### Economics 359M

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

### Exam 1

Spring 2000

Question 1 (2 parts, 16 points)

1. Describe and discuss the Coase proposition.

2. To find the efficient allocation of a good over several time periods economists usually recommend maximizing the present value of social surplus. Is it ethical to discount the future? How should one choose the discount rate? Discuss.

Question 2 (3 parts, 24 points total)

Used automobile batteries can be a serious environmental problem. If they are dumped into landfills, the lead in the batteries can leach out and contaminate nearby aquifers. To explore this issue, consider the following scenario. A particular town has 100,000 people, each of whose demand for car batteries per year is given by P= 200–300Qi. In addition, suppose that the cost of a battery is \$50, and the interest rate is 5%. Please note that because the demand is batteries per year, Qi does not have to be an integer – if it were 1.5, for example, that would be 3 batteries every two years.

1. Please derive the market demand curve for batteries in a given year. Using it, determine the market equilibrium price and quantity of batteries.

2. Now let’s consider the disposal problem. Suppose that each battery is used for 6 years and then thrown in a landfill. After it has been in the landfill for 15 more years (i.e., in year 21), there is a 25% chance that the lead in it will begin to leach out. Once it begins leaching, the lead causes damage every year forever. The magnitude of the damage is not certain, however. With 90% probability, it is only \$0.10 per year (ten cents) but there is a 10% chance it will be \$10.00 per year. Calculate the expected present value of the damages associated with the purchase of a battery. Be sure to show all your work!

3. Using your answer to part (b), find the efficient price and quantity of new batteries. If we were to achieve this by taxing batteries, what should the tax rate be? What will be the total dollar effect of this on consumer surplus? On government revenue? On the externality problem? What is the overall welfare gain?

Question 3 (1 part, 8 points total)

Suppose you are asked to decide on the appropriate use of a scenic canyon. At the moment, the canyon is used as a park but a mining company has proposed converting it into a coal mine. You are given the following information:

• There are 10,000 people who visit the park each year and their use is nonrival.
• Each visitor’s marginal benefits from Qi visits are given by MBi= AB*Qi
• The park is free and there are 30,000 visits each year
• As an experiment, a few years ago visitors were charged \$2 for each visit. The total number of visits dropped to 25,000.
• The mining company would be willing to pay \$1 million for the land.
• The interest rate is 10%.
1. Calculate the total social benefits that visitors receive from the park each year when no entry fee is charged. Be sure to show your work and make your reasoning clear. Using this information, determine what should be done with the land and then explain your result in words.