Fall 2007 Economics 431 Mid-Term Exam Prof. Hamilton Name: KEY Question 1A. (15 points) Externalities and Monopoly Markets Demonstrate on a diagram that the deadweight loss from a negative production externality is larger under competition than under monopoly for sufficiently damaging pollutants. Carefully label the axes and all relevant variables. Briefly explain. $/Q MSC P* Pm MPC MR MPB Q* Qm Qc Quantity In the diagram, the private market equilibrium occurs where MPB = MPC (at quantity Qc) in a competitive industry and where MR = MPC (at quantity Qm) in a monopoly industry. The social optimum occurs where MPB = MSC (at quantity Q*) must involve smaller DWL (the red shaded triangle) than DWL in the competitive equilibrium (the cross-hatched triangle) whenever Q* < Qm < Qc. Question 1B. (10 points) According to the diagram you have drawn, would the optimal externality policy for a monopolist involve a tax, a subsidy, or no policy at all? If drawn (as above) such that Q* < Qm, the optimal policy for a monopoly market is a tax. If drawn such that Qm < Q*, the optimal policy for a monopoly market is a subsidy.
Question 2. (25 points). Transferable Permits 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. Draw a diagram that shows the socially optimal level of pollution to be allocated between the two firms and the efficiency gain from a transferable permit policy in the case of an equal allocation of permits to each firm. Label the equilibrium permit price on your diagram. $/X MSC P 2 P* P 1 MB T = Total pollution demand MB 1 MB 2 X 1 * X 2 * 0 X 1 χ*/2 χ* X 2 0 χ 0 Pollution The permit price is P* and the shaded regions represent the efficiency gain from trading.
Question 3. (25 points) The Coase Theorem A paper mill pollutes a river. The total benefit of pollution (X) to the mill is B(X) = 10X 0.25X 2. A few miles downstream from the paper mill is a popular fly fishing area. The pollution from the paper mill damages fish and imposes total costs on fly fishers given by c(x) = 0.75X 2. Suppose there are no other benefits and costs associated with water pollution in the river. A. Define the Coase Theorem, state its corollary and the requirements necessary for it to hold. Coase Theorem: The private market achieves a Pareto optimal resource allocation whenever: 1) Property rights are clear and enforceable, 2) Property rights are transferable, 3) Economic agents have full information (no uncertainty), 4) Transaction costs are low. Corollary: the ability of economic agents to achieve a Pareto optimal allocation does not depend on which economic agent is given the property rights. B. Suppose a local court order gives the paper mill the right to pollute the water. If the fly fishers do not offer any compensation to reduce pollution, how much pollution will the firm generate? Denote this quantity of pollution as Xc. FP: Max. B(X) 10X 0.25X 2 FOC: B (X) = 10 0.5X = 0 Xc = 20 C. Pollution abatement (A) refers to the amount of pollution reduced from the unregulated level Xc; that is, actual pollution (X) is given by X = Xc A. What is the marginal benefit to the fly fishers from pollution abatement? What is marginal abatement cost for the firm? Provide a graph that shows pollution abatement (A) on the horizontal axis, the marginal benefit of abatement to fly fishers and marginal abatement cost (MAC). MC(X) = c (X) = 1.5X Fly fishers incur significant damages when Xc = 20. The marginal cost fly fisher incur for the last unit of pollution is MC(20) = 1.5(20) = 30. That is, the last unit of pollution by the paper mill causes $30 of opportunity cost to be incurred in fly fishing costs. Because the demand among fly fishers for pollution reduction must equal the opportunity cost of pollution: Since X = 20 A, MB(A) = 1.5(20 A) = 30 1.5A is the marginal benefit of abatement In words, the 20th unit of pollution causes $30 in damage to fly fishers, the 19 th unit causes the Troop MC(19) = 1.5(19) = $27.50 in damages, and so on, so that the marginal benefit of pollution abatement has an intercept of $30 and a slope of 1.5. Marginal abatement cost for the firm is the lost value incurred by the firm for each unit of pollution abated. Since X = 20 A, MAC = 10-0.5(20 A) = 0.5A is the marginal abatement cost
In words, with 20 units of pollution, the MB of the last unit is MB(20) = 10 0.5(20) = 0. (This must be true, because this is how we determined where the firm stops polluting in part C.) Similarly, the marginal abatement cost of the 19 th unit is the foregone marginal benefit to the firm, MB(19) = 10 0.5(19) = 0.5, and so on. The MAC starts at zero and rises at slope 0.5 as pollution is abated: MAC = 0.5Q. D. Graph Fly Fishers 30 MB -Abatement MC - Pollution Paper Mill 10 $7.50 $7.50 0 Pollution (X) A* = 15 (X* = 5) 20 Pollution abatement (A) E. What is the equilibrium level of pollution abatement, A*, after negotiation takes place? What is the fair bargaining price for a unit of pollution abated by the paper mill? What cash transfer does the paper mill receive from the fly fishers to abate water pollution? The socially efficient level of abatement occurs where MB(A) = MAC for abatement units, or: 30 1.5A = 0.5A => A* = 15. That is, starting from 20 units of pollution, it is optimal to abate A* = 15 units, leaving X* = 5 units of pollution. The fair bargaining price to obtain this outcome can be found from either MB or MAC at A* = 15 units of abatement. MAC(15) = 0.5(15) = $7.50. So, P* = $7.50. (This would be the same bargaining price if the fly fishers received the property right and the paper mill paid the fly fishers for pollution. Why?) The cash transfer the paper mill receives from the fly fishers in the equilibrium negotiation is C = $7.50(A*) = 15(7.50) = $112.50.
