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ChapterFiveChoice消费者最优选择
WhereAreWeDoinginThisChapter?Aftermodelingaconsumer’schoicesetandhispreference(representedbyutilityfunctions),wenowputthemtogetherandmodelhowhe/shemakesoptimalchoice.Inmathematicalterms,thisisaconstrainedmaximizationproblem;Ineconomics,thisisarationalchoiceproblem.
RationalConstrainedChoiceAffordable
bundlesx1x2Morepreferred
bundles
RationalConstrainedChoiceThemostpreferredaffordablebundleiscalledtheconsumer’sORDINARYDEMANDatthegivenpricesandbudget.Ordinarydemandswillbedenotedby
x1*(p1,p2,m)andx2*(p1,p2,m).
RationalConstrainedChoiceWhenx1*0andx2*0thedemandedbundleisINTERIOR.Ifbuying(x1*,x2*)costs$mthenthebudgetisexhausted.
RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.
(a)(x1*,x2*)exhauststhe
budget;p1x1*+p2x2*=m.
RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.
(b)Theslopeoftheindiff.
curveat(x1*,x2*)equals
theslopeofthebudget
constraint.
RationalConstrainedChoice(x1*,x2*)satisfiestwoconditions:(a)thebudgetisexhausted;
p1x1*+p2x2*=m(b)theslopeofthebudgetconstraint,-p1/p2,andtheslopeoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).
ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.
ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.
Then
ComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSis
ComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSis
At(x1*,x2*),MRS=-p1/p2so(A)
ComputingOrdinaryDemands-aCobb-DouglasExample.(x1*,x2*)alsoexhauststhebudgetso(B)
ComputingOrdinaryDemands-aCobb-DouglasExample.Sowehavediscoveredthatthemost
preferredaffordablebundleforaconsumer
withCobb-Douglaspreferences
is
ComputingOrdinaryDemands-aCobb-DouglasExample.x1x2
Ratio
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