Question

Fred and Barney are fishermen who operate fishing ships out of Nantucket. They own similar ships that can each

carry a day’s catch of 800 pounds of cod. Marginal costs of fishing are constant at $4 per pound (for simplicity,

assume they have no fixed -- or sunk -- costs). For the current discussion, assume that Fred and Barney are the only

fishermen and that the aggregate demand for Nantucket cod is characterized by the demand function Q = 1600 -

100P, where P is the price per pound of cod and Q is in pounds of cod. This corresponds to an inverse demand

function of P = 16 - .01Q, where Q = qF+ qB. Finally, the fish market operates in the following manner: fishermen go

out in the morning and catch fish, then they return to the dock and drop the catch on the dock. Customers gather

around and a market-clearing price is announced, at which point sales commence.

(f) If Barney expects Fred to catch qF, what is Barney’s best response function BRB(qF)?

(g) Using the fact that each fisherman’s equilibrium catch is a best response to the other’s, solve for the equilibrium

catch sizes qBCN and qFCN

(h) What will be the resulting price?

(i) Show that each fisherman’s Cournot duopoly profits will be $1600.

Answer 1