### Economics 359M

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

### Exam 1

Fall 1993

#### Section I, Short essay (3 parts, 21 points total)

Answer each of the following questions. Explain your position as completely as possible in the time allowed. If you use graphs, be sure to explain what each one is intended to show.
1. Give an example of a negative externality and explain in nontechnical language why it would cause a competitive market to reach an undesirable equilibrium.
2. Suppose you are asked to allocate Q units of a resource over T periods in such a way as to maximize the net present value of social surplus. Demand is the same in every year but marginal extraction costs are falling due to improvements in technology. If the interest rate is 5% per year and costs are falling at 3% per year, prove that efficiency requires the price to rise at 2% per year.
3. Discuss the NIMBY problem.

#### Section II, Problem 1 (2 parts, 14 points total)

Suppose there are exactly three deposits of a particular natural resource. Each deposit contains 30 units of the resource but has a different marginal extraction cost. For the first deposit, the MEC is \$10 per unit, for the second it is \$20 per unit and for the third it is \$30 per unit. Consider allocating this resource across two periods. Each period has a demand curve given by P = 70 - 2Q and the interest rate is 0.
1. Find the efficient total production of the resource. What quantity should each period consume? What should the royalty be in each period? What should the price be?
2. Now suppose the resource is common property and is produced by price taking firms in a competitive market. What quantity will be supplied in each period? What will the price be in each period? Explain why this allocation is undesirable. Calculate the benefits that could be achieved by moving to the best allocation.

#### Section III, Problem 2 (2 parts, 14 points total)

Consider allocating a resource across three periods. Each period's demand curve is given by P = 54 - 9Q. The resource is subject to increasing marginal extraction costs as follows: MEC = 3 Qt where Qt is total extraction of the resource to date. The interest rate is zero.
1. Find the efficient total production of the resource. What quantity should each period consume? What should the royalty be in each period? What should the price be?
2. Now suppose the resource is controlled by a profit-maximizing monopolist. What price will the monopolist charge? What will total output be? What quantity will each period consume?