The Concept Of Critical Loss For A Group Of Differentiated Products

In a recent article, Daljord, Sørgard, and Thomassen criticize Katz and Shapiro for applying the standard formula for critical loss to the case in which the price of only one product of the candidate market is increased. They argue that the standard formula does not hold in that case and suggest another expression. We show that this argument is correct, but that the formula proposed by Daljord, Sørgard, and Thomassen does not capture the essence of what critical loss really is. We propose another formula that does. Daljord, Sørgard, and Thomassen also modify the Katz–Shapiro aggregate diversion ratio rule for deciding whether a candidate market is an antitrust market. We show that their rule happens to be correct for the single-price-increase case and that the Katz–Shapiro rule remains valid for uniform price increases, but that in both cases this is for different reasons than mentioned by the authors. We believe that the confusion is due to the fact that the critical-loss concept, which was originally designed for a single homogeneous product, needs some further explanation before it can be applied in a setting of multiple differentiated products. Such explanation is given in this article.