Question

Suppose that three firms, 1, 2, and 3, produce a homogeneous product in a market with
market demand Q = 40 – 2p. Each firm has constant marginal cost c = 2 and has no other costs.
(a) If the three firms are Cournot competitors who simultaneously and independently choose
outputs, what is the equilibrium industry output?
(b) If the firms can collude to jointly choose output to maximize their total profit, what would
be the industry output?
(c) Now suppose that output collusion by the firms to maximize the industry profit is illegal,
but it can be discovered by the antitrust agency only with probability 0.1, in which case each
firm will receive a penalty that is equal to F. Assume that firms are risk neutral, and they
equally share the total profit under collusion. How high should penalty F be in order to deter
firms from collusion?

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Please include explanation

Answer 1