### 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.
1. Find the efficient number of species to preserve. Show all your work and explain the key steps as clearly as you can.
2. 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.