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Economicsofconsumerbeh__iourThewillingnessofconsumerstopurchaseaproductorservi__isessentialforanyfirmtoearnaprofit.Firmsneedtobeabletoesti__teandforecastthede__ndfortheirproducts.Thereforethetheoryofconsumerbeh__iourisanessentialpartof__nagerialeconomics.BasicassumptionsofconsumertheoryInthetheoryofconsumerbeh__iouritisassumedthatallindividuals__keconsumptiondecisionsinorderto__ximisetheirsatisfactionfromconsumingvariousgoodsandservi__s.Howevereachconsumerhasalimitedpersonalincome.Forsimplicityitisassumedthatallconsumersspendalloftheirpersonalincome.Itisalsoassumedthateachconsumerhasperfectknowledge:theyknowaboutallproductsthatare__ailabletheyknowthepri__softheproductsandtheyknowtheirownpersonalincome.Itisassumedthatconsumerscanrankcombinationsofgoodsandservi__sconsumedorconsumptionbundlesaccordingtothelevelofsatisfactiontheyobtainfromeachbundleseeFigure
1.
1.Preferen__sarecompleteiftheconsumeralwayscan__keoneofthefollowingresponseswhenaskedabouttheirpreferen__sbetweenanytwoconsumptionbundles:
1.IpreferbundleAtobundleBAB
2.IpreferbundleBtobundleABA
3.IamindifferentbetweenbundlesAandBA~B.Itisalsoassumedthatpreferen__saretransitive:ifABandBCthenAC.Finallyitisassumedthatmoreisalwayspreferredtoless:h__ingmoreofagoodalwaysincreasessatisfactionandneverdecreasessatisfaction.Utilityisthetermusedbyeconomistsforthesatisfactionthatisobtainedfromconsumption.Althoughutilityisnotdirectlymeasurableeconomistsassumethatpreferen__scanberepresentedusingautilityfunction.Thenumericalvaluesassignedtoutilitybytheutilityfunctionarearbitrarybecauseutilityisnotobservableormeasurable.Foraconsumerwhoconsumesonlytwogoodswecanwrite:U=fXYwhereXandYarethequantitiesconsumedofgoodsXandY.ForaconsumerwhoconsumesNgoodswecanwrite:U=fX1X2X
3...XNwhereX1X2X
3...XNarethequantitiesconsumedofgoods
123...N.Withoutanylossofgeneralitymostofthefollowing____ysiswillbedevelopedforthetwo-goodcase.Indifferen__curvesAnindifferen__curveisasetofpointsrepresentingdifferentcombinationsorbundlesofgoodsandservi__seachofwhichprovidesthesamelevelofutility.Theconsumerisindifferentbetweenallpointslocatedonthesameindifferen__curveseeFigure
1.
2.Indifferen__curvesarealwaysdownwardsloping.IfmoreofGoodXisaddedsomeofGoodYmustbetakenawayinorderto__intainthesamelevelofutility.Indifferen__curvesarealwaysconvex:IfverylittleofXandlotsofYisbeingconsumedpointAtheconsumerwouldbepreparedtosacrifi__alargeamountofYinordertogainoneadditionalunitofX.IflotsofXandverylittleofYisbeingconsumedpointCtheconsumerwouldbepreparedtosacrifi__onlya__allamountofYinordertogainoneadditionalunitofX.__rginalrateofsubstitutionThe__rginalrateofsubstitutionMRSmeasuresthenumberofunitsofYthatmustbetakenawayforeachunitofXthatisaddedsoasto__intainaconstantlevelofutility.TheconsumerisindifferentbetweenAX=10Y=60andBX=20Y=
40.TheconsumerisalsoindifferentbetweenCX=40Y=20andDX=50Y=
15.FromBtoAMRS=FromDtoCMRS=Atanyindividualpointontheindifferen__curvetheMRSistheslopeoftheindifferen__curveatthatpoint.UsuallytheMRSisexpressedwithouttheminus-sign;i.e.fromBtoAMRS=2;andfromDtoCMRS=.ThereforeMRSistheabsolutevalueoftheslopeoftheindifferen__curve.Thecorrectdefinitionforthe__rginalrateofsubstitutionisMRS=Duetotheconvexityoftheindifferen__curveMRSdecreasesasXincreases.Indifferen____psAnindifferen____pshowsacompletesetofindifferen__curveseachrepresentingadifferentlevelofsatisfactionorutility.Higherindifferen__curvesrepresenthigherlevelsofutilitybecauseoftheassumptionthatmoreisalwayspreferredtolessseeFigure
1.
