If instead the government used a pollution permit system, what permit price would achieve a cost-effective allocation of abatement? Compare the costs of this allocation to the costs of using the uniform standard described in part (b).

Question

Assume that there are two firms, each emitting 20 units of pollutants into the environment, for a total of 40 units in their region. The government sets an aggregate abatement standard (AST) of 20 units. The polluters' cost functions are as follows, where the dollar values are in thousands:
Polluter 1: TAC1 = 10 + 0.75(A1)2, Polluter 2: TAC2 = 5 + 0.5(A2)2, MAC1 = 1.5A1, MAC2 = A2.

Answer 1

Under a tradeable permit system, the government issues (or sells) an aggregate number of permits equal to the level of pollution deemed acceptable by the objective. In this case, 20 units of abatement are required to reduce the existing 40 levels of pollution down to 20. Hence, the government will issue 20 one-unit permits to the two polluters, who may then exchange these with one another in an open market. The two polluters will buy and sell permits as long as there are gains from trading. The high-cost abater would be willing to purchase permits as long as the selling price is lower than its MAC. The low-cost abater would be willing to sell a permit as long as it receives a price higher than its MAC. Trading will continue until the price reaches the point where neither firm has anything further to gain from an exchange. This occurs when both polluters are abating at the point where their MACs are equal.
Solving this algebraically, the two MAC functions should be set equal to one another, subject to the abatement constraint of 20 units.
MAC1 = MAC2,subject to A1 + A2 = 20
? 1.5A1 = A2
1.5(20 – A2) = A2
A2 = 12, so
A1 = 8
At these abatement levels, MAC1 = MAC2 = $12 thousand. What this means is that a permit price of $12 thousand yields a cost-effective solution. Notice that TAC1 = 10 + 0.75(8)2 =$58thousand and TAC2= 5 + 0.5(12)2$77thousand, for a total abatement cost in the region of $135 thousand. This is $93.39thousand lower than the costs incurred using the uniform standard analyzed in part (b).