Generalized Critical Loss for Market Definition

• Date: 06 April 2007
• DOI: https://doi.org/10.1016/S0193-5895(06)22003-7
• Pages: 41-58
• Published date: 06 April 2007
• Author: Malcolm B. Coate,Mark D. Williams

GENERALIZED CRITICAL LOSS

FOR MARKET DEFINITION

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Malcolm B. Coate and Mark D. Williams

ABSTRACT

This paper generalizes the critical loss concept of Harris and Simons to

account for a broader range of possible cost structures. Our analysis

presents a specialized market-level equilibrium for a relatively homo-

geneous good in which the Harris and Simons’ critical loss structure is

appropriate for market definition. Then, we broaden the equilibrium and

propose a generalized critical loss analysis. Of course, for relatively

differentiated goods, market definition analysis would use firm-level

modeling and therefore the standard market-level critical loss modeling

could be inappropriate.

1. INTRODUCTION

For over 15 years, critical loss analysis has played an important role in the

market definition analysis. Introduced by Barry Harris in the geographic

market analysis of the Occidental/Tenneco merger and further developed in

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The analyses and conclusions set forth in this paper are those of the authors and do not

purport to represent the views of the Federal Trade Commission, any individual Commissioner

or any Commission Bureau.

Research in Law and Economics, Volume 22, 41–58

Published by Elsevier Ltd.

ISSN: 0193-5895/doi:10.1016/S0193-5895(06)22003-7

41

a paper by Harris and Simons (1989), the analysis computed the maximum

level of lost sales (‘‘the critical loss’’) that could be profitably accepted by a

hypothetical cartel when applying the Merger Guidelines-based small, but

significant and non-transitory increase in price (SSNIP) test. Evidence,

showing the hypothetical cartel (i.e. the hypothetical monopolist) would

lose more than the critical level of sales if a SSNIP occurred, would lead to

a rejection of the proposed market definition. By contrast, if a SSNIP ap-

peared profitable, the proposed market would be accepted as relevant and

a full investigation would be needed to determine the merger’s likely

competitive effect. Critical loss analysis has played an important role in

a number of merger litigations, as well as countless merger enforcement

investigations.

1

Critical loss methodology is best seen as an empirical application of the

SSNIP market definition test that serves to improve the understanding of

certain complex real world situations. Scheffman and Simons (2003) re-

cently noted that critical loss is nothing more than a simple application of

arithmetic designed to explore the likelihood of a price increase. However, it

is important to understand that the basic methodology presumes that a

group of firms can set a single market price, therefore, the goods traded in

the market must be relatively homogeneous. If the products, offered for sale

in the market, are differentiated, the simplifying assumptions of critical loss

analysis will not apply and therefore a naı

¨ve application of the analysis may

be misleading.

2

In this paper, we define a set of conditions under which the critical

loss structure defined by Harris and Simons will accurately reflect the re-

alities facing firms in homogeneous product markets and then provide

a method to generalize the analysis to a more complex industry cost

structure.

3

We start with an exploration of the theoretical support for

the standard critical loss methodology within a homogeneous goods frame-

work. Assuming a Bertrand equilibrium structure, we observe that the

original Harris–Simons calculation for the Merger Guidelines market

definition algorithm may be based on a capacity-constrained equilibrium.

4

Our presentation then generalizes the industry cost structure by adding

an elasticity parameter for marginal cost to the critical loss algorithm.

As shown below, this generalization results in a small change in the value

of critical loss for some elasticity parameters and a large change for other

parameters. Thus, the need to apply the sophisticated version of the criti-

cal loss concept turns on the underlying cost structure of the market in

question.

MALCOLM B. COATE AND MARK D. WILLIAMS42