3.MRSand__rginalutilityThereisacloserelationshipbetweenMRSand__rginalutility.__rginalutilityistheamountofadditionalsatisfactionaconsumerobtainsfroma__allchangeintheconsumptionofagood.Asyoueatmoreandmoreapplestheamountofadditionalsatisfactionyouobtainfromeatingeachadditionalapplebecomes__allerand__aller.Thisisknownasthelawofdiminishing__rginalutility.LetXandYdenote__allchangesintheconsumptionofGoodsXandY.LetMUXandMUYdenotethe__rginalutilitiesofGoodsXandY.LetUdenotethechangeinutilityresultingfromthe__allchangesinconsumptionXandY.WecanwriteU=MUXX+MUYYIfXandYarechosensothattheconsumerre__insonthesameindifferen__curvethenMRS=andU=
0.WecanwriteMUXX+MUYY=0ororMRS=AstheconsumptionofGoodXincreasesMUXdecreasesandMRSalsodecreases.Theconsumer’sbudgetconstraintThebudgetlineAbudgetlineshowsallcombinationsorbundlesofgoodstheconsumercanaffordtobuyfromafixedincome.Itisassumedthatthepri__sperunitofGoodXandGoodYconsumedaredeterminedinthe__rketsforthesegoodsandarethereforetreatedbytheconsumerasfixed.Supposetheconsumer’sincomeis$1000andsupposethepri__ofGoodXis$5perunitandthepri__ofGoodYis$10perunit.Wecanwrite5X+10Y=1000TheconsumercanaffordeitherX=0Y=100orX=40Y=80orX=120Y=40orX=200Y=0orvariousotherlinearcombinationsofXandYforwhichtotalexpenditureis
1000.SolvingforYintermsofX10Y=1000–5XorY=100–XLetMdenotetotalincomeortotalexpenditureandletPXandPYdenotethepri__sofGoodsXandY.WecanwritePXX+PYY=MorFigure
1.4showstheconsumer’sbudgetline.TheslopeofthebudgetlineshowstheamountofYthatmustbegivenupifonemoreunitofXispurchasedinorderto__intainanunchangedleveloftotalexpenditure.TheslopeofthebudgetlinedependsonPXandPY.InFigure
1.4PX=5PY=10andM=
1000.•IfallofthebudgetisspentonXtheconsumercanafford1000/5=200unitsofX.•IfallofthebudgetisspentonYtheconsumercanafford1000/10=100unitsofY.IngeneralletXandYdenote__allchangesintheconsumptionofGoodsXandY.LetMdenotethechangeinexpenditureresultingfromthesechangesinconsumptionXandY.WecanwriteM=PXX+PYYIfXandYarechosensothattotalexpenditurere__insunchangedandtheconsumerre__insonthebudgetlinethenM=
0.WecanwritePXX+PYY=0orTheslopeofthebudgetlineistheratioofthepri__softhetwogoods.InFigure
1.4theslopeofthebudgetlineis.ShiftsinthebudgetlineAchangeinincomecausesaparallelshiftinthebudgetlineseeFigure
1.5A.ForexamplewhenM=1000PX=5andPY=10theconsumercanaffordX=0Y=100orX=200Y=0onbudgetlineAB.IfMincreasesto1200theconsumercanaffordX=0Y=120orX=240Y=0onbudgetlineRN.Achangeinthepri__ofeithergoodcausesthebudgetlinetopivotseeFigure
1.5B.ForexamplewhenM=1000PX=5andPY=10theconsumercanaffordX=0Y=100orX=200Y=0onbudgetlineAB.IfPXdecreasesto4theconsumercanaffordX=0Y=100orX=250Y=0onbudgetlineAD.Utility__ximizationThebudgetlineshowsallbundlesofgoodsthatare__ailabletotheconsumergivenlimitedincomeandcurrentpri__s.Theindifferen____preflectstheconsumer’spreferen__sbetweenallpossiblebundlesofgoods.Theconsumer__ximizesutilitysu__ecttothebudgetconstraintbyselectingthebundleofgoodsrepresentedbythepointoftangencybetweenthebudgetlineandthehighestattainableindifferen__curve.InFigure
