Consider a homogeneous product market with infinitely many quantity-setting firms. The inverse demand function is given by P(q) = a − q, where q is industry quantity. The cost function of each firm is Cs(qi) = csqi + Fs for qi > 0 and Cs(0) = 0. Suppose that parameters are such that, in any equilibrium, more than one firm is active (i.e., produces a positive quantity). For simplicity, the analysis below should be carried out under the assumption that the number of firms is a real number.

(a) Characterize the free-entry equilibria of the game in which all firms simultaneously set quantities. Determine the equilibrium quantity of each active firm, the equilibrium price, the industry quantity, the number of active firms and consumer welfare.

(b) Consider a single merger between two firms. Suppose that the merged firm has cost function Cm(qi) = cmqi +Fm for qi > 0andCm(0) = 0 and that cm = cs. Under what condition on Fm is a merger profitable, assuming that there is free entry before and after the merger?

(c) In the setting of part (b) is a profitable merger welfare-increasing? Or is a profitable merger welfare-decreasing? Interpret.

(d) Consider now a single merger after which the merged firm’s cost function is Cm(qi)= cmqi + Fm with Fm = Fs. Under what condition on cm is a merger profitable, as- suming that there is free entry before and after the merger?

(e) In the setting of part (d), is a profitable merger welfare-increasing? Or is a profitable merger welfare-decreasing? Interpret.