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1、Chapter9OverlappingGenerationsModelsThischapterdescribesthepureexchangeoverlappinggenerationsmodelofPaulSamuelson(1958).Webeginwithanabstractpresentationthattreatstheover-lappinggenerationsmodelasaspecialcaseofthechapter8generalequilibriummodelwithcompletemarketsandall
2、tradesoccurringattime0.Apeculiartypeofheterogeneityacrossagentsdistinguishesthemodel.Eachindividualcaresaboutconsumptiononlyattwoadjacentdates,andthesetofindividualswhocareaboutconsumptionataparticulardateincludessomewhocareaboutconsumptiononeperiodearlierandotherswhoc
3、areaboutconsumptiononepe-riodlater.Weshallstudyhowthisspecialpreferenceanddemographicpatternaffectssomeoftheoutcomesofthechapter8model.Whileithelpstorevealthefundamentalstructure,allowingcompletemar-ketswithtime0tradinginanoverlappinggenerationsmodelstrainscredulity.The
4、formalismenvisionsthatequilibriumpriceandquantitysequencesaresetattime0,beforetheparticipantswhoaretoexecutethetradeshavebeenborn.Forthatreason,mostappliedworkwiththeoverlappinggenerationsmodeladoptsasequential-tradingarrangement,likethesequentialtradeinArrowsecurities
5、describedinchapter8.Thesequential-tradingarrangementhasalltradesexecutedbyagentslivinginthehereandnow.Nevertheless,equilibriumquantitiesandintertemporalpricesareequivalentbetweenthesetwotradingarrangements.Therefore,analyticalresultsfoundinonesettingtransfertotheother.
6、Laterinthechapter,weuseversionsofthemodelwithsequentialtradingtotellhowtheoverlappinggenerationsmodelprovidesaframeworkforthinkingaboutequilibriawithgovernmentdebtand/orvaluedfiatcurrency,intergener-ationaltransfers,andfiscalpolicy.–315–316OverlappingGenerationsModels9.1
7、.EndowmentsandpreferencesTimeisdiscrete,startsatt=1,andlastsforever,sot=1,2,....Thereisaninfinityofagentsnamedi=0,1,....Wecanalsoregardiasagenti’speriodofbirth.Thereisasinglegoodateachdate.Thegoodisnotstorable.Thereisnouncertainty.Eachagenthasastrictlyconcave,twiceconti
8、nuouslydifferentiable,one-periodutilityfunctionu(c),whichisstrictlyincreasinginconsumptioncoftheonegood.Agenticonsumes