MB (polluter) MC (pollutee) Water Pollution. Full pollution. Zero pollution

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1 Fall 2011 Economics 431 Final Exam Name KEY Question 1. (30 points) The Coase Theorem A firm pollutes a local river and causes damage to a swim club downstream. The line MB represents the firms Marginal Benefit from polluting and the line MC represents the Marginal Cost of the pollution damages to swimmers. State your answers to each of the following questions in terms of the areas A, B, C, D, E, and F. Firm Swim Club MB (polluter) MC (pollutee) A F B E C D Q* Zero pollution Water Pollution Full pollution a) If the swim club is given the property right to the river, what area represents the minimum total payment the swim club would be willing to accept to allow the firm to pollute the river to the efficient level? Area C b) If the swim club has the property right for the river, what area represents the maximum total payment that the firm would be willing to pay to pollute the water to the efficient level? Area A+B+C c) If the swim club has the property right for the river, what area represents the swim club s gain from trading water rights with the firm at the fair bargaining price? Area B d) If the firm has the property right to pollute the water, what area represents the minimum total payment the firm would be willing to accept to reduce water pollution to the efficient level? Area D e) If the firm has the property right to pollute the water, what area represents the swim club s gain from trading water rights with the firm at the fair bargaining price? Area F f) In light of the properties necessary for the Coase Theorem to hold, would you expect an efficient outcome to be more likely when property rights were given to the swim club or firm? And why? The Coase Theorem may be more likely to hold when the swim club has the property rights, and the reason is that transaction costs exist in resolving the common property problem the club would face in collecting payments from swim club members.

2 Question 2. Transferable Permits (30 points). Suppose two firms pollute a common water medium, and the water medium is well-mixed so that the damage from water pollution does not depend on the identity of the polluter. Firm 1 receives total benefit B 1 (X 1 ) from polluting and firm 2 receives total benefit B 2 (X 2 ) from polluting and these benefits differ; i.e., B 1 (X) B 2 (X) for any (common) pollution level X. Pollution creates external costs in the economy and marginal external cost is increasing in the pollution level. a) (20 points) Draw a diagram that shows the socially optimal level of pollution to be allocated between the two firms. Label the region(s) that represent the efficiency gain from a transferable permit policy in the case where all permits are given to firm 1. Label the equilibrium permit price on your diagram. $/X MSC P* P 1 MB T = Total pollution demand MB 2 MB 1 X 2 * X 1 * X 2 0 * X Pollution The permit price is P * and the shaded regions represent the efficiency gain from trading. Firm 1 sells permits from * to X 1 * at price P * and gives up the area under MB1 in pollution benefits. Firm 2 buys X 2 * = ( * - X 1 * ) permits and receives consumer surplus in the permit market as the total pollution benefit (area under MB 2 curve) less permit cost of P * X 2 *. b) (10 points) Show by formally considering the pollution decision of firm(s) that the socially optimal outcome arises in a competitive permit market regardless of the initial distribution of permits across firms. FP (consider firm 1 with initial allocation of permits): max B 1 (X 1 ) + P( X 1 ) = B 1 (X 1 ) - P X 1 +P The first-order condition of the firm is: B 1 (X 1 ) P = 0. This condition is independent of the initial allocation of permits (whatever happens to be). The same holds for firm 2, so B 1 (X 1 ) = B 2 (X 2 ) = P and the same allocative efficiency criterion is met for any initial distribution of permits.

