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Chapter 34

Chapter 34. Externalities. Externalities. An externality is a cost or a benefit imposed upon someone by actions taken by others. A benefit caused by someone else (externally imposed ) is a positive externality . An externally imposed cost is a negative externality.

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Chapter 34

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  1. Chapter 34 Externalities

  2. Externalities • An externality is a cost or a benefit imposed upon someone by actions taken by others. • A benefit caused by someone else (externally imposed ) is a positive externality. • An externally imposed cost is a negative externality.

  3. Examples of Negative Externalities • Air or water pollution. • Loud parties next door (to which you’re not invited). • Traffic jams. • Passive smoking. • Increased insurance premiums because others drink, smoke or drive carelessly. • A perfume worn by the person next to you to which you have an allergic reaction.

  4. Examples of Positive Externalities • A pleasant perfume worn by the person seated next to you. • Flowers in your neighbour’s garden which look pretty from your window. • Improved driving habits that reduce accident risks. • A shift of travelling from cars to public transport which reduces air pollution.

  5. Externalities and Efficiency • The whole argument why competitive markets result in Pareto efficiency presupposes that there are no externalities. • 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 externality.

  6. Inefficiency & Negative Externalities • Consider two agents, A and B, and two commodities, money and smoke. • A is a smoker - both smoke and money are good( thing)s for A. • B doesn’t smoke and doesn’t like smoke. Money is a good and smoke is a bad for B. • They share a room and therefore breathe the same (equally smoke-filled) air.

  7. Agent A is endowed with yA SEK. • Agent B is endowed with yB SEK. • Smoke intensity is measured on a scale from 0 (no smoke) to 1 (maximum concentration).

  8. Smoke Money and smoke areboth goods for Agent A. 1 0 yA moneyA OA

  9. Smoke 1 Better 0 yA mA OA

  10. Smoke But smoke is a “bad” for B, not a “good”. 1 Better 0 yB MoneyB OB

  11. Better Turn the diagram for B around to make an Edgeworth Box Smoke 1 0 mB yB OB

  12. What are the efficient allocations of smoke and money? Smoke Smoke 1 1 0 0 mB mA OA OB

  13. Efficient allocations of smoke and money. Smoke 1 1 Smoke 0 0 yA yB OA OB mA mB

  14. Efficient allocations Smoke Smoke 1 1 0 0 yA yB OA OB mA mB

  15. Suppose there is no means by which money can be exchanged for changes in smoke level. • What then is A’s most preferred allocation? • Is this allocation efficient?

  16. Smoke Smoke The choices A has – income yA and some amount of smoke 1 1 0 0 yA yB OA OB mA mB

  17. A’s most preferred choiceis income yA and as much smoke as possible. This choiceis inefficient 1 1 Smoke Smoke 0 0 yA yB OA OB mA mB

  18. B’s most preferred choiceis income yB and no smoke. This choiceis inefficient too. Smoke Smoke 1 1 0 0 yA yB OA OB mA mB

  19. So if A and B cannot trade money for changes in smoke intensity, then the outcome is inefficient. • There is no market for smoke-filled or smoke-free air because there are no property rights. • If property rights are introduced: • Either A can have the right to smoke which is tantamount to giving A ownership of the air in the room. • Or B can have the right to breathe smoke-free air which is tantamount to giving the ownership to B.

  20. Suppose Agent B is assigned ownership of the air in the room. • Agent B can now sell “rights to smoke”. • Will there be any smoking? • If so, how much smoking and what will be the price for this amount of smoke? • Let p*s be the price paid by Agent A to Agent B in order to be allowed to create a smoke intensity of s.

  21. A line from (yA,0) with the slope -p is a budget constraint for A. Smoke Smoke 1 1 Initial endowments 0 0 yA yB OA OB mA mB

  22. p*sA transferred from A to B Smoke Smoke 1 1 Both agents gain and there is a positive amount of smoking. sA 0 0 yA yB OA OB mA mB

  23. Smoke Smoke 1 1 Both agents gain and there is a positive amount of smoking. sA 0 0 yA yB OA OB mA mB

  24. Internalising externalities • At the smoke level s, A compensates B for the smoke – bears the cost of the external negative effect caused by A’s smoking. • Making a producer of an externality to bear the full external cost or to enjoy the full external benefit is called internalizing the externality.

  25. Suppose instead that A is assigned the ownership of the air in the room. • B can now pay A to reduce the smoke intensity. • How much smoking will there be? • How much money will B pay A?

  26. Smoke Smoke 1 1 0 0 yA yB OA OB mA mB

  27. Smoke Smoke 1 1 0 0 yA yB OA OB mA mB

  28. Smoke Smoke p*sB 1 1 sB 0 0 yA yB OA OB mA mB

  29. Smoke Smoke p(sB) 1 1 Both agents gain and there is a reduced amount of smoking. sB 0 0 yA yB OA OB mA mB

  30. Notice that the • agent given the property right (asset) is better off than at her own most 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. • A general problem in cases like this is that both parties may consider that they should have the property rights.

