课件大纲中级微观济学

第十第十四章Consumer’s消费者剩MoneyequivalentofutilitygainstoConsumer’sChangesinconsumer’sCompensatingvariations补偿变Producer’ssurplus生产者剩2MonetaryMonetaryMeasuresofGains-Youcanbuyasmuchasyouwishatfixedprice.Q:WhatisthemostyouwouldA:thevalueofthegains-to-Howcansuchgains-to-tradebe3MonetaryMeasuresMonetaryMeasuresofGains-ThreesuchmeasuresConsumer’sEquivalentVariationCompensatingVariation补偿变4MoneyMoneyEquivalentUtilitySupposegasolinecanbeboughtonlyinlumpsofonegallon(discreteUser1todenotethemostasingleconsumerwouldpayfora1stgalloncallthisherreservationprice保留forthe1stgallon.r1isthemoneyequivalentofthemarginalutilityofthe1stgallon.5MoneyEquivalentMoneyEquivalentUtilityNowthatshehasonegallon,user2todenotethemostshewouldpayfora2ndgallon--thisisherreservationpriceforthe2ndgallon.r2isthemoneyequivalentofthemarginalutilityofthe2ndgallon.6MoneyEquivalentUtilityMoneyEquivalentUtilityGenerally,ifshealreadyhasn-1gallonsofgasolinethenrndenotesthemostshewillpayforannthrnisthemoneyequivalentofmarginalutilityofthe7MoneyEquivalentUtilityMoneyEquivalentUtilityr1+…+rnwillthereforebethemoneyequivalentofthetotalchangetoutilityfromacquiringngallonsofgasolineatapriceof$0.willber1+…+rn-moneyequivalentofthetotalchangetoutilityfromacquiringngallonsofgasolineatapriceof$pGeach.8MoneyEquivalentUtilityReservationPriceCurveformoneyvalueofnetutility($)Res.r10r26r4prMoneyEquivalentUtilityReservationPriceCurveformoneyvalueofnetutility($)Res.r10r26r4pr50G123456Gasoline9MoneyEquivalentUtilityifgasolinecanbepurchasedinanyquantity,MoneyEquivalentUtilityifgasolinecanbepurchasedinanyquantity,thereservationpricecurvemoneyvalueofnetutilityConsumer’sConsumer’sAconsumer’sreservation-pricecurveisdifferentfromtheordinarydemandcurveduetoincomeeffects.对一种商品的保留价格取决于其他商品的消Areservation-pricecurvedescribessequentiallythevaluesofsuccessivesingleunitsofacommodity;Anordinarydemandcurvedescribesthemostthatwouldbepaidforqunitsofacommoditypurchasedsimultaneously.MoneyMoneyEquivalentUtilityAsanapproximation,thereservation-pricecurveisreplacedwiththeconsumer’sordinarydemandcurve.Consumer’sSurplusisdefinedastheareaundertheordinarydemandcurvebutabovethepriceIftheconsumer’sutilityfunctionisquasi-linearinincome,thentherearenoincomeeffectsandConsumer’sSurplusisanexactmoneymeasureofgains-to-trade.Consumer’sTheconsumer’sutilityConsumer’sTheconsumer’sutilityfunctionisquasilinearinx2.U(x1,x2)v(x1)x2Takep2=ThenthechoiceproblemistoU(x1,x2)v(x1)x2subjectp1x1x2Quasi-Linearp1x1Quasi-Linearp1x1x2U(x1,x2)v(x1)Reservationpricesforthefirst3v(0)+m=v(1)+m-r1r1=v(1)-v(1)+m-r2=v(2)+m-2r2r2=v(2)-v(2)+m-2r3=v(3)+m-3r3r3=v(3)-r1+r2+r3=v(3)-Thisisthegrossbenefit（总收益）ofconsuming3unitsofgoodx.Quasi-LinearGrossbenefit=($)Res.r10r2r3r4r501Quasi-LinearGrossbenefit=($)Res.r10r2r3r4r50123456GasolineQuasi-LinearU(xQuasi-LinearU(x1,x2)v(x1)p1x1x2Whenx1=3,x2=m-U(3,m-3p)=v(3)+m-Ifconsume0goodx1,thenx2=mU(0,m)=mThenetbenefitofconsumingx1U(3,m-3p)–U(0,m)=v(3)-3pIfnunitsofxthenutilitygainisv(n)–pnnetutilityornetbenefit（净收益Quasi-LinearNetbenefit=v(3)-($)Res.r10r2r3r4r50Quasi-LinearNetbenefit=v(3)-($)Res.r10r2r3r4r50p123456GasolineConsumer’sTheconsumer’sutilityConsumer’sTheconsumer’sutilityfunctionisquasilinearinx2.U(x1,x2)v(x1)x2Takep2=ThenthechoiceproblemistoU(x1,x2)v(x1)x2subjectp1x1x2Consumer’sThatConsumer’sThatis,choosex1tov(x1)mThefirst-orderconditionv'(x1)p1p1v'(x1ThatThisistheequationoftheconsumer’sordinarydemandforcommodity1.Consumer’sOrdinarydemandcurve,v'(x1p1Consumer’sOrdinarydemandcurve,v'(x1p1 CS01v'(x1)dx1v(x')v(0)p'1 isexactlytheutilitygainfromconsumingx1’1.111Consumer’sConsumer’sConsumer’sSurplusisameasureofutilitygainedfromconsumingcommodity1whentheconsumer’sutilityfunctionisquasi-linearincommodity2.OtherwiseConsumer’sSurplusisanThechangetoaconsumer’stotalutilityduetoachangetop1isapproximatelythechangeinherConsumer’sSurplus.Consumer’sp1(x1),inverseordinarydemandcurveforcommodity1. 