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Models, Mathematics and Critical Loss


Malcolm B. Coate


U.S. Federal Trade Commission (FTC)

Joseph J. Simons


Paul, Weiss, Rifkind, Wharton & Garrison LLP

April 2010


Abstract:     
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: http://ssrn.com/abstract=1520069. 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 http://ssrn.com/abstract=1562006.

Number of Pages in PDF File: 43

Keywords: critical loss, market definition, merger analysis

JEL Classification: K21, L40

working papers series


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Date posted: February 19, 2009 ; Last revised: April 13, 2010

Suggested Citation

Coate, Malcolm B. and Simons, Joseph J., Models, Mathematics and Critical Loss (April 2010). Available at SSRN: http://ssrn.com/abstract=1346067 or http://dx.doi.org/10.2139/ssrn.1346067

Contact Information

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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