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oopicstobeGeneralEquilibriumEfficiencyinEquityandEfficiencyinoopicstobeTheGainsfromFreeAnOverview:TheEfficiencyofCompetitiveMarketsWhyMarketsGeneralGeneralEquilibriumUptothispoint,wehavebeenfocusedonpartialequilibriumanalysisActivityinonemarkethaslittleornoeffectonothermarketsMarketinterrelationshipscanbeComplementsandIncreaseinfirms’inputdemandcancausemarketpriceoftheinputandproducttoriseGeneralGeneralEquilibriumTostudyhowmarketsinterrelate,wecanusegeneralequilibriumanalysisSimultaneousdeterminationofthepricesandquantitiesinallrelevantmarkets,takingintoaccountfeedbackeffectsThefeedbackeffectisthepriceorquantityadjustmentinonemarketcausedbypriceandquantityadjustmentsinEfficiencyEfficiencyinWeshowedbeforethatcompetitiveandproducersurplusesaremaximizedWecanstudythisinmoredetailbyexamininganexchangeeconomyMarketinwhichtwoormoreconsumerstradetwogoodsamongthemselvesSamefortwoEfficiencyinEfficiencyinAnefficientallocationofgoodsisonewherenoonecanbemadebetteroffwithoutmakingsomeoneelseworseoff◦ParetoVoluntarytradebetweentwopartiesismutuallybeneficialandincreaseseconomicefficiencyGainGainfromradeTwoconsumersTwoBothpeopleknoweachother’sExchanginggoodsinvolveszerotransactionJamesandKarenhaveatotalof10unitsoffoodand6unitsofclothingGainfromradeTodetermineiftheyGainfromradeTodetermineiftheyarebetteroff,weneedtoknowthepreferencesforfoodandclothing-1F,+1F,-GainGainfromradeJames’MRSoffoodforclothingisonlyHewillgiveup½unitofclothingfor1unitofKarenhasalotofclothingandlittleMRSoffoodforclothingisToget1unitoffood,shewillgiveup3unitsofclothingGainGainfromradeThereisroomforJamesvaluesclothingmorethanKarenvaluesfoodmorethanKareniswillingtogiveup3unitsofclothingtoget1unitoffood,butJamesiswillingtotakeonly½unitofclothingfor1unitoffoodActualtermsoftradearedeterminedthroughbargainingTradefor1unitoffoodwillfallbetween½and3unitsofclothingGainGainfromradeSupposeKarenoffersJames1unitofclothingfor1unitoffoodJameswillhavemoreclothing,whichhevaluesmorethanfoodKarenwillhavemorefood,whichshevaluesWhenevertwoconsumers’MRSsaredifferent,thereisroomformutuallybeneficialtradeAllocationofresourcesisGainfromGainfromradeFromthisanalysisweobtainanimportantAnallocationofgoodsisefficientonlyifthegoodsaredistributedsothatthemarginalrateofsubstitutionbetweenanypairofgoodsisthesameforallTheTheEdgeworthBoxAdiagramshowingallpossibleallocationsofeithertwogoodsbetweentwopeopleoroftwoinputsbetweentwoproductionprocessesiscalledanEdgeworthBoxLet’sconsideranexchangeTheEdgeworthTheEdgeworthJames’AExchangeinanEdgeworthExchangeinanEdgeworthJames’B-AGainsfromradGainsfromradEfficiencyinEfficiencyinEfficientEfficientHowdothesepartiesreachanefficientWhenthereisnomoreroomforWhentheirMRSsareTheywillkeeptrading,reachinghigherindifferencecurves,untiltheycannolongerdosoandstillmakeeachbetteroffThisiswhenindifferencecurvesaretangenttheyhavethesameslopeandsameEfficiencyinAnymoveoutsidetheEfficiencyinAnymoveoutsidethetheirorigin)Bisamutuallybeneficialtrade--higherindifferencecurveforeachpersonTrademaybebeneficialbutnotefficientMRSisequalwhenindifferencecurvesaretangentandtheallocationisefficient0K0JJames’TheTheContractTofindallpossibleefficientallocationsoffoodandclothingbetweenKarenandJames,wewouldlookforallpointsoftangencybetweeneachoftheirindifferencecurvesThecontractcurveshowsalltheconsumers,oroftwoinputsbetweentwoproductionfunctionsTheContractTheContractJames’E,F,&ParetoGFEContractContractAllpointsoftangencybetweentheindifferencecurvesareefficientMRSofindividualsistheNomoreroomforThecontractcurveshowsallallocationsthatareParetoefficientParetoefficientallocationoccurswhenfurthertradewillmakesomeoneworseoffParetosetitselfdoesnotdependontheinitialMarketMarketradeWhatwouldhappenifthetwopersonsareinacompetitivemarket?Bothareprice-Supposewehaveathirdpartywhoactsasan“auctioneer”forthetwoagentsAtanypricesannouncedbytheauctioneer,ifthereisexcessdemandorsupply,thenshewillchangethepricessuchthatdemandequalsdemandforanyConsumerEquilibriuminaCompetitiveMarketKaren’sBeginatEachJamesbuys2Candsells2FmovingfromUJ1toUJ2,whichispreferred(AtoConsumerEquilibriuminaCompetitiveMarketKaren’sBeginatEachJamesbuys2Candsells2FmovingfromUJ1toUJ2,whichispreferred(AtoPricePBeginatEachKarenbuys2Fandsells2CmovingfromU1toU2,KKispreferred(AtoCAU1JJames’WalrasianWalrasianAmarketequilibriumorWalrasianequilibriumisasetofpricesatwhichthequantitydemandedequalsthequantitysuppliedineverymarketAlsocalledcompetitivearefacingthesameprice,soallconsumerswillhavethesamemarginalrateofsubstitutionbetweenanytwoWalrasianAttheequilibriumpricesp*,we(p*,p*)Xi(WalrasianAttheequilibriumpricesp*,we(p*,p*)Xi(p*,p*)WiWi(iiX 2 2ABThismeans(Xi*Wi)(Xi*Wi)AABBLetusdenotetheexcessdemandgoodibyagentjXi(p,p)Wi(jA,j jThen,we)e(,p)e(p1,p2zi(p,ii BZ(p1,p2)representstheaggregateexcessdemandforgoodiWalrasianTheareequilibriumprices(WalrasianTheareequilibriumprices(p*,p* z(p,p)0,z(p*,p*)** 2 2TheequilibriumpriceswillclearallmarketssimultaneouslyInordertounderstandthenatureoftheseconditions,weneedtoknowWalras’LawTheWalras’p1z1(p1,p2)p2z2(p1,pTheWalras’p1z1(p1,p2)p2z2(p1,p2)Attheoptimalbundles(X1(p*),X2(AAp (p*)pX2(p*)pW1pWpp1 p (p*)pX2(p*)pW1pWpp1 p e1)p(e2e2)1 B Bp1z1(p1,p2)p2z2(p1,p2)KMoregenerally,pkzk(p)kmarketwillalsoclearThereareonly(K-1)independentNotethatp*andtp*arebothequilibriumprices,andbysettingt=1/p1,thenthereareonly(K-1)relativepricesIngeneralwecallgood1asEquilibriumEquilibriumandAsshownbefore,wecanseethattheallocationinacompetitiveequilibriumiseconomicallyefficientTheefficientpointmustoccurwherethetwoindifferencecurvesaretangentIfnot,oneoftheconsumerscanincreasetheirutilityandbebetteroffAProofofEfficiencyinMarketThiscanbeprovenbywayofcounterSupposeAProofofEfficiencyinMarketThiscanbeprovenbywayofcounterSupposeamarketequilibriumisNOTefficient,thenitimpliesthatthereisanotherfeasibleallocation(yA,yB)suchyiWiW(i1,2)ABAB12(y,y (X1,X2AAAAA12(y,y(X1,X2BBBBBAProofofEfficiencyinMarket(yA)isbetterthanthebundle(xAAProofofEfficiencyinMarket(yA)isbetterthanthebundle(xA)Achoosing,thenitmustcostmorethanAcanafford,similarlyforBThatpy1pW1pW(jA, Addingthesetwoequations,wep( y1)p(y2y2)p(W1W1)p(WW211AB2AB1AB2ABThiscontradictswiththefeasibilityconditionwithequalityFirstFirstTheoremofWelfareMarketequilibriaareParetoIfeveryonetradesinacompetitivemarketplace,allmutuallybeneficialtradeswillbecompletedandtheresultingeconomicallyefficientWelfareeconomicsinvolvesthenormativeevaluationofmarketsandeconomicpolicyEquilibriumandThefirstEquilibriumandThefirstwelfaretheoremisthebestillustrationofAdamSmith’sinvisibleEconomywillautomaticallyallocateallresourcesefficientlywithoutneedforinterventionandmorehighlycompetitiveMarketsuseminimuminformationtofunctionwell(comparethiswiththecentralizedplanning)UnderlyingUnderlyingForthefirsttheoremtohold,thereareseveralimplicitassumptions:NoexternalityorpublicNomonopolypowerinsettingNoasymmetricinformation:marketscanbemissingduetotheasymmetricinformationEquityEquityandAlthoughtherearemanyefficientequitableallocation?WecanshowthatthereisnoreasontobelievethatefficientallocationfromcompetitivemarketswillgiveanequitableTheTheUtilityPossibilitiesFromtheEdgeworthBox,weshowedatwopersonexchangeTheutilitypossibilitiesfrontierrepresentsallallocationsthatareefficientintermsoftheutilitylevelsofthetwoShowsthelevelsofsatisfactionthatarereachedthecontractcurveTheUtilityPossibilitiesLETheUtilityPossibilitiesLEFHGJames’TheTheUtilityPossibilitiesFrompreviousexample,onecanseethataninefficientallocationmightbemoreequitablethananefficientoneButhowdowedefineanequitableItdependsonwhatwebelieveequitytoRequiresinterpersonalcomparisonsofSocialSocialWelfareutilitytodeterminewhatissociallyHowtheseweightsareappliedcomesfromthesocialwelfarefunctionsTheutilitarianfunctionweightseveryone’sutilitytomaximizeutilityforthewholesocietySocialSocialWelfareEachsocialwelfarefunctionisassociatedwithaparticularviewofequitySomeviewsofequitydonotassignweightsandcannotberepresentedbyawelfarefunctionCompetitivemarketprocessisequitablebecauseitrewardsthosewhoaremostableandworkhardestBelievescompetitiveequilibriumwouldbemostequitableSocialSocialWelfareTheRawlsianviewisthatindividualsknowwhattheirendowmentwillRawlsarguesthatifyoudon’tknowyourownfate,youwilloptforthesysteminwhichtheleastwell-offpersonistreatedThemostequitableallocationmaximizestheutilityoftheleastwell-offpersoninsocietySocialSocialWelfareAnegalitarianviewbelievesthatgoodsshouldbeequallysharedbyallindividualsinsocietyCouldhavesituationwheremoreproducingmoregoodsandthenhavingmoretoreallocatetoallofsocietyFourViewsofAllmembersFourViewsofAllmembersofsocietyreceiveequalamountofgoodsMaximizetheutilityoftheleast-well-offpersonMaximizethetotalutilityofallmembersofsocietyMarket-ThemarketoutcomeisthemostAAcompetitiveequilibriumcanoccuratanypointonthecontractcurvedependingontheinitialallocationSincenotallcompetitiveequilibriaareequitable,werelyonthegovernmenttoPublicEfficiencyandEfficiencyandMustasocietythatwantstobemoreequitablenecessarilyoperateinaninefficientworld?SecondTheoremofWelfareIfindividualpreferencesareconvex,theneveryefficientallocation(everypointonthecontractcurve)isacompetitiveequilibriumforsomeinitialallocationofEfficiencyandPriceEfficiencyandPricePCWAWhyAreConvexWhyAreConvexPricePCWAImplicationsoftheSecondImplicationsoftheSecondTheproblemofdistributionandefficiencycanbeseparatedPricesplaytworolesinthemarketallocativevs.TheallocativeroleofpricesistoreflectrelativescarcitywhilethedistributiveroleistodeterminethevaluesoftheendowmentsLetpricesallocateresourcesandgovernmentredistributewealthorincomeusing(lump-sum)subsidyortaxesDon’tmixupthesetwoBerkeleyBerkeleyEconomicsBerkeleyBerkeleyEconomicsSemesterAbroadAselectgroupofinternationalstudentstakeasemester,upperlevelcoursesinBerkeleyFall2013andSpring12Deadline:Jan15andApril15,YoumustapplybeforeJan10,Requirement:TOEFL(iBT)88,雅思Tuition$8250(coveredbyGuanghua)andpaylivingNoofficeNoofficehoursonDec23andOfficehours:1:00-5pm,Jan2,Rm.Final7-9pm,JanRm.102、202、112、ChapterChapterGeneralEquilibriumwithTheTheRobinsonCrusoeThiseconomyischaracterizedbyoneconsumer,onefirm,andtwogoodsRobinsonCrusoeplaysadualrole:consumerplusproducerHecanspendtimeloafingonthebeachbyconsumingleisureorgatheringcoconutsHowtoallocatetimeonconsumptionandvs.vs.ExtendedExtendedRobinsonCrusoeandacoconutmarketatthesametimeCrusoehasmultipleShareholderofthefirmwhocollectsWorkerwhodecideshowmuchlabortoProducerwhodecidestheemploymentandFirm:Profit-Firm:Profit-Consumer’sBudgetConsumer’sBudgetConsumer’s_MaxConsumer’s_Maxu(c,L__s.t.pcw(LL)*wLpc*PuttingThemogethePuttingThemogetheBudgetEfficiencyEfficiencyinUsingtheEdgeworthBoxdiagram,wecanshowefficientuseofinputsinproductionLaboronhorizontalCapitalonvertical50hoursoflaborand30hoursofcapitalEachoriginisanProductioninanEdgeworthLaborinClothingProductioninanEdgeworthLaborinClothingCapitalinLaborinFoodAProductionProductioninanEdgeworthEachpointintheboxrepresentsthelaborandcapitalinputsintheproductionoffoodandclothingCanuseproductionisoquantstoshowlevelsofoutputproducedwitheachcombinationofinputs3isoquantsrepresenting50,60and80unitsoffood3isoquantsrepresenting10,25and30unitsofclothingProductioninanEdgeworthLaborinClothingProductioninanEdgeworthLaborinClothingCapitalinCLaborinFoodProductionProductioninanEdgeworthTofindefficientproduction,mustfinddifferentcombinationsofinputsusedtoproducethetwooutputsAnallocationofinputsistechnicallyefficientiftheoutputofonegoodcannotbeincreasedwithoutdecreasingtheoutputofanothergoodProductionProductioninanEdgeworthProductionatpointAisinefficientsincewecanincreaseproductionofbothgoodsShadedareaindicatesincreasesinproductionofbothgoodsifbeginatAAllocationAcouldexistifalaborunionmarkethasenforcedinefficientworkrulesProductioninanEdgeworthLaborinClothingProductioninanEdgeworthLaborinClothingCapitalinCLaborinFoodProductionProductioninanEdgeworthPointsBandCareefficientallocationsandthereforelieontheproductioncontractcurveCurveshowingalltechnicallyefficientcombinationsofinputsCurveconnectstheoriginsOFandAllpointsoncurvearetangenciesbetweentwoisoquantsProductioninanEdgeworthLaborinClothingProductioninanEdgeworthLaborinClothingCapitalinCLaborinFoodProducerProducerEquilibrium–CompetitiveIfinputmarketsarecompetitive,anefficientpointwillbeachievedIncompetitiveinputWagerate,w,willbeequalinallRentalrateofcapital,r,willbeequalinallProducerEquilibriumProducerEquilibrium–CompetitiveWesawbeforethatifproducersminimizecosts,theywillchooseinputstothepointwheretheratioofthemarginalproductsofthetwoinputsisequaltotheratioofinputprices:ProducerEquilibriumProducerEquilibrium–CompetitiveRatioofmarginalproductsisthesameasthemarginalrateoftechnicalsubstitutionoflaborforcapital:ProducerProducerEquilibrium–CompetitiveTheMRTSistheslopeoftheisoquant,socompetitiveequilibriumexistsonlyif:SlopesoftheisoquantsareequaltooneThesealsoequaltheratioofthepricesoftwoinputsCompetitiveequilibriumliesontheproductioncontractcurve,andthecompetitiveequilibriumisefficientinProductionProductionPossibilitiesPPFshowsthevariouscombinationsoftwogoodsthatcanbeproducedwithfixedquantitiesofinputsFrontierisderivedfromtheproductionPointsonPPFshowefficientlyproducedlevelsofbothgoodsProductionPossibilitiesBCADProductionPossibilitiesBCADProductionProductionPossibilitiesPPFisdownwardInordertoproducemoreofonegood,mustgiveupproducingsomeoftheothergoodPPFisSlopeistheMRTSwhichincreasesasthelevelofproductionoffoodincreasesProductionProductionPossibilitiesMarginalrateoftransformation(MRT)offoodforclothingisthemagnitudeoftheslopeofthefrontierateachpointAmountofonegoodthatmustbegivenuptoproduceoneadditionalunitofasecondgoodHowmuchclothingmustbegivenuptoproduceoneadditionalunitoffoodAsweincreasetheproductionoffoodbymovingalongthePPF,theMRTincreasesMarginalMarginalRateofransformationTheproductivityoflaborandcapitaldiffersdependingonwhethertheinputsareusedtoproducemorefoodorStartingwhereonlyclothingisproduced,MPoflaborandcapitalarerelativelylowTransferringsometofoodproductionwhereMPisrelativelyhighAswedothis,MPinfooddecreasesandMPinclothingincreasesProductionPossibilitiesMRTProductionPossibilitiesMRT<B→MRT=MRT>D→MRT=MarginalRateofMarginalRateofransformationCanalsodescribeintermsof◦WhenproducingatOF,theMCoffoodisverylowandtheMCofclothingisveryhighWhenMRTislow,soistheratiooftheMCofproducingfoodtoclothingSlopeofPPFmeasurestheMCofproducingonegoodrelativetotheMCofproducingtheother◦◦OutputOutputForGoodproducedatminimumMustbeproducedincombinationsthatpeople’swillingnesstoMRS=consumer’sWTPforadditionalfoodbyconsuminglessclothingMRT=costofadditionalunitoffoodintermsofproducinglessclothingEfficiencymeansMRS=OutputOutputWhatifMRTConsumerwillingtogiveup2unitsofclothingtoget1unitoffoodCostofgettingadditionalfoodisonly1unitoflostclothingToolittlefoodisbeingFoodproductionmustincrease,MRSfallsandMRTincreasesuntiltwoareequalagainOutputMRS=OutputMRS=IndifferenceEfficiencyinEfficiencyinOutputForperfectlycompetitivemarkets,allconsumersallocatetheirbudgetssotheirMRSbetweentwogoodsareequaltotheratioofpricesProfitmaximizingfirmsproduceoutputtothepointwherepriceisequaltoMCMRTisequaltotheEfficiencyinOutputEfficiencyinOutputEfficiencyincompetitivemarketsisachievedwhenthereisseparateproductionandconsumptionMarketpriceratioofP1FCFoodandclothingareproducedatAwherepriceratioequalsMRTThispricecausesconsumertomaximizeutilityandconsumeatBEfficiencyinOutput1CABC2EfficiencyinOutput1CABC2COverview–EfficiencyofCompetitiveMarkets Efficiencyin=◦Overview–EfficiencyofCompetitiveMarkets Efficiencyin=◦◦=P/P= Efficiencyintheuseofinputsin=◦◦=w/r=Overview–Overview–EfficiencyofCompetitiveMarkets