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1、NotesonDiscreteTimeEconomicModels:TheGrowthModelRodyManuelliDepartmentofEconomics.UniversityofWisconsin-MadisonAugust8,2007iiContentsIntroductionvii1BasicResultsinDynamicOptimization11.1ConcavityandOptimization.....................11.2OptimizationSubjecttoConstraints................21
2、.3ATwoPeriodModel.........................41.4AnExtensionoftheKuhn-TuckerTheorem............82TheBasicGrowthModel:SteadyStates152.1TheBasicGrowthModel......................152.2ThePlanner’sProblem........................162.3SteadyStateAnalysis........................193TheBasicGrowth
3、Model:Dynamics273.1GlobalDynamics...........................273.1.1TheE?ectsofPermanentShocks..............363.1.2TheE?ectsofTemporaryShocks..............373.2LocalDynamics............................483.3Applications..............................493.3.1ConstantSavingRates............
4、........493.3.2PopulationGrowthandTechnicalChange.........494CompetitiveEquilibrium534.1BasicResults.............................534.2TaxesandDe?cits..........................684.3TheStructureofTaxation:SteadyStateImplications......754.3.1BasicSteadyStateAnalysis.................774.3
5、.2ChangingtheTaxRateonCapitalIncome........794.3.3ADigression:TheUserCostofCapital..........814.3.4ChangingtheTaxRateonLaborIncome.........824.3.5Digression:PartialEquilibriumAnalysis..........834.3.6IndividualandCorporateTaxation.............874.3.7ABalancedBudget(RevenueNeutral)Chan
6、geinTaxRates934.3.8TaxationandHumanCapital................97iiiivCONTENTS4.4Heterogeneity.............................1014.4.1TheDistributionofIndividualConsumption.......1044.4.2TheTimePathofConsumptionInequality........107PrefaceThesenoteswereoriginallydevelopedaspartofthe?rstyearMa
7、croeconomicTheorycourseattheUniversityofWisconsin.Severalgenerationsofstudentsdeservecreditfor?ndingnumerouserrors,andpointingalternativewaysofdiscussingandpresentingthematerial.Theydeserverecognition.Thelastiterationhasbene?ttedfromdetailedcommentsbyNickMader.vviPREFACEIntroductionTh
8、epurp
