1、Chapter Thirty-Two,Externalities,Externalities,An 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. An externally imposed benefit is a positive externality. An externally imposed cost is a negative e

2、xternality.,Examples of Negative Externalities,Air pollution. Water pollution. Loud parties next door. Traffic congestion. Second-hand cigarette smoke. Increased insurance premiums due to alcohol or tobacco consumption.,Examples of Positive Externalities,A well-maintained property next door that rai

3、ses the market value of your property. A pleasant cologne or scent worn by the person seated next to you. Improved driving habits that reduce accident risks. A scientific advance.,Externalities and Efficiency,Crucially, an externality impacts a third party; i.e. somebody who is not a participant in

4、the activity that produces the external cost or benefit.,Externalities and Efficiency,Externalities cause Pareto inefficiency; typically too much scarce resource is allocated to an activity which causes a negative externality too little resource is allocated to an activity which causes a positive ex

5、ternality.,Externalities and Property Rights,An externality will viewed as a purely public commodity. A commodity is purely public if it is consumed by everyone (nonexcludability), and everybody consumes the entire amount of the commodity (nonrivalry in consumption). E.g. a broadcast television prog

6、ram.,Inefficiency U(m,s) = m + f(s).,Coases Theorem,Coases Theorem is: If all agents preferences are quasilinear in money, then the efficient level of the externality generating commodity is produced no matter which agent is assigned the property right.,Production Externalities,A steel mill produces

7、 jointly steel and pollution. The pollution adversely affects a nearby fishery. Both firms are price-takers. pS is the market price of steel. pF is the market price of fish.,Production Externalities,cS(s,x) is the steel firms cost of producing s units of steel jointly with x units of pollution. If t

8、he 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,Production Externalities,The first-order profit-maximizationconditions are,Production Externalities,The first-order profit-maximizationconditions are,and,Producti

9、on Externalities,states that the steel firm,should produce the output level of steel for which price = marginal production cost.,Production Externalities,states that the steel firm,should produce the output level of steel for which price = marginal production cost.,is the rate at which the firms,int

10、ernal production cost goes down as the pollution level rises,Production Externalities,states that the steel firm,should produce the output level of steel for which price = marginal production cost.,is the rate at which the firms,internal production cost goes down as the pollution level rises, so,is

11、the marginal cost to the firm of pollution reduction.,Production Externalities,is the marginal cost to the firm of pollution reduction.,What is the marginal benefit to the steel firm from reducing pollution?,Production Externalities,is the marginal cost to the firm of pollution reduction.,What is th

12、e marginal benefit to the steel firm from reducing pollution? Zero, since the firm does not face its external cost. Hence the steel firm chooses the pollution level for which,Production Externalities,and the first-order profit-maximizationconditions are,and,E.g. suppose cS(s,x) = s2 + (x - 4)2 andpS

13、 = 12. Then,Production Externalities,determines the profit-max.,output level of steel; s* = 6.,Production Externalities,determines the profit-max.,output level of steel; s* = 6.,is the marginal cost to the firm,from pollution reduction. Since it gets no benefit from this it sets x* = 4.,Production E

14、xternalities,determines the profit-max.,output level of steel; s* = 6.,is the marginal cost to the firm,from pollution reduction. Since it gets no benefit from this it sets x* = 4.,The steel firms maximum profit level isthus,Production Externalities,The cost to the fishery of catching f units of fis

15、h 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 Externalities,The cost to the fishery of catching f units of fish when the steel mill emits x units of pollution is cF(f,x).

16、Given f, cF(f,x) increases with x; i.e. the steel firm inflicts a negative externality on the fishery. The fisherys profit function isso the fisherys problem is to,Production Externalities,The first-order profit-maximizationcondition is,Production Externalities,The first-order profit-maximizationcon

17、dition is,Production Externalities,The first-order profit-maximizationcondition is,Higher pollution raises the fisherysmarginal production cost and lowers bothits output level and its profit. This is the external cost of the pollution.,Production Externalities,E.g. suppose cF(f;x) = f2 + xf and pF =

18、 10.The external cost inflicted on the fishery by the steel firm is xf. Since the fishery has no control over x it must take the steel firms choice of x as a given. The fisherys profit function is thus,Production Externalities,Given x, the first-order profit-maximizationcondition is,Production Exter

19、nalities,Given x, the first-order profit-maximizationcondition is,So, given a pollution level x inflicted uponit, the fisherys profit-maximizing outputlevel is,Production Externalities,Given x, the first-order profit-maximizationcondition is,So, given a pollution level x inflicted uponit, the fisher

20、ys profit-maximizing outputlevel is,Notice that the fishery produces less, andearns less profit, as the steel firmspollution level increases.,Production Externalities,The steel firm, ignoring its external cost inflicted upon the fishery,chooses x* = 4, so the fisherysprofit-maximizing output level g

