Now find the cost-effective solution.
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.
To find the cost-effective solution, the MACs must be set equal, subject to the abatement constraint that the sum of the two abatement levels, A1 + A2, must equal 15 units. This is found as follows:
Cost-effectiveness requires: 3.2A1 = 0.8A2
Abatement standard requires: A1 + A2 = 15
Solving simultaneously: 3.2(15 – A2) = 0.8A2
Therefore: 48 – 3.2A2 = 0.8A2, so A2 = 12, and
A1 = 15 – A2 = 3
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