# Problem 8 Assume that there are two firms each emitting 40 units of pollutants into the environment for a total of 80 units in their region. The government sets an aggregate abatement standard of 30 units. The polluters’ total abatement cost functions are as follows:

Problem 8

Assume that there are two firms each emitting 40 units of pollutants into the environment for a total of 80 units in their region. The government sets an aggregate abatement standard of 30 units. The polluters’ total abatement cost functions are as follows:

Polluter 1: TAC1 = 450 + 4.6(A1)2 + 0.20(A1)3 Polluter 2: TAC2 = 370 + 10.2(A2)2 + 0.20(A2)3

where Ai = the amount of abatement by polluter I and costs are in dollars.

a. Suppose the government allocates the abatement responsibility equally such that each polluter must abate 15 units of pollution. Graphically illustrate this allocation and analytically assess the cost implications (i.e., use the above formulas in a mathematical

analysis). Your analysis should include the total cost to each firm, the marginal cost to each firm, and the total cost to society.

b. Now, assume that the government institutes an emission fee of \$900 per unit of pollution. How many units of pollution would each polluter abate? Is the \$900 fee a cost-effective strategy for meeting the standard? Explain.

c. What allocation of abatement responsibility will reach the abatement goal of 50 units at the lowest social cost? What will be the MAC for each firm and for society under this optimal allocation?

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