[精选]消费者最优选择(3).pptx

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1、ChapterFiveChoice消费者最优选择WhereAreWeDoinginThisChapter?Aftermodelingaconsumer’schoicesetandhispreference(representedbyutilityfunctions),wenowputthemtogetherandmodelhowhe/shemakesoptimalchoice.Inmathematicalterms,thisisaconstrainedmaximizationproblem;Ine

2、conomics,thisisarationalchoiceproblem.RationalConstrainedChoiceAffordablebundlesx1x2MorepreferredbundlesRationalConstrainedChoiceThemostpreferredaffordablebundleiscalledtheconsumer’sORDINARYDEMANDatthegivenpricesandbudget.Ordinarydemandswillbedenote

3、dbyx1*(p1,p2,m)andx2*(p1,p2,m).RationalConstrainedChoiceWhenx1*>0andx2*>0thedemandedbundleisINTERIOR.Ifbuying(x1*,x2*)costs$mthenthebudgetisexhausted.RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.(a)(x1*,x2*)exhauststhebudget;p1x1*+p2x2*=m

4、.RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.(b)Theslopeoftheindiff.curveat(x1*,x2*)equalstheslopeofthebudgetconstraint.RationalConstrainedChoice(x1*,x2*)satisfiestwoconditions:(a)thebudgetisexhausted;p1x1*+p2x2*=m(b)theslopeofthebudge

5、tconstraint,-p1/p2,andtheslopeoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.ComputingOrdinaryDemands-aCobb-DouglasExample.Supposethattheconsu

6、merhasCobb-Douglaspreferences.ThenComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSisComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSisAt(x1*,x2*),MRS=-p1/p2so(A)ComputingOrdinaryDemands-aCobb-DouglasExample.(x1*,x2*)alsoexhauststhebudgetso

7、(B)ComputingOrdinaryDemands-aCobb-DouglasExample.SowehavediscoveredthatthemostpreferredaffordablebundleforaconsumerwithCobb-DouglaspreferencesisComputingOrdinaryDemands-aCobb-DouglasExample.x1x2RationalConstrainedChoiceWhenx1*>0andx2*>0and(x1*,x2*)

8、exhauststhebudget,andindifferencecurveshaveno‘kinks’,theordinarydemandsareobtainedbysolving:(a)p1x1*+p2x2*=y(b)theslopesofthebudgetconstraint,-p1/p2,andoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).RationalConstrainedChoiceBut