3 Question 3. Monopoly Permit Market (40 points) An issue with pollution markets, as with any market, is the potential for firm(s) to corner the market by acquiring all the permits and then selling them at monopoly prices. Suppose a permit market consists of two polluting firms: Firm 1 has total benefit from pollution (X) given by B 1 (X 1 ) = 100X 1 0.5X 1 2, and firm 2 has total benefit from pollution given by B 2 (X 2 ) = 100X 2 X 2 2. The total external cost of pollution is given by the damage function D(X) = 50X, where X = X 1 + X 2. A. (10 points). Calculate the socially optimal pollution level (X*) and the optimal distribution of pollution across the two firms (X 1 * and X 2 *) W = B 1 (X 1 ) + B 2 (X 2 ) - D(X) = 100X 1 0.5X X 2 0.5X (X 1 + X 2 ) FOC: dw/dx 1 = X 1-50 = 0 => X * 1 = 50 dw/dx 2 = X 2-50 = 0 => X * 2 = 50 and X * = 100 B. (5 points). If firm 1 acquires all the permits, calculate the marginal cost (MAC) for selling permits. If firm 1 is allocated all X=100 permits, the firm could use all of them and receive a positive MB for each c unit of pollution (X 1 =100 is the unregulated optimum for firm 1). If the firm chooses to sell permits, the marginal cost of selling a permit in the permit market is the opportunity cost of not polluting that unit. Since not polluting a unit for the sake of selling the unit to firm 2 entails abating a unit of pollution, the marginal cost of selling a permit is MAC: That is, abatement is A = X 1, so B 1 (X 1 ) = X 1 = (100 - A) MC = MAC = A (where A = abatement = number of permits sold) C. (5 points) For firm 2, calculate the (inverse) demand for permits. Calculate the marginal revenue function facing plant 1 in the permit market. Firm 2 has no pollution rights and therefore must buy a permit for each unit of pollution. The (inverse) demand for permits for firm is the marginal benefit of pollution: P = B 2 (X 2 ), or P = 100 X 2 Since firm 2 must purchase a permit for each unit of pollution, X 2 = A (the amount abated by firm 1). Inverse demand for permits is therefore P = 100 A. Marginal revenue has twice the slope of linear (inverse) demand, so: MR = 100 2A (Formally, TR = (100 A) A = 100A A 2 => MR = 100 2A

4 3D. (10 points) Draw a graph that shows the monopoly outcome and the socially optimal allocation. Show the deadweight loss from the monopoly permit market on your graph. $/A p M =66.67 DWL MAC = A p * =50 MR=100 2A p =100 A A M =33.33 A* = A E. (10 points) How many permits will a monopolist operating firm 1 sell to firm 2 in the permit market? What is the monopoly permit price? How much will each firm pollute? Explain why this outcome is inefficient. A monopoly permit seller sets MR = MC => 100 2A = A => 100 = 3A => A M = The monopoly permit price is a point on inverse demand, so: p M = p() = = $ A monopoly permit seller rations permit sales to drive permit prices up. In the monopoly equilibrium, the pollution levels are X 2 M = A M = and X 1 M = = 67.33; The outcome is inefficient, because allocative efficiency is not met.

5 Question 4. (30 points) Controlling Pollution at the Widget Factory Suppose a firm uses two inputs to produce widgets, labor (L) and capital (K). Capital pollutes and labor does not. Suppose further that the output level of the firm at an optimal allocation is 20 percent lower than the current (unregulated) level. Draw a diagram that shows that a standard on output that requires the firm to produce 20 percent less output is suboptimal. Show the optimal solution on your diagram, explain how it is different than a standard requiring a 20 percent reduction of output, and describe 2 types of alternative policies that could attain the optimum. L L* L 0 L 1 Q 0 Q 1 K* K 1 K 0 C/r* C 1 /r C 0 /r K The initial production level is shown as the isoquant Q 0. The cost of producing Q 0 is C 0, where C 0 = wl + rk is the isocost line. The K-intercept is therefore C 0 /r. If a production standard is implemented requiring a 20% reduction in output to Q 1, the firm scales back production proportionately by selecting (roughly) 20% less labor (L 1 L 0 ) and 20% less capital (K 1 K 0 ). This is not optimal, since input prices in the economy do not fully reflect negative external costs. Specifically, since K polluted and L does not, the rental rate on capital is not high enough (r < r*). The social price that reflects the marginal social cost of capital is r* and the optimal mix of inputs that achieves the isoguant line Q 1 at the social price level is L* and K*, which involves less capital and an additional input substitution effect away from capital and towards labor due to the relative price change. The optimal policy involves L* and K* at the optimal production level Q 1. Two policies that can achieve this result: (1) a standard on K* and L*; or (2) a tax of t*= E(K*) on polluting capital Question 5. Deposit-Refund System (40 points)

