Microeconomics Slides Ch 6-8 PDF

Chapter 6: Externalities Varian, Chapter 24 114 Ch 6.1: Introduction I What is an externality? 115 Ch 6.1: Introduction 116 Ch 6.1: Introduction Definition 6.1 (Externality) An externality is p...

Chapter 6: Externalities Varian, Chapter 24 114 Ch 6.1: Introduction I What is an externality? 115 Ch 6.1: Introduction 116 Ch 6.1: Introduction Definition 6.1 (Externality) An externality is present whenever the well-being of a consumer or the production possibilities of a firm are directly a↵ected by the actions of another agent in the economy. I Definition given in Mas-Colell, Whinston and Green (1995), Ch. 11.B. I When we say “directly” we mean to exclude any e↵ects which are mediated by prices. 117 Ch 6.1: Introduction 118 Ch 6.1: Introduction I If the well-being of a consumer is a↵ected we will speak of a consumption externality. I If the production possibility of a firm is a↵ected we will say it is a production externality. I An externality can be negative or positive. I Smoking in a restaurant and taking a flu vaccine both have a consumption externality. I A chemical plant which pollutes a lake will have a negative production externality on the local fishery. On the other hand, a bee-keeper and an orchard will have positive externality on each other. 119 Ch 6.1: Introduction 120 Ch 6.1: Introduction 121 Ch 6.1: Introduction 122 Ch 6.2: A production externality I A steel mill produces upstream of a fishery. I The steel mill produces steel s from labor according to the production function @ @2 s = (`s ) with > 0, < 0. @`s @`2s I When producing s units of steel, the mill unavoidably produces ⇢(s) units of waste (with @⇢(s) @s > 0), which is expelled into the river. 123 Ch 6.2: A production externality I The fishery produces f units of fish which depends on the amount of labor `f employed and the amount of pollution in the river ⇢. I The production function of the fishery is given by f = (`f , ⇢) with @ @2 @ @2 > 0, < 0, < 0, < 0. @`f @`2f @⇢ @`f @⇢ 124 Ch 6.2: A production externality I The steel mill and the fishery are price takers. I Let p, q and w be the prices of steel, fish and labor. I The profit function of the steel mill is ⇡s (`s |p, w) = p (`s ) w`s while the profit function of the fishery is ⇡f (`f |q, w, `s ) = q (`f , ⇢( (`s ))) w`f. 125 Ch 6.2: A production externality I The steel mill chooses `0s so that @ (`s ) p = w. @`s `s =`0s I Given ⇢0 = ⇢( (`0s )), the fishery chooses `0f so that @ (`f , ⇢0 ) q = w. @`f `f =`0f I The market allocation is then (`0s , `0f ). 126 Ch 6.2: A production externality I This allocation is inefficient. I Suppose the steel mill reduces production by some small amount d`s < 0. The change in its profit is given by " # @ (`s ) d⇡s = p w d`s = 0. `s =`0s @`s `s =`0s | {z } =0 I On the other hand, this reduction in `s impacts the fishery’s profits in a positive way: @ (`f , ⇢) @⇢( ) @ (`s ) d⇡f = q d`s > 0. @⇢ | @{z } @`s |{z} | {z } | {z } 0 127 Ch 6.2: A production externality I The efficient outcome is the solution to max ⇡s + ⇡f. `s ,`f From the FOC with respect to `s we obtain d ! (⇡s + ⇡f ) = 0 d`s   @ (`s ) @ (`f , ⇢) @⇢( ) @ (`s ) p w + q =0 @`s @⇢ @ @`s  @ (`s ) @ (`f , ⇢) @⇢( ) p+q =w (1) @`s @⇢ @ | {z } `0f and f ⇤ > f 0. 129 Ch 6.3: Solutions I The problem is that the steel mill does not take into account the negative externality that it exerts on the fishery. I Several solutions have been proposed, each with some deficiencies: I Pigovian taxes I Property rights I Missing markets/Coase theorem 130 Ch 6.3: Pigovian taxes Arthur Cecil Pigou (1877-1959) Cambridge (succeeded Alfred Marshall) 131 Ch 6.3: Pigovian taxes I From this perspective, the steel mill faces the wrong price. I p does not include the e↵ect of steel production on the fishery. I If we imposed an appropriate tax on steel production, the steel mill would “internalize” the pollution externality. I The optimal Pigou tax is !✓ ◆ ⇤ ⇤ @ (`⇤f , ⇢) @⇢( ) t = q >0 @⇢ ⇢=⇢⇤ @ = ⇤ 132 Ch 6.3: Pigovian taxes I Now, the profit function of the mill is ⇡s (`s |p, w, t⇤ ) = (p t⇤ ) (`s ) w`s I and the mill chooses `s in order to maximize post-tax profits. I The FOC of the mill is @ (`s ) (p t⇤ ) =w @`s I and it is easy to see that this is the same as the efficiency condition in Eq. (1). 133 Ch 6.3: Pigovian taxes I An example of a Pigou tax is the proposed “carbon tax”. I A problem with Pigou taxes is that it requires a lot of information. I But, optimality is a high standard. Even if we don’t set the tax optimally, a small Pigou tax will improve the outcomes. 