Now, assume that the government institutes an emission fee of $16 thousand per unit of pollution. How many units of pollution would each polluter abate? Is the $16 thousand fee a cost-effective strategy for meeting the standard? Explain.

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.

Faced with a $16 thousand pollution charge, each polluter will abate as long as its MAC is less than $16 thousand and pay the fee when the opposite condition holds. Hence, polluter 1 will abate up to the point where MAC1 equals $16 thousand. Algebraically, this is found as follows:
MAC1 = 16
1.5(A1) = 16, which implies A1 = 10.67 units.
Analogously, polluter 2 abates up to the point where MAC2 equals $16 thousand, found as:
MAC2 = 16
A2 = 16 units
Notice that although the pollution charge brings about equal MACs across polluters, the total abatement level for the region is 26.67 units, which is higher than what is required. This means that the fee is set too high to meet the standard and too manyresources are being allocated to pollution abatement.Total costs of abatement are: TAC1 = 10 + 0.75(10.67)2 =$95.39 thousand and TAC2= 5 + 0.5(16)2= $133 thousand, or $228.39 thousandfor the entire region. This result underscores the difficulty in setting the appropriate level of a pollution charge to meet a given abatement level.