6 Suppose consumers derive total benefit of B(Q) = 10Q 0.25Q 2 from consuming fluorescent lights (Q), where Q denotes fluorescent bulbs (in hundred millions). The total cost of producing fluorescent lights is given by c(q) = Q Q 2. After consumption, fluorescent lights can be recycled at a recycling center (R) or disposed in a landfill (D), so that Q = R+D. Recycling fluorescent lights requires that consumers travel to a recycling center (e.g., Home Depot), which is a hassle, and the total cost of recycling for consumers is C(R) = 0.5R 2. It is much easier for consumers to simply discard fluorescent lights in the garbage (D); however, fluorescents contain toxic chemicals such as argon and mercury that contaminate the environment through their accumulation in landfill waste. According to the Environmental Protection Agency (EPA), approximately 800 million fluorescent bulbs are improperly disposed of every year. Suppose the environmental damage of fluorescents disposed in landfills is given by E(D) = 2D 2. A. (20 points) What is the welfare-maximizing mix of recycled and disposed fluorescents (R*, D*)? B(Q) = 10Q 0.25Q 2 = 10(D + R) 0.25(D + R) 2 c(q) = Q Q 2 = (D + R) (D + R) 2 W = 10(D + R) 0.25(D + R) 2 - (D + R) (D + R) 2-0.5R 2 2D 2 FOC: (1) dw/dr = (D + R) 1 0.5(D + R) R = 0 => (1) 9 (D + R) = R (2) dw/dd = (D + R) 1 0.5(D + R) 4D = 0 => (2) 9 (D + R) = 4D Solving (1) and (2) together => R = 4D Plugging this value into (1): 9 (D+4D) = 4D => 9 = 9D => D* = 1 Noting that R = 4D => R* = 4 B. (10 points) What is the outcome in an unregulated, competitive market for fluorescents? CP: Max CS = B(Q) pq 0.5R 2, where Q = D + R CS = 10(D + R) 0.25(D + R) 2 p(d + R) 0.5R 2 FOC: (1) dcs/dr = (D + R) p R = 0 => p = (D + R) - R (2) dcs/dd = (D + R) p = 0 => p = (D + R) Notice that these 2 conditions can only be met when R c = 0. The equilibrium price equates supply and demand in the fluorescent market, where Q = D. Formally, the firm s problem (FP) is: Max = pq - Q Q 2 FOC: d/dq = p 1 0.5Q = 0 => p = Q Market Equilibrium: p = MB = MC => Q = Q => Q c = D c = 9 P c = $5.50 and R c = 0

