Question

Consider question 1. Suppose that Fred wakes up earlier than Barney and decides how many pounds of cod to catch and calls the dock manager to tell him how many pounds of cod to bring to dock. When Barney wakes up, he realizes that Fred’s output is already announced, and he has to decide how many pounds of cod to catch accordingly.
(a) Write Barney’s best response function (Hint: Similar to what you found in question 1).
(b) What is Fred’s profit as a function of his catch qF?
(c) Solve for the equilibrium catch sizes qBS and qFS .
(d) What will be the resulting price?
(e) Find each fisherman’s Stackelberg duopoly profits.

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.

Answer 1