武汉大学MBA管理经济学第三章

DEMANDANALYSISOVERVIEWofChapter3DemandRelationshipsDemandElasticitiesIncomeElasticitiesCrossElasticitiesofDemandAppendix3A:IndifferenceCurvesHealthCare&CigarettesRaisingcigarettetaxesreducessmokingInCanada,$4forapackofcigarettesreducedsmoking38%inadecadeButcigarettetaxesalsohelpsfundhealthcareinitiativesTheissuethen,shouldwefindataxratethatmaximizestaxrevenues?Orataxratethatreducessmoking?DemandAnalysisAnimportantcontributortofirmriskarisesfromsuddenshiftsindemandfortheproductorservice.Demandanalysisservestwomanagerialobjectives:(1)itprovidestheinsightsnecessaryfor effectivemanagementofdemand,and(2)itaidsinforecastingsalesandrevenues.DemandCurves

IndividualDemandCurve

thegreatestquantityofagooddemandedateachpricetheconsumersareWillingtoBuy,ceterisparibus.WillingtoBuyUnwillingtoBuy$/QQ/timeunitTheMarketDemandCurve

isthehorizontalsumoftheindividualdemandcurves.

TheDemandFunction

includesallvariablesthatinfluencethequantitydemanded

437Sam DianeMarketQ=f(P,Ps,Pc,

I,W,E)

++-??+SupplyCurvesFirmSupplyCurve

-thegreatestquantityofagoodsuppliedateachpricethefirmisprofitablyabletosupply,ceterisparibus.$/QQ/timeunitAbletoProduceUnabletoProduce

TheMarketSupplyCurve

isthehorizontalsumofthefirmsupplycurves.

TheSupplyFunction

includesallvariablesthatinfluencethequantitysupplied

437Acme UniversalMarketQ=g(P,W,R,

TC)

+--+Equilibrium:NoTendencytoChangeSuperimposedemandandsupplyIfNoExcessDemandandNoExcessSupplyNotendencytochangeDSPewilling&ableQPDownwardSlopeReasonsthatpriceandquantityarenegativelyrelatedinclude:incomeeffect--asthepriceofagooddeclines,theconsumercanpurchasemoreofallgoodssincehisorherrealincomeincreased.substitutioneffect--asthepricedeclines,thegoodbecomesrelativelycheaper.Arationalconsumermaximizessatisfactionbyreorganizingconsumptionuntilthemarginalutilityineachgoodperdollarisequal:OptimalityConditionisMUA/PA=MUB/PB=MUC/PC=... IfMUperdollarinAandBdiffer,theconsumercanimproveutilitybypurchasingmoreoftheonewithhigherMUperdollar.ComparativeStatics

andtheSupply-DemandModelSupposeashiftinIncome,andthegoodisa“normal”goodDoesDemandorSupplyShift?Supposewagesrose,whatthen?DSe1PQElasticityasSensitivityElasticityismeasureofresponsivenessorsensitivityBewareofusingSlopesbushels hundredtonsprice priceper perbu. buSlopeschangewithachangeinunitsofmeasurePriceElasticityEP=%changeinQ/%changeinPShortcutnotation:EP=

%

Q/%

PApercentagechangefrom100to150Apercentagechangefrom150to100ArcPriceElasticity--averagesoverthetwopointsDarcpriceelasticityArcPriceElasticityExampleQ=1000atapriceof$10ThenQ=1200whenthepricewascutto$6FindthepriceelasticitySolution:EP=

%

Q/%

P=+200/1100 -4/8or-.3636.Theanswerisanumber.A1%increaseinpricereducesquantityby.36percent.PointPriceElasticityExampleNeedademandcurveordemandfunctiontofindthepriceelasticityatapoint. EP=

%

Q/%

P=(

Q/

P)(P/Q) IfQ=500-5•P,findthepointprice elasticityatP=30;P=50;andP=80EQ•P=(

Q/

P)(P/Q)=-5(30/350)=-.43EQ•P=(

Q/

P)(P/Q)=-5(50/250)=-1.0EQ•P=(

Q/

P)(P/Q)=-5(80/100)=-4.0PriceElasticity(bothpointpriceandarcelasticity)IfEP=-1,unitelasticIfEP>-1,inelastic,e.g.,-0.43IfEP<-1,elastic,e.g.,-4.0priceelasticregionunitelasticinelasticregionStraightlinedemandcurveTRandPriceElasticities

