Economics 359M

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

Exam 1

Fall 1995

Question 1 (12 points)

Suppose there are 10 people with identical willingness to pay for some good. There are 20 units of the good available and the marginal cost is zero.
  1. If the people all live in a single period how should the good be allocated? Explain why.
  2. If instead the people live in 10 consecutive periods (one to a period), would the allocation change? Why or why not? If the two allocations are different, explain thoroughly and in nontechnical language why you would want to treat the same people differently in these two circumstances.

Question 2 (12 points)

Suppose a 1200 acre parcel of land contains a forest of giant redwood trees. The trees take hundreds of years to grow and are very beautiful. However, the wood from the trees is also valuable as lumber. Given the following facts, please answer the questions below:
You may assume that once an acre of trees is cut down it never grows back, and that the scenic beauty of the trees is a nonrival, nonexclusive good.
  1. How much land should be logged and how much left in its natural state? Why? When should the logging be done? Why?
  2. How much land will be logged if the first period ignores later periods in making its decision? Will this be a problem? Explain why or why not.

Question 3 (6 points)

Suppose you've been assigned to debate deforestation in developing countries. Your opponent opens with the statement "People in developing countries deforest too rapidly because they don't understand how valuable rainforests are." How would you reply? (That is: Is deforestation too rapid? If so, how do you know? What causes it?)

Question 4 (6 points)

Pesticides reduce the costs of farmers but they also get into the water supply and inflict costs on people downstream. Consider a specific example. Suppose the MC of growing a ton of tomatoes without pesticides is $200. With pesticides it drops to $100, but people downstream suffer $50 damage per ton of tomatoes. If the demand for tomatoes is P=1000-Q, what is the efficient production of tomatoes? What will happen if the market is left to itself? What tax might be applied to tomatoes to reach efficiency? Are there likely to be any political problems with this? Explain.

Question 5 (12 points)

Consider allocating 100 units of aquifer water between two periods. To make things a bit different, let the two periods be generations. You are given the following facts:
  1. The MB of a unit of water in each period is $500.
  2. Marginal costs in each period are given by: MCi=4Qi, where MCi and Qi are the marginal cost and quantity in period i.
  3. Used water is gone and does not return to the aquifer.
  4. The interest rate is 100% (one hundred percent).
The interest rate is large because the two generations are many years apart.
  1. Find the efficient allocation of water. Show your work. If the government wanted to allocate the water by selling it, how much should it charge?
  2. Suppose someone else proposed splitting the water evenly. Use an appropriate diagram to show what problem this would cause and explain it in words. Calculate the size of the problem.