范里安现代观点课件-南开大学中级微观经济学

ChapterSixDemand2021/5/271PropertiesofDemandFunctionsComparativestaticsanalysisofordinarydemandfunctions--thestudyofhowordinarydemandsx1*(p1,p2,y)andx2*(p1,p2,y)changeaspricesp1,p2andincomeychange.2021/5/272Own-PriceChangesHowdoesx1*(p1,p2,y)changeasp1changes,holdingp2andyconstant?Supposeonlyp1increases,fromp1’top1’’andthentop1’’’.2021/5/273

x1x2p1=p1’Fixedp2andy.p1x1+p2x2=yOwn-PriceChanges2021/5/274Own-PriceChangesx1x2p1=p1’’p1=p1’Fixedp2andy.p1x1+p2x2=y2021/5/275Own-PriceChangesx1x2p1=p1’’p1=

p1’’’Fixedp2andy.p1=p1’p1x1+p2x2=y2021/5/276p1=p1’Own-PriceChangesFixedp2andy.2021/5/277x1*(p1’)Own-PriceChangesp1=p1’Fixedp2andy.2021/5/278x1*(p1’)p1x1*(p1’)p1’x1*Own-PriceChangesFixedp2andy.p1=p1’2021/5/279x1*(p1’)p1x1*(p1’)p1’p1=p1’’x1*Own-PriceChangesFixedp2andy.2021/5/2710x1*(p1’)x1*(p1’’)p1x1*(p1’)p1’p1=p1’’x1*Own-PriceChangesFixedp2andy.2021/5/2711x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’)p1’p1’’x1*Own-PriceChangesFixedp2andy.2021/5/2712x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’)p1’p1’’p1=p1’’’x1*Own-PriceChangesFixedp2andy.2021/5/2713x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’)p1’p1’’p1=p1’’’x1*Own-PriceChangesFixedp2andy.2021/5/2714x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’’)x1*(p1’’)p1’p1’’p1’’’x1*Own-PriceChangesFixedp2andy.2021/5/2715x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’’)x1*(p1’’)p1’p1’’p1’’’x1*Own-PriceChangesOrdinary

demandcurve

forcommodity1Fixedp2andy.2021/5/2716x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’’)x1*(p1’’)p1’p1’’p1’’’x1*Own-PriceChangesOrdinary

demandcurve

forcommodity1Fixedp2andy.2021/5/2717x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’’)x1*(p1’’)p1’p1’’p1’’’x1*Own-PriceChangesOrdinary

demandcurve

forcommodity1p1price

offer

curveFixedp2andy.2021/5/2718Own-PriceChangesThecurvecontainingalltheutility-maximizingbundlestracedoutasp1changes,withp2andyconstant,isthep1-priceoffercurve.Theplotofthex1-coordinateofthep1-priceoffercurveagainstp1istheordinarydemandcurveforcommodity1.2021/5/2719Own-PriceChangesWhatdoesap1price-offercurvelooklikeforCobb-Douglaspreferences?2021/5/2720Own-PriceChangesWhatdoesap1price-offercurvelooklikeforCobb-Douglaspreferences?Take

Thentheordinarydemandfunctionsforcommodities1and2are2021/5/2721Own-PriceChangesandNoticethatx2*doesnotvarywithp1sothe

p1priceoffercurveis2021/5/2722Own-PriceChangesandNoticethatx2*doesnotvarywithp1sothe

p1priceoffercurveisflat2021/5/2723Own-PriceChangesandNoticethatx2*doesnotvarywithp1sothe

p1priceoffercurveisflatandtheordinary

demandcurveforcommodity1isa2021/5/2724Own-PriceChangesandNoticethatx2*doesnotvarywithp1sothe

p1priceoffercurveisflatandtheordinary

demandcurveforcommodity1isa

rectangularhyperbola.2021/5/2725x1*(p1’’’)x1*(p1’)x1*(p1’’)Own-PriceChangesFixedp2andy.2021/5/2726x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*Own-PriceChangesOrdinary

demandcurve

forcommodity1

isFixedp2andy.2021/5/2727Own-PriceChangesWhatdoesap1price-offercurvelooklikeforaperfect-complementsutilityfunction?2021/5/2728Own-PriceChangesWhatdoesap1price-offercurvelooklikeforaperfect-complementsutilityfunction?Thentheordinarydemandfunctions

forcommodities1and2are2021/5/2729Own-PriceChanges2021/5/2730Own-PriceChangesWithp2andyfixed,higherp1causes

smallerx1*andx2*.2021/5/2731Own-PriceChangesWithp2andyfixed,higherp1causes

smallerx1*andx2*.As2021/5/2732Own-PriceChangesWithp2andyfixed,higherp1causes

smallerx1*andx2*.AsAs2021/5/2733Fixedp2andy.Own-PriceChangesx1x22021/5/2734p1x1*Fixedp2andy.Own-PriceChangesx1x2p1’

’p1=p1’

’