Ifyouraiseprice,doesTRrise?Supposedemandiselastic,andraiseprice.TR=P•Q,so,%

TR=%

P+%

QIfelastic,P,butQalotHenceTRFALLS!!!Supposedemandisinelastic,andwedecidetoraiseprice.WhathappenstoTRandTCandprofit?AnotherWaytoRememberLineardemandcurveTRonothercurveLookatarrowstoseemovementinTRElasticUnitElasticInelasticTRQQ1979DeregulationofAirfaresPricesdeclinedPassengersincreasedTotalRevenueIncreasedWhatdoesthisimplyaboutthepriceelasticityofairtravel?DeterminantsofthePriceElasticityThenumberofclose

substitutesmoresubstitutes,moreelasticTheproportionofthebudgetlargerproportion,moreelasticThelongerthe

time

periodpermittedmoretime,generally,moreelasticconsiderexamplesofbusinesstravelversusvacationtravelforallthreeabove.IncomeElasticity

EI=

%

Q/%

I=(

Q/

I)(I/Q)

arcincomeelasticity:supposedollarquantityoffoodexpendituresoffamiliesof$20,000is$5,200;andfoodexpendituresrisesto$6,760forfamiliesearning$30,000.Findtheincomeelasticityoffood %

Q/%

I

=(1560/5980)•(10,000/25,000)=.652DefinitionsIfEIispositive,thenitisanormalorincomesuperiorgoodsomegoodsareLuxuries:EI

>1somegoodsareNecessities:EI<1IfEQ•Iisnegative,thenit’san

inferior

goodconsider:ExpendituresonautomobilesExpendituresonChevroletsExpenditureson1993ChevyCavalierPointIncomeElasticityProblemSupposethedemandfunctionis:

Q=10-2•P+3•IfindtheincomeandpriceelasticitiesatapriceofP=2,andincomeI=10So:Q=10-2(2)+3(10)=36EI=(

Q/

I)(I/Q)=3(10/36)=.833EP=(

Q/

P)(P/Q)=-2(2/36)=-.111Characterizethisdemandcurve!CrossPriceElasticitiesEX=

%

Qx/%

Py

=(

Qx/

Py)(Py/Qx)Substituteshavepositivecrosspriceelasticities:Butter&MargarineComplementshavenegativecrosspriceelasticities:VCRmachinesandtherentalpriceoftapesWhenthecrosspriceelasticityiszeroorinsignificant,theproductsarenotrelatedHOMEWORKPROBLEM:

Findthepointpriceelasticity,thepointincomeelasticity,andthepointcross-priceelasticityatP=10,I=20,andPs=9,ifthedemandfunctionwereestimatedtobe:

Qd=90-8·P+2·I+2·Ps.

Isthedemandforthisproductelasticorinelastic?Isitaluxuryoranecessity?Doesthisproducthaveaclosesubstituteorcomplement?Findthepointelasticitiesofdemand.IndifferenceCurveAnalysis

Appendix3AConsumersattempttomaxhappiness,orutility:U(X,Y)Subjecttoanincomeconstraint:

I=Px•X+Py•YGraphin3-dimensionsYXUUoUo

ConsumerChoice-assumeconsumerscanrankpreferences,thatmoreisbetterthanless(nonsatiation),thatpreferencesaretransitive,andthatindividualshavediminishingmarginalratesofsubstitution.

Thenindifferencecurvesslopedown,neverintersect,andareconvextotheorigin.XY567976convexUoU1U2giveup2XforaYXYYUoU1acdemandbIndifferenceCurves

• Wecan"derive"ademandcurvegraphicallyfrommaximizationofutilitysubjecttoabudgetconstraint.Aspricefalls,wetendtobuymoredueto(i)the

IncomeEffectand(ii)theSubstitution Effect.PyConsumerChoice&LagrangiansTheconsumerchoiceproblemcanbemadeintoaLagrangianMaxL=U(X,Y)-

{Px•X+Py•Y-I} i)

L/

X=

U/

X-

Px=0 MUx=Px ii)

L/

Y=

U/

Y-

Py=0