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101/ECON EEP 125 Prof. Zilberman GSIs: Alix, McKim, Schoengold Problem Set # 2 Due Tuesday, March 5 (Assignments turned in after the beginning of lecture will not be graded) Numerical problems 1. Assume that manufacturing of PVC tubing, which produces large amounts of carcinogenic byproducts, is undertaken by two firms. The total benefits that the firms derive from releasing this cancer-causing stuff into the environment are given by: 2 B1 = 75 X 1 - 1 X 12 and B2 = 100 X 2 - X 2 . A combination of experts from the School 4 of Public Health and the Department of Resource Economics have assessed the marginal damage function to be: MEC = 10 + 3 X where X = X 1 + X 2 . Using this information, 4 please answer the following questions both graphically and using mathematics. a) Find the aggregate demand function of firms for carcinogens and show it on your graph. b) Find the amount of carcinogens released by the two firms in the absence of regulation. Label these points Q1 and Q2 on your graph. c) What is the socially optimal level of pollution? d) Suppose now that the government decides to impose a system of pollution permits. They are not allowed to trade. The government is considering two different forms of permit allocation. In the first, each firm receives permission to release of the socially optimal amount of pollution. The other option is to allocate the socially optimal number of permits based upon historical emissions levels. Show graphically and calculate the marginal benefit to each firm from emitting their permitted levels of pollution in each case. e) Now suppose trade is allowed. How many pollution permits will each firm buy/sell under the uniform allocation scheme? Under the historical scheme? 2. Assume there are ten farmers who plant corn on a hillside in some unspecified country. Each farmer employs fixed-proportions technology and produces different amounts of corn (Q). The hillside upon which they are located is above a stream that surrounding villages use for drinking, washing clothes and other water-related activities. The farmers all employ different amounts of labor (L), pesticides and fertilizers. In the following table we have summarized the water pollution (Z) resulting from their runoff as well as the other characteristics associated with each farmer. Farmer Amartya Bhoutros Claudio Dionysis Ed Federico Gerhardt Hans Ivan Jun Q 27 58 76 65 27 38 20 26 25 102 L 24 35 41 60 10 19 11 18 17 30 Z 10 10 10 10 10 10 10 10 10 10 Suppose also that the following things are true: 1. Price per unit of corn (P)is $5 2. Per unit wages (W) are $6 3. There is a pollution tax (T) of $6 Given this information, answer please the following questions: a) Which firm has both the lowest labor per output rate and the lowest pollution per output rate? Calculate the numerical values. Consider first the situation where there is no tax. Which farmers will be able to compete? Determine the total aggregate output and pollution level of the surviving firms. Consider now the situation where you impose the tax specified above. Identify which farmers will continue to farm and calculate their aggregate production and pollution levels. Now suppose that you want to get rid of the tax in favor of a uniform standard. If you want to produce the same level of pollution that you had with the tax, what is the maximum level of pollution per corn unit that you would allow each farmer to produce? Compare the aggregate output that you have under the tax and the standard. Which is more efficient? As a policymaker, why might you choose one over the other? b) c) d) e) 3. Imagine the unlikely scenario where the Kyoto Protocol has been signed and will be enforced. President George W. Bush, having fallen into the clutches of Ralph Nader and Hunter S. Thompson, has agreed to reduce emissions to their 1990 level of 12 tons per month. You are the head of the EPA, and have chosen to implement this strategy through a tax on oil (x) used for industrial purposes. Let y be output from oil-using industry whose aggregate production function is f(x) = 2x1/2. The relationship between petroleum use and pollution (z) is given by g(x) = 3x1/3. The price (w) of oil is $2 per barrel and the price of output is $20 per unit. Armed with this information, you need to answer the following questions: a) Find the output for unregulated industry. b) Find the optimal second best pollution tax to reach the target level. c) Find the optimal second best input tax to reach the target level. d) Interpret the multiplier on the constraint. Essay 4. You have graduated from Berkeley with a degree in resource economics and policy. Eager to travel the world, you have accepted a job with the Mexican version of the EPA. Your first assignment is no small task - attack the smog caused by excessive vehicles and unregulated industry in Mexico City. You must present arguments to Congress detailing the pros and cons of taxes/subsidies (incentive based) vs. standards (direct control) to help address this problem. You should discuss at least 3 different considerations that might favor one type of policy over the other. Like politicians the world over, the senators who are your audience suffer from short attention spans. You should be concise yet thorough in your discussion.

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