北大微观经济学课件(英文版)ch5Choice

ChapterFiveChoice选择2023/7/22中级微观经济学StructureRationalconstrainedchoiceComputingordinarydemandsInteriorsolution（内在解）Cornersolution（角点解）“Kinky”solutionExample:Choosingtaxes2023/7/22中级微观经济学EconomicRationalityTheprincipalbehavioralpostulateisthatadecision-makerchoosesitsmostpreferredalternativefromthoseavailabletoit.Theavailablechoicesconstitutethechoiceset.Howisthemostpreferredbundleinthechoicesetlocated?2023/7/22中级微观经济学RationalConstrainedChoicex1x2Affordable

bundlesMorepreferred

bundles2023/7/22中级微观经济学RationalConstrainedChoiceAffordable

bundlesx1x2Morepreferred

bundles2023/7/22中级微观经济学RationalConstrainedChoicex1x2x1*x2*2023/7/22中级微观经济学RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isthemost

preferredaffordable

bundle.2023/7/22中级微观经济学RationalConstrainedChoiceThemostpreferredaffordablebundleiscalledtheconsumer’sORDINARYDEMAND（一般需求）atthegivenpricesandbudget.Ordinarydemandswillbedenotedby

x1*(p1,p2,m)andx2*(p1,p2,m).2023/7/22中级微观经济学RationalConstrainedChoiceWhenx1*>0andx2*>0thedemandedbundleisINTERIOR.Ifbuying(x1*,x2*)costs$mthenthebudgetisexhausted.2023/7/22中级微观经济学RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.(x1*,x2*)exhauststhe

budget.2023/7/22中级微观经济学RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(a)(x1*,x2*)exhauststhe

budget;p1x1*+p2x2*=m.2023/7/22中级微观经济学RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(b)Theslopeoftheindiff.

curveat(x1*,x2*)equals

theslopeofthebudget

constraint.2023/7/22中级微观经济学RationalConstrainedChoice(x1*,x2*)satisfiestwoconditions:(a)thebudgetisexhausted;

p1x1*+p2x2*=m(b)tangency:theslopeofthebudgetconstraint,-p1/p2,andtheslopeoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).2023/7/22中级微观经济学MeaningoftheTangencyConditionConsumer’smarginalwillingnesstopayequalsthemarketexchangerate.Supposeataconsumptionbundle(x1,x2),MRS=-2,-P1/P2=-1Theconsumeriswillingtogiveup2unitofx2toexchangeforanadditionalunitofx1Themarketallowshertogiveuponly1unitofx2toobtainanadditionalx1(x1,x2)isnotoptimalchoiceShecanbebetteroffincreasingherconsumptionofx1.2023/7/22中级微观经济学x1x1x22023/7/22中级微观经济学ComputingOrdinaryDemandsSolvefor2simultaneousequations.TangencyBudgetconstraintTheconditionsmaybeobtainedbyusingtheLagrangianmultipliermethod,i.e.,constrainedoptimizationincalculus.2023/7/22中级微观经济学ComputingOrdinaryDemandsHowcanthisinformationbeusedtolocate(x1*,x2*)forgivenp1,p2andm?2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.

TheMRSis2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.At(x1*,x2*),MRS=-p1/p2sothetangencycondition(MRS=-p1/p2)is

(A)2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.(x1*,x2*)alsoexhauststhebudgetso(B)2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.Sonowweknowthat(A)(B)2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.Thesolutiontothesimultaneousequationsis:2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.Sowehavediscoveredthatthemost

preferredaffordablebundleforaconsumer

withCobb-Douglaspreferences

is2023/7/22中级微观经济学ComputingOrdinaryDemands-aCobb-DouglasExample.x1x22023/7/22中级微观经济学RationalConstrainedChoice:SummaryWhenx1*>0andx2*>0

and(x1*,x2*)exhauststhebudget,

andindifferencecurveshaveno

‘kinks’,theordinarydemandsareobtainedbysolving:(a)p1x1*+p2x2*=y(b)theslopesofthebudgetconstraint,-p1/p2,andoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).2023/7/22中级微观经济学RationalConstrainedChoiceButwhatifx1*=0?Orifx2*=0?Ifeitherx1*=0orx2*=0thentheordinarydemand(x1*,x2*)isatacornersolution(角点解)totheproblemofmaximizingutilitysubjecttoabudgetconstraint.2023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-12023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1>p2.2023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1>p2.2023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1>p2.2023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1<p2.2023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCaseSowhenU(x1,x2)=x1+x2,themost

preferredaffordablebundleis(x1*,x2*)

whereandifp1<p2ifp1>p2.2023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1=p2.2023/7/22中级微观经济学ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2Allthebundlesinthe

constraintareequallythe

mostpreferredaffordable

whenp1=p2.2023/7/22中级微观经济学ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Better2023/7/22中级微观经济学ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x22023/7/22中级微观经济学ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Whichisthemostpreferred

affordablebundle?2023/7/22中级微观经济学ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundle2023/7/22中级微观经济学ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundleNoticethatthe“tangencysolution”

isnotthemostpreferredaffordable

bundle.2023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax12023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=0U(x1,x2)=min{ax1,x2}x2=ax12023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-¥MRS=0U(x1,x2)=min{ax1,x2}x2=ax12023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-¥MRS=0MRSisundefinedU(x1,x2)=min{ax1,x2}x2=ax12023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax12023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1Whichisthemost

preferredaffordablebundle?2023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1Themostpreferredaffordablebundle2023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1x1*x2*2023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1x1*x2*(a)p1x1*+p2x2*=m2023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1x1*x2*(a)p1x1*+p2x2*=m

(b)x2*=ax1*2023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCase(a)p1x1*+p2x2*=m;(b)x2*=ax1*.Substitutionfrom(b)forx2*in(a)givesp1x1*+p2ax1*=m

whichgives2023/7/22中级微观经济学Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax12023/7/22中级微观经济学ChoosingTaxes:VariousTaxes