Efficiencyintheoutput◦◦◦◦MRTFC=MRSFC(forallconsumers)PF=MCF,PC=MCCresultinginMRTFC=MCF/MCC=PF/PC;thereforeMRSFC=MRTFCWhyWhyMarketsMarketThosewithmarketpowerchoosethepriceandquantityLessoutputissoldthanincompetitiveCanhavemarketpowerasproducersorasWhyWhyMarketsIncompleteConsumersmusthaveaccurateinformationaboutmarketpricesorproductionqualityformarketstooperateefficientlyLackofinformationcanchangeBuyproductswithnoDon’tbuyenoughofproductswithSomemarketsmayneverMaybeimpossibletogetinsurancebecausesuppliersofinsurancelackinformationWhyWhyMarketsMarketpricesdonotalwaysreflecttheactivitiesofeitherproducersorconsumersConsumptionorproductionhasindirecteffectonotherconsumptionorproductionnotreflectedinmarketpricesWhyWhyMarketsPublicNonexclusive,nonrivalgoodsthatcanbemadeavailablecheaplybutwhich,onceavailable,aredifficulttopreventothersfromCompanythinkingaboutresearchinganewtechnologyifcan’tgetpatentOnceit’smadepubic,otherscanduplicateChapterChapterExternalityPublicAnAnexternalityisacostorabenefitimposeduponaconsumerorafirmbyactionstakenbyothers.ThecostorbenefitisthusgeneratedexternallytotheconsumerorthefirmAnexternallyimposedbenefitisapositiveAnexternallyimposedcostisanegativeExamplesExamplesofNegativeAirWaterLoudpartiesnextTrafficIncreasedhealthinsurancepremiumduetoalcoholortobaccoconsumption.ExamplesExamplesofPositiveAwell-maintainedpropertynextdoorthatraisesthemarketvalueofyourownApleasantcologneorscentwornbythepersonseatednexttoyouImproveddrivinghabitsthatreduceAscientificExternalitiesExternalitiesandExternalitiesoccurwhenone’sactionordecisiondirectlyentersotherpeople’spayofffunction(utilityorprofits)ThecrucialfeatureofanexternalityisthattherearegoodspeoplecareaboutthatarenotsoldonmarketsItisthislackofmarketsforexternalitiesthatcausesproblemsExternalitiesExternalitiesandExternalitiescauseParetoinefficiency;toomuchscarceresourceisallocatedtoanactivitywhichcausesanegativeexternalitytoolittleresourceisallocatedtoanactivitywhichcausesapositiveexternality.InefficiencyInefficiency&NegativeConsideranexampleoftworoommates,AandB,andtwocommodities,moneyandsmoke.AgentA.AgentB.SmokeisapurelypubliccommoditywhichisnonrivalryandnonexcludableInefficiencyInefficiency&NegativeAgentAisendowedwithAgentBisendowedwithSmokeintensityismeasuredonascalefrom0(nosmoke)to1(maximumHencethereisonlyoneamountofsmokethattheymustbothconsumeInefficiencyInefficiency&NegativeInefficiency&Negative1Clean0Inefficiency&Negative1Clean0Inefficiency&Negative100Inefficiency&Negative100InefficiencyInefficiency&NegativeSupposethereisnomechanismbywhichmoneycanbeexchangedforchangesinsmokelevel.WhatthenisAgentA’smostIsthisallocationInefficiency&Negative10 Inefficiency&Negative10 InefficiencyInefficiency&NegativeContinuetosupposethereisnomechanismbywhichmoneycanbeWhatisAgentB’smostIsthisallocationInefficiency&NegativeB’s10 Inefficiency&NegativeB’s10 Inefficiency&NegativeB’s1OB0 Inefficiency&NegativeB’s1OB0 