A polluting firm (A) releases 1000 units of acid into a river, and the firm's clean-up cost is is 50 + 0.25x. x is the number of units of acid. The marginal costs of the pollution rise as the firm reduces its level of acids towards zero. Meanwhile, another firm's (B) water purification costs decline, as firm A reduces it level of acids runoff. The marginal benefits of less pollution are constant and equal to $200/unit reduction of runoff.

Suppose the government steps in and decides to tax pollution.

a. What is the optimal tax per unit of acid released? How much pollution will result?

b. Imagine the government decides to pay firm A a subsidy for each gallon reduction of its acid release. What is the optimal subsidy per gallon reduction? How much pollution will result?

c. What is the relationship between the optimal tax and subsidy per gallon that was in a and b? Will this relationship always hold?