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1、AdvancedMicroeconomicsTopic2:IndividualPreferencesPrimaryReadings:DL–Chapter4;JR-Chapter3;Varian–Chapter7Inmosteconomicmodels,westartwithanagent'sutilityfunction.Theutilityfunctionbasicallymapsfrombundlesthattheagentmightchoose,totherealline.Theutilityfunctionisqui
2、teconvenient:itcanbemaximizedandmanipulatedusingmathematicaltools.Butthequestionis:Isitvalidtoreduceasimple,real-valuefunction,somethingascomplicatedasanagent'spreferencesoverawidevarietyofbundles?Whatdoesitreallymeanabouttheagent'spreferences?Areweimposingsomehidd
3、enordesirableassumptionswhenwetakethisapproach?Inthislecture,wewilltrytoanswerthesequestionsbyanalyzingtherelationshipsbetweenaxiomsaboutanagent'spreferences,andthenestablishingtheexistenceofautilityfunctionthatrepresentstheagent'spreferences.2.1TheConsumer'sPrefer
4、ences2.1.1ConsumptionSetWelettheconsumptionset,X,representthesetofallalternatives,orcompleteconsumptionplans,thattheconsumercanconceive-whethersomeofthemwillbeachievableinpracticeornot.EveryelementofXiscalledaconsumptionbundleoraconsumptionplan.·Xcapturestheunivers
5、eofallpossiblechoicesaconsumermayhave.Forthisreason,theconsumptionsetisalsoknownasthechoiceset.·Normally,XÌRm+-theentirenonnegativeorthantoftherealspaceRm.·WewillalwaysassumethatXisaclosedandconvexset.2.1.2BasicProperties&AxiomsofPreferences·Forx,yÎX,whenwewritexy,
6、wemeanthat"theconsumerthinksthatthebundlexisatleastasgoodasbundley."WecallapreferencerelationonX.·Wesay,"xis(weakly)preferredtoy".·ItisclearthatisabinaryrelationdefinedonX.Asthefinalpurposeofintroducingapreferencerelationistoorderthesetofconsumptionbundles,weneedto
7、assumeanumberofaxioms.Theseaxiomsofconsumerchoiceareintendedtogiveformalmathematicalexpressiontofundamentalaspectsofconsumerbehaviorandaltitudestowardtheobjectsofchoice.AXIOM1:(Completeness)"x,yÎX,(xy)Ú(yx).(Note:Ú="or")·Tosatisfythecompletenessaxiom,thepreferencec
8、annotbedefinedsothatxyÛxj³yj,"j.(Reason:itisonlyapartialordering.)(Note:Whilethisaxiomappearsinnocuous,incombinationwiththeusualconfinementofthec