’y/p22021/5/2735p1x1*Fixedp2andy.Own-PriceChangesx1x2p1’p1’’p1=p1’’’’’’’’y/p22021/5/2736p1x1*Fixedp2andy.Own-PriceChangesx1x2p1’p1’’p1’’’p1=p1’’’’’’’’’’’’y/p22021/5/2737p1x1*Ordinary

demandcurve

forcommodity1

isFixedp2andy.Own-PriceChangesx1x2p1’p1’’p1’’’y/p22021/5/2738Own-PriceChangesWhatdoesap1price-offercurvelooklikeforaperfect-substitutesutilityfunction?Thentheordinarydemandfunctions

forcommodities1and2are2021/5/2739Own-PriceChangesand2021/5/2740Fixedp2andy.Own-PriceChangesx2x1Fixedp2andy.p1=p1’<p2’2021/5/2741Fixedp2andy.Own-PriceChangesx2x1p1x1*Fixedp2andy.p1’p1=p1’<p2’’2021/5/2742Fixedp2andy.Own-PriceChangesx2x1p1x1*Fixedp2andy.p1’p1=p1’’=p22021/5/2743Fixedp2andy.Own-PriceChangesx2x1p1x1*Fixedp2andy.p1’p1=p1’’=p22021/5/2744Fixedp2andy.Own-PriceChangesx2x1p1x1*Fixedp2andy.p1’p1=p1’’=p2’’2021/5/2745Fixedp2andy.Own-PriceChangesx2x1p1x1*Fixedp2andy.p1’p1=p1’’=p2p2=p1’’2021/5/2746Fixedp2andy.Own-PriceChangesx2x1p1x1*Fixedp2andy.p1’p1’’’p2=p1’’2021/5/2747Fixedp2andy.Own-PriceChangesx2x1p1x1*Fixedp2andy.p1’p2=p1’’p1’’’p1price

offercurveOrdinary

demandcurve

forcommodity12021/5/2748Own-PriceChangesUsuallyweask“Giventhepriceforcommodity1whatisthequantitydemandedofcommodity1?”Butwecouldalsoasktheinversequestion“Atwhatpriceforcommodity1wouldagivenquantityofcommodity1bedemanded?”2021/5/2749Own-PriceChangesp1x1*p1’Givenp1’,whatquantityis

demandedofcommodity1?2021/5/2750Own-PriceChangesp1x1*p1’Givenp1’,whatquantityis

demandedofcommodity1?

Answer:x1’units.x1’2021/5/2751Own-PriceChangesp1x1*x1’Givenp1’,whatquantityis

demandedofcommodity1?

Answer:x1’units.Theinversequestionis:

Givenx1’unitsare

demanded,whatisthe

priceof

commodity1?2021/5/2752Own-PriceChangesp1x1*p1’x1’Givenp1’,whatquantityis

demandedofcommodity1?

Answer:x1’units.Theinversequestionis:

Givenx1’unitsare

demanded,whatisthe

priceof

commodity1?Answer:p1’2021/5/2753Own-PriceChangesTakingquantitydemandedasgivenandthenaskingwhatmustbepricedescribestheinversedemandfunctionofacommodity.2021/5/2754Own-PriceChangesACobb-Douglasexample:istheordinarydemandfunctionandistheinversedemandfunction.2021/5/2755Own-PriceChangesAperfect-complementsexample:istheordinarydemandfunctionandistheinversedemandfunction.2021/5/2756IncomeChangesHowdoesthevalueofx1*(p1,p2,y)changeasychanges,holdingbothp1andp2constant?2021/5/2757IncomeChangesFixedp1andp2.y’<y’’<y’’’2021/5/2758IncomeChangesFixedp1andp2.y’<y’’<y’’’2021/5/2759IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’2021/5/2760IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurve2021/5/2761IncomeChangesAplotofquantitydemandedagainstincomeiscalledanEngelcurve.2021/5/2762IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurve2021/5/2763IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvex1*yx1’’’x1’’x1’y’y’’y’’’2021/5/2764IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvex1*yx1’’’x1’’x1’y’y’’y’’’Engel

curve;good12021/5/2765IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvex2*yx2’’’x2’’x2’y’y’’y’’’2021/5/2766IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvex2*yx2’’’x2’’x2’y’y’’y’’’Engel

curve;good22021/5/2767IncomeChangesFixedp1andp2.y’<y’’<y’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvex1*x2*yyx1’’’x1’’x1’x2’’’x2’’x2’y’y’’y’’’y’y’’y’’’Engel

curve;good2Engel

curve;good12021/5/2768IncomeChangesandCobb-DouglasPreferencesAnexampleofcomputingtheequationsofEngelcurves;theCobb-Douglascase.Theordinarydemandequationsare2021/5/2769IncomeChangesandCobb-DouglasPreferencesRearrangedtoisolatey,theseare:Engelcurveforgood1Engelcurveforgood22021/5/2770IncomeChangesandCobb-DouglasPreferencesyyx1*x2*Engelcurve

