Cournot and Stackelberg Mergers.

Consider a Cournot model in which prior to merger there is one low cost firm with marginal cost equal to 12 and 2 high cost firms with marginal cost equal to 24. Fixed costs are zero and inverted market demand is given by P = 48 – Q. In the post-merger setting the low cost firm merges with one of the high cost firms. The merged firm has marginal cost equal to 12 (i.e. equal to the marginal cost of the low cost firm). Outsider marginal cost remains at 24.

a) Solve for the pre-merger level of (i) output and profit for each firm (ii) Herfindahl index and (iii) Welfare.

b) Solve for the post-merger level of (i) output and profit for each firm (ii) Herfindahl index and (iii) Welfare assuming that the merged firm acts like a Cournot firm. Is the merger profitable for the insiders? Does it raise welfare? Does it increase concentration?

c) Repeat b) except assume that the merged firm acts like a Stackelberg leader and the non-merged firms act like Stackelberg followers.