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.

(d) suppose that the government imposes a tax on the oil refiner that makes the oil refiner pay $t per unit of output produced. is there a t that induces the pareto efficient level of o?

(e) suppose that the fishery has the right to a pollution-free environment. suppose that given this the fishery can bargain with the oil refiner over o, and suppose that the bargaining process is such that the fishery makes a take-it-or-leave it offer to the oil refiner, and the offer can either be accepted or rejected. the offer allows the refiner to produce a certain level of o in exchange for a payment from the refiner to the fishery. if the offer is rejected the oil refiner is not allowed to produce. what will be the outcome of this bargaining process in terms of the quantity of o produced?