Let market demand be given by Q( P) = 200 - P. Each firm's cost function is C(qi ) = 20qi , where i = 1, 2.
(a) Using the Cournot model, find each firm's output, profit, and price.
(b) Graph each firm's reaction function. Show the Cournot equilibrium.
(c) Suppose that the duopolists collude. Find their joint profit-maximizing price, output, and profit; find each firm's output and profit.
(d) Does each firm have an incentive to increase output? What is the optimal defection for each firm? What does this imply about the stability of their collusive agreement?
(e) Suppose that the cost function is now C(qi ) = 20qi + 400. What is the free-entry number of firms?