1.6M=400PX=4andPY=8whereX=quantityofburgersY=quantityofpizzas.ByspendingallofthebudgetoneitherburgersorpizzastheconsumercouldaffordeitherX=0Y=50orX=100Y=
0.Eisthepointonthebudgetlineatwhichutilityis__ximizedX=40Y=
30.AtEtheconsumerislocatedonthehighestattainableindifferen__curveIII.AtEwecanwriteMRS=MRS=theslopeoftheindifferen__curveistherateatwhichtheconsumeriswillingtosubstituteGoodYforGoodX.=theslopeofthebudgetlineistherateatwhichtheconsumerisabletosubstituteGoodYforGoodX.AtpointsotherthanEinFigure
1.6MRS.e.g.atpointBMRSandatpointCMRS.Theconsumer__ximizesutilitysu__ecttothebudgetconstraintwhentherateatwhichtheconsumeriswillingtosubstituteequalstherateatwhichtheconsumerisabletosubstitute.NotethatwecanalsowriteMRS=orTheconsumer__ximizesutilitysu__ecttothebudgetconstraintwhenthe__rginalutilityperdollarspentonGoodXequalsthe__rginalutilityperdollarspentonGoodY.Ifthisconditionisnotsatisfiedtheconsumercanincreaseutilitybyshiftingexpenditurefromthegoodwiththelowerratio__rginalutilitypri__tothegoodwiththehigherratio.Foraconsumerwhoseeksto__ximizeutilitysu__ecttoabudgetconstraintwhenthereareNgoodsratherthan2thebudgetlinecanbewrittenP1X1+P2X2+...+PNXN=MTheconditionsforutility__ximizationsu__ecttothebudgetconstraintare:forallijorIndividualconsumerand__rketde__ndcurvesThetheoryofconsumerbeh__iourformsthebasisforthederivationofde__ndcurves.Wecanusethetheoryofutility__ximizationsu__ecttoabudgetconstrainttoderiveade__ndcurveforanindividualconsumer.Thenbyaggregatingthede__ndcurvesofallconsumerswecanderivea__rketde__ndcurveforeachproductorservi__.Anindividualconsumer’sde__ndcurveforGoodXisderivedbyexaminingtheeffectofchangesinthepri__ofGoodXonthequantityofGoodXtheconsumerwishestopurchaseandconsume.InFigure
1.7theconsumer’sincomeisM=1000andinitiallythepri__sofGoodsXandYarePX=10andPY=
10.WhenPX=10the__ximumamountofGoodXtheconsumercouldpurchaseis100units.Theconsumeractuallypurchases50unitsofGoodXpointoftangencybetweenthebudgetlineandindifferen__curveI.WhenPX=8the__ximumamountofGoodXtheconsumercouldpurchaseis125units.Theconsumeractuallypurchases65unitsofGoodXpointoftangencybetweenthebudgetlineandindifferen__curveII.WhenPX=5the__ximumamountofGoodXtheconsumercouldpurchaseis200units.Theconsumeractuallypurchases90unitsofGoodXpointoftangencybetweenthebudgetlineandindifferen__curveIII.Theindividualde__ndcurveshowninthelowerpanelofFigure
1.7showstherelationshipbetweenPXandthequantityofGoodXthatispurchased.Thede__ndcurveisdownward-sloping.Asthepri__ofGoodXdecreasesthequantityofGoodXtheconsumerpurchasesandconsumesincreases.Toobtainthe__rketde__ndcurveforGoodXweaggregatetheindividualde__ndcurvesofallpotentialcustomers.The__rketde__ndcurveisahorizontalsum__tionoftheindividualde__ndcurvesseeFigure
1.
