Peter J. Wilcoxen

Department of Economics

University of Texas at Austin

*Spring 1995*

From time to time, Congress considers opening the Arctic National Wildlife Refuge--an essentially untouched part of Alaska's North Slope--to oil drilling. The refuge is very remote and its ecosystem is very fragile (it would take a very long time to recover from any disturbance). For the purpose of this question, you may regard drilling as a complete and irreversible change in the use of the land.

- What valuation method(s) would be appropriate for this decision? Why? Discuss the strengths and weaknesses
of the method(s) you advocate.

- How do irreversibility and technical change influence the decision?

Consider allocating natural gas consumption among all future periods. Demand in each period is identical and is given by: P=17-(Q/1,000,000). There is an initial proven reserve of 80 million units of gas available at zero marginal cost. In addition, more gas can be discovered by exploratory drilling. Each exploratory well costs 1.5 million dollars to drill and will yield either 0, 1 million or 2 million units of gas with probabilities of 50%, 25% and 25%, respectively. Assuming the interest rate is zero, please answer the following questions.

- Find the efficient price and quantity in each period. If marginal user costs play a role, calculate them and
explain why they are present. When will exploratory drilling be done? How many wells will be drilled in each year?

- The
*Limits to Growth*study made extensive use of "reserve ratios", the ratio of proven reserves to annual use. Given the results from part (1), what is the reserve ratio for the first period in this problem? Discuss the*Limits to Growth*approach in light of this.

Suppose you are given the following facts about the copper industry:

- The demand for copper is given by Q=100-P.
- The private cost of producing copper from a mine is constant at $40/ton.
- Copper mining is unsightly and generates an external cost of $20/ton.
- Copper can be obtained by recycling, which does not create an externality.
- The
*marginal*cost of recycling is $2*x*, where*x*is the number of tons recycled.

Please answer the following questions:

- Find the market outcome when firms take prices as given and the industry ignores the externality. Find the
price, the total quantity produced, the amount produced by mining, and the amount produced by recycling (if any).

- Using an appropriate graph, show that the outcome in part (1) is not efficient. Explain the graph in words.
Find the efficient price, total output, amount of raw production and quantity of recycling. Suggest a policy
*other than a tax on raw production*that could move the industry from the outcome in part (1) to efficiency. Calculate the values of any important variables in your proposal (for a tax policy, this would be the tax rate).

Suppose that in the absence of human intervention, salmon reproduce according to the function G(b)=10,000*b-5b*b,
where *b* is the stock of fish. In addition, suppose that salmon may be caught either of two ways: using fish
traps at the mouths of rivers, or using trawlers and nets on the open ocean. Catching salmon using fish traps has
zero marginal cost. Catching the fish at sea requires *E* units of effort to harvest h=0.008bE fish, and the
cost of each unit of effort is $1000. Finally, the price of salmon is $25.

- Find the efficient sustainable harvest of salmon. Also calculate the stock of fish and the amount of profits,
if any. Which fishing technique should be used? Why?

- If there is free entry into the industry, what fishing method will be used? What will the equilibrium harvest
and stock be? Why does this differ from the result in part (1)? Discuss.

- A regulator is considering prohibiting the principal fishing method from part (2). What good would that do? (Be specific and numerical!) Can you suggest any alternatives that might be better? How much better is your approach in dollar terms?

For each of the assertions below, indicate whether it is true or false and then *give a short argument in
support of your answer*. Credit will be given on the basis of your argument; no credit will be given for "true"
or "false" without an explanation.

- "A tax on gasoline would be a good way to increase U.S. energy security"

- "One disadvantage of using an emissions tax or other market-based policy to control pollution is that some firms might just pay the tax and go on polluting."