微观经济学课件：第33章 外部效应

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1、Chapter Thirty-ThreeExternalities外部效应外部效应StructureuDefinitionuConsumption externalityuProduction externalityuThe tragedy of commonsExternalitiesuAn externality is a cost or a benefit imposed upon someone by actions taken by others.The cost or benefit is thus generated externally to that somebody.uAn

2、 externally imposed benefit is a positive externality.uAn externally imposed cost is a negative externality.Examples of Negative ExternalitiesuAir pollution.uWater pollution.uLoud parties next door.uTraffic congestion.uSecond-hand cigarette smoke.Examples of Positive ExternalitiesuA well-maintained

3、property next door that raises the market value of your property.uA pleasant cologne or scent worn by the person seated next to you.uImproved driving habits that reduce accident risks.uEducation.Externalities and EfficiencyuCrucially,an externality impacts a third party;i.e.somebody who is not a par

4、ticipant in the activity that produces the external cost or benefit.Externalities and EfficiencyuExternalities cause Pareto inefficiency;typicallytoo much scarce resource is allocated to an activity which causes a negative externalitytoo little resource is allocated to an activity which causes a pos

5、itive externality.Externalities and Property RightsuAn externality is viewed as a purely public commodity.uA commodity is purely public ifit is consumed by everyone(nonexcludability),andeverybody consumes the entire amount of the commodity(nonrivalry in consumption).uE.g.a broadcast television progr

6、am.Consumption ExternalityuPareto efficient amount of smokeuInefficient equilibrium with negative externalityuProperty rights and price mechanismuQuasi-linear utility and the Coase theorem(科斯定理科斯定理)uConsider two agents,A and B,and two commodities,money and smoke.uBoth smoke and money are goods for A

7、gent A.uMoney is a good and smoke is a bad for Agent B.uSmoke is a purely public commodity.Consumption ExternalityuAgent A is endowed with$yA.uAgent B is endowed with$yB.uSmoke intensity is measured on a scale from 0(no smoke)to 1(maximum concentration).Consumption ExternalityOA10SmokemAyAMoney and

8、smoke areboth goods for Agent A.Consumption ExternalityOA10SmokemAyAMoney and smoke areboth goods for Agent A.BetterConsumption ExternalityOB10SmokemByBMoney is a good and smokeis a bad for Agent B.BetterConsumption ExternalityOB10SmokemByBMoney is a good and smokeis a bad for Agent B.BetterConsumpt

9、ion ExternalityPareto Efficient AllocationsuWhat are the efficient allocations of smoke and money?OA10SmokemAyAOB10SmokemByBPareto Efficient AllocationsOA10SmokemAOB10SmokemByAyBPareto Efficient AllocationsOA10SmokemAOB10SmokemByAyBPareto Efficient AllocationsOA10SmokemAOB10SmokemByAyBPareto Efficie

10、nt AllocationsOA10SmokemAOB10SmokemByAyBEfficientallocationsPareto Efficient AllocationsInefficiency&Negative ExternalitiesuSuppose there is no means by which money can be exchanged for changes in smoke level.uWhat then is Agent As most preferred allocation?uIs this allocation efficient?Inefficiency

11、&Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsInefficiency&Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsAs choicesInefficiency&Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocations As mostpreferred choiceis inefficientInefficiency&Negative

12、 ExternalitiesuContinue to suppose there is no means by which money can be exchanged for changes in smoke level.uWhat is Agent Bs most preferred allocation?uIs this allocation efficient?Inefficiency&Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsBs choicesInefficiency&Negative E

13、xternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocations Bs mostpreferred choiceInefficiency&Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocations Bs mostpreferred choiceis inefficientInefficiency&Negative ExternalitiesuSo if A and B cannot trade money for changes in smoke intensity

14、,then the outcome is inefficient.uEither there is too much smoke(As most preferred choice)or there is too little smoke(Bs choice).Externalities and Property RightsuRonald Coases insight is that most externality problems are due to an inadequate specification of property rights and,consequently,an ab

15、sence of markets in which trade can be used to internalize external costs or benefits.Externalities and Property RightsuCausing a producer of an externality to bear the full external cost or to enjoy the full external benefit is called internalizing the externality(外外部效应内部化部效应内部化).Externalities and

16、Property RightsuNeither Agent A nor Agent B owns the air in their room.uWhat happens if this property right is created and is assigned to one of them?Externalities and Property RightsuSuppose Agent B is assigned ownership of the air in the room.uAgent B can now sell“rights to smoke”.uWill there be a

17、ny smoking?uIf so,how much smoking and what will be the price for this amount of smoke?Externalities and Property RightsuLet p(sA)be the price paid by Agent A to Agent B in order to create a smoke intensity of sA.Externalities and Property RightsOA10SmokemAOB10SmokemByAyBExternalities and Property R