forgood1Engelcurve

forgood22021/5/2771IncomeChangesandPerfectly-ComplementaryPreferencesAnotherexampleofcomputingtheequationsofEngelcurves;theperfectly-complementarycase.Theordinarydemandequationsare2021/5/2772IncomeChangesandPerfectly-ComplementaryPreferencesRearrangedtoisolatey,theseare:Engelcurveforgood1Engelcurveforgood22021/5/2773Fixedp1andp2.IncomeChangesx1x22021/5/2774IncomeChangesx1x2y’<y’’<y’’’Fixedp1andp2.2021/5/2775IncomeChangesx1x2y’<y’’<y’’’Fixedp1andp2.2021/5/2776IncomeChangesx1x2y’<y’’<y’’’x1’’x1’x2’’’x2’’x2’x1’’’Fixedp1andp2.2021/5/2777IncomeChangesx1x2y’<y’’<y’’’x1’’x1’x2’’’x2’’x2’x1’’’x1*yy’y’’y’’’Engel

curve;good1x1’’’x1’’x1’Fixedp1andp2.2021/5/2778IncomeChangesx1x2y’<y’’<y’’’x1’’x1’x2’’’x2’’x2’x1’’’x2*yx2’’’x2’’x2’y’y’’y’’’Engel

curve;good2Fixedp1andp2.2021/5/2779IncomeChangesx1x2y’<y’’<y’’’x1’’x1’x2’’’x2’’x2’x1’’’x1*x2*yyx2’’’x2’’x2’y’y’’y’’’y’y’’y’’’Engel

curve;good2Engel

curve;good1x1’’’x1’’x1’Fixedp1andp2.2021/5/2780IncomeChangesx1*x2*yyx2’’’x2’’x2’y’y’’y’’’y’y’’y’’’x1’’’x1’’x1’Engel

curve;good2Engel

curve;good1Fixedp1andp2.2021/5/2781IncomeChangesandPerfectly-SubstitutablePreferencesAnotherexampleofcomputingtheequationsofEngelcurves;theperfectly-substitutioncase.Theordinarydemandequationsare2021/5/2782IncomeChangesandPerfectly-SubstitutablePreferences2021/5/2783IncomeChangesandPerfectly-SubstitutablePreferencesSupposep1<p2.Then2021/5/2784IncomeChangesandPerfectly-SubstitutablePreferencesSupposep1<p2.Thenand2021/5/2785IncomeChangesandPerfectly-SubstitutablePreferencesSupposep1<p2.Thenandand2021/5/2786IncomeChangesandPerfectly-SubstitutablePreferencesyyx1*x2*0Engelcurve

forgood1Engelcurve

forgood22021/5/2787IncomeChangesIneveryexamplesofartheEngelcurveshaveallbeenstraightlines?

Q:Isthistrueingeneral?A:No.Engelcurvesarestraightlinesiftheconsumer’spreferencesarehomothetic.2021/5/2788HomotheticityAconsumer’spreferencesarehomotheticifandonlyif

foreveryk>0.Thatis,theconsumer’sMRSisthesameanywhereonastraightlinedrawnfromtheorigin.Û(x1,x2)(y1,y2)(kx1,kx2)(ky1,ky2)

pp2021/5/2789IncomeEffects--ANonhomotheticExampleQuasilinearpreferencesarenothomothetic.

Forexample,2021/5/2790Quasi-linearIndifferenceCurvesx2x1Eachcurveisaverticallyshiftedcopyoftheothers.Eachcurveintersects

bothaxes.2021/5/2791IncomeChanges;QuasilinearUtilityx2x1x1~2021/5/2792IncomeChanges;QuasilinearUtilityx2x1x1~x1*yx1~Engel

curvefor

good12021/5/2793IncomeChanges;QuasilinearUtilityx2x1x1~x2*yEngel

curvefor

good22021/5/2794IncomeChanges;QuasilinearUtilityx2x1x1~x1*x2*yyx1~Engel

curvefor

good2Engel

curvefor

good12021/5/2795IncomeEffectsAgoodforwhichquantitydemandedriseswithincomeiscallednormal.Thereforeanormalgood’sEngelcurveispositivelysloped.2021/5/2796IncomeEffectsAgoodforwhichquantitydemandedfallsasincomeincreasesiscalledincomeinferior.Thereforeanincomeinferiorgood’sEngelcurveisnegativelysloped.2021/5/2797IncomeChanges;Goods

1&2Normalx1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvex1*x2*yyx1’’’x1’’x1’x2’’’x2’’x2’y’y’’y’’’y’y’’y’’’Engel

curve;good2Engel

curve;good12021/5/2798IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x12021/5/2799IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x12021/5/27100IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x12021/5/27101IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x12021/5/27102IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x12021/5/27103IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1Income

offercurve2021/5/27104IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1x1*yEngelcurve

forgood12021/5/27105IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1x1*x2*yyEngelcurve

forgood2Engelcurve

forgood12021/5/27106OrdinaryGoodsAgoodiscalledordinaryifthequantitydemandedofitalwaysincreases