Exam 1 Spring 1995

Economics 359M

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

Exam 1

Spring 1995

Question 1: Short Essay (7 points)

Economists often assume that the best way to allocate a resource over time is to maximize the net present value of social surplus. Why is this a reasonable criterion?

Question 2: Biodiversity (14 points)

Imagine you're responsible for managing the number of species of large mammals (wolves, bears, elk, etc.) in a national park and you have collected the following information:

Each visitor's benefit from Q species is given by B=100Q-2Q*Q.
There are exactly 1 million visitors to the park and their use of the park is non-rival.
The marginal cost of protecting species is zero for the first 15 species. After 15 species the cost rises by 4 million dollars with each species. In other words, the marginal cost is zero until Q hits 15, after which it is given by MC=$4M (Q-15).
There are initially 30 species.

Please answer the following questions:

Find the efficient number of species to preserve. Show all your work and explain the key steps as clearly as you can.
Now suppose that this biodiversity provides external benefits to a large group of people who never visit the park. How large would the external benefit per species have to be in order to make it worthwhile to preserve all of the species?

Question 3: Technical Change (14 points)

Consider managing an exhaustible resource with the following features over two periods:

Each period's demand is given by Pi=500-20Qi (Pi and Qi are the price and quantity in period i).
There are 25 units of the resource available.
Marginal extraction costs are $200 per unit in period 1 and $100 per unit in period 2.
The interest rate is zero.

Please answer the following questions:

Determine the optimal allocation of the resource between the two periods. Solve for the prices, quantities, and royalties in each period (show all your work). Discuss the patterns in prices and royalties over time.
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.

Question 4: Backstops (14 points)

Consider allocating a resource over 5 periods subject to the following conditions:

Each period's demand curve is given by Pi=100-Qi (Pi and Qi are the price and quantity in period i).
The interest rate is zero.
The resource can produced by mining subject to a marginal extraction cost curve of the form: MEC=Qt/10, where Qt is the total amount of the resource mined to date.
The resource can also be produced using a backstop technology at the following cost: MCb = 20 (MCb is the marginal cost of the backstop).

Please answer the following questions:

Find the optimal price and total consumption of this resource. How much will be produced by mining? How much from the backstop?
In what year will the backstop begin to be used? For each of the five years find the price of the resource, the marginal cost, the royalty and the total amount consumed.