18、ightsOA10SmokemAOB10SmokemByAyBExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sA)sAExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sA)Both agentsgain andthere is apositiveamount ofsmoking.sAExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sA)sAEstablishinga mar

19、ket fortrading rightsto smoke causes an efficientallocation tobe achieved.Externalities and Property RightsuSuppose instead that Agent A is assigned the ownership of the air in the room.uAgent B can now pay Agent A to reduce the smoke intensity.uHow much smoking will there be?uHow much money will Ag

20、ent B pay to Agent A?Externalities and Property RightsOA10SmokemAOB10SmokemByAyBExternalities and Property RightsOA10SmokemAOB10SmokemByAyBExternalities and Property RightsOA10SmokemAOB10SmokemByAyBsBp(sB)Externalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sB)Both agentsgain andthere is are

21、ducedamount ofsmoking.sBExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sB)Establishinga market fortrading rightsto reducesmoke causes an efficientallocation tobe achieved.sBExternalities and Property RightsuNotice that theagent given the property right is better off than at her own mos

22、t preferred allocation in the absence of the property right.amount of smoking that occurs in equilibrium depends upon which agent is assigned the property right.Externalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sB)p(sA)sA sBsBsAExternalities and Property RightsuIs there a case in which th

23、e same amount of smoking occurs in equilibrium no matter which agent is assigned ownership of the air in the room?Externalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sB)p(sA)sA=sBExternalities and Property RightsOA10SmokeOB10SmokeyAyBp(sB)p(sA)sA=sBFor both agents,the MRS is constant asmone

24、y changes,for given smoke intensity.Externalities and Property RightsOA10SmokeOB10SmokeyAyBp(sB)p(sA)sA=sBSo,for both agents,preferences must bequasilinear in money;U(m,s)=m+f(s).Coases TheoremuCoases Theorem is:If all agents preferences are quasilinear in money,then the efficient level of the exter

25、nality generating commodity is produced no matter which agent is assigned the property right.Production ExternalitiesuA steel mill produces jointly steel and pollution.uThe pollution adversely affects a nearby fishery.uBoth firms are price-takers.upS is the market price of steel.upF is the market pr

26、ice of fish.Issues of InterestuIndependent firmsuMerger and internalizationuNon-merger solutionsProperty rights and price mechanismCoase theoremProduction ExternalitiesucS(s,x)is the steel firms cost of producing s units of steel jointly with x units of pollution.uIf the steel firm does not face any

27、 of the external costs of its pollution production then its profit function is and the firms problem is to ssss xp scs x(,)(,)Production Externalitiesmax(,)(,).,s xssss xp scs x The first-order profit-maximizationconditions areProduction Externalitiesmax(,)(,).,s xssss xp scs x The first-order profi

28、t-maximizationconditions arepcs xsss (,)0 cs xxs(,).andProduction Externalitiespcs xsss (,)states that the steel firmshould produce the output level of steelfor which price=marginal production cost.Production Externalitiespcs xsss (,)states that the steel firmshould produce the output level of steel

29、for which price=marginal production cost.cs xxs(,)is the rate at which the firmsinternal production cost goes down as thepollution level risesProduction Externalitiespcs xsss (,)states that the steel firmshould produce the output level of steelfor which price=marginal production cost.cs xxs(,)is the

30、 rate at which the firmsinternal production cost goes down as thepollution level rises,so cs xxs(,)is the marginal cost to thefirm of pollution reduction.Production Externalities cs xxs(,)is the marginal cost to thefirm of pollution reduction.What is the marginal benefit to the steelfirm from reduci

31、ng pollution?Production Externalities cs xxs(,)is the marginal cost to thefirm of pollution reduction.What is the marginal benefit to the steelfirm from reducing pollution?Zero,since the firm does not face itsexternal cost.Hence the steel firm chooses the pollutionlevel for which cs xxs(,).0Producti

32、on Externalities024 ().xand the first-order profit-maximizationconditions are122 s()2(4).mMCxx andE.g.suppose cS(s,x)=s2+(x-4)2 andpS=12.ThenProduction Externalitiespss 122,determines the profit-max.output level of steel;s*=6.Production Externalitiespss 122,determines the profit-max.output level of

33、steel;s*=6.24()xis the marginal cost to the firmfrom pollution reduction.Since it getsno benefit from this it sets x*=4.Production Externalitiespss 122,determines the profit-max.output level of steel;s*=6.24()xis the marginal cost to the firmfrom pollution reduction.Since it getsno benefit from this

34、 it sets x*=4.ssxssx(*,*)*(*)()$36.1241266442222The steel firms maximum profit level isthusProduction ExternalitiesuThe cost to the fishery of catching f units of fish when the steel mill emits x units of pollution is cF(f,x).Given f,cF(f,x)increases with x;i.e.the steel firm inflicts a negative ext