134 Ch 6.3: Pigovian taxes 135 Ch 6.3: Missing markets/Coase theorem I From this perspective, the steel mill actually produces two outputs: steel and pollution. I There is no market for pollution. I If there was a market, and the price for pollution was t⇤ , the mill would produce the efficient output. I But the markets for pollution as production externality would likely be thin — there is no reason to expect the competitive price t⇤. I Pollution as consumption externality has attributes of a public good, and the market would likely not provide incentives for pollution reduction. 136 Ch 6.3: Missing markets/Coase theorem I Coase provides a similar argument without having to rely on markets to find the efficient price. I Suppose the mill had the right to pollute. The fisher would have an incentive to pay the mill in order for the mill to reduce the output. I Similarly, suppose the fishery had the right to clean water. The mill would be willing to pay the fishery to the right to pollute. I Coase Theorem: If there are no transaction costs, then independently of the initial allocation of property rights the parties will reach the efficient allocation through voluntary bargaining. 137 Ch 6.3: Missing markets/Coase theorem Ronald Coase (1910-2013) University of Chicago Nobel Memorial Prize in Economics (1991) 138 Ch 6.3: Missing markets/Coase theorem I Coase Theorem seems to solve the problem of externalities, and does so without relying on the state’s knowledge of detailed information (like Pigou). I But, there are problems with this solution too: I If the externality a↵ects many parties, bargaining is difficult due to the free rider problem. If you drive a car, can you negotiate with every person who inhales some of your exhausts? I Also, if the impact of externalities is private knowledge of the agents, then the Coase Theorem breaks — there is actually no mechanism that will lead to the efficient outcome (known as the Myerson-Satterthwaite Theorem). 139 Ch 6.3: Property Rights I Note that if the steel mill and fishery merged, their joint profits would be higher than the sum of their individual profits. I Thus, it would be profitable for one firm to buy the other one. I This will not solve the consumption externalities, or the externalities that are spread out among many firms. 140 Chapter 7: Public goods Varian, Chapter 23 141 Ch 7.1: Introduction I A good is said to be excludable if it is possible to exclude individuals from consuming the good. I An apple is an excludable good. You have to pay the store in order to consume it. I Quiet during the night is not excludable. I A good is said to be nonrival if one individual’s consumption does not diminish the amount available to others. I If I eat an apple, nobody else can eat it. I However, if I sleep well because it is quiet during the night, this does not prevent anyone else from also enjoying the quiet. 142 Ch 7.1: Introduction I If a good is both exludable and rival, we say it is a private good. I An apple is a private good. Until now, we have dealt only with private goods. I If a good is excludable, but it is nonrival, we say it is a club good. I For example, Spotify and Netflix. I A good which is not excludable, but it is rival is called a common good. I For example, fishing in the ocean. I Finally, if a good is not excludable and is nonrival, then we speak of a public good. I A typical example is national defense. 143 Ch 7.1: Introduction I We will focus on discrete public goods. I That is, goods which are either provided (if enough is invested) or not. I A dam to protect against floods. I A sewage treatment plant. I On the other hand we have continuous goods, where investing more provides better, or more, public goods. I For example, national defense. I For simplicity, we consider only the case of two agents. 144 Ch 7.2: Efficient provision of a public good I Suppose there are two agents and two goods, a private good and a public good. I Each agent has some initial endowment of resources !i which can be spent on the private good xi or the public good gi such that xi + gi  !i. I Agents have a strongly increasing utility ui (G, xi ). I Public good is discrete and costs c to provide: ( 1 if g1 + g2 c G= (2) 0 if g1 + g2 < c. 145 Ch 7.2: Efficient provision of a public good I When is it Pareto efficient to provide the public good? I An allocation in this setting is a vector of private good consumption and investment in public good (x1 , g1 , x2 , g2 ). An allocation is feasible if: x1 + g 1 + x2 + g 2  !1 + !2. I Suppose that the maximum willingness to pay of agent i for the public good is ri : ui (1, wi ri ) = ui (0, !i ). 