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Problem: Consider a market with n firms. Marginal cost is constant and equal to c. The inverted market demand for each firm is given by pi = a - qi - dQ-i where qi is the output of firm i and Q-i represents the output of firm i's rivals. Fixed cost = F in the pre-merger setting and for outsiders in the post-merger setting. Fixed cost = 2F - x for the insiders in the post-merger setting.
Required:
a) Find the differentiated Cournot equilibrium profits per firm prior to merger.
b) Now suppose that two firms merge. Find the differentiated Cournot profits of each of the merging firms (insiders) after the merger.
c) Let a = 130, c = 10, n = 5, d = 1⁄2. For what values of x is the merger profitable. Does a profitable merger increase welfare?
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