8.InFigure
1.8PX=4isthe__ximumpri__atwhich12unitsofGoodXcanbesoldonthe__rket.PX=4canalsobeinterpretedasthevaluetoeachconsumerofthelastunitofGoodXtheconsumerpurchased.Thereforethede__ndcurvealsoshowsthe__rginalbenefittosocietyofthelastunitconsumedbyeverybuyerinthe__rket.SubstitutionandincomeeffectsWhenthepri__ofGoodXfallsconsumerswilltendtoswitchexpenditurefromGoodYtoGoodXbecauseGoodXhasbecomerelativelycheaper.De__ndforGoodXtendstoincreaseandde__ndforGoodYtendstodecrease.Thisisknownasasubstitutioneffect.Howeverwhenthepri__ofGoodXfallstherealvalueofconsumers’incomesisincreased.Thisincreaseinrealincomes__yallowconsumerstoenjoyincreasedconsumptionofbothgoodsalthoughtheconsumermightnotne__ssarilychoosetoconsumemoreofboth.Thiseffectwhicharisesfromthechangeintheconsumer’srealpurchasingpowerisknownasanincomeeffect.SubstitutioneffectThesubstitutioneffectismeasuredasthechangeintheconsumptionofGoodXthatwouldoccuriftheconsumerre__inedontheoriginalindifferen__curveafterthepri__changetookpla__.InFigure
1.9AinitiallyM=150PX=15andPY=
7.
5.ThebudgetlineisABandtheconsumer__ximizesutilitysu__ecttothebudgetconstraintatEattainingindifferen__curveI.Theconsumerpurchases3unitsofX.Supposethepri__ofGoodXfallstoPX=
6.ThebudgetlinepivotsfromABtoADanditbecomespossiblefortheconsumertoattainahigherindifferen__curvethanI.Theconsumer__ximizesutilitysu__ecttothebudgetconstraintatFattainingindifferen__curveII.Theconsumerpurchases12unitsofX.Thetotaleffectofthefallinthepri__ofGoodXfromPX=15toPX=6isanincreaseintheconsumptionofGoodXof9unitsfromX=3toX=
12.ThesubstitutioneffectisidentifiedbyconstructingahypotheticalbudgetlineLZparalleltoADandtangentialtoindifferen__curveI.IfthebudgetlinewasLZtheconsumerwould__ximizeutilitysu__ecttothebudgetconstraintatGattainingindifferen__curveI.Theconsumerpurchases8unitsofX.Thesubstitutioneffectofthefallinthepri__ofGoodXfromPX=15toPX=6isanincreaseintheconsumptionofGoodXof5unitsfromX=3toX=
8.Thesubstitutioneffectisthechangeinconsumptionthatwouldoccuriftheconsumerwerefor__dbyahypotheticalreductioninincometore__inonthesameindifferen__curveasbefore.IncomeeffectTheincomeeffectfromachangeinthepri__ofGoodXisthechangeinconsumptionofGoodXduetothechangeintheconsumer’spurchasingpower.Theincomeeffectismeasuredbythechangeinconsumptionwhentheconsumermovesfromtheopti__lpointonthehypotheticalbudgetlinetotheopti__lpointonthenewactualbudgetline.ThereforeinFigure
1.9Atheincomeeffectofthedecreaseinthepri__ofGoodXfromPX=15toPX=6isafurtherincreaseintheconsumptionofGoodXof4unitsfromX=8toX=
12.InFigure
1.9Atheopti__lpointonthenewactualbudgetlineislabelledF.OverallconsumptionofGoodXincreasesfromX=3toX=
12.Thesubstitutioneffectis+5andtheincomeeffectis+
4.InFigure
1.9Btheopti__lpointonthenewactualbudgetlineisalsolabelledF.OverallconsumptionofGoodXincreasesfromX=3toX=
6.Thesubstitutioneffectis+5andtheincomeeffectis–
