Chapter6 DemandCourse:MicroeconomicsText:Varian’sIntermediateMicroeconomics

1IntroductionInChapter5,wetalkabouttheoptimalchoiceunderthebudgetconstraint.Here,weconsiderhowthechangesofexogenousvariablesaffectdecisions.Recall

endogenousvariables:quantitiesofgoodsx1,x2

exogenousvariables:pricesandincome.2Own-PriceChangesConsiderthetwo-goodcase.Denotetheordinarydemandfunctionsasx1*(p1,p2,m),x2*(p1,p2,m).Howdoesx1*(p1,p2,m)changeasp1changes,holdingp2andmconstant?Supposeonlyp1increases,fromp1’top1’’andthentop1’’’.3Own-PriceChanges4x1x2p1=p1’Fixedp2andm.p1x1+p2x2=mOwn-PriceChanges5x1x2p1=p1’’p1=p1’Fixedp2andm.p1x1+p2x2=mOwn-PriceChanges6x1x2p1=p1’’p1=

p1’’’Fixedp2andy.p1=p1’p1x1+p2x2=mx1*(p1’)Own-PriceChangesp1=p1’Fixedp2andy.7x1*(p1’)p1x1*(p1’)p1’x1*Own-PriceChangesFixedp2andm.p1=p1’8x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’)p1’p1’’x1*Own-PriceChangesFixedp2andm.9x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’’)x1*(p1’’)p1’p1’’p1’’’x1*Own-PriceChangesFixedp2andm.10x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’’)x1*(p1’’)p1’p1’’p1’’’x1*Own-PriceChangesOrdinary

demandcurve

forcommodity1Fixedp2andm.11x1*(p1’’’)x1*(p1’)x1*(p1’’)p1x1*(p1’)x1*(p1’’’)x1*(p1’’)p1’p1’’p1’’’x1*Own-PriceChangesOrdinary

demandcurve

forcommodity1p1price

offer

curveFixedp2andm.12Own-PriceChangesThecurvecontainingalltheutility-maximizingbundlestracedoutasp1changes,withp2andyconstant,isthep1-priceoffercurve.Theplotofthex1-coordinateofthep1-priceoffercurveagainstp1istheordinarydemandcurveforcommodity1.13OrdinaryGoodsAgoodiscalledanordinarygoodifthequantitydemandedofitalwaysincreasesasitsownpricedecreasesandviceversa(negativelyrelated),holdingallotherfactors,suchasprices,incomeandpreferenceconstant.OrdinaryGoodsFixedp2andy.x1x2p1price

offer

curvex1*Downward-sloping

demandcurveGood1is

ordinary?p1GiffenGoodsIfthequantitydemandedofagooddecreasesasitsown-pricedecreasesandviceversa(i.e.positivelyrelated)holdingallotherfactorsconstant,thenthegoodiscalledaGiffenGood.Note:weneedtoholdotherfactorsconstant.Thus,ifthepricechangeisalsoassociatedwithchangeinincomeorpreference,thenevenifthere’sapositiverelationbetweenpriceandquantity,itisnotcharacterizedasGiffengood.GiffenGoodsFixedp2andy.x1x2p1priceoffercurvex1*Demandcurvehas

apositivelyslopedpartGood1is

Giffen?p1Own–PriceChanges–

PerfectComplementsWhatdoesap1price-offercurvelooklikeforaperfect-complementsutilityfunction?Own-PriceChanges–PerfectComplementsOwn-PriceChanges–PerfectComplementsWithp2andyfixed,higherp1causes

smallerx1*andx2*.AsAsFixedp2andy.x1x2Own-PriceChange—

PerfectComplementsp1x1*Fixedp2andy.PerfectComplementx1x2p1’p1=p1’

’

’y/p2p1x1*Fixedp2andy.PerfectComplementx1x2p1’p1’’p1=p1’’y/p2p1x1*Fixedp2andy.PerfectComplementx1x2p1’p1’’p1’’’p1=p1’’’’’’y/p2p1x1*Ordinary

demandcurve

forcommodity1

isFixedp2andy.PerfectComplementx1x2p1’p1’’p1’’’y/p2OwnPriceChanges–

PerfectSubstitutesWhatdoesap1price-offercurvelooklikeforaperfect-substitutesutilityfunction?Own-PriceChanges–

PerfectSubstitutesandFixedp2andy.PerfectSubstitutesx2x1p1x1*Fixedp2andy.p1’p1=p1’<p2Fixedp2andy.PerfectSubstitutesx2x1p1x1*Fixedp2andy.p1’p1=p1’’=p2Fixedp2andy.PerfectSubstitutesx2x1p1x1*Fixedp2andy.p1’p1=p1’’=p2Fixedp2andy.PerfectSubstitutesx2x1p1x1*Fixedp2andy.p1’p1=p1’’=p2p2=p1’’Fixedp2andy.PerfectSubstitutesx2x1p1x1*Fixedp2andy.p1’p1’’’p2=p1’’Fixedp2andy.PerfectSubstitutesx2x1p1x1*Fixedp2andy.p1’p2=p1’’p1’’’p1price

offercurveOrdinary

demandcurve

forcommodity1InverseDemandFunctionUsuallyweask“Giventhepriceforcommodity1whatisthequantitydemandedofcommodity1?〞Butwecouldalsoasktheinversequestion“Atwhatpriceforcommodity1wouldagivenquantityofcommodity1bedemanded?〞Takingquantitydemandedasgivenandthenaskingwhatmustbepricedescribestheinversedemandfunctionofacommodity.InverseDemandFunctionp1x1*p1’Givenp1’,whatquantityis

demandedofcommodity1?

Answer:x1’units.x1’InverseDemandFunctionp1x1*p1’x1’Givenp1’,whatquantityis

demandedofcommodity1?