21、iven thesteel firms choice of pollution level isf* = 3, giving the fishery a maximumprofit level of,Notice that the external cost is $12.,Production Externalities,Are these choices by the two firms efficient? When the steel firm ignores the external costs of its choices, the sum of the two firms pro

22、fits is $36 + $9 = $45. Is $45 the largest possible total profit that can be achieved?,Merger and Internalization,Suppose the two firms merge to become one. What is the highest profit this new firm can achieve?,Merger and Internalization,Suppose the two firms merge to become one. What is the highest

23、 profit this new firm can achieve? What choices of s, f and x maximize the new firms profit?,Merger and Internalization,The first-order profit-maximizationconditions are,The solution is,Merger and Internalization,And the merged firms maximum profitlevel is,This exceeds $45, the sum of the non- merge

24、d firms.,Merger and Internalization,Merger has improved efficiency. On its own, the steel firm produced x* = 4 units of pollution. Within the merged firm, pollution production is only xm = 2 units. So merger has caused both an improvement in efficiency and less pollution production. Why?,Merger and

25、Internalization,The steel firms profit function is,so the marginal cost of producing x units of pollution is,When it does not have to face the external costs of its pollution, the steel firm increases pollution until this marginal cost is zero; hence x* = 4.,Merger and Internalization,In the merged

26、firm the profit function is,The marginal cost of pollution is thus,Merger and Internalization,In the merged firm the profit function is,The marginal cost of pollution is,Merger and Internalization,In the merged firm the profit function is,The marginal cost of pollution is,The merged firms marginal p

27、ollution cost is larger because it faces the full cost of its own pollution through increased costs of production in the fishery, so less pollution is produced by the merged firm.,Merger and Internalization,But why is the merged firms pollution level of xm = 2 efficient?,Merger and Internalization,B

28、ut why is the merged firms pollution level of xm = 2 efficient? The external cost inflicted on the fishery is xf, so the marginal external pollution cost is,Merger and Internalization,But why is the merged firms pollution level of xm = 2 efficient? The external cost inflicted on the fishery is xf, s

29、o the marginal external pollution cost is The steel firms cost of reducing pollution is,Merger and Internalization,But why is the merged firms pollution level of xm = 2 efficient? The external cost inflicted on the fishery is xf, so the marginal external pollution cost is The steel firms cost of red

30、ucing pollution is Efficiency requires,Merger and Internalization,Merger therefore internalizes an externality and induces economic efficiency. How else might internalization be caused so that efficiency can be achieved?,Coase and Production Externalities,Coase argues that the externality exists bec

31、ause neither the steel firm nor the fishery owns the water being polluted. Suppose the property right to the water is created and assigned to one of the firms. Does this induce efficiency?,Coase and Production Externalities,Suppose the fishery owns the water. Then it can sell pollution rights, in a

32、competitive market, at $px each. The fisherys profit function becomes,Coase and Production Externalities,Suppose the fishery owns the water. Then it can sell pollution rights, in a competitive market, at $px each. The fisherys profit function becomes Given pf and px, how many fish and how many right

33、s does the fishery wish to produce? (Notice that x is now a choice variable for the fishery.),Coase and Production Externalities,The profit-maximum conditions are,Coase and Production Externalities,The profit-maximum conditions are,and these give,(fish supply),(pollution right supply),Coase and Prod

34、uction Externalities,The steel firm must buy one right for every unit of pollution it emits so its profit function becomes Given pf and px, how much steel does the steel firm want to produce and how many rights does it wish to buy?,Coase and Production Externalities,The profit-maximum conditions are

35、,Coase and Production Externalities,The profit-maximum conditions are,and these give,(steel supply),(pollution right demand),Coase and Production Externalities,In a competitive market for pollution rights the price px must adjust to clear the market so, at equilibrium,Coase and Production Externalit

36、ies,In a competitive market for pollution rights the price px must adjust to clear the market so, at equilibrium,The market-clearing price for pollution rights is thus,Coase and Production Externalities,In a competitive market for pollution rights the price px must adjust to clear the market so, at

37、equilibrium,The market-clearing price for pollution rights is thus,and the equilibrium quantity of rights traded is,Coase and Production Externalities,Coase and Production Externalities,So if ps = 12 and pf = 10 then,This is the efficient outcome.,Coase and Production Externalities,Q: Would it matte

38、r if the property right to the water had instead been assigned to the steel firm? A: No. Profit is linear, and therefore quasi-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 ri

39、cher.),The Tragedy of the Commons,Consider a grazing area owned “in common” by all members of a village. Villagers graze cows on the common. When c cows are grazed, total milk production is f(c), where f0 and f”0. How should the villagers graze their cows so as to maximize their overall income?,The

40、Tragedy of the Commons,c,Milk,f(c),The Tragedy of the Commons,Make the price of milk $1 and let the relative cost of grazing a cow be $pc. Then the profit function for the entire village isand the villages problem is to,The Tragedy of the Commons,The income-maximizing number of cows to graze, c*, satisfies,i.e. the marginal income gain from the last cow grazed must equal the marginal