Two large manufacturing firms are major sources of airborne pollutants in a metropolitan area. Currently, each firm generates about 15 million units of pollution per year. The firms’ costs of reducing pollution are C1 = 2Q1 + .1Q12 and C2 + .15Q22, where Q1 and Q2 denote the amounts of pollution cleaned up by the respective firms. The social benefit of reducing pollution is estimated to be B = 9Q - .2Q2, where Q denotes the total amount of pollution cleaned up; that is, Q = Q1 + Q2.
a. Write the expressions for the marginal benefit and marginal costs of cleanup, that is, MB, MC1, and MC2.
b. Suppose the EPA seeks to implement pollution standards that maximize net benefits to society (B - C1 - C2). Find the optimal values of Q1 and Q2 by setting MB = MC1 = MC2. Explain why the firms face different quantity standards.
c. Suppose, instead, that the regulator sets a uniform pollution tax of $4 per unit. How much pollution will each firm clean up?
d. What tax should the regulator set to implement the optimal cleanup amounts in part (b)? Explain.