Peter J. Wilcoxen

Department of Economics

University of Texas at Austin

*Fall 1995*

Suppose that oil can be obtained from either a large underground reservoir or from a backstop technology. The
quantity of oil in reservoir is know to be 120 units and the marginal cost of extracting it is constant at $20
per unit.** **Oil can be produced by the backstop method at a constant marginal cost of $40 per unit. Finally,
suppose that we're interested in allocating the oil over 5 identical periods. Each period has a demand curve given
by Pi = 80-Qi (where Pi and Qi are the price and quantity in period i) and the interest rate is ... 0 (whew!).

- Find the efficient allocation of oil. What will be the price, quantity and marginal user cost in each period?
When will the backstop be used?

- Suppose that the reservoir is
*very*large in area and underlies property owned by many people. If ownership of oil is governed by the right of capture (whoever extracts it owns it), and it is too expensive to store once extracted, what will be the price and quantity of oil in each period? When will the backstop be used? Explain why this outcome is different from part (1). If there is a welfare gain or loss, calculate it.

- Now suppose the resource (both sources of it) is owned by a profit-maximizing monopolist. Find the price and quantity of oil in each period. Will the monopolist use the backstop? If so, when?

Suppose that in the absence of human intervention, swordfish reproduce according to the function G(S) = S -
(1/20000)(S*S), where *S* is the stock of fish and S*S is S squared. In addition, suppose the technology of
catching swordfish can be represented by the equation h=E*S/20 where *h* is the harvest and *E* is the
amount of effort devoted to fishing. The cost of each unit of effort is $1000 and the price of swordfish is $20.

- What is the maximum sustainable yield for this fishery? What stock is required to support that harvest?

- Determine the efficient values of the following: effort, harvest, stock, total costs, total revenue and profits.
(Be sure to show your work.)

- If there is free entry into the industry, what will the market equilibrium values be of the following variables:
effort, harvest, stock, total costs, total revenue and profits. (Show your work.) Why does this differ from the
result in part (2)?

- Suppose the government wants to cure the problem in part (3) by imposing a tax on the harvest of swordfish.
Once the tax is imposed, people in the industry receive $20(1-
*T*) instead of $20 for each unit of swordfish, where*T*is the tax rate. Calculate the tax rate needed to move the industry in part (3) to the efficient outcome.

- Is the policy in part (4) likely to be popular with people in the industry? Explain. Suppose the government were to use a tradable permit policy instead. How many permits should be issued? (You may assume one permit entitles the owner to catch one unit of swordfish each year forever.) What will the market value of a permit be if the interest rate is about 10 percent? What problems from part (4) could this policy solve? Discuss.

This section consists of three short essay questions on environmental amenities.

- What is an environmental amenity? Give some examples. Why do markets generally not produce the efficient amounts
of amenities? (Be specific about the characteristics of amenities that cause them to be produced in the wrong amounts.)
Explain.

- Discuss how one might go about computing the value of an amenity. What methods are available? What are the
main strengths and weaknesses of each approach?

- Unlike most other natural resources, it is likely that amenities are becoming more scarce and valuable over time. Why? Explain in detail.