146 Ch 7.2: Efficient provision of a public good Proposition 7.1 Consider the allocation xi = !i and gi = 0 for i = 1, 2. It is a Pareto improvement to provide a public good if and only if r1 + r2 > c. 147 Ch 7.3: Market provision of a public good I When goods are private, the First Welfare Theorem tells us that any Walrasian equilibrium will be Pareto efficient. I Will market provision be efficient when goods are public? I Consider the following example: r1 = 100, r2 = 50 and c = 120. According to the result above, it is efficient to provide the public good. I The game is as follows: there is a price for the public good p, and each agent decides whether to pay p or not. The public good is provided only if the sum of paid prices is at least c. 148 Ch 7.3: Market provision of a public good I Depending on p we get the following 3 games. (Why games now, when with private goods we did not have any games?) I First, suppose that p < 60: contributes does not contributes p, p p, 0 does not 0, p 0, 0 149 Ch 7.3: Market provision of a public good I Next, suppose that 60  p < 120: contributes does not contributes 100 p, 50 p p, 0 does not 0, p 0, 0 I Finally, suppose that 120  p: contributes does not contributes 100 p, 50 p 100 p, 50 does not 100, 50 p 0, 0 150 Ch 7.3: Market provision of a public good I Bottom line: the market is likely to under-provide public goods. I We must look for alternative mechanisms for provision of such goods. I An obvious answer is to turn to the government for the provision of such goods. I But how should a government know if the good should be provided? I Maybe the people can vote on whether they want the good or not. 151 Ch 7.3: Voting for a public good 152 Ch 7.3: Voting for a public good I Suppose we have three consumers voting on whether to provide a public good at a cost c = 99. I If the good is provided each consumer pays equally a share of the cost. I If the good is not provided, nobody pays anything. I Suppose consumers vote in favor if and only if their value of receiving the good is greater than the price. I Their reservation prices are r1 = 90, r2 = 30 and r3 = 30. I Thus, it is efficient to provide the public good. 153 Ch 7.3: Voting for a public good I However, if the public good is provided, each consumer will have to pay 99/3 = 33. I Thus, only consumer 1 votes in favor of providing the good and the good is not provided! I In this example, voting leads to uderprovision of the public good, like the market does. 154 Ch 7.3: Voting for a public good I Next, suppose the cost is still 99 but the reservation prices are now r1 = r2 = 40 and r3 = 10. I Now it is not efficient to provide the public good. I But, since the cost is only 33 per person, consumers 1 and 2 vote in favor of the public good. I Now, voting leads to overprovision of the public good! I Clearly, we will need to find a way to incorporate (probably private) information about each agent’s reservation price in both the decision to provide the public good, and in the way the costs are shared. I This (and much more general questions!) is the subject of study of mechanism design, a topic we will explore in the last chapter of this class. 155 Chapter 8: Market Power Jehle and Reny, Chapter 4.2 156 Ch 8.1: Introduction I The results that market outcomes are Pareto efficient depend on the assumption that all agents in the economy act as price takers. I For example, in the Robinson Crusoe economy, we have written the optimization problem of the firm as max ph↵ wh h I However, large firms are aware that they can influence the market price of their products. How does this a↵ect efficiency of equilibria? 157 Ch 8.1: Simple model I Let us consider this question in a simple partial equilibrium model. I Suppose that there is a market for some good, and that the market demands quantity Q if the price of the good is P (Q) = a bQ. I Suppose further that this good can be produced at some marginal cost c. 158 Ch 8.1: Efficient quantity I An outcome is efficient if everyone who values the good more than it costs to produce it, gets the good. I The quantity produced is efficient if P (Q) = c which gives the efficient quantity as a c Q⇤ = b 159 Ch 8.1: Efficient quantity 160 Ch 8.1: Monopoly I Now suppose there is a single firm which can produce the good. That firm chooses the quantity to maximize its profit: max P (q)q cq q or equivalently max (a bq)q cq. q I Solving this yields the monopoly quantity a c qM = 2b 161 Ch 8.1: Monopoly 162 Ch 8.1: Monopoly 163 Ch 8.1: Oligopoly I What would happen if there were N firms choosing quantities simultaneously? ! Cournot model: 0 1 N X max P @ qj Aqi cqi qi j=1 I We can solve this and find that the equilibrium quantity chosen by each firm is 1 a c qN = n+1 b and the total quantity supplied to the market is n a c n QN = = Q⇤ n+1 b n+1 164 Ch 8.1: Oligopoly 165 Ch 8.1: Oligopoly 166 Ch 8.1: Solutions I What should we do about the inefficiencies caused by market power? I Should we make sure there are no large firms with significant market power? 167 Ch 8.1: Solutions I US: - Sherman Act of 1890 - Clayton Act of 1914 I EU: - TFEU Art. 101 and 102 - Council Regulation (EC) No 139/2004 I Switzerland - Federal Act on Cartels and other Restraints of Competition (Kartellgesetz, 1995) 168