Consider a three-firm Cournot oligopoly in a homogeneous product. Each firm has the same constant marginal...

 

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Consider a three-firm Cournot oligopoly in a homogeneous product. Each firm has the same constant marginal cost of production, c. The firms are indexed i = 1, 2, 3. The inverse market demand for the good is given by P = a – bQ, where Q is the total output of the firms. The reaction function for each firm i is given by a - c-bE9 2b Suppose firms 1 and 2 merge. We now have a Cournot duopoly. Is this merger privately profitable? That is, is the profit of the merged firm higher than the sum of the profits of the two individual firms before the merger? Do the results change when all three firms merge? More generally, consider an industry with n symmetric firms. Let m firms participate in a merger. What is the condition on m so that the firms that merge are better off than before the merger? Consider a three-firm Cournot oligopoly in a homogeneous product. Each firm has the same constant marginal cost of production, c. The firms are indexed i = 1, 2, 3. The inverse market demand for the good is given by P = a – bQ, where Q is the total output of the firms. The reaction function for each firm i is given by a - c-bE9 2b Suppose firms 1 and 2 merge. We now have a Cournot duopoly. Is this merger privately profitable? That is, is the profit of the merged firm higher than the sum of the profits of the two individual firms before the merger? Do the results change when all three firms merge? More generally, consider an industry with n symmetric firms. Let m firms participate in a merger. What is the condition on m so that the firms that merge are better off than before the merger?

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