Question

An industry producing a homogeneous commodity is comprised of N(≥ 2) firms. Assume that each firm faces a marginal cost of 1 and no other costs. The industry inverse demand function is P(Q) = 11 − Q, where Q is industry output.

(a) Assuming that the firms choose quantities simultaneously, derive the profits of each firm in equilibrium.

(b) Two of the firms are considering a merger. A merger simply means that these two firms become one firm, with the same marginal cost of 1. Retaining the assumption of Cournot-Nash behaviour in the post-merger equilibrium, derive the condition under which a merger would be profitable; that is under which the equilibrium profits of the new merged firm are greater than the combined profits of the two merging firms pre-merger. What is the largest value of N for which a merger between the two firms would be undertaken? Given this observation, would the merger ever be undertaken?

Pls give the process.

Answer 1