Anderson, PUBLIC FINANCE Chapter 4 End-of-chapter problems with solutions 1 1. In which of the following situations is the Coase Theorem likely to apply? Explain. a. The neighbor who lives below you in the apartment building loves to play old John Denver records at loud volume early in the morning. In fact, his favorite song seems to be Thank God I m a Country Boy. You hate old John Denver songs and this one in particular. b. You have just moved to Los Angeles and quickly discover that you are allergic to smog. It causes you great pain in breathing and limits your ability to work. Furthermore, you have medical expenses related to treatment for its health effects on you. c. Medical research in the 1990s has revealed a specific cause of birth defects related to a certain drug prescribed for pregnant women in the 1960s. d. The water in the huge underground Ogallala aquifer in the Great Plains region of the U.S. is being nitrate contaminated due to agricultural fertilizer use throughout the region. As a homeowner in this region, you find that your water must be treated in order to be safe for drinking. The Coase Theorem applies to situation a. In situation a, it is quite likely the property right to either have quiet or the option to play loud music can be assigned with little complication. The number of parties involved is small and well defined (the residents of the property building, or perhaps just the two residents directly affected by the loud John Denver music), and the transaction costs of negotiation will be minimal. In situations b, c, and d, the number of parties to the transactions is too large for the Coase Theorem to apply. In situation b, the number of contributors to smog is enormous; in situation c, finding all the women and their children affected by the drug prescribed 30 years earlier will be a huge undertaking; and in situation d, the sources of nitrates in the water in the Ogallala aquifer are numerous and quite dispersed. In all three cases the transactions costs will be far greater than zero. 2. One of the most striking aspects of cities in the Former Soviet Union is the poor condition of public places. Streets, parks, libraries, museums, concert halls, and public gathering places of every description are all in very poor condition, revealing years of neglect and lack of maintenance. Explain this phenomenon in light of the definition of property rights and the transition from socialism to a market economy. The public places and facilities described all provide positive externalities when they are well maintained and in good condition (as do all public goods). It is often said that when everyone owns an asset, however, no one owns the asset. That may be the source of the problem in the former Soviet Union. Since the demise of the Soviet Union as a political entity many public facilities once carefully maintained by the
2 government are no longer maintained adequately. That may have occurred for two reasons. First, the many new regional governments that have replaced the single government of the Soviet Union may not have clearly established property rights to the former state assets. Consequently, no one will properly maintain those assets due to a lack of property rights definitions. Transition is occurring in a context where the state once owned everything and the move to a market oriented economy requires privatization and clear establishment of property rights for all assets, including state assets. Lack of clear and comprehensive property rights definitions are at the heart of many of the difficulties associated with transition economies. Second, recall the Samuelson Rule from chapter 3 and note that the efficient allocation of resources to public goods depends on both the sum of residents marginal benefits and the marginal cost of providing the public good. If transition reduced residents marginal benefits, then a smaller quantity of public goods is justified. One way to have less public infrastructure is to stop investment and maintenance and allow the facilities to depreciate. 3. Suppose that the marginal benefit associated with corn production is MB = 2.5. Marginal private cost of production is MPC = 2 + 0.1 Q, where Q measures bushels of corn produced in thousands. The marginal damages caused by pollution in corn production are given by MD = 0.05Q. a. Compute the privately optimal output and the socially optimal output. b. Compute new solutions for in MB to MB = 3. Explain what has happened and why. c. Demonstrate the effects of an increase in MD to MD = 0.075 compared to the solutions in part a. a. Privately optimal output rate is found by setting the private marginal benefit equal to the private marginal cost: 2.5 = 2.0 + 0.1Q. Solving for Q we obtain Q=5. The socially optimal output rate is found by setting the private marginal benefit equal to the marginal social cost: 2.5 = 2.0 + 0.1Q +0.05Q. Solving for Q provides Q=3.33. b. When the marginal benefit rises to MB=3, the private solution changes to Q=10 and the social solution changes to 6.67. Since the marginal benefit has risen, larger outputs can be justified (recall that both marginal private cost and marginal social cost are rising with output). c. A larger marginal damage reduces the socially optimal solution in part (a) to Q=2.86. The privately optimal solution is unaffected, of course, because it does not take marginal damages into account. 4. Policy analysts in the Department of Natural Resources have estimated that the marginal benefits from water pollution abatement are given by the function MB = 0.90-0.03A where A is a measure of the abatement intensity. Industry experts have estimated that the marginal cost of abatement activity is MC = 0.30 + 0.09A. a. Determine the optimal level of abatement activity. b. Explain what happens when new technology reduces the marginal cost of abatement
to MC = 0.25 + 0.06A. 3 a. Setting the marginal benefit of abatement equal to the marginal cost gives: 0.90-0.03A = 0.30 + 0.09 A. Solving for A gives A=5. b. When new technology reduces the marginal cost of abatement, the optimal level of abatement increases to A=7.22. 5. Use the information in the policy study Downwind from a Soviet Research Center to construct graphs analyzing the production of Soviet military research and ceramics at Compound 19 and the downwind ceramics factory. Explain the economics of the externality in the problem and how it affects the both the research center and the ceramics factory. $ MSC = MD + MPC MPC MB 0 Xs Xp Anthrax Production
4 $ MC2 MC1 MB 0 X2 X1 Ceramics Production The bottom graph shows the increased marginal cost of ceramics production due to the anthrax blowing from the research center in Compound 19. The top graph shows the marginal social cost, including the marginal damage done by anthrax production in the form of the higher cost of ceramics production, of anthrax. The optimal level of production of both goods decreases as a result of the externality produced by the research center. 6. Consider the issue of emissions trading introduced in the policy study The Kyoto Protocol. a. What is the economic rationale for permitting emissions trading? b. If the objective is to minimize the cost of emissions reductions, explain what economic principle should be followed in allocating emissions reductions among two countries. c. Suppose the marginal cost curves for emissions reductions in countries A and B are given as follows: MC A = 10+ 0.04q A, MC B = 5+ 0.02 q B. What is the most efficient allocation of an emission reduction of q 0 among the two countries? (Assume that the emissions reductions of the two countries must add up to the total emissions reduction: q 0 = q A +q B.) a. Since the cost of emissions reductions differs among countries, we can minimize the total cost of a given amount of emissions reduction by allocation those reductions among countries appropriately.
b. Allocate emissions reductions among countries so that the marginal cost on the last unit if emissions reduction is equal in the two countries: MC A = MC B. c. Set the two marginal costs equal and include the constraint that the emissions reductions add up to the total required: 10+ 0.04q A = 5+ 0.02 [q 0 - q A ]. Solve for q A = (1/3)q 0-5/0.06 and q B = (2/3)q 0 + 5/0.06. 5