How Bad is the Merger Paradox?

The merger paradox is a classic, counter-intuitive result from the literature of Industrial Organization saying that merging firms typically experience a decline in their overall profit compared to their total pre-merger profit. This phenomenon is more striking in small oligopolistic markets, where mergers increase market concentration and may hence trigger a substantial increase in prices. In this paper, we investigate the severity of the merger paradox in Cournot oligopoly markets. Namely, we study the worst-case magnitude of this profit loss in quantity-setting market games. We consider convex, asymmetric production costs for the firms, and we show that the profit loss can be substantial even in small markets. That is, two merging firms can lose half of their pre-merger profit, but no more than half in markets with concave demand functions. On the positive side, we show that in markets with affine demand two firms can never lose more than 1/9 of their profit when merging, and this bound is tight. We also study the asymptotic loss in larger markets, where it is easy to show that the profit loss can be arbitrarily large when multiple firms merge; we give bounds that characterize the profit loss from a merger as a function of the market size and the number of merging firms.