Models, Mathematics and Critical Loss

43 Pages Posted: 19 Feb 2009 Last revised: 13 Apr 2010

Malcolm B. Coate

U.S. Federal Trade Commission (FTC)

Joseph J. Simons

Paul, Weiss, Rifkind, Wharton & Garrison LLP

Date Written: April 2010


Critical Loss Analysis is an empirical implementation of the hypothetical monopolist test for market definition contained in the Department of Justice and Federal Trade Commission Horizontal Merger Guidelines. As usually applied, the test accepts the proposed market definition as relevant for antitrust analysis whenever the predicted Actual Loss from a small, but significant and non-transitory price increase is less than the computed break-even Critical Loss. While the traditional analysis does not posit an analytical link between the predicted Actual Loss and the break-even Critical Loss, some economists claim the two concepts are mathematically related. They believe that the Critical Loss test will almost never generate broad market definitions in high margin markets. We suggest that the critics overstate their case, because they have only identified a special case modeling structure which may have limited applicability. Revised analyses, drawing on the concepts introduced in this paper, are available elsewhere on SSRN. Text based on Sections II and IV form the core of Coate, Malcolm B. and Joseph J. Simons, “Critical Loss: Modeling and Application Issues,” 2009. Available at SSRN: Text building on Section III, along with Appendix A was published as Coate, Malcolm B. and Joseph J. Simons, “Critical Loss vs. Diversion: Clearing up the Confusion,” GCP Antitrust Chronicle, Dec. 2009. Through the courtesy of the editors, this paper is also available at

Keywords: critical loss, market definition, merger analysis

JEL Classification: K21, L40

Suggested Citation

Coate, Malcolm B. and Simons, Joseph J., Models, Mathematics and Critical Loss (April 2010). Available at SSRN: or

Malcolm B. Coate (Contact Author)

U.S. Federal Trade Commission (FTC) ( email )

601 Pennsylvania Avenue, NW
Washington, DC 20580
United States

Joseph J. Simons

Paul, Weiss, Rifkind, Wharton & Garrison LLP ( email )

New York, NY 10019
United States

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