Peter J. Wilcoxen

Department of Economics

University of Texas at Austin

*Spring 1999*

**Question 1 (2 parts, 14 points)**

- Describe and discuss the Coase proposition.

- A given area of rainforest can be used for logging today or preserved to allow researchers to search for new
medicines. If used for logging, it immediately produces a one-time payment of $200 million and is then worthless
for research. On the other hand, if it is preserved, there is a 90% chance that a discovery worth $10 million per
year will eventually be made and a 10% chance that the discovery will be worth $1
*billion*a year instead. However, the time until the discovery is made is also uncertain: there is a 50% chance that the research project will begin paying off in year 11 and a 50% chance that it won’t start paying off until year 21. The interest rate is 10%. What should be done with the land and why?

**Question 2 (3 parts, 21 points total)**

A major problem in international negotiations on controlling global warming has been the division of responsibilities
between developed and developing countries. Geographically, developed countries tend to be in the northern hemisphere
and developing countries in the south, so let’s refer to the two groups as *N* and *S*. Developed countries
(*N*) are the source of much of the emissions but some people believe that developing countries (*S*)
could reduce their emissions more easily. At the same time, people in *N* seem to care the most about controlling
global warming while people in *S* are much more worried about economic growth and development.

- Suppose that each person in
*N*is willing to pay $0.01 (one cent)*per unit*of greenhouse gas emissions abated in order to prevent global warming. Each person in*S*is not willing to pay anything. In addition, suppose that current emissions are about 6,000 units and that global warming will be*completely prevented*if emissions are reduced to 5,000 units. If there are one billion people in*N*and four billion in*S*, what is the marginal social benefit of abating greenhouse gas emissions? Draw an appropriate graph and explain how you got your answer.

- Now suppose that the marginal cost of abating greenhouse emissions in
*N*is $8 million per unit (that is,*MCn*= $8 million) and the marginal cost of abating emissions in*S*is given by*MCs*= $10,000*Qs.*What is the efficient amount of abatement in each country? What is the total amount of abatement? Be sure to show your work. - What is the total cost of abatement to each country in part (b)? What is the total benefit to each? Is this
policy likely to be popular in
*N*? In*S*? If not, what could you do to improve the situation? Discuss.

**Question 3 (2 parts, 14 points total)**

Suppose that a given highway is designed to carry 10,000 cars per hour. When fewer cars are using it, everyone
can travel at the speed limit and the road is completely uncongested. Above 10,000 cars per hour, however, the
road becomes congested and every car’s travel time increases. Suppose that the amount of extra time, *T*,
taken by every vehicle is related to the total number of cars on the road, *Q*, as follows: *T* = (*Q*-10,000)/40,000.
(In other words, when there are 12,000 cars on the road, each one is taking 0.05 hours extra, or an additional
3 minutes, to get to its destination.) In addition, suppose that car drivers value their time at $20 per hour and
that the total demand for rush hour trips on the highway is given by *P* = 10 – *Q*/2000.

- In the absence of any kind of government intervention, how many cars will use the road at rush hour? Is this
efficient? Explain. Use an appropriate graph if it would help.

- Now show that the marginal social cost of adding a vehicle to the highway when it is congested is given by
*MSC*= (2*Q*-10,000)/2000. (BE SURE TO SHOW YOUR WORK BECAUSE YOU’LL BE GRADED ON YOUR REASONING.) What is the efficient number of vehicles on the highway during rush hour? If you could impose a fee for the use of the highway, what would it be? What is the total value of time wasted at the market equilibrium in (a)?