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problem+set+7+solutions

# problem+set+7+solutions - Econ 1 Fall 2010 University of...

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Econ 1, Fall 2010 Problem Set 7 Solutions University of California, Berkeley Page 1 of 8 Problem Set #7 Solutions 1. Externalities: Suppose that we have a demand for energy: Q D = 2,000,000 – 25 P , where Q D is the total amount of energy consumption in gigawatt hours (GW h) and P is the price of power per gigawatt hour. Suppose, further, that we have a competitive industry of power plants that can produce up to 2,000,000 GW h of energy at a constant marginal cost price of \$40,000 per gigawatt hour. Suppose, further, that each GW h of energy produced imposes \$1 of acid rain damage on fish, buildings, and forests. a. What is the equilibrium price and quantity in the free-market equilibrium? Since this is a competitive market, the supply function is given by P = MC = 40,000 for all quantities such that Q S 2,000,000. Therefore, the free-market equilibrium occurs where P = 40,000, and Q D = 2,000,000 – 25(40,000) = 1,000,000 GW h. b. What is the best pollution-control tax to impose on the power plant? Why? In general, the optimal tax is equal to the marginal damage cost at every quantity level. This way, the marginal damage cost will be incorporated in the marginal cost calculations of the decision maker, and the externality will be effectively internalized. In this case, the marginal damage cost is a constant \$1 per GW h for all quantity levels, so the optimal tax is also a constant \$1 per GW h for all quantity levels. c. What is the equilibrium price and quantity in the optimal tax equilibrium? Incorporating the optimal tax, the virtual supply curve is P = 40,000 + 1 = 40,001, so the equilibrium price with the tax in place is P = 40,001, and the equilibrium quantity with the tax is Q D = 2,000,000 – 25(40,001) = 999,975 GW h. d. What do you think is the best way to use the tax revenue raised by the pollution control tax? This is a subjective question with many possible answers. Nevertheless, it seems particularly appropriate to spend the \$999,975 of tax revenue on measures designed to mitigate the resulting acid rain damage.

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Econ 1, Fall 2010 Problem Set 7 Solutions University of California, Berkeley Page 2 of 8 2. Externalities: Reconsider question 1. Assume that the demand curve, supply curve, and marginal damage cost curve are the same as in the statement of question 1. a. Suppose that you are not allowed—for political reasons—to impose a tax, and instead Production Distribution Coordination (PDC) imposes a limit on how much of power plant capacity can be operated. What should that limit be? The socially optimal quantity to produce is found where the marginal benefit to society (given by the demand function) intersects the marginal social cost—that is, the sum of the marginal cost to producers plus any marginal damage cost. The equilibrium quantity with the optimal tax found in question 1c is the socially optimal quantity of energy to produce.
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