Lec21

ChapterThirty-FourExternalitiesWhenthemarketworksasitshould…Recall:AdamSmith’s“invisiblehand〞ofthemarketplaceleadsself-interestedbuyersandsellersinamarkettomaximizethetotalbenefitthatsocietycanderivefromamarket.Butmarketfailurescanstillhappen.ExternalitiesAnexternalityisacostorabenefitimposeduponsomeonebyactionstakenbyothers.Thecostorbenefitisthusgeneratedexternallytothatsomebody.Anexternallyimposedbenefitisapositiveexternality.Anexternallyimposedcostisanegativeexternality.EXTERNALITIESANDMARKETINEFFICIENCY

NegativeExternalitiesAutomobileexhaustCigarettesmokingBarkingdogs(loudpets)LoudstereosinanapartmentbuildingEXTERNALITIESANDMARKETINEFFICIENCYPositiveExternalitiesImmunizationsRestoredhistoricbuildingsResearchintonewtechnologiesExamplesofNegativeExternalitiesAirpollution.Waterpollution.Loudpartiesnextdoor.Trafficcongestion.Second-handcigarettesmoke.Increasedinsurancepremiumsduetoalcoholortobaccoconsumption.ExamplesofPositiveExternalitiesAwell-maintainedpropertynextdoorthatraisesthemarketvalueofyourproperty.Apleasantcologneorscentwornbythepersonseatednexttoyou.Improveddrivinghabitsthatreduceaccidentrisks.Ascientificadvance.ExternalitiesandEfficiencyCrucially,anexternalityimpactsathirdparty;i.e.somebodywhoisnotaparticipantintheactivitythatproducestheexternalcostorbenefit.ExternalitiesandEfficiencyExternalitiescauseParetoinefficiency;typicallytoomuchscarceresourceisallocatedtoanactivitywhichcausesanegativeexternalitytoolittleresourceisallocatedtoanactivitywhichcausesapositiveexternality.ExternalitiesandPropertyRightsAnexternalitywillviewedasapurelypubliccommodity.Acommodityispurelypublicifitisconsumedbyeveryone(nonexcludability),andeverybodyconsumestheentireamountofthecommodity(nonrivalryinconsumption).E.g.abroadcasttelevisionprogram.Inefficiency&NegativeExternalitiesConsidertwoagents,AandB,andtwocommodities,moneyandsmoke.BothsmokeandmoneyaregoodsforAgentA.MoneyisagoodandsmokeisabadforAgentB.Smokeisapurelypubliccommodity.Inefficiency&NegativeExternalitiesAgentAisendowedwith$yA.AgentBisendowedwith$yB.Smokeintensityismeasuredonascalefrom0(nosmoke)to1(maximumconcentration).Inefficiency&NegativeExternalitiesOA10SmokemAyAMoneyandsmokeare

bothgoodsforAgentA.Inefficiency&NegativeExternalitiesOA10SmokemAyAMoneyandsmokeare

bothgoodsforAgentA.BetterInefficiency&NegativeExternalitiesOB10SmokemByBMoneyisagoodandsmokeisabadforAgentB.BetterInefficiency&NegativeExternalitiesOB10SmokemByBMoneyisagoodandsmokeisabadforAgentB.BetterInefficiency&NegativeExternalitiesWhataretheefficientallocationsofsmokeandmoney?Inefficiency&NegativeExternalitiesOA10SmokemAyAOB10SmokemByBInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsInefficiency&NegativeExternalitiesSupposethereisnomeansbywhichmoneycanbeexchangedforchangesinsmokelevel.WhatthenisAgentA’smostpreferredallocation?Isthisallocationefficient?Inefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsA’schoicesInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsA’smost

preferredchoice

isinefficientInefficiency&NegativeExternalitiesContinuetosupposethereisnomeansbywhichmoneycanbeexchangedforchangesinsmokelevel.WhatisAgentB’smostpreferredallocation?Isthisallocationefficient?Inefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsB’schoicesInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsB’smost

preferredchoiceInefficiency&NegativeExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsB’smost

