Pure Exchange Equilibrium of Dynamic Models Dav...

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1、JOURNALOFECONOMICTHEORY6,12-36(1973)PureExchangeEquilibriumofDynamicEconomicModels*DAVIDGALEDepartmentofIndustrialEngineeringandOperationsResearch,Universityof’California,Berkeley,Califbrnia94720ReceivedFebruary14,1972Thispaperstudiescompetitiveequilibrium

2、overtimeofaonegoodmodelinwhichtheagentsaremembersofapopulationwhichgrowsataconstantrate.Eachagentlivesfornperiodsandinthei-thperiodofhislifereceivesanendowmentofeiunitsofgoods.Goodscanneitherbeproducednorstored.Themodelisthusthen-periodgeneralizationofthet

3、wo-andthree-periodmodelsstudiedbySamuelsonin[4].Weseektoascertainthestructureofthetimepathsofconsumptioninthesemodels.Ourresultscanbesummarizedroughlyasfollows:Ingeneral,therewillexisttwokindsofsteadystatepaths,(i)goldenrulepathsinwhichtherateofinterestequ

4、alsthegrowthrateofpopulationand(ii)“balanced”pathsinwhichtheaggregateassetsorindebtednessofthesocietyasawholeiszero(afundamentalfactaboutdynamicmodelsisthatitispossibleforaggregatedebtnottoequalaggregatecreditasitmustinthestaticcase).Amodelistermedclassica

5、lifinthegoldenrulestateaggregateassetsarenegative(ordebtpositive)andSamuelson(following[4])intheoppositecase.ItisconjecturedthatthegoldenruleprogramisgloballystableintheclassicalcaseandthebalancedprogramisstableintheSamuelsoncase.Thisisestablishedforthespe

6、cialcasen=2.I.STRUCTUREANDBEHAVIOROFTHEMODELS1.IntroductionThisstudyrepresentspartofacontinuinginvestigationofthepropertiesofgeneralequilibriummodelsinwhichinsteadofworkingwithafixedsetofeconomicagentswepostulatea“population,”thatis,astreamorsequenceofagen

7、tseachassociatedwithaparticularperiodorinterval*ThisresearchwasdonewhiletheauthorheldaResearchProfessorshipwiththeMillerInstituteforResearchinSciencesattheUniversityofCalifornia,Berkeley.IthasalsobeenpartiallysupportedbytheOfficeofNavalResearchunderContrac

8、tNOOO14-69-A-0200-1010andtheNationalScienceFoundationunderGrantGP-30961XwiththeUniversityofCalifornia.ReproductioninwholeorinpartispermittedforanypurposeoftheUnitedStatesGovernment.12Copyright01973byAcademicP