Ch33Externalities(中级微观经济学-北大-赵耀辉).ppt

ExternalitiesuAn externality is a cost or a benefit imposed upon a consumer or a firm by actions taken by others. The cost or benefit is thus generated externally to the consumer or the firm.uAn 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 suffered by a non-smoker.uIncreased health insurance premia due to alcohol or tobacco consumption.Examples of Positive ExternalitiesuA well-maintained property next door that raises the market value of your own property.uA pleasant cologne or scent worn by the person seated next to you.uImproved driving habits that reduce accident risks.uA scientific advance.Externalities and EfficiencyuThe crucial feature of an externality is that it impacts a third party; that is, somebody who is not directly a participant in the activity which 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 positive externality.Externalities and Property RightsuAn externality will be taken to be 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 program.Inefficiency & Negative ExternalitiesuConsider an example of two agents, A and B, and two commodities, money and smoke.uBoth smoke and money are goods for Agent A.uMoney is a good and smoke is a bad for Agent B.uSmoke is a purely public commodity.Inefficiency & Negative ExternalitiesuAgent 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).Inefficiency & Negative ExternalitiesOA10SmokemAyAMoney and smoke areboth goods for Agent A.Inefficiency & Negative ExternalitiesOA10SmokemAyAMoney and smoke areboth goods for Agent A.BetterInefficiency & Negative ExternalitiesOB10SmokemByBMoney is a good and smokeis a bad for Agent B.BetterInefficiency & Negative ExternalitiesOB10SmokemByBMoney is a good and smokeis a bad for Agent B.BetterInefficiency & Negative ExternalitiesuWhat are the efficient allocations of smoke and money?Inefficiency & Negative ExternalitiesOA10SmokemAyAOB10SmokemByBInefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBInefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBInefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBInefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsInefficiency & Negative ExternalitiesuSuppose there is no mechanism by which money can be exchanged for changes in smoke level.uWhat then is Agent As most preferred allocation?uIs this allocation efficient?Inefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsInefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocationsAs choicesInefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocations As mostpreferred choiceis inefficientInefficiency & Negative ExternalitiesuContinue to suppose there is no mechanism 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 ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocations Bs mostpreferred choiceInefficiency & Negative ExternalitiesOA10SmokemAOB10SmokemByAyBEfficientallocations Bs mostpreferred choiceis inefficientInefficiency & Negative ExternalitiesuSo if neither A nor B can trade money for changes in smoke intensity, 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 absence 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.Externalities and 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 that Agent B is assigned ownership of the air in the room.uAgent B can now sell “rights to smoke”.uWill there be any smoking?uIf so, how much smoking with there be and what will be the equilibrium 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 RightsOA10SmokemAOB10SmokemByAyBExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sA)sAExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sA)Both agentsgain andthere is apositiveamount ofsmoking.sAExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sA)sAEstablishinga market 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 Agent 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 areducedamount ofsmoking.sBExternalities and Property RightsOA10SmokemAOB10SmokemByAyBp(sB)Establishinga market fortrading rightsto reducesmoke causes an efficientallocation tobe achieved.sBExternalities and Property RightsuNotice that the agent given the property right (asset) is better off than at his/her own most preferred allocation in the absence of the property right.uNotice also that the amount of smoking that occurs in equilibrium typically 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 the same amount of smoking occurs in equilibrium no matter which of the agents 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 asmoney 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 externality generating commodity is produced no matter to which agent its property right is assigned.Production ExternalitiesuConsider a steel mill which 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 price of fish.Production 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 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 profit-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 steelfor 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 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 reducing 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( , ).0Production Externalities ss xssx( , )() 12422and the first-order profit-maximizationconditions are122 s024 ().xandE.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 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 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 externality 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 fisherys 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 first-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 fisheryby 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, 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 fisherys 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-maximizing 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 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 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 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 pollution.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( )() 24and, since 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 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()( ).xMCxsThe 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 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 the fishery is xf, so