Peter J. Wilcoxen
Department of Economics
University of Texas at Austin
Question 1 (2 parts, 16 points total)
Suppose a particular pollutant is produced by three sources. Initially, none of the sources is abating emissions
and each is emitting 30 tons of pollution. The marginal abatement costs of the sources are as follows: MC1 = $100,
MC2 = $200, MC3 = $300. (That is, the marginal cost of abating pollution from source 1 is $100 for each unit eliminated,
etc.) The marginal benefit of abatement is given by MB = $1000 - 16 Qa, where Qa is the total quantity of abatement.
- Find the efficient amount of abatement for each firm. Be sure to show all your work and explain your reasoning.
Also, calculate the cost to each firm of cleaning up its emissions. Do you think the firms would regard this as
- Now consider solving the problem by using a tradable permit policy. What quantity of permits should be issued?
What will the market price of a permit be? How would you distribute them if you wanted to equalize the overall
cost of abatement across all three firms? (Please calculate the specific quantity of permits to be given to each
firm.) Would the firms prefer this or an emissions tax policy? Explain.
Question 2 (2 parts, 16 points total)
Consider a city of one million people trying to cope with a pollution problem. The pollutant is produced by
dozens of sources, each of which has a different marginal cost of abatement. Moreover, for most of the sources
the marginal cost of abatement is unknown. Public health studies suggest that when more than 100 tons of the pollutant
are emitted, 5 people will die from diseases caused by it. However, when less than 100 tons are emitted, the pollutant
causes no health problems. At all levels of emission the pollutant causes no problems other than its effects on
health. At the moment, 150 tons of pollution are being produced. In addition, an economist has estimated that individuals
in the city are willing to pay $1 for each 1/1,000,000 reduction in the risk of death.
- Propose a specific policy to deal with this problem. By "specific" I mean that you must indicate
the specific numerical value of any key part of the policy. Explain in detail why you chose the policy you did.
- Now suppose that the legislature put the policy you recommended above into place and a couple of years have
passed. The firms have had a chance to react to the policy. Suppose that you, as the economist, are still unable
to observe the marginal abatement cost curves of the individual firms. (That is, you can't get a MC of abatement
curve for each of the firms, either because there are too many firms or because the information is a trade secret.)
How would you decide whether the policy was actually efficient? Explain.
Question 3 (1 part, 8 points)
Suppose you pick up a newspaper one day and come across a story about the world oil supply. The author of the
story is very concerned that world oil reserves are about to be exhausted. His argument is based on two propositions:
(1) at current rates of consumption, proven reserves of oil will only last for another X years, and (2) the oil
market does not take future consumers into account. What is wrong with this analysis? Please explain in detail.
(If this question looks familiar, that's a reward for studying -- it's identical to one from an old exam.)
Question 4 (2 parts, 16 points)
Technological progress in the exhaustible resource industry has often been very rapid. This problem asks you
to examine how anticipated progress affects the allocation of a resource. Consider an exhaustible resource that
is to be allocated across two periods. You are given the following information:
- Demand in period 1: P1 = 100 - Q1
- Demand in period 2: P2 = 100 - Q2
- Marginal extraction cost in period 1: $40
- Marginal extraction cost in period 2: $20 (known in advance to be lower than MEC1)
- Total quantity of the resource is 50 units
- The interest rate is 100% (suppose the two periods are a generation apart)
Notice that extraction costs are known from the beginning to be lower in period 2 than in period 1 and that
the cost reduction does not depend on how much has been extracted.
- Find the efficient allocation of the resource between the two periods. Determine the price, royalty, quantity
extracted and marginal extraction cost for both periods. Show all your work.
- Now suppose that there's a backstop technology available in either period at a price of $60. Find the new efficient
allocation, including all of the following variables for each period: the price, marginal extraction cost, royalty,
quantity of raw extraction and quantity of backstop production. Explain in non-technical language how the backstop
affects the problem. You may assume that everyone knows about the backstop at the beginning of period 1.
Check your answer here.