### Economics 359M

Peter J. Wilcoxen
Department of Economics
University of Texas at Austin

### Exam 1

Spring 1998

#### Question 1 (2 parts, 14 points total)

1. To find the efficient allocation of a good over several time periods economists usually recommend maximizing the present value of social surplus. Is it ethical to discount the future? How should one choose the discount rate? Discuss.

2. Is biodiversity likely to be provided efficiently by an unaided market? Discuss in detail.

#### Question 2 (2 parts, 14 points total)

Suppose a small town needs a new water treatment plant to clean up its sewage. The town consists of two neighborhoods which we'll call "H" and "L". The population of H is 10,000 and each resident has a willingness to pay for treating sewage given by P = 75-QH, where QH is the amount of water treated per year. The population of L is 30,000 and each of its residents has a willingness to pay for sewage treatment given by P=25-QL.
1. Derive an equation for the total annual demand for sewage treatment. Suppose that the plant will be able to treat sewage at a marginal cost of \$10 per unit; how much sewage would the plant have to handle each year? How much consumer surplus would be received by residents in each neighborhood?

2. OK, now let's consider where the plant should be built. Suppose (!) that people in this town don't like having a sewage treatment plant in their neighborhood. In fact, residents of H are each willing to pay \$750 to avoid having the plant in H, and residents of L are each willing to pay \$120 to avoid the plant. In which neighborhood should the plant be built? Why? If any compensation is needed to keep this decision from making anyone worse off, calculate how much it should be. Is there any tension between efficiency and equity in this decision? Discuss, and be specific about dollar amount, where possible. Finally, suppose we did the calculation in terms of willingness to accept (W2A) instead of willingness to pay. Moreover, suppose area H's W2A was \$750 but area L's was no longer \$120. Would the decision have been the same? Discuss.

#### Question 2 (3 parts, 21 points total)

Imagine that you've been put in charge of cleaning up VOC air pollution in Austin. Suppose the marginal benefit of each ton of VOCs reduced has been estimated to be \$2,000. Moreover, suppose VOCs come from two principle sources: cars and power plants. Each source is currently uncontrolled and is emitting 500 tons, for a total of 1000. For cars, the marginal cost of abatement is given by MC1=500*Q1 (where MC1 and Q1 are the marginal abatement cost and quantity of abatement for cars), and for power plants the marginal cost of abatement is MC2=5*Q2.
1. Please calculate the following things: (1) the efficient amount of VOC abatement for each source, (2) the total amount of VOCs to be abated, (3) the cost of abatement to each firm, and (4) the total cost of abatement. Be sure to show your work and explain what you're doing.

2. Now suppose that two policies have been proposed to deal with VOCs. Policy A would require each source to cut its pollution by a percentage equal to the percent by which emissions were cut in part (a). (That is, if you found that emissions should be reduced by 20% in total, this policy would achieve that by requiring each source to reduce by 20%.) Policy B would impose a tax on emissions. Please determine the tax that would be needed in policy B. Explain how you found it. Then calculate the effects of each policy on both car drivers and power plants. Which policy would be preferred by car drivers? Which by power plant operators? Which by economists? Discuss.

3. Now suppose Capitol Metro comes up with a plan to reduce VOCs by building a light rail system (more or less an above-ground subway, if you can stand the oxymoron!). Capitol Metro estimates that it will cost \$2.5 million to build the system, which will have to be paid immediately. Construction will take 10 years. Beginning in year 11, however, the system will reduce VOCs in Austin by 250 tons a year forever. You may assume that once the project is built, it would cost nothing to operate. The interest rate is 10%. Is is a good idea to go ahead with this project? What would your answer be if the interest rate were 5% instead? Please show all your work. Would the existence of this option change your answer to part (a)? Explain.