Answer:x1’units.Theinversequestionis:

Givenx1’unitsare

demanded,whatisthe

priceof

commodity1?Answer:p1’Cross-PriceEffectsIfanincreaseinp2,holdingp1constant,increasesdemandforcommodity1thencommodity1isagrosssubstituteforcommodity2.

reducesdemandforcommodity1thencommodity1isagrosscomplementforcommodity2.GrossSubstitutesandComplementsSubstitutes:ifthepriceishigherforonegood,youturntobuyothergoodstogiveyousatisfaction.

E.g.drinks:bubbleteavsfruitjuice;

entertainment:movievsmagazine.Complements:thingstendtobeusedtogethersowhenoneofthepricesincreases,thedemandfortheotherwilldecrease.

E.g.:cameraandmemorycards38Cross-PriceEffectsAperfect-complementsexample:soThereforecommodity2isagrosscomplementforcommodity1.Cross-PriceEffectsp1x1*p1’p1’’p1’’’Increasethepriceof

good2fromp2’top2’’

andCross-PriceEffectsp1x1*p1’p1’’p1’’’Increasethepriceof

good2fromp2’top2’’

andthedemandcurveforgood1shiftsinwards

--good1isa

complementforgood2.CrossPriceEffectForperfectsubstitutes,howwillthequantitydemandedx1changewhenp2increases?Note:itonlychangesthepointwherex1startstobepositive.42Cross-PriceEffectsp1x1*p1’p1’’p1’’’Generally,anincreasethepriceofgood2fromp2’top2’’andthedemandcurveforgood1shiftsoutwards

--good1isa

substituteforgood2.IncomeChangesHowdoesthevalueofx1*(p1,p2,m)changeasmchanges,holdingbothp1andp2constant?IncomeChangesFixedp1andp2.m’<m’’<m’’’IncomeChangesFixedp1andp2.x1’’’x1’’x1’x2’’’x2’’x2’m’<m’’<m’’’IncomeChangesFixedp1andp2.x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvem’<m’’<m’’’IncomeChangesAplotofincomeagainstquantitydemandediscalledanEngelcurve.IncomeChangesFixedp1andp2.m’<m’’<m’’’x1’’’x1’’x1’x2’’’x2’’x2’Income

offercurvex1*x2*yyx1’’’x1’’x1’x2’’’x2’’x2’m’m’’m’’’m’m’’m’’’Engel

curve;good2Engel

curve;good1IncomeChangesp1x1*p1’p1’’p1’’’Whenincomeincreases,thecurveshiftsoutwardforeachgiveprice,ifthegoodisanormalgood.IncomeEffectsAgoodforwhichquantitydemandedriseswithincomeiscallednormal.Thereforeanormalgood’sEngelcurveispositivelysloped.Generally,mostgoodsarenormalgoods.IncomeEffectsAgoodforwhichquantitydemandedfallsasincomeincreasesiscalledincomeinferior.Thereforeanincomeinferiorgood’sEngelcurveisnegativelysloped.E.g.:low-qualitygoods.IncomeChanges;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;good1IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1Income

offercurveIncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1x1*yEngelcurve

forgood1IncomeChangesandPerfectly-ComplementaryPreferencesAnotherexampleofcomputingtheequationsofEngelcurves;theperfectly-complementarycase.TheordinarydemandequationsareIncomeChangesandPerfectly-ComplementaryPreferencesRearrangedtoisolatey,theseare:Engelcurveforgood1Engelcurveforgood2Fixedp1andp2.IncomeChangesx1x2IncomeChangesx1x2y’<y’’<y’’’x1’’x1’x2’’’x2’’x2’x1’’’Fixedp1andp2.IncomeChangesx1x2y’<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.IncomeChangesx1*x2*yyx2’’’x2’’x2’y’y’’y’’’y’y’’y’’’x1’’’x1’’x1’Engel

curve;good2Engel

curve;good1Fixedp1andp2.IncomeChangesandPerfectly-SubstitutablePreferencesAnotherexampleofcomputingtheequationsofEngelcurves;theperfectly-substitutioncase.TheordinarydemandequationsareIncomeChangesandPerfectly-SubstitutablePreferencesyyx1*x2*0Engelcurve

forgood1Engelcurve

forgood2Supposep1<p2Itistheoppositewhenp1>p2.IncomeEffects--ANonhomotheticExampleQuasi-linearpreferences

Forexample,IncomeChanges;QuasilinearUtilityx2x1x1~IncomeChanges;QuasilinearUtilityx2x1x1~x1*x2*yyx1~Engel

curvefor

good2Engel

curvefor

good1IncomeChanges;Good2IsNormal,Good1BecomesIncomeInferiorx2x1x1*x2*yyEngelcurve

forgood2Engelcurve

forgood1ProportionalChangeinIncomeandPricesIfincomeandpricesallchangebythesameproportionk,howdoestheconsumerdemandchange?(e.g.samerateofinflationforpricesandincome)Recallthatpricesandincomeonlyaffectsthebudgetconstraint:p1x1+p2x2=m.

Nowitbecomes:kp1x1+kp2x2=km.

Whichclearlygetsbacktotheoriginalone.

Thus,xi(kp1,kp2,km)=xi(p1,p2,m)

Wesometimescallthisnomoneyillusion.70Example:Cobb-DouglasUtilityHowarethedemandcurvesandEngelcurveslooklikeforaCobb-Douglasutility?RecalltheCobb-Douglasutilityfunction:OnsolvingusingtheMRS=p1/p2andthebudgetconstraint,youwillhave:71Cobb-DouglasUtilityThentheordinarydemandfunctionsforcommodities1and2areCobb-DouglasUtilityOwn-Priceeffect:inverse