In our paper Critical Loss vs. Diversion Analysis: Clearing up the Confusion, we tried to bridge the gap between the merger analysts that prefer to begin the market definition exercise with firm level relationships (e.g., the Lerner Index) in conjunction with diversion ratios and those of us that prefer to start at the group or market level and to apply natural experiment and other evidence within the Critical Loss construct. In our article, we developed the concept of the Retention Rate to link firm level to market level analysis. Given a theoretical estimate of the firm's sales diverted to rivals within the market in response to a single-firm price increase, the Retention Rate defines the share of those initially diverted sales that are "retained" within the market in response to an across-the-board price increase. The retained portion of the theoretical diversion can then be used as an adjustment to the Critical Loss analysis. Farrell & Shapiro's comment presents a graphical illustration of our Retention Rate concept. Either approach can be used to describe how sales are diverted to rivals in the hypothetical market in response to a market-wide small, but significant and non-transitory increase in price ("SSNIP").
In this rejoinder, we will first elaborate on the Critical Loss consensus identified in the Farrell & Shapiro paper and then move on to address the areas of misunderstanding associated with our work. As noted in our original paper, we do not disagree with the mathematics of Farrell & Shapiro's single-firm SSNIP analysis applied to a linear demand structure.