preferredchoice

isinefficientInefficiency&NegativeExternalitiesSoifAandBcannottrademoneyforchangesinsmokeintensity,thentheoutcomeisinefficient.Eitherthereistoomuchsmoke(A’smostpreferredchoice)orthereistoolittlesmoke(B’schoice).ExternalitiesandPropertyRightsRonaldCoase’sinsightisthatmostexternalityproblemsareduetoaninadequatespecificationofpropertyrightsand,consequently,anabsenceofmarketsinwhichtradecanbeusedtointernalizeexternalcostsorbenefits.ExternalitiesandPropertyRightsCausingaproducerofanexternalitytobearthefullexternalcostortoenjoythefullexternalbenefitiscalledinternalizingtheexternality.ExternalitiesandPropertyRightsNeitherAgentAnorAgentBownstheairintheirroom.Whathappensifthispropertyrightiscreatedandisassignedtooneofthem?ExternalitiesandPropertyRightsSupposeAgentBisassignedownershipoftheairintheroom.AgentBcannowsell“rightstosmoke〞.Willtherebeanysmoking?Ifso,howmuchsmokingandwhatwillbethepriceforthisamountofsmoke?ExternalitiesandPropertyRightsLetp(sA)bethepricepaidbyAgentAtoAgentBinordertocreateasmokeintensityofsA.ExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBp(sA)sAExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBp(sA)Bothagentsgainandthereisapositiveamountofsmoking.sAExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBp(sA)sAEstablishingamarketfortradingrightstosmokecausesanefficientallocationtobeachieved.ExternalitiesandPropertyRightsSupposeinsteadthatAgentAisassignedtheownershipoftheairintheroom.AgentBcannowpayAgentAtoreducethesmokeintensity.Howmuchsmokingwilltherebe?HowmuchmoneywillAgentBpaytoAgentA?ExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBsBp(sB)ExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBp(sB)Bothagentsgainandthereisareducedamountofsmoking.sBExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBp(sB)Establishingamarketfortradingrightstoreduce

smokecausesanefficientallocationtobeachieved.sBExternalitiesandPropertyRightsNoticethattheagentgiventhepropertyright(asset)isbetteroffthanatherownmostpreferredallocationintheabsenceofthepropertyright.amountofsmokingthatoccursinequilibriumdependsuponwhichagentisassignedthepropertyright.ExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBp(sB)p(sA)sA

1sBsBsAExternalitiesandPropertyRightsIsthereacaseinwhichthesameamountofsmokingoccursinequilibriumnomatterwhichagentisassignedownershipoftheairintheroom?ExternalitiesandPropertyRightsOA10SmokemAOB10SmokemByAyBp(sB)p(sA)sA=sBExternalitiesandPropertyRightsOA10SmokeOB10SmokeyAyBp(sB)p(sA)sA=sBForbothagents,theMRSisconstantas

moneychanges,forgivensmokeintensity.ExternalitiesandPropertyRightsOA10SmokeOB10SmokeyAyBp(sB)p(sA)sA=sBSo,forbothagents,preferencesmustbe

quasilinearinmoney;U(m,s)=m+f(s).Coase’sTheoremCoase’sTheoremis:Ifallagents’preferencesarequasilinearinmoney,thentheefficientleveloftheexternalitygeneratingcommodityisproducednomatterwhichagentisassignedthepropertyright.ProductionExternalitiesAsteelmillproducesjointlysteelandpollution.Thepollutionadverselyaffectsanearbyfishery.Bothfirmsareprice-takers.pSisthemarketpriceofsteel.pFisthemarketpriceoffish.ProductionExternalitiescS(s,x)isthesteelfirm’scostofproducingsunitsofsteeljointlywithxunitsofpollution.Ifthesteelfirmdoesnotfaceanyoftheexternalcostsofitspollutionproductionthenitsprofitfunctionis

andthefirm’sproblemistoProductionExternalitiesThefirst-orderprofit-maximization

conditionsareProductionExternalitiesThefirst-orderprofit-maximization

conditionsareandProductionExternalitiesstatesthatthesteelfirmshouldproducetheoutputlevelofsteelforwhichprice=marginalproductioncost.ProductionExternalitiesstatesthatthesteelfirmshouldproducetheoutputlevelofsteelforwhichprice=marginalproductioncost.istherateatwhichthefirm’sinternalproductioncostgoesdownasthepollutionlevelrisesProductionExternalitiesstatesthatthesteelfirmshouldproducetheoutputlevelofsteelforwhichprice=marginalproductioncost.istherateatwhichthefirm’sinternalproductioncostgoesdownasthepollutionlevelrises,soisthemarginalcosttothefirmofpollutionreduction.ProductionExternalitiesisthemarginalcosttothefirmofpollutionreduction.Whatisthemarginalbenefittothesteelfirmfromreducingpollution?ProductionExternalitiesisthemarginalcosttothefirmofpollutionreduction.Whatisthemarginalbenefittothesteelfirmfromreducingpollution?Zero,sincethefirmdoesnotfaceitsexternalcost.HencethesteelfirmchoosesthepollutionlevelforwhichProductionExternalitiesandthefirst-orderprofit-maximization

