Lectures 6 and 7 - Neoclassical Growth

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1、14.452EconomicGrowth:Lectures6and7,NeoclassicalGrowthDaronAcemogluMITNovember15and17,2011.DaronAcemoglu(MIT)EconomicGrowthLectures6and7November15and17,2011.1/71IntroductionIntroductionIntroductionRamseyorCass-Koopmansmodel:di¤ersfromtheSolowmodelonlybecauseitexplicitlymodelstheconsumersideandendo

2、genizessavings.Beyonditsuseasabasicgrowthmodel,alsoaworkhorseformanyareasofmacroeconomics.DaronAcemoglu(MIT)EconomicGrowthLectures6and7November15and17,2011.2/71IntroductionEnvironmentPreferences,TechnologyandDemographicsIIn…nite-horizon,continuoustime.Representativehouseholdwithinstantaneousutili

3、tyfunctionu(c(t)),(1)Assumptionu(c)isstrictlyincreasing,concave,twicecontinuouslydi¤erentiablewithderivativesu0andu00,andsatis…esthefollowingInadatypeassumptions:limu0(c)=∞andlimu0(c)=0.c!0c!∞Supposerepresentativehouseholdrepresentssetofidenticalhouseholds(normalizedto1).Eachhouseholdhasaninstant

4、aneousutilityfunctiongivenby(1).L(0)=1andL(t)=exp(nt).(2)DaronAcemoglu(MIT)EconomicGrowthLectures6and7November15and17,2011.3/71IntroductionEnvironmentPreferences,TechnologyandDemographicsIIAllmembersofthehouseholdsupplytheirlaborinelastically.Objectivefunctionofeachhouseholdatt=0:Z∞U(0)exp((ρn

5、)t)u(c(t))dt,(3)0wherec(t)=consumptionpercapitaatt,ρ=subjectivediscountrate,ande¤ectivediscountrateisρn.Objectivefunction(3)embeds:Householdisfullyaltruistictowardsallofitsfuturemembers,andmakesallocationsofconsumption(amonghouseholdmembers)cooperatively.Strictconcavityofu(
)Thuseachhouseholdmem

6、berwillhaveanequalconsumptionC(t)c(t)L(t)DaronAcemoglu(MIT)EconomicGrowthLectures6and7November15and17,2011.4/71IntroductionEnvironmentPreferences,TechnologyandDemographicsIIIUtilityofu(c(t))perhouseholdmemberattimet,totalofL(t)u(c(t))=exp(nt)u(c(t)).Withdiscountatrateofexp(ρt),obtain(3).Assumpt

7、ion40.ρ>n.Ensuresthatinthemodelwithoutgrowth,discountedutilityis…nite.Willstrengthenitinmodelwithgrowth.Startmodelwithoutanytechnologicalprogress.Factorandproductmarketsarecompetitive.Productionpossibilitiessetoftheeco