35、ernality on the fishery.Production ExternalitiesuThe cost to the fishery of catching f units of fish when the steel mill emits x units of pollution is cF(f,x).Given f,cF(f,x)increases with x;i.e.the steel firm inflicts a negative externality on the fishery.uThe fisherys profit function isso the fish

36、erys problem is to FFFf xp fcf x(;)(;)Production Externalitiesmax(;)(;).fFFFf xp fcf x The first-order profit-maximizationcondition isProduction Externalitiesmax(;)(;).fFFFf xp fcf x The first-order profit-maximizationcondition ispcf xfFF (;).Production Externalitiesmax(;)(;).fFFFf xp fcf x The firs

37、t-order profit-maximizationcondition ispcf xfFF (;).Higher pollution raises the fisherysmarginal production cost and lowers bothits output level and its profit.This is theexternal cost of the pollution.Production ExternalitiesE.g.suppose cF(f;x)=f2+xf and pF=10.The external cost inflicted on the fis

38、heryby the steel firm is xf.Since the fisheryhas no control over x it must take the steelfirms choice of x as a given.The fisherysprofit function is thus Ff xffxf(;)102Production ExternalitiesGiven x,the first-order profit-maximizationcondition is Ff xffxf(;)102102 fx.Production ExternalitiesGiven x

39、,the first-order profit-maximizationcondition isSo,given a pollution level x inflicted uponit,the fisherys profit-maximizing outputlevel isfx*.52 Ff xffxf(;)102102 fx.Production ExternalitiesGiven x,the first-order profit-maximizationcondition isSo,given a pollution level x inflicted uponit,the fish

40、erys profit-maximizing outputlevel is Ff xffxf(;)102Notice that the fishery produces less,andearns less profit,as the steel firmspollution level increases.fx*.52102 fx.Production Externalities The steel firm,ignoring its external cost inflicted upon the fishery,chooses x*=4,so the fisherysprofit-max

41、imizing output level given thesteel firms choice of pollution level isf*=3,giving the fishery a maximumprofit level of.9$343310*xf*f*f10)x*;f(22F Notice that the external cost is$12.fx*.52Production ExternalitiesuAre these choices by the two firms efficient?uWhen the steel firm ignores the external

42、costs of its choices,the sum of the two firms profits is$36+$9=$45.uIs$45 the largest possible total profit that can be achieved?Merger and InternalizationuSuppose the two firms merge to become one.What is the highest profit this new firm can achieve?Merger and InternalizationuSuppose the two firms

43、merge to become one.What is the highest profit this new firm can achieve?uWhat choices of s,f and x maximize the new firms profit?ms f xsfsxfxf(,)().12104222Merger and Internalization ms f xsfsxfxf(,)().12104222The first-order profit-maximizationconditions are mmmssffxxxf 12201020240.().The solution

44、 issfxmmm 642.Merger and Internalization mmmmmmmmmm msfxsfsxfxf(,)()()$48.12104126104624424222222And the merged firms maximum profitlevel isThis exceeds$45,the sum of the non-merged firms.Merger and InternalizationuMerger has improved efficiency.uOn its own,the steel firm produced x*=4 units of poll

45、ution.uWithin the merged firm,pollution production is only xm=2 units.uSo merger has caused both an improvement in efficiency and less pollution production.Why?Merger and Internalization ss xssx(,)()12422The steel firms profit function is so the marginal cost of producing x unitsof pollution isMCxxs

46、()()24When it does not have to face theexternal costs of its pollution,the steelfirm increases pollution until this marginalcost is zero;hence x*=4.Merger and InternalizationIn the merged firm the profit function is ms f xsfsxfxf(,)().12104222The marginal cost of pollution is thusMCxfmx()()24Merger

47、and InternalizationIn the merged firm the profit function is ms f xsfsxfxf(,)().12104222The marginal cost of pollution isMCxfmx()()24 24()().xMCxsMerger and InternalizationIn the merged firm the profit function is ms f xsfsxfxf(,)().12104222The marginal cost of pollution isMCxfmx()()24 24()().xMCxsT

48、he merged firms marginal pollution costis larger because it faces the full cost ofits own pollution through increased costsof production in the fishery,so lesspollution is produced by the merged firm.Merger and InternalizationuBut why is the merged firms pollution level of xm=2 efficient?Merger and

49、InternalizationuBut why is the merged firms pollution level of xm=2 efficient?uThe external cost inflicted on the fishery is xf,so the marginal external pollution cost isMCfxE .Merger and InternalizationuBut why is the merged firms pollution level of xm=2 efficient?uThe external cost inflicted on th