conditionsareandE.g.supposecS(s,x)=s2+(x-4)2and

pS=12.ThenProductionExternalitiesdeterminestheprofit-max.outputlevelofsteel;s*=6.ProductionExternalitiesdeterminestheprofit-max.outputlevelofsteel;s*=6.isthemarginalcosttothefirmfrompollutionreduction.Sinceitgetsnobenefitfromthisitsetsx*=4.ProductionExternalitiesdeterminestheprofit-max.outputlevelofsteel;s*=6.isthemarginalcosttothefirmfrompollutionreduction.Sinceitgetsnobenefitfromthisitsetsx*=4.Thesteelfirm’smaximumprofitlevelis

thusProductionExternalitiesThecosttothefisheryofcatchingfunitsoffishwhenthesteelmillemitsxunitsofpollutioniscF(f,x).Givenf,cF(f,x)increaseswithx;i.e.thesteelfirminflictsanegativeexternalityonthefishery.ProductionExternalitiesThecosttothefisheryofcatchingfunitsoffishwhenthesteelmillemitsxunitsofpollutioniscF(f,x).Givenf,cF(f,x)increaseswithx;i.e.thesteelfirminflictsanegativeexternalityonthefishery.Thefishery’sprofitfunctionis

sothefishery’sproblemistoProductionExternalitiesThefirst-orderprofit-maximization

conditionisProductionExternalitiesThefirst-orderprofit-maximization

conditionisProductionExternalitiesThefirst-orderprofit-maximization

conditionisHigherpollutionraisesthefishery’s

marginalproductioncostandlowersboth

itsoutputlevelanditsprofit.Thisistheexternalcostofthepollution.ProductionExternalitiesE.g.supposecF(f;x)=f2+xfandpF=10.

Theexternalcostinflictedonthefisherybythesteelfirmisxf.Sincethefisheryhasnocontroloverxitmusttakethesteelfirm’schoiceofxasagiven.Thefishery’sprofitfunctionisthusProductionExternalitiesGivenx,thefirst-orderprofit-maximization

conditionisProductionExternalitiesGivenx,thefirst-orderprofit-maximization

conditionisSo,givenapollutionlevelxinflictedupon

it,thefishery’sprofit-maximizingoutput

levelisProductionExternalitiesGivenx,thefirst-orderprofit-maximization

conditionisSo,givenapollutionlevelxinflictedupon

it,thefishery’sprofit-maximizingoutput

levelisNoticethatthefisheryproducesless,and

earnslessprofit,asthesteelfirm’s

pollutionlevelincreases.ProductionExternalitiesThesteelfirm,ignoringits

externalcostinflicteduponthefishery,

choosesx*=4,sothefishery’s

profit-maximizingoutputlevelgiventhe

steelfirm’schoiceofpollutionlevelis

f*=3,givingthefisheryamaximum

profitlevelofNoticethattheexternalcostis$12.ProductionExternalitiesArethesechoicesbythetwofirmsefficient?Whenthesteelfirmignorestheexternalcostsofitschoices,thesumofthetwofirm’sprofitsis$36+$9=$45.Is$45thelargestpossibletotalprofitthatcanbeachieved?MergerandInternalizationSupposethetwofirmsmergetobecomeone.Whatisthehighestprofitthisnewfirmcanachieve?MergerandInternalizationSupposethetwofirmsmergetobecomeone.Whatisthehighestprofitthisnewfirmcanachieve?

