Consider a standard Cournot oligopoly with n ≥ 2 identical firms, P(x) = a - bX, X ≥ 0, and C(x) = cx2.
a. Find the Cournot equilibrium output and profit.
b. If m firms wish to merge, what would be their cost function, assuming that they can use all their m production plants but that they otherwise do not have any eciency gains as a result of the merger?
c. Given the cost function from part b, when is an m-firm merger profitable to the merged entity? To the non merging firms?
d. Give a precise economic intuition explaining your answer relative to the usual (linear cost) case.