### Economics 359M

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

### Exam 1

Spring 1996

#### Question 1 (3 parts, 27 points total)

1. Explain in non-technical language (that is, explain in a way that someone who is NOT an economist would understand) what externalities are and explain why they cause problems. Give examples of positive and negative externalities and discuss each briefly.

2. To find the efficient allocation of a good over several time periods economists usually recommend maximizing the present value of net social surplus. In such a calculation the benefits received by future periods are discounted. Does this mean we care less about the future than the present? Discuss.

3. Suppose a particular piece of land can be used for one of three purposes: mining, housing or a park. If the land is mined, it will produce \$100,000 per year for 4 years, with the first payment arriving in 1 year (that is, the payments occur in years 1, 2, 3 and 4). After year 4 the land could no longer be used for any purpose and would be worth nothing. If the land is to be used for housing, a developer is willing to buy it for \$350,000 now (year 0). If the land is used as a park it generates \$33,000 per year forever beginning in year 1. If the interest rate is 10%, which of these is the best use for the land? Explain. What would be best if the interest rate were 5% instead? If the answer is different, explain (in non-technical language) why it changes.

#### Question 2 (4 parts, 36 points total)

Imagine that you work for an economic consulting company and have been asked evaluate a proposed bus system for a small city. You are given the following pieces of information:
• There are 1000 people who would use the bus system;
• Each person has an identical willingness to pay for bus trips given by the following equation: P=A - BQi , where Qi is the number of trips taken by individual i and A and B are constants that are the same across all individuals;
• The marginal cost of a bus trip is \$4 (per person);
• An experimental study of bus ridership by three randomly-chosen individuals has been conducted. Each individual was charged a different price and the number of times he or she rode the bus was observed. The results were as follows: person 1 was charged \$2 per ride and took 9 trips, person 2 was charged \$4 per ride and took 8 trips, and person 3 was charged \$8 and took 6 trips.
1. Use the information above to show that the market demand for bus trips will be given by the equation: P=20-Qt/500, where Qt is the total quantity consumed. SHOW YOUR WORK AND EXPLAIN WHAT YOU'RE DOING! Since the answer is given, points will ONLY be awarded for deriving the answer correctly.

2. Now find the market equilibrium price and quantity. Explain in non-technical language why this quantity is efficient.

3. Now suppose that riding the bus creates a positive externality of \$2 per trip. Explain why the outcome from (b) is no longer efficient. Also, suggest a specific tax or subsidy policy that could move the equilibrium to efficiency. (By "specific" I mean that you should calculate the numerical value of the optimal tax or subsidy). Explain briefly why your policy would work and use a graph to illustrate your explanation.

4. Finally, thoroughly evaluate the distributional effects of the policy from part (c). Calculate the total amount of the subsidy and explain as specifically as you can where it goes. Use a graph if that would help. What are the pros and cons of the policy?

#### Question 3 (2 parts, 18 points total)

Consider the allocation of a fixed amount of oil between two periods. The total stock of oil is know to be 2000 barrels. To keep things simple, assume the cost of extracting the oil from the ground is zero. Each period's demand for oil is identical and given by P=1500-Qi. The overall interest rate between periods is 50% (that is, treat the periods as though they were 1 year apart with an interest rate of 50%).
1. Find the efficient allocation of oil between the two periods. What will prices be in the two periods? Draw an appropriate graph and be sure to label it completely. If this allocation does not give an equal amount of oil to each period, explain in non-technical language why.

2. Now suppose we're not certain exactly what next period's demand will be like. In particular, suppose there's a 75% chance that period 2's demand curve will be identical to period 1's, and a 25% chance that oil will be a lot more valuable and the demand curve will instead be P=3000-Q2 (where Q2 is period 2's allocation). How much oil should period 1 use in this case? Explain why.