In the Name of God. Sharif University of Technology. Microeconomics 2. Graduate School of Management and Economics. Dr. S.

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1 In the Name of God Sharif University of Technology Graduate School of Management and Economics Microeconomics ( nd term) - Group 2 Dr. S. Farshad Fatemi Chapter 11: Externalities & Public Goods

2 We have seen that the resulting allocation of a competitive equilibrium is Pareto optimal. On the other hand, any Pareto optimal allocation can be achieved by redistribution of wealth through competitive markets (assuming suitable convexity). However, there are situation where some of our assumptions for welfare theorems do not hold and consequently markets fail to deliver optimal results. Such situations are referred to as market failures. Microeconomics 2 Dr. F. Fatemi Page 83

3 Definition (MWG 11.B.1): An externality exists whenever a consumer s utility or a firm s profit is directly (excluding any effects mediated by prices) affected by the actions of another agent. If the externality is favorable to the recipient, it is called a positive externality, otherwise it is a negative externality. Microeconomics 2 Dr. F. Fatemi Page 84

4 Examples of Negative Externality: Polluting industries: A chemical firm discharges waste into a lake & ruins the fishing for fishers Playing loud music by neighbours Congestion on roads A smoker who smokes in a room & creates discomfort for the others A farmer whose cattle create greenhouse gases & increases the possible risk of global warming Microeconomics 2 Dr. F. Fatemi Page 85

5 Examples of Positive Externality: Lighting a lamp in front of your house in the street A resident in a street who spends money on a nice front garden & neighbours also enjoy it Somebody who vaccinates himself against a potentially epidemic disease & reduces the risk of epidemic for the others as well Investing in educating the young Microeconomics 2 Dr. F. Fatemi Page 86

6 Production Externality / External Costs / Negative Exernality Ignoring the external costs associated with the manufacture of paper products, firms will base their production and pricing decisions on S1 (Marginal Private Costs). If they consider external costs, such as the cost of pollution, they will operate on S2 (Marginal Social Cost), producing Q1. The shaded area abc shows the amount by which the marginal cost of production of Q2 Q1 units exceeds the marginal benefits to consumers and the inefficiency of the private market. Microeconomics 2 Dr. F. Fatemi Page 87

7 Consumption Externality / External Benefits / Positive Exernality Ignoring the external benefits of getting flu shots, consumers will base their purchases on D1 (Marginal Private Benefit) instead of D2 (Social Private Benefit). Fewer shots will be purchased than could be justified economically. Because the marginal benefit of each shot between Q1 and Q2 exceeds its marginal cost of production. External benefits are not being realized. The shaded area abc indicates market inefficiency. Microeconomics 2 Dr. F. Fatemi Page 88

8 Bilateral Externality Consider a two-agent partial equilibrium model (two consumers i = 1,2 who are price-takers): L traded goods An action h R + taken by consumer 1 which has an effect on consumer 2 s welfare Each consumer s utility function: u i (x 1i,, x Li, h) Assume: u 2 (x 12,, x L2, h) h 0 Microeconomics 2 Dr. F. Fatemi Page 89

9 Each consumer s utility maximization problem: v i (p, w i, h) = max x i 0 u i (x i, h) s. t. p. x i w i Assuming quasilinear utility functions: v i (p, w i, h) = φ i (p, h) + w i Since consumers are price-takers: v i (p, w i, h) = φ i (h) + w i Microeconomics 2 Dr. F. Fatemi Page 90

10 Consumer 1 chooses level of h to maximize φ 1 (h): φ 1 (h) 0, with equality if h > 0 However, the Pareto optimal level should solve: max h 0 φ 1 (h) + φ 2 (h) So: φ 1 h φ 2 h, with equality if h > 0 Microeconomics 2 Dr. F. Fatemi Page 91

11 The Limits on Government Intervention Sometimes the distortion resulting from externality effect is negligible. Then little can be gained by government intervention. Government Action itself generates an external cost which should be considered whenever government decides to intervene in a market. Over the long-run some of the externalities might internalize which government action may delay or destroy this process. Microeconomics 2 Dr. F. Fatemi Page 92

12 Solutions to the externality problem Quotas: Imposing quotas and/or standards on all producers. Taxes: Taxing the polluting industries (1. find alternative technologies to pollute less 2. reducing the number of units consumed) / Tax credits for the installation of pollution controls Microeconomics 2 Dr. F. Fatemi Page 93

13 Assignment of Property Rights: Assignment of land rights to cattle owner in order to eliminate overgrazing Persuasion / Providing Information: Advertisements to urge people not to litter or to risk forest fires / Not to drink and drive / To cultivate the land so as to minimize erosion / To conserve water and gas / publishing studies showing the external costs of smoking. (Such efforts are limited in their effect) Microeconomics 2 Dr. F. Fatemi Page 94

14 Government Production: Nationalization of schools, public health services, national and state parks, transportation systems (it might reduce the competition and therefore reduce efficiency) Standards / Minimum Quality: Forcing the firms to consider some features in their production (ABS in cars) Microeconomics 2 Dr. F. Fatemi Page 95