  31. Smoke Smoke p(sB) p(sA) 1 1 sB sA¹ sB and the net incomes also depend on who “owns the air” sA 0 0 yA yB OA OB mA mB

  32. Is there a case in which the same amount of smoking occurs in equilibrium no matter which agent is assigned ownership of the air in the room? • If for both agents, preferences are quasilinear in money; U(m,s) = m + f(s), we have seen (exc. 6.3) that demand for smoke doesn’t depend on income. • In this special case, the amount of smoke at the efficient point does not depend on who has the property right.

  33. Coase’s Theorem • Coase’s 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.

  34. Production Externalities • A chemical factory produces jointly herbicides and pollution. • The pollution causes allergies and asthma in children living nearby. • The local health clinic treats the children. • ph is the market price of herbicides. • cx is the medical cost that come from an increase of pollution by one unit. • For simplicity we ignore the “intangible costs” of illness – the argument would be analogous if we can attach a value to the loss of well-being.

  35. ch(h,x) is the chemical firm’s cost of producing s units of herbicide jointly with x units of pollution. • If the chemical firm does not face any of the external costs of its pollution production then its profit function is • and the firm’s problem is to maximise this function.

  36. First-order maximization conditions In other words, production is carried on up to the point where the marginal cost of increasing production of herbicides is equal to the price and where the marginal gain from increasing pollution is zero.

  37. is the rate at which the firm’s internal production cost goes down as the pollution level rises Conversely is the marginal cost to the firm of pollution reduction. The marginal benefit to the firm of pollution production is zero since it does not pay the health care costs.

  38. But the marginal social cost is cx • If the firm had to pay the health care costs it caused it it would only increase production of pollution until • If we assume that the marginal benefit of increasing pollution is decreasing, this means that a firm that was made responsible for the damage it caused would produce less pollution (and less herbicides). • Because the cost of treating allergies is external to the firm, it overproduces. • An emissions tax of cx would increase efficiency and welfare.

  39. Production Externalities: A numerical example: A foundry produces steel (s) and pollution (x) Its cost function is: cS(s,x) = s2 + (x - 4)2 Assume that pS = 12 The profit function will be: Π(s, x) = 12s - s2- (x - 4)2 and the first order conditions for maximum are: Π’s(s, x) =12 -2s = 0 s = 6 Π’x(s, x) =2(x-4) = 0 x = 4 Π(6, 4) = 72 – 36 – 0 = 36

  40. Downstreams from the foundry is a fishery whose production depends (negatively) on the level of pollution in the water. • The cost to the fishery of catching f units of fish (which it can sell at a price of pF = 10) when the steel mill emits x units of pollution is cF(f, x) = f2 + xf • Given f, cF(f,x) increases with x; i.e. the steel firm inflicts a negative externality on the fishery.

  41. The fishery’s profit function is • and the first order condition • Π’F = 10 - 2f - x = 0 • Without any pollution f = 5 and Π = 25 • With a pollution of x=4, f = 3 and Π = 9 • Thus, production and profits are lower in the presence of pollution. This is the external cost of the pollution.

  42. Are these choices by the two firms efficient? • When the steel firm ignores the external costs of its choices, the sum of the two firm’s profits is 36 + 9 = 45. • Is 45 the largest possible total profit that can be achieved? • What happens if the two firms merge?

  43. Merger and Internalization • Profits of the new firm are. • First order conditions for maximum: • 12-2s = 0 (1) • 10 – 2f – x = 0 (2) • -2(x-4)- f = 0 (3) • (1)  s = 6 • (2)  x = 10 –2 f (4) • (3) & (4)  -2(10-2f-4) = f  f = 4; x = 2 • Note that: and

  44. And the merged firm’s maximum profit level is • Without merger, total profits were 45 and pollution was 4. • After a merger, profits are 48 and pollution is 2. • The merger has internalised the externality. • Efficiency has increased. • Pollution is decreased.

  45. In the merged firm the profit function is The marginal cost of pollution is The merged firm’s marginal pollution 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.

  46. Merger and Internalization • How else might internalization be caused so that efficiency can be achieved? • Property rights (create a market) • Taxes • Tradeable emission quotas • Restrictions on production or emissions

  47. Coase argues that the externality exists because neither the steel firm nor the fishery owns the water being polluted. • Property right to the water can be created and assigned to one of the firms. This would induce efficiency (and benefit whoever got the property rights). • To give the fishery the rights would agree with the Polluter Pays Principle

  48. Tradeable emissions quotas: The government sets a target for reduction of emissions. Each firm is given or allowed to buy a certain quantity of emission-rights. A firm that emits less than its quota can sell the right to emit to somebody else. Reductions will be made where it is cheapest to make them.

  49. Taxing pollution Assume that the foundry has to pay a tax of t*x where t is a tax rate. If t is set so that at the socially optimal level of x, the MC of polluting to the foundry will be equal to the social MC and it will reduce pollution to the optimal level. In the example, set t = 4 and solve the foundry’s profit maximisation problem! This kind of tax is called a Pigouvian tax. They are good if they are set correctly but to set them correctly requires knowledge of the optimal level of pollution.

  50. 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 f’>0 and f”<0. • How should the villagers graze their cows so as to maximize their overall income?

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