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1、14.452EconomicGrowth:Lectures5,FoundationsofNeoclassicalGrowthDaronAcemogluMITNovember10,2011.DaronAcemoglu(MIT)EconomicGrowthLecture5November10,2011.1/60PreliminariesIntroductionFoundationsofNeoclassicalGrowthSolowmodel:constantsavingrate.Moresatisfactorytospecifythepreferenceo
2、rderingsofindividualsandderivetheirdecisionsfromthesepreferences.Enablesbetterunderstandingofthefactorsthata¤ectsavingsdecisions.Enablestodiscussthe“optimality”ofequilibriaWhetherthe(competitive)equilibriaofgrowthmodelscanbe“improvedupon”.Notionofimprovement:Paretooptimality.Dar
3、onAcemoglu(MIT)EconomicGrowthLecture5November10,2011.2/60PreliminariesPreliminariesPreliminariesIConsideraneconomyconsistingofaunitmeasureofin…nitely-livedhouseholds.I.e.,anuncountablenumberofhouseholds:e.g.,thesetofhouseholdsHcouldberepresentedbytheunitinterval[0,1].Emphasizeth
4、ateachhouseholdisin…nitesimalandwillhavenoe¤ectonaggregates.CanalternativelythinkofHasacountablesetoftheformH=f1,2,...,MgwithM=∞,withoutanylossofgenerality.Advantageofunitmeasure:averagesandaggregatesarethesameSimplertohaveHasa…nitesetintheformf1,2,...,MgwithMlargebut…nite.Accep
5、tableformanymodels,butwithoverlappinggenerationsrequirethesetofhouseholdstobein…nite.DaronAcemoglu(MIT)EconomicGrowthLecture5November10,2011.3/60PreliminariesPreliminariesPreliminariesIIHowtomodelhouseholdsinin…nitehorizon?1“in…nitelylived”orconsistingofoverlappinggenerationswit
6、hfullaltruismlinkinggenerations!in…niteplanninghorizon2overlappinggenerations!…niteplanninghorizon(generally...).DaronAcemoglu(MIT)EconomicGrowthLecture5November10,2011.4/60PreliminariesPreliminariesTimeSeparablePreferencesStandardassumptionsonpreferenceorderingssothattheycanber
7、epresentedbyutilityfunctions.Inparticular,eachhouseholdihasaninstantaneousutilityfunctionui(ci(t)),ui:R+!Risincreasingandconcaveandci(t)istheconsumptionofhouseholdi.Noteinstantaneousutilityfunctionisnotspecifyingacompletepreferenceorderingoverallcommodities—hereconsumptionlevels
8、inalldates.Sometimesalsoreferredtoasthe“felicit
