Problem
Consider a standard Cournot oligopoly with n ≥ 2 identical firms, an inverse demand function P(X) = a - bX, and cost function C(x) = K + cx if x > 0, and 0 if x = 0, meaning K is a fixed cost.
a. Find the Cournot equilibrium output and profit. How many firms (as a function of K) can survive at the equilibrium?
b. When is an m-firm merger profitable to the merged entity? To the nonmerging firms?
c. Give a precise economic intuition as to why most mergers are not profitable in the usual model with K = 0. How is it different when K > 0?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.