Let market demand be given by the inverse demand function P = 300-2Q, where Q = q1 +q2 +...+qn. The cost function for each firm in the industry is c(qi) = F +20qi+q 2 i . Firms are Cournot competitors.
(a) Find each firm’s equilibrium output and profit (dependent on F and n).
(b) Find the range of F so that there will be 6 firms in the long run.
(c) If F = 1, 000, find n in the long run. Also find each firm’s profit, consumer surplus, and deadweight loss.