## Consider a case where there are three firms contributing to the pollution of the Cabernet airshed. Their demand functions for the right to pollute are given as follows:

Consider a case where there are three firms contributing to the pollution of the Cabernet airshed. Their demand functions for the right to pollute are given as follows:

Firm A: Q = 64 – P Firm B: Q = 32 – 1/3P Firm C: Q = 30 – 2/3P

where Q is the amount of pollution in tons per year and P is the willingness to pay in dollars per ton.

a. Draw the individual and aggregate demand functions for the right to pollute in the Cabernet airshed (Hint: Note that the aggregate is not a simple summation. If this problem gives you trouble, you may want to review the tutorial on aggregating cost and demand curves that is on the class web site).

Emissions Demand Curves for Individual Firms and Industry Aggregate

b. What is the total amount of unabated air pollution in this airshed?

c. Now draw the marginal abatement cost (MAC) curve.

d. Suppose that the Cabernet environmental agency determines that the MED function for emissions is MED = 50 for the entire range of emissions. Draw the marginal abatement benefit (MAB) curve onto the MAC curve

e. What is the efficient level of abatement in this case? The efficient level of emissions?

f. What is the total cost of abatement to reach the efficient level of emissions?

Aggregate Marginal Abatement Cost Curve And Marginal Abatement Benefit Curve with Total Abatement Cost

g. What is the allocatively efficient level of abatement for each firm? What is the total cost of abatement to each firm?

Problem 3

Adapted from problem 5, p111 in text

The Great Fracking Natural Gas company has just established a new well in the ranching community of Grassville, USA. It turns out that some of the chemicals used in the Fracking process are contaminating the groundwater. The total damage to ranchers due to livestock losses from drinking the water is 50p2, where p is the level of pollution in this case. The

total damage to families who must travel to town and purchase clean water each month is 300p2. The marginal savings to Great Fracking for being allowed to pollute is 4000 – 40p.

a. Find the aggregate (including both types of consumers) marginal damage for the public bad.

b. Graph the marginal savings and aggregate marginal damage curves with pollution on the horizontal axis.

c. How much will Great Fracking pollute in the absence of any regulation or bargaining? What is this society’s optimal level of pollution?

d. Starting from the uncontrolled level of pollution calculated in part (c), find the marginal willingness to pay for pollution abatement, A, for each consumer class (abatement reduction in pollution; zero abatement would be associated with the uncontrolled level of pollution). Find the aggregate marginal willingness to pay for abatement.

e. Again starting from the uncontrolled level of pollution, what is the firm’s marginal cost of pollution abatement? What is the optimal level of A?

Are the problems of optimal provision of the public bad (pollution) and the public good (abatement) equivalent? Explain why or why not.