Firm S produces steel with a cost function cS(s,x) = s^2 + 10 − (12x − x^2), where s is units of steel and x is units of a pollutant that is a byproduct of steel production. Another firm F produces fish with a cost function cF(f,x)=3f^2+fx,where f is units of fish. Hence, pollution raises F’s costs. Steel and fish are sold in internationally competitive markets, where the price of steel is $20 and the price of fish is $72.

(a) Sketch S’s marginal benefit curve (or negative marginal cost) from pollution and F’s marginal cost curve from pollution.

(b) Suppose S can freely dump its pollution into the lake used by F . What will be the quantity of pollution, x∗, in the unregulated competitive equilibrium? How much fish and how much steel will be produced in this equilibrium?

(c) What is the socially efficient quantity of pollution, x∗∗?