Question

There is an oil refinery located on a river. A fish farm is located in the bay, and is adversely affected by the oil refiner’s water pollution. More oil produces more pollution, and more pollution increases the fish farmer’s costs. The price for refining a barrel of crude oil is po = 200, and the price of a unit of fish is pf = 500. Let o and f represent the quantities of oil refined and fish produced by the two firms, respectively. The oil refiner’s cost is Co(o) = o^2, and the fish farmer’s cost function is Cf(f,o) = f^2+o^2. The fact that o shows up in Cf reflects the negative externality.

(a) How much do the firms produce in a decentralized market equilibrium?

(b) Show that the decentralized market solution is Pareto inefficient.

(c) Find the Pareto efficient allocation of o.