资源描述：
《Chapter 2Preference and Choice(高级微观经济学-上海.pdf》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Chapter2:PreferenceandChoice•Twoapproachestomodelingindividualchoicebehavior:1.Preference-basedapproach:preferencerelation2.Choice-basedapproach:revealedpreference•Aset(X)ofpossible(mutuallyexclusive)alternativesfromwhichtheindividualmustchoose.2.A:PreferenceRelations•Preferencerelations≿,whichisab
2、inaryrelationonthesetofalternativesXWereadx≿yas“xisatleastasgoodasy”,wherex,.y∈X1.x≿ybutnoty≾x⇔xfy2.x≿yandy≾x⇔x~y•Definition2.1:Thepreferencerelation≿isrational,ifitsatisfies:Axiom1:Completeness.Forallx,y∈X,wehavethatx≿yory≾xorboth.Axiom2:Transitivity.Forallx,y,z∈X,ifx≿yandy≿z,thenx≿z.⇒Theindividua
3、lcancompletelyrankanyelementsinX.However:Dowereallyknowourownpreferences?Areourpreferencesreallytransitive?Justperceptibledifferences,theframingproblem,collectivedecision(Condorcetparadox)12.B:ChoiceRules•Achoicestructure(B,C(•)),whereBisafamilyofnonemptysubsetsofX,C(•)isachoicerule.•Theweakaxiomof
4、revealedpreference:ifforsomeB∈Bwithx,y∈Bwehavex∈C(B),thenforanyB'∈Bwith'x,y∈Bandy∈C(B'),wemustalsohavex∈C(B').Example:X={}x,y,z,andB={{x,y},{x,y,z}}C:C(){}x,y={x},C({x,y,z})={x}yes111C:C(){}x,y={x},C({x,y,z})={x,y}no2222.C:Therelationshipbetweenpreferencerelationsandchoicerules•Definition2.2:Givena
5、choicestructure,therevealedpreferencerelation≿*isdefinedby:x≿*y⇔thereissomeB∈Bsuchthatx,y∈Bandx∈C(B).?DoestherevealedpreferencesatisfyAxiom1&2?•Definition2.3:Givenarationalpreference,thegeneratedchoicestructureis(B,C*(•,≿))suchthatC*(B,≿)={x∈B:x≿yforeveryy∈B}.2•Theorem2.4:Supposethat≿isarationalpre
6、ferencerelation.Thenthechoicestructuregeneratedby≿,(B,C*(•,≿)),satisfiestheweakaxiom.Proof:SupposethatforsomeB∈Bwehavex,y∈Bandx∈C*(B,≿).BythedefinitionofC*(B,≿),thisimpliesx≿y.SupposethatforsomeB’∈Bwithx,y∈B'wehavey∈C*(B’,≿).Thisimpliesthaty≿zforallz∈B'.Hence,accordingtotransitivityaxiom,wehavex≿z.
7、Wecanconcludethatx∈C*(B’,≿).Itispreciselytheconclusionthattheweakaxiomdemands.•Theorem2.5:If(B,C(•))isachoicestructuresuchthat:(1)theweakaxiomissatisfied,(2)BincludesallsubsetsofXofuptothreeelements,thenthe