Whatchoicesofs,fandxmaximizethenewfirm’sprofit?MergerandInternalizationThefirst-orderprofit-maximization

conditionsareThesolutionisMergerandInternalizationAndthemergedfirm’smaximumprofit

levelisThisexceeds$45,thesumofthenon-mergedfirms.MergerandInternalizationMergerhasimprovedefficiency.Onitsown,thesteelfirmproducedx*=4unitsofpollution.Withinthemergedfirm,pollutionproductionisonlyxm=2units.Somergerhascausedbothanimprovementinefficiencyandlesspollutionproduction.Why?MergerandInternalizationThesteelfirm’sprofitfunctionissothemarginalcostofproducingxunitsofpollutionisWhenitdoesnothavetofacetheexternalcostsofitspollution,thesteelfirmincreasespollutionuntilthismarginalcostiszero;hencex*=4.MergerandInternalizationInthemergedfirmtheprofitfunctionisThemarginalcostofpollutionisthusMergerandInternalizationInthemergedfirmtheprofitfunctionisThemarginalcostofpollutionisMergerandInternalizationInthemergedfirmtheprofitfunctionisThemarginalcostofpollutionisThemergedfirm’smarginalpollutioncostislargerbecauseitfacesthefullcostofitsownpollutionthroughincreasedcostsofproductioninthefishery,solesspollutionisproducedbythemergedfirm.MergerandInternalizationButwhyisthemergedfirm’spollutionlevelofxm=2efficient?MergerandInternalizationButwhyisthemergedfirm’spollutionlevelofxm=2efficient?Theexternalcostinflictedonthefisheryisxf,sothemarginalexternalpollutioncostisMergerandInternalizationButwhyisthemergedfirm’spollutionlevelofxm=2efficient?Theexternalcostinflictedonthefisheryisxf,sothemarginalexternalpollutioncostisThesteelfirm’scostofreducingpollutionisMergerandInternalizationButwhyisthemergedfirm’spollutionlevelofxm=2efficient?Theexternalcostinflictedonthefisheryisxf,sothemarginalexternalpollutioncostisThesteelfirm’scostofreducingpollutionisEfficiencyrequiresMergerandInternalizationMergerthereforeinternalizesanexternalityandinduceseconomicefficiency.Howelsemightinternalizationbecausedsothatefficiencycanbeachieved?CoaseandProductionExternalitiesCoasearguesthattheexternalityexistsbecauseneitherthesteelfirmnorthefisheryownsthewaterbeingpolluted.Supposethepropertyrighttothewateriscreatedandassignedtooneofthefirms.Doesthisinduceefficiency?CoaseandProductionExternalitiesSupposethefisheryownsthewater.Thenitcansellpollutionrights,inacompetitivemarket,at$pxeach.Thefishery’sprofitfunctionbecomes

CoaseandProductionExternalitiesSupposethefisheryownsthewater.Thenitcansellpollutionrights,inacompetitivemarket,at$pxeach.Thefishery’sprofitfunctionbecomes

Givenpfandpx,howmanyfishandhowmanyrightsdoesthefisherywishtoproduce?(Noticethatxisnowachoicevariableforthefishery.)CoaseandProductionExternalitiesTheprofit-maximumconditionsareCoaseandProductionExternalitiesTheprofit-maximumconditionsareandthesegive(fishsupply)(pollutionrightsupply)CoaseandProductionExternalitiesThesteelfirmmustbuyonerightforeveryunitofpollutionitemitssoitsprofitfunctionbecomes

Givenpfandpx,howmuchsteeldoesthesteelfirmwanttoproduceandhowmanyrightsdoesitwishtobuy?CoaseandProductionExternalitiesTheprofit-maximumconditionsareCoaseandProductionExternalitiesTheprofit-maximumconditionsareandthesegive(steelsupply)(pollutionrightdemand)CoaseandProductionExternalitiesInacompetitivemarketforpollutionrightsthepricepxmustadjusttoclearthemarketso,atequilibrium,CoaseandProductionExternalitiesInacompetitivemarketforpollutionrightsthepricepxmustadjusttoclearthemarketso,atequilibrium,Themarket-clearingpriceforpollutionrightsisthusCoaseandProductionExternalitiesInacompetitivemarketforpollutionrightsthepricepxmustadjusttoclearthemarketso,atequilibrium,Themarket-clearingpriceforpollutionrightsisthusandtheequilibriumquantityofrightstradedisCoaseandProductionExternalitiesCoaseandProductionExternalitiesSoifps=12andpf=10thenThisistheefficientoutcome.CoaseandProductionExternalitiesQ:Woulditmatterifthepropertyrighttothewaterhadinsteadbeenassignedtothesteelfirm?A:No.Profitislinear,andthereforequasi-linear,inmoneysoCoase’sTheoremstatesthatthesameefficientallocationisachievedwhicheverofthefirmswasassignedthepropertyright.(Andtheassetownergetsricher.)TheTragedyoftheCommons