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1、MARSHALLIANDEMANDCURVESANDCOMPENSATEDDEMANDCURVESMarshalliandemandcurvesarethe“regular”demandcurvestypicallyseenintextbooksandexamples.Theyshowtherelationshipbetweenpriceandquantity.Demandcurvestaketheform:X1*=d1(P1,P2,...PN,I),whereX=demandforgood1,P=priceofgoodan
2、dI=income.Thissetupimpliesthatdemanddependsonpreferences,allprices,andincome.X1*=theutilitymaximizingchoiceoftheindividual.Weusuallysimplifythedemandcurveforpresentationpurposesasfollows:Xx*=dx(PX,PY,I).Thisallowsustographthedemandcurveintwodimensions.Fornormalgood
3、s,MX/MPX<0.Thisimpliesthatthedemandcurveslopesdown.Notethatthreefactorswereheldconstantinderivingthisdemandcurve:1.Income2.Thepricesofallothergoods3.Theindividual’spreferences.Changesinanyofthesethreewillshiftthedemandcurve.Forexample,ifincomeincreases,thedemandcur
4、vewouldshiftoutward,withmoreXdemandedateachprice.Traditionally,theterm“increaseindemand”referstoshiftsoutwardinthedemandcurve;theterm“anincreaseinthequantitydemanded”referstomovementalongagivendemandcurvecausedbyachangeinPX.Figures1and2illustratehowaanindividual’sd
5、emandcurveisderived.CompensatedDemandCurvesRecallthattheactuallevelofutilityvariesalongthedemandcurve.Asshowninfigure1asPXfalls,theindividualismadebetteroffbytheutilityincreasesfromU0toU1toU2.ThedeclineinPXcausesindividual’srealincometoincrease(realpurchasingpowero
6、ftheindividualhasincreased).AnotherwaytoconstructademandcurveistoholdutilityconstantwhileallowingPXtovary.Todothis,atleaseasathoughtexperiment,asPXfalls,theindividual’sincomeisreduced,preventinganyincreaseinutility.Inotherwords,theeffectsofthepricechangeare“compens
7、ated,”tokeeptheindividualonagivenindifferencecurve.Thisimpliesthatreactionstopricechangesincludeonlysubstitutioneffects(i.e.,noincomeeffects).Formally,wedefineacompensateddemandcurveasfollows:X*=dX(PX,PY,U).Notethatutilityisanexplicitelementofthedemandfunction.This
8、setupassumesutilityisheldconstant.Figures3and4illustratethederivationofacompensateddemandcurve.RelationshipBetweenCompensatedandUncompensatedDema
