Peter J. Wilcoxen

Department of Economics

University of Texas at Austin

*Spring 1996*

Suppose you pick up a newspaper one day and come across a story about the world oil supply. The author of the
story is very concerned that world oil reserves are about to be exhausted. His argument is based on two propositions:
(1) at current rates of consumption, proven reserves of oil will only last for another X years, and (2) the oil
market does not take future consumers into account. What is wrong with this analysis? Please explain *in detail*.

Suppose you've been asked to decide whether a particular scenic area now used as a park should be converted to a housing development. The two uses are mutually exclusive. At the moment, no admission fee is charged and 400 people visit the park each day. A researcher has interviewed a sample of the visitors and concluded that they come from 5 geographic zones. She has collected the following information, where "Travel Cost" is the round-trip transportation cost of visiting the park:

Zone

Travel Cost

Population

Visitors

1

1

5000

250

2

2

2500

100

3

3

1250

37.5

4

4

625

12.5

5

5

800

0

Total

400

- Using the travel cost method calculate the number of people who would visit the park if an admission fee of
$1 were imposed.
- It is also known that the total number of visits to the park (including people from all zones) is given by
an equation of the form: P=A-BQ, where P is the admission fee, Q is the number of visitors, and A and B are constants.
Using this fact and the information above (including, if necessary, the results from part 1) calculate the daily
value of keeping the land as a park. If the value of the housing development is $900 per day what should be done
with the land? Explain.
- Is the value of the park calculated in part (2) likely to understate or overstate the true value? If so, explain why and discuss how you could improve the estimate. How does this affect the decision in part (2), if at all?

Suppose you've been put in charge of cleaning up water pollution in a river. The marginal benefit of cleaning
up the pollutant is given by MB=500-Q, where *Q* is the total quantity of abatement, measured in tons. Pollution
is currently uncontrolled and totals 1000 tons. It comes from two sources, each of which is now emitting 500 tons.
For source 1, the marginal cost of abatement is given by MC1=Q1 (where MC1 and Q1 are the marginal cost and quantity
of abatement for source 1) while for source 2 the marginal cost is constant: MC2=100.

- Show that the efficient total amount of pollution is 600 tons. Calculate the amount of abatement that should
be done by each firm.
*Show your work and explain what you're doing! Since the answer is given, points will only be awarded for deriving the answer correctly.* - Suppose that the legislature becomes concerned about this problem and passes a law requiring each source to
reduce emissions by 40%. Would this be efficient? If so, explain why. If not, explain as specifically and non-technically
as you can why it is not and calculate the deadweight loss of the policy.
- What emissions tax policy would achieve efficiency? Calculate how much such a policy would cost each firm including
both abatement costs and taxes. Would the firms prefer this policy or the one from part (2)? Explain why and be
specific.
- Now suppose the legislature is a bit more enlightened and passes a law requiring emissions to be reduced to
600 tons in such a way that the firms share the burden equally. (That is, their total costs must be equal -- they
do
*not*necessarily need to reduce emissions by the same amounts.) Design a tradable permit policy that would accomplish this. How many permits would you give to each source? Why?

Suppose a natural resource can be produced from either raw ore or recycled scrap. The marginal cost of production from ore is given by MEC=Qt/10 where Qt is the total amount of ore extracted to date. The marginal cost of production from scrap is given by MRC=20. Consider allocating the resource over the indefinite future (that is, over an infinite number of future periods), where each period has a demand curve given by P=60-Q/2. You may assume the interest rate is zero and that there is always plenty of scrap.

- Find the efficient allocation of the resource. Calculate the efficient prices,
*MECs*, royalties and quantities for all periods. In what period does recycling begin? Explain why you can solve this problem for an infinite number of periods. - Now suppose that production from ore creates an externality of $10 per unit but no externality is associated with recycling. Would this change the efficient allocation of the resource? If so, describe what would change as precisely as you can. Calculate numerical results, if appropriate.