1LostConsumer’sp1(x1),inverseordinarydemandcurveforcommodity1. 1Lost1111CompensatingVariationCompensatingVariationEquivalentTwoadditionalmoneymeasuresofthetotalutilitychangecausedbyapricechangeareCompensatingVariationandEquivalentVariation.CompensatingCompensatingp1Whatistheleastextraincomethat,atthenewprices,justrestorestheconsumer’soriginalutilitylevel?Compensatingp2isx2 'm1p1xCompensatingp2isx2 'm1p1x1p2x2p"x" 22p"x'"pm2 CV=m2-x1111EquivalentEquivalentp1Whatistheleastextraincomethat,attheoriginalprices,justrestorestheconsumer’soriginalutilitylevel?价格变化以前，要让消费者境况跟价Equivalentp2isx2 'm1Equivalentp2isx2 'm1p1x1p2x2p"x" 22 p'x'"2 EV=m1-x 1111Consumer’sSurplus,Consumer’sSurplus,VariationandEquivalentWhentheconsumer’spreferencesarequasi-linear,allthreemeasuresarethesame.ConsiderfirstthechangeConsumer’sSurpluswhenp1fromp1’top1”.Consumer’sSurplus,VariationandEquivalentU(x1,x2)Consumer’sSurplus,VariationandEquivalentU(x1,x2)v(x1)x2CS(p')v(x')v(0)p'11 andsothechangeinCSwhenp1risesfromp1’top1”isCSCS(p')CS(p"11v(x')v(0)p'x'v(x")v(0)1 1 v(x')v(x")(p'x'p"x"11 Consumer’sSurplus,VariationandEquivalentConsumer’sSurplus,VariationandEquivalentNowconsiderthechangeinTheconsumer’sutilityforgivenp1v(x*(p))mpx*(p)11 1CVistheextraincometobegiven(atthenewprice)tomaketheconsumers’utilitysameasattheoldConsumer’sSurplus,VariationandEquivalentv(x'Consumer’sSurplus,VariationandEquivalentv(x')mp'1 v(x")mCV1 CVv(x')v(x")(p'p"x"11 Consumer’sSurplus,VariationandEquivalentConsumer’sSurplus,VariationandEquivalentNowconsiderthechangeinTheconsumer’sutilityforgivenp1v(x*(p))mpx*(p)11 1EVistheextraincometotakeaway(attheoldprice)tomaketheconsumer’sutilitysameasatthenewConsumer’sSurplus,VariationandEquivalent(x)m’EVConsumer’sSurplus,VariationandEquivalent(x)m’EVp11(x)"""mpx11ThatEVv(x')v(x")(p'p"x"11 Consumer’sSurplus,Consumer’sSurplus,VariationandEquivalentSowhentheconsumerhasquasilinearCV=EV=EV<CS<CV(whenpriceProducer’schangesinafirm’sProducer’schangesinafirm’swelfarecanbemeasuredindollarsmuchasforaconsumerOutputpriceMarginalyRvenue=pProducer’sOutputpriceMarginalProducer’sOutputpriceMarginalVariableCost可变成本ofProducingyunitsisthesumofthemarginalyBenefit-CostBenefit-CostCanwemeasureinmoneyunitsthenetgain,orloss,causedbyamarketintervention;e.g.,theimpositionortheremovalofamarketregulation?Yes,byusingmeasuressuchastheConsumer’sSurplusandtheProducer’sSurplus.Benefit-CostThefree-marketequilibriumandthegainsfromtradegeneratedbyBenefit-CostThefree-marketequilibriumandthegainsfromtradegeneratedbyQD,q0Benefit-CostThegainfromfreelytradingtheq1thunit.QBenefit-CostThegainfromfreelytradingtheq1thunit.QD,qq10 Benefit-CostThegainsfromfreelytradingtheunitsfromtoBenefit-CostThegainsfromfreelytradingtheunitsfromtoQD,qq10 Benefit-CostAnexcisetaximposedatarateof$tperunitdestroysthesegains.pbBenefit-CostAnexcisetaximposedatarateof$tperunitdestroysthesegains.pbtQD,qq10Benefit-CostAnexcisetaximposedatarateof$tpertradedBenefit-CostAnexcisetaximposedatarateof$tpertradedunitdestroystheseSodoesapricesetatpfQD,qq10Benefit-C