15 Quotas and Taxes Suppose there exists a negative externality (h > h ), government can impose a quota on the externality equal to h. Then consumer 1 will limit the level of externality at the optimal level. Instead, a tax equal to t h = φ 2 h > 0 can be imposed on the externality (Pigouvian tax). In this case, consumer 1 will choose the level of externality which solves: max h 0 φ 1 (h) t h h So the FOC results: φ 1 (h) t h, with equality if h > 0 Microeconomics 2 Dr. F. Fatemi Page 96

16 Note: The optimality can also be achieved by subsidizing the reduction of externality. Pigouvian tax should be implemented directly on the production of externality. In order to achieve optimality by imposing a quota or a tax, the government should have access to the information about the benefits and costs of the externality. Microeconomics 2 Dr. F. Fatemi Page 97

17 Assignment of property rights (bargaining over externality) Suppose we assign the property right to consumer 2 and she makes an offer to consumer 1. The offer includes a lump-sum payment T in return of permission to generate the externality level of h. Then consumer 2 solves this maximization problem: max h 0,T φ 2 (h) + T s. t. φ 1 (h) T φ 1 (0) The constraint is binding, then T = φ 1 (h) φ 1 (0) Microeconomics 2 Dr. F. Fatemi Page 98

18 So the consumer 2 s optimization problem becomes: max h 0,T φ 2 (h) + φ 1 (h) φ 1 (0) The solution to this problem is h. Proposition (Coase Theorem): If Trade of the externality is possible, then bargaining will lead to an efficient allocation no matter how property rights are allocated. In assigning property rights, government does not need to have the sort of information which is needed for imposing quotas or taxes. Microeconomics 2 Dr. F. Fatemi Page 99

19 Missing markets If the property rights are well defined and enforceable, then it is possible to suggest creating a market for the externality. Consumer 1 s problem: max h 0 φ 1 (h) p h h With the FOC: φ 1 (h) p h, with equality if h > 0 Consumer 2 s problem: max h 0 φ 2 (h) + p h h With the FOC: φ 2 (h) p h, with equality if h > 0 Microeconomics 2 Dr. F. Fatemi Page 100

20 In a competitive equilibrium, the two solutions can be rewritten as: φ 1 (h) φ 2 (h), with equality if h > 0 Which the equilibrium price of the externality is: p h = φ 1 h = φ 2 h The problem is the assumption of a competitive outcome form a bilateral situation is unrealistic. However, the competitive equilibrium is achievable in multilateral setting. Microeconomics 2 Dr. F. Fatemi Page 101

21 Public Goods Definition (MWG 11.C.1): A public good is a commodity for which the use of the good by one agent does not preclude its use by other agents. More precisely, a pure public good is both Non-Excludable: It is impossible to exclude anyone from consumption. Non-Rivalrous: It is technically possible for one person to consume without reducing the amount available for others. Microeconomics 2 Dr. F. Fatemi Page 102

22 The following classification is possible: Excludable Rivalrous Private Good food; dental treatment Non-Rivalrous Club Good satellite television Non-Excludable Common Good grazing grounds; fish Public Good national defense; air Microeconomics 2 Dr. F. Fatemi Page 103

23 Consider the following model: I consumers L traded goods One public good q R + The quantity of the public good has no effect of the prices of other goods Consumers utility functions are quasi-linear wrt the same numeraire Each consumer s utility from public good: φ i (q) where φ i (. ) > 0 and φ i (. ) < 0 The cost function of producing public good: c(q) where c (. ) > 0 and c (. ) > 0 Microeconomics 2 Dr. F. Fatemi Page 104

24 Since the utility function are quasi-linear then any Pareto optimal allocation should maximize the total surplus: max q 0 φ i (q) i c(q) The FOC: φ i q i c q, with equality if q > 0 In an interior solution: φ i q i = c q marginal social benefit = marginal cost Microeconomics 2 Dr. F. Fatemi Page 105

25 Private provision of public good Suppose there is a market for the public good where the supply side consisting a single price-taking profit-maximizing firm. At a competitive equilibrium with price p for the public good, each consumer s utility maximizing decision is (q i = q k k i ): max q i 0 φ i (q i + q i ) p q i The FOC: φ i (q i + q i ) p, with equality if q i > 0 Or φ i (q ) p, with equality if q i > 0 Microeconomics 2 Dr. F. Fatemi Page 106

26 The firm should solve: max q 0 p q c(q) The FOC: p c (q ), with equality if q > 0 In the equilibrium (letting δ i = 1 if q i > 0 and δ i = 0 if q i = 0): δ i [φ i (q ) c (q )] i = 0 Microeconomics 2 Dr. F. Fatemi Page 107

27 Then whenever I > 1 and q > 0: φ i (q ) > c (q ) i In general, in our model only the consumer with the highest marginal benefit pays for the public good and all others are free-riders. Lindahl Equilibrium The equilibrium in personalized markets for public good. Microeconomics 2 Dr. F. Fatemi Page 108

