Consider Cournot competition with n identical firms. Suppose that the inverse demand function is linear with P(X) = a - bX, where X is total industry output, a; b > 0. Each firm has a linear cost function of the form C(x) = cx, where x stands for per firm output. It is assumed that a > c.
a. At the symmetric equilibrium, what are the industry output and price levels? What are the equilibrium per firm output and profit levels? What is the equilibrium social welfare (defined as the difference between the area under the demand function and total cost)?
b. Now let m out of n firms merge. Show that the merger is profitable for the m merged firms if and only if it involves a pre-merger market share of 80 percent.
c. Show that each of the (n - m) non merged firms is better off after the merger.
d. Show that the m-firm merger increases industry price and also lowers consumer welfare.