If the state uses a uniform standard, show that such a ruling would not be cost-effective. Which firm should be abating more, and which firm should be abating less?

Consider the environmental problem created by two paint companies that release chromium wastes into a nearby stream. The state authorities set a standard for the waterway that requires a combined abatement level (A) for chromium of 15 units. Suppose that the two firms, firm 1 and firm 2, face the following marginal abatement cost equations: MAC1 = 3.2A1 and MAC2 = 0.8A2, where costs are measured in thousands of dollars.

Based on a uniform standard, each firm would abate half of the aggregate standard, or 7.5 units. Therefore, MAC1 = 3.2(7.5) = $ 24 thousand and MAC2 = 0.8(7.5) = $6 thousand. Since the MACs are unequal, cost-effectiveness is not achieved. Based on the relative dollar values, Firm 1 should abate less, and Firm 2 should abate more, since Firm 2 clearly can clean up more cheaply than Firm 1 at the margin.