Asymmetric Price Increase In Critical Loss Analysis: A Reply To Daljord, Sørgard, And Thomassen

When products produced by merging firms or in an antitrust candidate market are differentiated, imposing an asymmetric price increase can be more profitable than raising prices similarly for all products. Critical loss and diversion ratio analyses attempt to model the implications of mergers on competition and antitrust market definition in differentiated markets, and have been a major focus over the last decade by authors such as Michael Katz and Carl Shapiro. James Langenfeld and Wenqing Li, and Øystein Daljord, Lars Sørgard, and Øyvind Thomassen, derive the critical loss formula when the price of only one differentiated product is raised due to a merger. However, they arrive at different results. This article corrects the derivation in Daljord, Sørgard, and Thomassen, and provides the appropriate formula of critical loss with asymmetric price. It then shows how failure to correct Daljord, Sørgard, and Thomassen's formulation of critical loss can lead to incorrect conclusions about market definition and competitive effects in merger analysis, resulting in antitrust markets that tend to be too broad.