivity26EffectofanIncreaseinProductivity27TheFirmThefirmmaximizesprofitssubjecttotheproductionfunctionProfitπ:outputminuscost28GraphicalProfitMaximization29OptimizationResultSlopeofproductionfunctionequalsslopeofcostcurve

Thisisaverygeneralresult:theMPofanyfactorofproductionisgivenbyitsprice!30MathematicalProfitOptimizationThemaximizationproblem:First-ordercondition:Wageequalsmarginalproductoflabor31EquilibriumRequirementsforequilibrium:ConsumermaximizesutilityFirmmaximizesprofitsDemandequalssupplyineverymarketCombiningfirmandhouseholdoptimization,weget32WhatistheSimpleModelGoodfor?TheultimatetaskofanyeconomicmodelistoshedlightontherealworldTheonlythingthemodelcouldbegoodforisexplaininglabor-leisurechoiceDoesthemodelexplainU.S.data?33AverageWorkweekinU.S.34AverageWorkweekinU.S.35HowistheModelEvaluated?ModelabstractsfrommanypotentialfactorsWanttoknowwhethermodelissufficienttoexplaindeclineintimeworkedNeedtospecifymodelmoreprecisely36MakingtheModelMorePreciseNocapitalforsimplicityVariables:C:consumptionl:leisureN:laborw:wagez:totalfactorproductivityg:growthrateofzProductivitygrowsovertimeWanttodetermineNasafunctionofz37ChoosingFunctionalFormsProductionfunction:Utilityfunction:Budgetandtimeconstraints:38ProfitMaximization

Firstordercondition:

39UtilityMaximizationThemaximizationproblem:First-ordercondition:Laborconstant,independentofwage!40WhatdoesItMean?Modelappearstobeacompletefailure!Reason:withlogutility,incomeandsubstitutioneffectsonlaborsupplycancel(i.e.,theyhaveequalsizeandoppositesign)Isthisrealisticinthecross-section?41UsingtheModelforCross-CountryComparisionEuropeancountries(France,Germany,Swedenetc.)havehighertaxesandhighertransfersIslikeanegativesubstitutioneffect:incometaxlowerstheperceivedwageModelpredictslessworkandmoreleisureinEurope42WhatElseCouldExplaintheFacts?Therearealternativeexplanations:Labor-forceparticipationTaxationRelativeproductivityof“leisure”sectorTrynewmodelsincaseoffailure43IntertemporalChoiceMostofmacroeconomicsisaboutchangesovertimeSofar,havejusconsideredthedecisionofworkversusleisureNeedtoaddchoiceoftodayversustomorrow44ExamplesSomeintertemporalchoices:BorrowingandsavingbyconsumersInvestmentbyfirmsHumancapitalinvestmentbystudentsFamilydecisions45ImportantFactorsforIntertemporalChoice:Preferencesovertime(patience)ExpectedreturnoninvestmentExpectedfutureeconomicconditions46ModelingIntertemporalChoiceForsimplicity:LookatoneconsumerinisolationTwoperiodsonlyVariables::consumptiontodayandtomorrow:discountfactor(measurespatience):incometodayandtomorrow:saving:interestrate(returnonsaving)47TheSetupUtilityfunction:Budgetconstraints:Wanttoknowhowanddependon(intertemporalpreferences)(economicconditions)(returnoninvestment)48MathematicalSolutionSubstituteconstraintsintoutilityfunction:Settingderivativewrt.stozero:49OutcomeMRS=InterestrateSameasbefore–SimpleModel:ChoicebetweenleisureandlaborMRS(l,C)=Relativeprice(l,C)Intertemporalmodel:ChoicebetweentodayandtomorrowMRS=Relativeprice50ThePresent-ValueBudgetConstraintPresentvalueofxdollarstomorrow:Amountneededtobesavedtodaytohavexdollarstomorrow

Solvingperiod-2constraintfors:51ThePresent-ValueBudgetConstraintPluggingtheresultintotheperiod-1constraint:PV(totalconsumption)=PV(totalincome)52GraphicalAnalysisLifetimewealth:we=PV(totalincome)Rewritingthebudgetconstraint:Cannowrepresentchoiceinstandarddiagram

53TheDiagram54OutcomeMRS=RelativepricePureincomeeffect(increaseineitheror)willincreasebothandImpliesthatsincreaseswhenrisesImpliesthatsfallswhenrisesOnlypresentvalueofincomematters,distributionirrelevantforconsumption55Example:LogUtilityFOCforand

56ComputingConsumptionExampleI:ExampleII:

57ConclusionsModelpredictsstrongconsumptionsmoothing:timingofincomedoesnotmatterResultreliesonperfectcapitalmarketEvenso,evidenceforconsumptionsmoothingisstrong58ConsumptionSmoothinginPracticeLife-cycleconsumption:borrowearlyinlife,thensaveforretirement59InformalCapitalMarketsDefaultriskpreventssomepeoplefromborrowingSocietyoftenfindswaysaroundthatproblem:TransfersfromparentsandrelativesGiftgivingandneighborhoodhelpSocialinsurance60ANeoclassicalGrowthModelOverlappinggenerations:EachconsumerlivesfortwoperiodsEachyear,oneoldandoneyoungconsumerarealiveTheyoungworkoneunitoftimeTheoldareretiredandsupplycapital61GenerationalStructure62TheDecisionProblemofaConsumerBornatTimetUtilityfunction:Budgetconstraints:Noticethat:ThereisnoincomeintheoldperiodSavingsarecapitalintheoldperiod63SolvingtheConsumer’sProblemChoosetosolve:First-ordercondition:Solution:

64TheProfit-MaximizationProblemoftheFirmFirmmaximizesproductionminuscost:First-orderconditionsare:65ClosingtheModelMarketclearingforcapitalandlabor:Assumeconstantproductivity(fornow):66WorkingoutthePredictionsoftheModelUsingmarket-clearingconditionsinequationsforwandr:Usingwageequationinsavingequationofhousehold:67UsingtheLawofMotionforCapitalHavederivedalawofmotionforcapital(capitaltomorrowdependingoncapitaltoday)Startingatanyinitialcapital,candeterminehowcapitalwilldevelopinthefutureCancomputeproductionandgrowthratesovertime68ExampleParameterchoices:

Thelawofmotionis:69GraphoftheLawofMotion70Convergence71CapitalOverTime72ResultModelpredictsconvergenceacrosscountrieswithdifferentinitialcapitalIntuition:ReturnstocapitalaredecreasingWageincreaseslessthanproportionallywithcapitalSavingsincreaselessthanproportionallywithcapital73Long-runPredictionsCapitalconvergencetosteadystateSolvingforcapitalinsteadystate:74WhatHappensifthereisProductivityGrowth?Steady-statelevelofcapitaldependsonproductivityzSteadystateshiftsupwardsifproductivityincreasesAssumeconstantproductivitygrowthg:75TheLawofMotionafteraChangeinProductivity76ImplicationsInthelongrun,capitalkgrowsatthesamerateasproductivity:Whathappen