Peter J. Wilcoxen

Department of Economics

University of Texas at Austin

*Spring 2000*

**Question 1 (2 parts, 16 points)**

- Compare and contrast three basic policy approaches for dealing with a pollutant: command and control, an emissions
tax, and a tradable permit system. What are the strengths and weaknesses of each?

- Does a competitive market allocate an exhaustible resource like oil efficiently?
*Explain why or why not as thoroughly as you can.*

**Question 2 (2 parts, 16 points total)**

Imagine that the government is considering what, if anything, should be done about a carcinogenic air pollutant in a city of 1 million people. No epidemiological studies of the substance are available. There has been a single clinical study in which a dose of 100 units of the chemical were shown to cause 10 fatal cases of cancer in a population of 1000 rats. However, the usual dose that people are exposed to in the environment is 1 unit.

- Suppose that a pollution abatement policy is available that would reduce the average dose to 0.5 units at a
total cost of $15 million. Under the usual assumptions used in risk analysis, how high would the population’s willingness
to pay per life saved have to be to justify this policy? How does this value compare to real world estimates of
the willingness to pay to save a life? Is this likely to be a good policy? Why or why not?

- Now suppose that a second clinical study is conducted, but at a higher dose. This time, 150 units of the chemical
produce 20 fatal cases of cancer per 1000 rats. The new study leads toxicologists to revise their opinion about
the dose-response function. One group believes that the function has the form:
*R*=*A*+*B**D, where*D*is the dose,*A*and*B*are unknown constants, and*R*is the number of cases of cancer per 1000 animals. The other group believes the function is quadratic:*R*=*E***D*+*F***D*^2, where*E*and*F*are constants. If the first group is right, would you want to adopt the abatement policy? Explain why or why not and calculate any numbers that are important for your argument. What would you want to do if the second group is right? Why? Again, calculate any important numbers and justify your answer.

**Question 3 (2 parts, 16 points total)**

Consider a city dealing with a severe ozone problem. Ozone levels are initially uncontrolled and there are 100
units of it in the atmosphere. The ozone results from emissions at two sources, each of which is responsible for
50 units. Source 1 can abate its emissions at a marginal cost given by *MC*1=2**Q*1, where *Q*1
is the amount of abatement it does. Source 2’s marginal abatement cost is *MC*2=4**Q*2. The marginal
benefits of abating the ozone are believed to be given by a function of the form: *MB*=*A*-*B***Q*,
where *A* and *B* are parameters and *Q* is the total amount of abatement.

- A hedonic pricing study has been done on the value of improving air quality. The study reports that the marginal
benefit for an improvement in air quality from the uncontrolled level would be $200. The authors also calculate
that if the ozone level were reduced to 75 units, the marginal benefit of abatement would fall to $150. Determine
the efficient level of abatement. How much should source 1 clean up? Source 2?

- Design a tradable permit policy that would achieve the efficient amount of abatement while spreading the overall cost equally between the two firms. How many permits would you distribute to each firm? What would the price of a permit be in equilibrium?

**Question 4 (3 parts, 24 points total)**

Suppose that a particular good can be produced from either raw materials or scrap. The marginal cost of raw
production depends on the total amount extracted to date and is given by the equation: *MEC* = $200 + $1**QT*,
where *QT* is the total amount produced to date. Producing the good by recycling scrap has a marginal cost
of $1000. The good is to be produced for 5 periods, each of which has a willingness to pay given by: *Pi*
= 2000 – 2.5**Qi*, where *Pi* and *Qi* are the price and quantity of the good in period *i*.

- Find the efficient pattern of production and use of this good. Solve for the price, quantity, marginal extraction
cost and royalty in each period. How much is produced from raw materials? How much by recycling? In what period
does recycling start?

- Now suppose that recycling produces a lot of pollution and that the damages associated with it are $200 per
unit recycled. What is the new efficient pattern of production and use of the good across the periods? What is
the efficient amount of raw production? What is the efficient amount of recycling?

- Suppose the economy is initially at the market equilibrium and a group of citizens becomes concerned about the $200 externality from recycling. They argue that since raw production doesn’t create the externality, it should be encouraged. In fact, they argue, it should receive a $200 subsidy per unit from the government. Evaluate this proposal and calculate any relevant numbers. Does it solve the problem? Discuss in detail. You can assume this debate occurs before any production has actually taken place.