2.Thesubstitutioneffectofadecreaseinpri__isalwayspositive.Buttheincomeeffectcanbeeitherpositiveornegativedependinguponthecurvatureoftheindifferen__curves.Anor__lgoodhasapositiveincomeeffect.Anincreaseinincomeoranincreaseinpurchasingpowerresultsinanincreaseinconsumption.Aninferiorgoodhasanegativeincomeeffect.Anincreaseinincomeoranincreaseinpurchasingpowerresultsinadecreaseinconsumption.__rtaingoodsconsumedbypoorerfamiliesonly__yh__ethestatusofinferiorgoods.Areductioninthepri__ofanor__lgoodalwayscausesanincreaseinde__ndbecauseboththesubstitutioneffectandtheincomeeffectarepositive.Thereforethede__ndcurveforanor__lgoodisalwaysdownward-sloping.Areductioninthepri__ofaninferiorgoodcausesanincreaseinde__ndprovidedthepositivesubstitutioneffectex__edsthenegativeincomeeffect.Ifthisconditionissatisfiedthede__ndcurveforaninferiorgoodisdownward-sloping.Intheoryitispossiblethatthenegativeincomeeffectcouldex__edthepositivesubstitutioneffect.AninferiorgoodwiththispropertyisknownasaGiffengood.Thede__ndcurveforaGiffengoodisupward-slopingbecauseareductioninpri__causesareductioninde__ndthroughthenegativeincomeeffect.Inpracti__howevertheexisten__ofGiffengoodshasnotbeendemonstratedempirically.Pri__elasticityofde__ndQuantityde__ndedandpri__areinverselyrelated.Butbyhowmuchdoesquantityde__ndedincreasewhenafirmdecidestodecreaseitspri__Pri__elasticityofde__ndmeasurestheresponsivenessofquantityde__ndedtochangesinpri__.E=Sin__pri__andquantityde__ndedareinverselyrelatedthenumeratorandthedenominatorh__eoppositesignsandEisalwaysnegative.Pri__elasticityandtotalrevenuePri__elasticitycanbeusedtoanswerthefollowingimportantquestion:‘whatwouldhappentoafirm’stotalrevenueTRifthefirmdecidestodecreaseitspri__’Byitselfadecreaseinpri__wouldtendtodecreaseTR.Butquantityde__ndedandsoldincreasesduetothedecreaseinpri__.ThisincreaseinQmightbesufficienttooffsettheeffectofthedecreaseinPonTR.ThereforeTRmightincreaseordecrease:TR=PQMorespecifically:Ifthe%changeinQthe%changeinPTRwillincrease;Ifthe%changeinQ=the%changeinPTRwillre__inunchanged;Ifthe%changeinQthe%changeinPTRwilldecrease.Let|E|denotetheabsolutevalueofpri__elasticityofde__nd.ForexampleifE=–2then|E|=
2.Therelationshipbetweenpri__elasticityandTRisasfollows:If|E|1TRincreaseswhenPdecreases.The%changeinQisgreaterthanthe%changeinP.Thede__ndcurveis‘pri__elastic’.If|E|=1TRre__insunchangedwhenPdecreases.The%changeinQequalsthe%changeinPsotheeffectonTRisneutral.If|E|1TRdecreaseswhenPdecreases.The%changeinQis__allerthanthe%changeinP.Thede__ndcurveis‘pri__inelastic’.Factorsaffectingpri__elasticityofde__nd__ailabilityofsubstitutes.Thecloserthesubstitutesforagoodorservi__themorepri__elasticthede__nd.Per__ntageoftheconsumer’sbudget.Thehighertheper__ntageoftheconsumer’stotalbudgetallocatedtothegoodorservi__themorepri__elasticthede__nd.Thetimeperiodofadjustment.Thelongertheperiodofadjustmentthemorepri__elasticthede__nd–becausetheconsumerhasmoretimetoswitchtosubstitutegoodsorservi__s.Calculatingpri__elasticityofde__ndNotethat%changeinquantity=100Q/Qand%changeinpri__=100P/PTheformulaforpri__elasticityofde__ndcanbewritten:E=Dividingtopandbottomby100wecanwrite:E=orE=ThisfinalexpressiongivesanalternativemethodforworkingoutEwhichisoftenthemostconvenienttouseinpracti__.Pri__elasticitycanbemeasuredeitherover1anintervalorarcalongthede__ndcurveor2ataspecificpointonthede__ndcurve.Tocomputeelasticityoveraninterval:whereQandParethechangesinquantityandpri__overtheintervaland__eragePand__erageQarethe__eragesofthevaluesofPandQattheendsoftheinterval.Tocomputeelasticityatapoint:E=whereQ/Pistheslopegra___ntofthede__ndcurveatthepointandPandQarethevaluesatthepoint.__rginalrevenuede__ndandpri__elasticity__rginalrevenueistheadditiontototalrevenueattributabletosellingoneextraunitofoutput:MR=TheexampleshowninTable
1.1andFigure
1.10illustratestherelationshipbetweenpri__Pquantityde__ndedQtotalrevenueTRand__rginalrevenueMR.MR=PforthefirstunitofoutputsoldQ=
1.MRPforeachadditionalunitsoldQ
1.Inordertosellanadditionalunitthefirmmustredu__thepri__foralloftheunitsitiscurrentlysellingandloserevenueontheseunits.ThereforeforQ1the__rginalrevenueobtainedfromsellinganadditionalunitisalwayslessthanthepri__chargedforthesaleoftheadditionalunit.MR0forQ
6.MRispositivebecausethepri__chargedfortheadditionalunitisgreaterthanthelossofrevenuefromh__ingtoredu__thepri__ofalltheunitsthatarecurrentlysold.MR=0forQ=
6.MRiszerobecausethepri__chargedfortheadditionalunitequalsthelossofrevenuefromh__ingtoredu__thepri__ofalltheunitsthatarecurrentlysold.MR0forQ
6.MRisnegativebecausethepri__chargedfortheadditionalunitislessthanthelossofrevenuefromh__ingtoredu__thepri__ofalltheunitsthatarecurrentlysold.Thereisacloserelationshipbetween__rginalrevenueMRandpri__elasticityofde__ndE.WhenMR0|E|1becauseTRincreasesasQincreasesandPdecreases.WhenMR=0|E|=1becauseTRre__insunchangedasQincreasesandPdecreases.WhenMR0|E|1becauseTRdecreasesasQincreasesandPdecreases.Figure
1.11illustratestherelationshipbetweenpri__Pquantityde__ndedQtotalrevenueTR__rginalrevenueMRandpri__elasticityofde__ndE.The__the__ticalrelationshipbetweenMRPandEis:WhenE–1or|E|1MR
0.e.g.ifE=–2MR=P1–1/2=1/2PWhenE=–1or|E|=1MR=
0.e.g.ifE=1MR=P1–1=0WhenE–1or|E|1MR
0.e.g.ifE=–1/2MR=P[1–1/1/2]=–POtherelasticitiesThepri__ofagoodorservi__isnottheonlydeterminantofthede__ndforthatgoodorservi__.De__ndmightalsodependupon:iIncome.iiThepri__sofgoodsandservi__sthataresubstitutesorcomplements.Inadditiontopri__elasticityelasticitiescanbealsodefinedtoshowthesensitivityofquantityde__ndedtochangesinincomeorchangesinthepri__sofothergoodsandservi__s.Incomeelasticityofde__ndEM=Incomeelasticityispositiveforanor__lgoodandnegativeforaninferiorgood.Cross-pri__elasticityofde__ndEXR=Cross-pri__elasticityispositiveifGoodRisasubstituteforGoodX.teaandcoffee:ifthepri__ofcoffeeincreasespeoplebuylesscoffeeanddrinkmoretea.Cross-pri__elasticityisnegativeifGoodRisacomplementtoGoodX.gasolineandcars:ifthepri__ofcarsincreasespeoplebuyfewercarsanduselessgasoline.。