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Econ 144B: Urban Economics II Nilopa Shah Assignment 3 (based on textbook Chapter 9) Question 1 (extensive version of Exercise 9.1 from textbook) Suppose there are two polluting factories, surrounded by two identical residential neighborhoods with no overlapping locations. The marginal damage curves are identical for the two neighborhoods, and they are given by and , where P is the level of pollution. The marginal benefit curves for the factories, however, are different. The marginal benefit curve for the first factory is , while the curve for the second factory, which uses a cleaner production process, is given by (both curves become zero once they hit they reach the horizontal axis). (a) Draw two diagrams, one for each neighborhood to illustrate the MD and MB curves for each respective factory. In each diagram, clearly label both axes, both lines as well as the x- and y-intercepts of the MB lines. (b) Identify the pollution levels chosen by each factory in the absence of government intervention. Find the level of social surplus (difference between total benefits and total damage) achieved in each neighborhood with no government intervention. (c) Find the socially optimal pollution levels in the two neighborhoods. Explain intuitively why the optimal levels of pollution for both neighborhoods are different. (d) Compute social surplus at the optimal pollution level in each neighborhood. Then, sum up the values across the two neighborhoods to get total welfare. This is the social welfare that would result from imposition of separate pollution standards on the two factories. (e) Now suppose that the government institutes a common pollution standard, which applies to both neighborhoods. This standard restricts pollution from any factory to a maximum value . Under this standard, how much does each factory pollute? (f) Compute the resulting level of social surplus in each neighborhood, and add the values to obtain the social welfare under a common pollution standard. (g) Consider the social welfare from parts (b), (d) and (f) i.e. social welfare with no government intervention, with separate pollution standards and with a common pollution standard for both neighborhoods. How does the common standard compare to separate pollution standards, and to the case where the government does not intervene at all? (h) Comment on the wisdom of using a common pollution standard. MD1 = P MD2 = P MB1 = 8 − P MB2 = 4 − P ̂P = 3 Department of Economics of UC Irvine1 3 Econ 144B: Urban Economics II Nilopa Shah Question 2 (table version of Exercise 9.2 from textbook) Suppose the marginal damage and marginal benefit curves in a polluted neighborhood are and . Also, suppose that transactions costs are low, so that the neighborhood residents and the firm can bargain. We saw that in this case, the socially optimal level of pollution is achieved. With this understanding, answer the following sub-questions. (a) Compute the socially optimal level of pollution. (b) Draw a diagram to represent the above information - label both axes; the lines MD, MB and their x- and y- intercepts; and also clearly indicate the areas that you will calculate in the sub-questions that follow. (c) Complete the table below that lists various possible bargaining scenarios - compute the amount of money transferred through the bargaining process; and indicate who pays whom (i.e., whether consumers pay the firm, or vice versa). Also, compute the gains to each party relative to the status quo (i.e., the starting point of the bargaining process). MD = P/3 MB = 4 − P P* P* Property Rights: Residents have the right to clean air Payment made by Firm/Residents (circle correct response) Residents Gain Firm Gains Firm is dominant in the bargaining process Residents are in the bargaining process - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Property Rights: Firm has the right to pollute Payment made by Firm/Residents (circle correct response) Residents Gain Firm Gains Firm is dominant in the bargaining process Residents are in the bargaining process - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Department of Economics of UC Irvine2 3 Econ 144B: Urban Economics II Nilopa Shah Question 3 (Exercise 9.3 from textbook) Suppose that pollution in a neighborhood comes from two factories, with marginal benefit curves given by and . The level of pollution in the neighborhood is given by . The government wants to limit pollution by instituting a pollution-rights market. (a) Suppose the government’s desired level of pollution is . So, it prints 10 pollution rights and offers them for sale to the firms. Find the equilibrium selling price of a pollution right, as well as the allocation of rights (and hence pollution levels) across the two factories. (b) Repeat the calculations from part (a) for the case where the government’s desired level of pollution is . (c) Comment on the usefulness of a pollution rights market in achieving efficient levels of pollution abatement. MB1 = 12 − P1 MB2 = 8 − P2 P = P1 + P2 ̂P = 10 ̂P = 14 Department of Economics of UC Irvine3 3