Economics 359M

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

Exam 2

Spring 1999

Question 1 (3 parts, 21 points)

  1. In a world without uncertainty, taxes and tradable permits would be equally efficient policies for dealing with an externality like pollution. In the real world, however, the costs and benefits of reducing pollution are seldom known with certainty. Explain in detail how this affects the choice between tax and permit policies.

  2. The ecosystem of Florida’s Everglades National Park is threatened by water pollution from surrounding areas. What method or methods would you recommend for estimating the benefits of reducing the problem? Why? In answering this question you may want to consider that the Everglades is the only national park in the northern hemisphere that has been named an "International Biosphere Reserve" and a "World Heritage Site" by the United Nations. How, if at all, would this affect your choice of method(s)?

  3. Does a competitive market allocate an exhaustible resource like oil efficiently? Explain why or why not as thoroughly as you can.

Question 2 (2 parts, 14 points total)

Suppose that clinical studies on a particular chemical indicate that in high doses it increases the risk of breast cancer by 1 in 1,000. That is, if 1,000 people were exposed to the high dose we would expect about 1 extra case of cancer. Furthermore, suppose that the clinical dose is about 100 times larger than the dose people actually receive in the environment, and toxicologists believe the dose-response relationship is linear. Finally, suppose that a study has been done of people’s willingness to pay for reducing a similar risk and it was found to be $2 million per life saved.

  1. Suppose that one million people are currently exposed to the chemical. Calculate the benefit of a policy that would cut the dose they receive in half. Would this policy be worth doing if it cost $8 million? Explain why or why not.

  2. Some of the steps in doing the calculation in part (a) are subject to a great deal of uncertainty. Which ones and why? Given this uncertainty, if you had to choose between two equally expensive policies, one which cut the dose in half and one which reduced the exposed population by 50%, which one would you choose? Explain why.

Question 3 (3 parts, 21 points total)

Suppose an exhaustible resource is to be allocated across five periods. Demand for the resource in each period i is given by Pi = 150 – Qi. The data in the table below has been collected about the resource’s distribution. You may assume that all areas where the resource might be found have been explored and that there are no undiscovered deposits. You may also assume that the interest rate is zero.

Grade of ore


















  1. Find the efficient allocation of the resource across the five periods. What will the price, quantity, marginal extraction cost and royalty be in each period? Be sure to show all your work. What would the US Geological Survey (USGS) report as "proven reserves" at the beginning of the first period? Will the resource be completely exhausted by the end of the fifth period? Explain why or why not.

  2. Now suppose that just before extraction begins in period 1, news arrives that a new backstop technology has been invented. The marginal cost of the backstop is $20. Determine how this changes the allocation of the resource across the periods. Does this change what the USGS would report as proven reserves? Explain and discuss.

  3. Over the years much use has been made of "reserve ratios" or "years of supply" calculations to indicate whether we’re about to run out of various exhaustible resources. Is this a good measure? Explain why or why not.

Question 4 (1 part, 7 points)

Suppose that a particular resource can be produced from either raw ore or by recycling. The marginal cost of production from raw ore is given by MEC = Qt where Qt is the total amount of ore extracted to date. The marginal cost of producing it from scrap is given by MRC = $120. In addition, producing the resource from raw ore causes an externality of $80 per unit but there is no externality associated with recycling.

Consider allocating the resource over four periods where each period has a demand curve given by Pi = 200 – Qi. You may assume the interest rate is zero and that there is always plenty of scrap. Find the total market production of the resource (that is, the total over all the periods). How much of this is produced from raw ore? How much by recycling? Is this efficient? Discuss why or why not in detail and illustrate your answer with an appropriate graph.

Check your answers here.