50、e fishery is xf,so the marginal external pollution cost isuThe steel firms marginal cost of reducing pollution is MCfxE .()2(4).mMCxx Merger and InternalizationuBut why is the merged firms pollution level of xm=2 efficient?uThe external cost inflicted on the fishery is xf,so the marginal external po

51、llution cost isuThe steel firms marginal cost of reducing pollution is uEfficiency requiresMCfxE .()2(4).mMCxx()2(4).EmxMCMCxfx Merger and Internalization.ExMCf()2(4).mMCxx 42xMerger and InternalizationuMerger therefore internalizes an externality and induces economic efficiency.uHow else might inte

52、rnalization be caused so that efficiency can be achieved?Coase and Production ExternalitiesuCoase argues that the externality exists because neither the steel firm nor the fishery owns the water being polluted.uSuppose the property right to the water is created and assigned to one of the firms.Does

53、this induce efficiency?Coase and Production ExternalitiesuSuppose the fishery owns the water.uThen it can sell pollution rights,in a competitive market,at$px each.uThe fisherys profit function becomes Ffxf xp ffxfp x(,).2Coase and Production ExternalitiesuSuppose the fishery owns the water.uThen it

54、can sell pollution rights,in a competitive market,at$px each.uThe fisherys profit function becomesuGiven pf and px,how many fish and how many rights does the fishery wish to produce?(Notice that x is now a choice variable for the fishery.)Ffxf xp ffxfp x(,).2Coase and Production Externalities FfFxfp

55、fxxfp 200 Ffxf xp ffxfp x(,).2The profit-maximum conditions areCoase and Production Externalities FfFxfpfxxfp 200 Ffxf xp ffxfp x(,).2The profit-maximum conditions areand these givefpxppxSfx*.2(fish supply)(pollutionright supply)Coase and Production ExternalitiesuThe steel firm must buy one right fo

56、r every unit of pollution it emits so its profit function becomesuGiven pf and px,how much steel does the steel firm want to produce and how many rights does it wish to buy?Ssxs xp ssxp x(,)().224Coase and Production Externalities SsSxspsxxp 20240()Ssxs xp ssxp x(,)().224The profit-maximum condition

57、s areCoase and Production Externalities SsSxspsxxp 20240()Ssxs xp ssxp x(,)().224The profit-maximum conditions areand these givespxpsDx*.242(steel supply)(pollutionright demand)Coase and Production ExternalitiesIn a competitive market for pollution rightsthe price px must adjust to clear the markets

58、o,at equilibrium,xpppxDxfxS*.422Coase and Production ExternalitiesIn a competitive market for pollution rightsthe price px must adjust to clear the marketso,at equilibrium,xpppxDxfxS*.422The market-clearing price for pollutionrights is thusppxf 283Coase and Production ExternalitiesIn a competitive m

59、arket for pollution rightsthe price px must adjust to clear the marketso,at equilibrium,xpppxDxfxS*.422The market-clearing price for pollutionrights is thusppxf 283and the equilibrium quantity of rightstraded isxxpDSf*.163Coase and Production ExternalitiesspfpxxpsxDSf*;*;*;2163ppxf 283.Coase and Pro

60、duction ExternalitiesspfpxxpsxDSf*;*;*;2163ppxf 283.So if ps=12 and pf=10 thensfxxpDSx*;*;*;.6424This is the efficient outcome.Coase and Production ExternalitiesuQ:Would it matter if the property right to the water had instead been assigned to the steel firm?uA:No.Profit is linear,and therefore quas

61、i-linear,in money so Coases Theorem states that the same efficient allocation is achieved whichever of the firms was assigned the property right.(And the asset owner gets richer.)The Tragedy of the Commons公地悲剧uConsider a grazing area owned“in common”by all members of a village.uVillagers graze cows

62、on the common.uWhen c cows are grazed,total milk production is f(c),where f0 and f”0 and f”0 and f”0.So the economic profit from introducing one more cow is positive.uSince nobody owns the common,entry is not restricted.(*)*(*)*(*)*ccf cp ccf ccpcc 0The Tragedy of the CommonsuEntry continues until t

63、he economic profit of grazing another cow is zero;that is,until()()().ccf cp ccf ccpcc 0The Tragedy of the CommonscMilkf(c)pccslope=f(c*)c*f ccpc()f(c*)cThe Tragedy of the CommonscMilkf(c)pccslope=f(c*)c*f ccpc()f(c*)The commons are over-grazed,tragically.cThe Tragedy of the CommonsuThe reason for t

64、he tragedy is that when a villager adds one more cow his income rises(by f(c)/c-pc)but every other villagers income falls.uThe villager who adds the extra cow takes no account of the cost inflicted upon the rest of the village.The Tragedy of the CommonsuModern-day“tragedies of the commons”includeover-fishing the high seasover-logging forests on public landsover-intensive use of public parks.urban traffic congestion.