Week of January 20-27 Practice Problems
Practice Problems for Chapter 3, 4 and 5:
Suppose marginal damages due to industrial chlorine emissions into a river system are defined
by the equation
MD = 2E
where E is the measure of pollution. Marginal abatement costs are defined by the equation
MAC = 1000 - ½E
(i) Calculate the pollution level in the absence of any pollution. If you were a policy maker and
were asked to set a target for emissions reduction, how large a reduction would you guess
ought to be pursued?
(ii) Calculate the optimal level of pollution. How good was your guess?
Answer to Question 1
(i) In the absence of any pollution, the firm will pollute up to the point where MAC = 0. The
MAC curve shows the marginal benefit of pollution to the firm, and as long as it is positive it
pays for the firm to pollute more. Set 1000 - ½E = 0 and solve to get E = 2000 units.
(ii) The optimal pollution level (E*)occurs where MD = MAC. Set 2E = 1000 - ½E and solve
for E, to get E* = 400. Pollution should be reduced in this case by 80 per cent (1600 units).
Now suppose that scientific evidence arises showing that the chlorine release is twice as
damaging as previously thought: so the MD curve is actually
MD = 4E
Should you order emissions be cut in half (from 400 down to 200)? Or more? Why or why not?
Answer to Question 2
Set 4E = 1000 - ½E and solve for E, to get E* = 222. Emissions should be cut by 44.5 per cent
(178 out of 400). While marginal damages have doubled, further cuts in emissions increase the
marginal cost of pollution abatement. Hence, it is not desirable to cut emissions by half, even
though marginal damages have doubled. Week of January 20-27 Practice Problems
Suppose two firms, 1 and 2, have the following marginal abatement cost curves:
MAC =1100 - 3 e1 MAC =250 - 2 e2
Find the least-cost allocation of emissions between the two firms that controls total emissions to
Answer to Question 3
We know that aggregate abatement costs between the two firms is minimized when their
marginal abatement costs are equal (the equi-marginal