Inefficiency&NegativeInefficiency&NegativeSoifneitherAnorBcantrademoneyforchangesinsmokeintensity,thentheoutcomeisTheonlyproblemariseswhenthepropertyrightsarenotwelldefinedinthiscaseEitherthereistoomuchsmoke(A’smostpreferredchoice)orthereistoolittlesmoke(B’schoice).ExternalitiesandPropertyExternalitiesandPropertyRonaldCoase’sinsightisthatexternalityproblemsareduetoinadequatespecificationpropertyand,consequently,absenceofinwhichtradecanbeusedtointernalizeexternalcostsorbenefits.ExternalitiesExternalitiesandPropertySupposethatAgentBisassignedownershipofthecleanairintheroom.AgentBcannowsell“rightstoWilltherebeanyIfso,howmuchsmokingwiththerebeandwhatwillbetheequilibriumpriceforthisamountofsmoke?ExternalitiesExternalitiesandPropertyLetp(sA)bethepricepaidbyAgentAtoAgentBinordertocreateasmokeintensityofsA.ExternalitiesandProperty100 ExternalitiesandProperty100 ExternalitiesandProperty10 ExternalitiesandProperty10 ExternalitiesandProperty10 ExternalitiesandProperty10 ExternalitiesandProperty1gainandthereisaamountofExternalitiesandProperty1gainandthereisaamountofsA0 ExternalitiesandProperty1amarketfortradingrightsExternalitiesandProperty1amarketfortradingrightstosmokecausesanallocationtobeachieved.sA0 OAExternalitiesExternalitiesandPropertySupposeinsteadthatAgentAisassignedtheownershipoftheairintheroom.thesmokeintensity.HowmuchsmokingwillthereHowmuchmoneywillAgentBpaytoAgentA?ExternalitiesandProperty100 ExternalitiesandProperty100 ExternalitiesandProperty1100 ExternalitiesandProperty1100 ExternalitiesExternalitiesandPropertyNoticethattheagentgiventhepropertyright(asset)isbetteroffthanathis/herownmostpreferredallocationintheabsenceofthepropertyright.Noticealsothattheamountofsmokingthatoccursinequilibriumtypicallydependsuponwhichagentisassignedthepropertyright.ExternalitiesandProperty1sAExternalitiesandProperty1sA0 ExternalitiesExternalitiesandPropertyIsthereacaseinwhichthesameamountofsmokingoccursinequilibriumnomatterwhichoftheagentsisassignedownershipoftheairintheroom?ExternalitiesandProperty11=ExternalitiesandProperty11=00 ExternalitiesandProperty11=ExternalitiesandProperty11=00 Forbothagents,theMRSisconstantmoneychanges,forgivensmokeExternalitiesandProperty11=ExternalitiesandProperty11=00 So,forbothagents,preferencesmustbequasilinearinmoney;U(m,s)=m+f(s).Digression:QuasilinearmaxDigression:QuasilinearmaxU(x,y)v(x)s.t.pxxpyyv'(x)px/pyxx*(/pyNoincomeCoase’sCoase’sCoase’sTheorem:Ifthepropertyrightsarewelldefinedandtransactioncostsarezero,thentheallocationwillbeefficientnomaterhowthepropertyrightsareassignedWhat’smore,ifallagents’preferencesarequasilinearinmoney,thentheefficientleveloftheexternalitygeneratingcommodityisproducednomattertowhichagentitspropertyrightisassignedProductionProductionConsiderasteelmillwhichproducesjointlysteelandpollutionandafisherywhichproducesfishThepollutionadverselyaffectsanearbyBothfirmsareprice-pSisthemarketpriceofpFisthemarketpriceofProductioncS(s,x)isProductioncS(s,x)isthesteelfirm’scostofproducingsunitsofsteeljointlywithxunitsofFishery’scostfunctionAssumecs(s,x)0,cf(f,x)ProductionThefirmmaxs(s,x)ProductionThefirmmaxs(s,x)psscs(s,s,cs(s,x)cs(s,x)F.O.C.,sTheFisherymax (f,x)pfcf(f,ffcf(f,F.O.C.,fProductioncs(s,x)istheProductioncs(s,x)isthemarginalbenefittofirmofincreasingpollutionWhatisthemarginalcosttothesteelfirmfromincreasingpollution?Zero,sincethefirmdoesnotfaceitsexternalcost.Hencethesteelfirmchoosesthelevelforcs(s,x)ProductionThefirst-orderprofit-maximizationconditionisProductionThefirst-orderprofit-maximizationconditioniscF(f;x)pFHigherpollutionraisesthefishery’smarginalproductioncostandlowersbothitsoutputlevelanditsprofit.Thisistheexternalcostofthepollution.MergerandMergerandArethesechoicesbythetwofirmsSupposethetwofirmsmergetobecomeone.Whatisthehighestprofitthisnewfirmcanachieve?Maxpsspffcs(s,x)cf(f,Maxpsspffcs(s,x)cf(f,F.O.C.:(s*,x*),(f*,sf(s*,x*) (f*,x*)Notethatinthepreviouscase,cs(s,x) 0,cs(s*,x*) (f*,x*)(s*,x*)cs(s,x), x 0-Socialx-SocialxMergerandMergerandMergerhasimprovedOnitsown,thesteelfirmproducedx0ofpollution.Withinthemergedfirm,pollutionproductionisonlyx*units.Somergerhascausedbothanimprovementinefficiencyandlesspollutionproduction.Why?Internalizationofexternality!MergerMergerandislargerbecauseitfacesthefullcostofitsownpollutionthroughincreasedofproductioninthefishery,solesspollutionisproducedbythemergedfirmMergerMergerandMergerthereforeinternalizesanexternalityandinduceseconomicHowelsemightinternalizationbecausedsothatefficiencycanbeachieved?SolutionsSolutionstoExternalityTherearetwomajorinterpretationswhyexternalitycausesproblemsThesteelfirmfacesthewrongpriceforThereisamissingmarketforPigouvianaxTheproductionofpollutioncostsitnothingandthereforeitisnecessarytoPigouvianaxTheproductionofpollutioncostsitnothingandthereforeitisnecessarytocorrectitbylettingthefirmfacethesocialcostofitsactionsPlaceataxonthepollutiongeneratedbytheMaxpsscs(s,x)F.O.C.s(f*,x*)t(s*,Coase’sTheCoase’sTheexternalityproblemarisesbecausethepolluterfacesazeropriceforanoutputgoodthatitproducesPeoplewouldbewillingtopaymoneytohavethatoutputlevelreducedFromasocialpointofview,theoutputofpollutionshouldhaveanegativeprice(i.e.,itshouldbecompensatedlowerlevel)forCoaseCoaseSupposethatthefisheryhadtherighttocleanwater,butcouldselltherighttoallowpollutionLetqbethepriceperunitofLetxbetheamountofpollutionthatthesteelmillproducesCoaseThefirm'sproblemMaxpssqxcsCoaseThefirm'sproblemMaxpssqxcs(s, qpsThefishery'sproblemMaxpffqxcf(f,qp,fqParetoCoaseSupposeCoaseSupposethatthesteelfirmhadtherighttopollutethewaterThefisherywouldhavetopaytoinducethesteelfirmtopollutelessSupposethatthesteelfirmhasthe_topolluteuptosomexCoaseThesteelfirm'sproblem_Maxpssq(xCoaseThesteelfirm'sproblem_Maxpssq(xx)cs(s, qpsThefishery'sproblem_Maxpffq(xx)cf(f,qp,fqParetoApplicationsApplicationsofCoaseTradingofpollutionpermitswhilethetotalnumberofpermitsisfixedInter-countytradeforpollutionTheredlinefor1.8billionarableland:thecurrentsystemfixesthelandquotaforeachcountyCanwetradeforarablelandquotasacrossregions?ThemarketforDiPiaoinChengduandTheragedTheragedoftheConsideragrazingareaowned“inbyallmembersofaVillagersgrazecowsontheWhenccowsaregrazed,totalproductionisf(c),wheref’>0andHowshouldthevillagersgrazetheircowsastomaximizetheiroverallTheraTheragedofthecTherTheragedoftheNormalizethepriceofaunitofmilkto$1andlettherelativecostofgrazingacowbe$pc.Ifthecommonsarerunlikeaprivatefirm,thentheprofitfunctionfortheentirevillageis(c)f(c