3. Lets consider an symmetric Cournot example with 3 firms. You are free to use any of the formula from the slides, but please indicate which formula you are using. Suppose that inverse demand is P(q) = 100 q1 q2 q3. The constant pre-merger marginal costs of the firms are c1 = 20, c2 = 20 and c3 = 20 and there are no fixed costs.. Assume that these marginal costs are such that all three firms have positive output in equilibrium.

(a) Suppose that firms 1 and 2 merge with no synergy. Is the merger profitable? (

b) Now suppose that the firms play an infinitely repeated game, setting quantities each period (i.e., the same model we considered for collusion). If they collude, each firm will produce an equal share of the joint monopoly output. For what discount factors can the firms support collusion without the merger? (Assume that they dont anticipate the merger). For what discount factors can the firms support collusion with the merger? Does this provide a possible alternative explanation for why the merger might be profitable