7 C. (10 points) Suppose it is impossible to monitor consumers and tax them for disposing fluorescents in garbage bins. Derive a deposit-refund system to achieve (R*, D*) with a combination of a tax on fluorescent bulbs and a refund on fluorescent bulbs returned to recycling centers. The policy levies a tax of $t per unit on all fluorescent bulbs and returns $s back to consumers on recycled fluorescents. The consumer s problem under the deposit-refund system is: CP: Max CS = B(Q) pq 0.5R 2 tq + sr, where Q = D + R CS = 10(D + R) 0.25(D + R) 2 p(d + R) 0.5R 2 t(d + R) + sr FOC: (1a) dcs/dr = (D + R) p R t + s = 0 => p = (D + R) R t + s (2a) dcs/dd = (D + R) p t = 0 => p = (D + R) t Substitution in from the firm s problem, p = (D+R), gives: (1a) 9 (D + R) = R + t s (2a) 9 (D + R) = t The goal is to line this solution up with the optimal outcome in equations (1) and (2) from part A. Equating (1) and (1a): From (1), 9 (D* + R*) = R*, so t* = s* in (1a) Equating (2) and (2a): From (2), 9 (D* + R*) = 4D*, so t = 4D* or t* = $4 Check: Plugging t* = 4 into equation (2a) and factoring gives: D + R = 5. Plugging t* = s* = 4 and D+R = 5 into (1a) gives: R c = R* = 4. Since D + R = 5 and R c = 4, D c = 1. Question 6. Valuation (30 points) a) (15 points) Suppose you are asked to value a program to protect Elephant Seals on breeding beaches near San Simeon. Classify the types of benefits Elephant Seals provide and assess whether these benefits would be appropriate to consider for the program in San Simeon? We can decompose the value of environmental amenities into two components; use value and non-use value. Use value is easier to quantify. Use values include recreation benefits of an environmental amenity, such as camping, fishing, hunting, and sight-seeing, which consumers may pay for in some fashion (either directly in markets, or indirectly through travel costs). These benefits can be measured using transactional (market) data by methods such as travel cost and hedonic regression. The idea behind the travel cost method is that the value of an amenity can be estimated by taking the sum of all the travel expenses taken to get there. Hedonic regression studies, on the other hand, assume that the value of an amenity (such as a beautiful view) is capitalized into the value of market goods, such as property value. Non-use values are such things as existence value (how much Elephant Seals are worth to you just knowing that they exist, even if you never visit San Simeon beaches to see them). Non-use benefits are not picked up by travel cost or housing market valuations, and usually require contingent valuation methods, i.e. simply asking people how much they would be willing to pay (WTP) to preserve Elephant Seals. If I was making the call on this one, I would not consider non-use values for Elephant Seals in San Simeon. The reason is that they are not endangered, so that existence values and other non-use values relating to overall population may be relatively small.

8 b) (15 points) Suppose you have three methods available to you for assessing values: Contingent Valuation, Travel Cost, and Housing Market Valuation (Hedonic Regression). Briefly list the advantages and disadvantages of each of these methods for estimating the value of Elephant Seals in San Simeon. Which method do you think is best suited for the job? CONTINGENT VALUATION: A. Advantages: 1) Measures non-use values as well as use-values. 2) Can provide an explicit dollar value for the amenity. B. Disadvantages 1) Strategic Bias: A respondent may not state their true WTP for strategic reasons, if they think their answer will somehow influence policy (such as change taxes). 2) Hypothetical Bias: A respondent may state a WTP greater than their income, knowing that they don t actually have to pay it. 3) Framing Bias: The answer given depends on the range of other choices available or the context given by the questionnaire. 4) Information Bias: The respondent may not be well informed about the issue, yet feel obligated to state an answer anyway. Also, the information provided in the survey may be one-sided and influence the results. TRAVEL COST: A. Advantages: 1) Avoids the issue of asking people difficult contingent valuation questions. 2) More adequately captures use-value than entry fees. B. Disadvantages: 1) There are a lot of variables to consider in the cost of travel. 2) Hard to measure the opportunity cost of people s time. 3) Only measures use-values. 4) People may travel to many areas on a single trip, which brings up the issue of allocating travel expenses between different sites. HOUSING MARKET VALUATION: A. Advantages: 1) Housing market data is readily available. B. Disadvantages: 1) There are a lot of variables to consider in the price of a house. 2) Amenities in remote areas can t be measured. 3) Only measures use-values. For the specific case of valuing Elephant Seals in San Simeon, it is unclear that property values or other market values would be affected given the remoteness of these beaches, which would limit the use of hedonic techniques. Travel cost methods among visitors to the beaches may be possible, and this seems like a reasonable choice. Contingent valuation is an attractive alternative for picking up non-use values; however, such techniques may be less reliable in terms of potential bias and may over-state the results. This is particularly true in the case of species that are not endangered, which would imply small non-use benefits for San Simeon. I would suggest travel cost as a good method for Elephant Seals in San Simeon, but I could be convinced otherwise