F. Suppose instead that the fly fishers received the property right to a clean river. What is the equilibrium level of pollution, X*, after negotiation takes place and how does this relate to A*? What is the fair bargaining price for a unit of pollution by the paper mill? What cash transfer do the fly fishers receive from the mill in equilibrium for allowing water pollution? If the fly fishers receive the property right, the equilibrium level of pollution will be X* = 20 A* = 20 15 = 5 The relationship between these values is X* + A* = Xc. The cash value of the fly fishers receive for allowing these 5 units of pollution is: C = $7.50(5) =$37.50 EXTRA CREDIT. In the context of this problem, what obstacle(s) might prevent bargaining between fly fishers and the paper mill from achieving the socially optimal outcome? The key is to pick one of the 4 requirements for the Coase Theorem to hold and explain why it may break down. One major issue is transaction costs. There may be thousands of fly fishers who use the river (or would wish to use it if it were less polluted) and organizing them together to negotiate with the paper mill can easily preclude negotiation. One aspect of this transaction cost is that a good fly fishing river is a public good, so that free riding can be a problem if fly fishers try to collect money to negotiate with the paper mill for abatement. (Alternatively, if fly fishers are to be given the property rights, some people who don t fly fish would rush out to Wal Mart and buy hats with fly fishing lures hanging off them to try to disguise themselves as fly fishers in the hope of receiving a share of the property right.) Question 4. (25 points) Uncertainty More than half the electricity in the U.S. comes from burning coal. Suppose a regulator in the U.S. wants to design a more efficient policy to control greenhouse gases (notably NOx, SOx, CO 2 and SO 2 ), particulates and toxic compounds such as mercury. The regulator estimates the total benefit of burning coal (X) at electric plants to be TB(X) = 100X 2X 2. Suppose the total social cost of burning coal is TSC(X) = 10X + 0.5X 2. The regulator wants an efficient policy and can select between a tax and a standard. A. Based on the information available on benefits and costs, what pollution tax (t^) would the regulator set to obtain the social optimum? What pollution standard (X^) would the regulator set to obtain the social optimum? MB(X) = 100 4X MSC(X) = 10 + X Social optimal allocation (with available information): 100 4X = 10 + X 5X = 90 X^ = 18 Associated tax: t^ = 100 4X^ = 100 4(18) t^ = $28
B. Suppose the total benefit of burning coal (X) is actually TB(X) = 90X 2X 2. What is the actual outcome that will occur under a tax of t^? Under a standard of X^? MB(X) = 90 4X MSC(X) = 10 + X Social optimal allocation (with actual information): 90 4X = 10 + X 5X = 80 X* = 16 At a tax of t^ = $28, electric utilities burn coal until MB(X) = 90 4X = 28 4X = 62 This implies an actual combustion level of: Xa t = 15.5 Under a standard of X^ = 18, electric plants combust Xa s = 18 units of coal (since MB(18) > 0) C. Provide a diagram that shows the true social optimum, the outcome under a pollution tax and the outcome under a pollution standard. P DWLstandard t^=28 DWLtax MSC Qa t =15.5 Q*=16 MBtrue Qa s =18 MB(X)est X D. See above. Taxes perform better, because MB of coal is inelastic. E. The regulator makes the following public statement: Because a transferable permit policy operates much the same as a pollution tax, a transferable permit policy performs equally well as a tax under uncertainty. Evaluate this statement. This statement is incorrect. Transferable permits are only like taxes in the sense that both obtain allocative efficiency. At the aggregate level, a standard of X^ = 18 units will lead to 18 units of coal being used. DWL under a standard without permit trading would be larger than the region depicted above to the extent that pollution is not allocated efficiently among regulated electric plants.