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1、Chapter7Recursive(Partial)Equilibrium7.1.AnequilibriumconceptThischapterformulatescompetitiveandoligopolisticequilibriainsomedynamicsettings.Uptonow,wehavestudiedsingle-agentproblemswherecomponentsofthestatevectornotunderthecontroloftheagentweretakenasgiven
2、.Inthischapter,wedescribemultiple-agentsettingsinwhichcomponentsofthestatevectorthatoneagenttakesasexogenousaredeterminedbythedeci-sionsofotheragents.Westudypartialequilibriummodelsofakindappliedinmicroeconomics.1Wedescribetwocloselyrelatedequilibriumconcep
3、tsforsuchmodels:arationalexpectationsorrecursivecompetitiveequilibrium,andaMarkovperfectequilibrium.The?rstequilibriumconceptjointlyrestrictsaBellmanequationandatransitionlawthatistakenasgiveninthatBellmanequation.Thesecondequilibriumconceptleadstopairs(int
4、heduopolycase)orsets(intheoligopolycase)ofBellmanequationsandtransitionequationsthataretobesolvedbysimultaneousbackwardinduction.Thoughtheequilibriumconceptsintroducedinthischaptertranscendlinearquadraticsetups,wechoosetopresenttheminthecontextoflinearquadr
5、aticexamplesbecausethisrenderstheBellmanequationstractable.1Forexample,seeRosenandTopel(1988)andRosen,Murphy,andScheinkman(1994)–227–228Recursive(Partial)Equilibrium7.2.Example:adjustmentcostsThissectiondescribesamodelofacompetitivemarketwithproducerswhofac
6、eadjustmentcosts.2Inthecourseoftheexposition,weintroduceandexploitaversionofthe‘bigK,littlek’trickthatiswidelyusedinmacroeconomicsandappliedeconomicdynamics.3Themodelconsistsofnidentical?rmswhosepro?tfunctionmakesthemwanttoforecasttheaggregateoutputdecision
7、sofother?rmsjustliketheminordertochoosetheirownoutput.Weassumethatnisalargenumbersothattheoutputofanysingle?rmhasanegligiblee?ectonaggregateoutputand,hence,?rmsarejusti?edintreatingtheirforecastofaggregateoutputasuna?ectedbytheirownoutputdecisions.Thus,oneo
8、fncompetitive?rmssellsoutputytandchoosesaproductionplantomaximize∞tβRt(7.2.1)t=0where2Rt=ptyt?.5d(yt+1?yt)(7.2.2)subjecttoy0beingagiveninitialcondition.Hereβ∈(0,1)isadiscountfactor,andd>0measuresacost
