Consider a standard Cournot oligopoly with n = 2k identical firms (with k ≥ 1), an inverse demand P(X), and a cost function C(x) with no fixed costs. Consider only two possible cases: C(x) convex and C(x) concave. Assume that there is always a unique symmetric equilibrium with per firm output xk and profit pk. Assume that there are k two-firm mergers.
a. List all conditions on the primitives of the model such that each firm is better o¤ after these mergers. Explain your answer (no proof needed).
b. Can such a set of mergers be expected to take place without regulatory intervention? Explain.
c. Under what conditions can such a set of mergers increase social welfare?