3. A steel firm produces jointly steel and pollution. The pollution adversely affects a nearby fishery. Both firms are price-takers. ps is the market price of steel. PF is the market price of fish....

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Extracted text: 3. A steel firm produces jointly steel and pollution. The pollution adversely affects a nearby fishery. Both firms are price-takers. ps is the market price of steel. PF is the market price of fish. Cs(s, x) is the steel firm's cost of producing s units of steel jointly with x units of pollution. CF(f,x) is the cost to the fishery of catching f units of fish when the steel mill emits x units of pollution. Suppose the steel firm does not face any of the external costs of its pollution production. (a) Write down the profit functions, and the first-order profit-maximization conditions for the two firms. 14, cs(s, x) = s² + (x – 5)² , and CF(f,x) = f + fx . Suppose ps Please answer the following questions. 10, Pf = (b) Derive the output level of the two firms. (c) Suppose the fishery firm owns the water and can sell pollution rights at px each. What is the equilibrium price and equilibrium quantity for pollution rights traded? (d) Suppose the two firms merge to become one. What is the highest profit this new firm can achieve?