MERGERS AND COORDINATED EFFECTS

QUESTION 3 (MERGERS AND COORDINATED EFFECTS ) Consider an infinitely re- peated Bertrand game with 3 firms. The discount factor across periods is o. Firms offer a homogenous product which can be produced at zero cost. Suppose that the total number of consumers in the market is 1 and that each consumer demands exactly one unit if the price is not higher than the reservation price of r > 0. At equal prices, consumers split evenly among the three firms. (a) Show that there is a collusive equilibrium where all firms choose the monopoly price (p = r). Determine the critical discount factor. (b) Suppose now that two firms merge. There are two effects of this merger: 1. the number of firms is reduced, 2. at equal prices, the merged firm receives a share of 2/3 of consumers and the outside firm a share of 1/3 of consumers. Discuss how the mergers affects firms’ incentives to collude.