28 Multilateral Externality The first issue regarding the multilateral externality is whether the externality is private or public: If the externality experienced by one agent reduces the total amount of externalities which will be felt by the others, then the externality is depletable (or private or rivalrous). On the other hand, nondepletable externalities share the characteristics of public good. Microeconomics 2 Dr. F. Fatemi Page 109

29 Depletable Externalities Consider a partial equilibrium model: J firms and I consumers who are price-takers L traded goods with price vector p An action h j R + taken by firm j which has negative externality Each firm s profit function over the amount of externality she generates given the price vector p: π j h j where π j (. ) > 0 & π j (. ) < 0 Each consumer s utility function over the amount of externality she experiences given the price vector p: φ i h i where φ i (. ) < 0 & φ i (. ) < 0 Microeconomics 2 Dr. F. Fatemi Page 110

30 At any competitive equilibrium: π j h j 0 with equality if h j > 0 The Pareto optimal level of externality is the solution to this problem: max h i,h j 0 φ i h i i + π j h j j s. t. h j j = h i i Microeconomics 2 Dr. F. Fatemi Page 111

31 The FOCs: φ i h i μ μ π j h j with equality if h i > 0, i with equality if h j > 0, j These two conditions with h j j = h i i are equivalent to the efficient conditions derived for a private good in a partial competitive equilibrium. If enforceable property rights can be defined over the externality and I and J are large enough (enough to make all agents price-takers), a market for externalities can lead to optimal allocation. Microeconomics 2 Dr. F. Fatemi Page 112

32 Nondepletable Externalities The only difference in this case is that all consumers are affected by the total amount of externality. The Pareto optimal level of externality now is the solution to this problem: max h j 0 φ i h j i j + π j h j j The FOC: φ i h j i j π j h j with equality if h j > 0 Microeconomics 2 Dr. F. Fatemi Page 113

33 The result is similar to the private provision of public good and therefore a standard market for externality fails to lead to the Pareto optimal allocation. One way to achieve the optimality is to impose a tax on externality. The optimal tax per unit is t h = φ i h j i j Microeconomics 2 Dr. F. Fatemi Page 114

34 Market for the Right to Produce Externality Another way to achieve the optimality is to impose a quota on externality, give each firm the right for generating a certain amount of externality (e.g. pollution permits), and then let the firms trade their permissions. If the number of firms is large enough, then firms in the market for permission are price-takers. Microeconomics 2 Dr. F. Fatemi Page 115

35 The optimal level of permits: h = h j j Firm j s final share of permits: h j such that j h j = h The equilibrium price for permits: p h Each firm s problem: max h j 0 π j h j + p h h j h j The FOC: π j h j p h with equality if h j > 0 Market clearing condition: j h j = h Then: p h = φ i h i Microeconomics 2 Dr. F. Fatemi Page 116

36 Example: Microeconomics 2 Dr. F. Fatemi Page 117

37 Reducing pollution is costly and adds to the costs of production, increasing product prices and reducing the quantities of products demanded. Therefore firms have a demand for the right to avoid pollution emission costs. The lower the price of such rights, the greater the quantity of rights that firms will demand. If the government issues ten pollution permits (suppose this is the optimal level of pollution), the price of the rights will settle at the intersection of the supply and demand curves here, about $1,500 regardless of initial allocation of permits. Microeconomics 2 Dr. F. Fatemi Page 118

38 Private Information and Second-Best Solutions Asymmetric information regarding the cost or benefit of externality for the agents Centralized and decentralized attempts fail to achieve optimality Start with the model of one firm (generating negative externality) and one consumer (affected by the externality) Microeconomics 2 Dr. F. Fatemi Page 119

39 Suppose the consumer s utility has the form: φ(h, η) And firm s profit: π(h, θ) η, θ R are type of consumer and firm respectively, only known by the agent herself. η, θ are independently distributed and their support is common knowledge. Assume G(η) and F(θ) are the distribution functions. Microeconomics 2 Dr. F. Fatemi Page 120

40 Decentralized Bargaining Now let s give the bargaining power to the consumer. She can make a take-it-or-leave-it offer to the firm: a pair of (h, T) For simplicity assume only two levels of externality is possible: 0 and h Consumer asks for a payment of T > c and wants to maximise her expected payoff: max T 1 G(T) (T c) The offer is accepted if and only if T < b. Quotas and Taxes Microeconomics 2 Dr. F. Fatemi Page 121

41 The best thing that the government can do is to determine the level of quota or tax based on the mean value of c and b This might be different from the optimal level Microeconomics 2 Dr. F. Fatemi Page 122

42 Other Mechanisms The regulator asks the two parties to report cost and benefit Assume they report c and b Regulator lets the externality to be generated if b c Pay consumer b, and tax the firm equal to c It is a weakly dominant strategy for both players to tell the truth It is why this mechanism is called truth-revealing mechanism. Microeconomics 2 Dr. F. Fatemi Page 123