Estimating Incremental Margins for Diversion Analysis

• Author: Seth B. Sacher and John D. Simpson
• Position: The authors are economists on the staff of the U.S. Federal Trade Commission
• Pages: 527-556

ESTIMATING INCREMENTAL MARGINS FOR

DIVERSION ANALYSIS

S

ETH

B. S

ACHER

J

OHN

D. S

IMPSON

*

Over the past 20 years, as part of the merger review process, antitrust agen-

cies have increasingly turned to economic tools such as diversion and pricing

pressure analyses to help determine which mergers to investigate, and then to

further identify which mergers to challenge. A key input in these analyses is

an estimate of the profit margin that the merging firms earn on incremental

sales (“incremental margin”).

1

All else being equal, the higher the merging

firms’ pre-merger incremental margins, the likelier the analysis will be to pre-

dict significant price increases post-merger.

Obtaining and compiling the information required to estimate incremental

margins can be difficult in practice. Thus, antitrust economists often use

proxies based on measures found in aggregate accounting data, such as the

difference between price and the cost of goods sold (the gross margin) or the

difference between price and average variable costs.

2

However, as noted by

economists in other contexts, such proxies sometimes provide a poor measure

of a firm’s market power and a poor measure of performance in an industry.

3

* The authors are economists on the staff of the U.S. Federal Trade Commission. This article

reflects the views of the authors and does not necessarily reflect the views of the U.S. Federal

Trade Commission or any individual Commissioner. Malcolm Coate, Arthur Del Buono, Jeffrey

Fischer, Daniel Greenfield, Kevin Hearle, Subbu Ramanarayanan, Paolo Ramezzana, David

Schmidt, Aileen Thompson, and Nathan Wilson provided helpful comments and suggestions.

Remaining errors are the authors’.

1

Incremental profits are the net change in profits associated with the specific change in out-

put over the time period relevant to the matter being considered. The incremental profit margin

(“incremental margin”) is the profit margin on these units of output; it is measured as the average

difference between price and incremental cost over this change in output. See U.S. Dep’t of

Justice & Fed. Trade Comm’n, Horizontal Merger Guidelines §§ 2.21, 4.1.3, 6.1 (2010) [herein-

after Merger Guidelines].

2

The cost of goods sold comprises all direct and indirect manufacturing costs required to

produce a good. Variable costs are those costs that vary with output.

3

See, e.g., Franklin M. Fisher, On the Misuse of the Profit-Sales Ratio to Infer Monopoly

Power, 18 RAND J. E

CON

. 384 (1987). There is a vast economic literature relating various

measures of industry performance, such as rates of return or price-cost margins, to economic

527

528

A

NTITRUST

L

AW

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OURNAL

[Vol. 83

In this article, we offer our views on how best to estimate incremental margins

given the shortcomings of measures based on aggregate accounting data.

I. USE OF INCREMENTAL MARGINS IN ANALYSIS OF MARKET

DEFINITION AND COMPETITIVE EFFECTS

A. D

IFFERENT

I

NCREMENTAL

M

ARGINS

M

EASURE

D

IFFERENT

T

HINGS

A discussion of diversion analysis, an economic tool commonly used in

antitrust analysis and described in the Merger Guidelines,

4

illustrates the im-

portance of accurate estimation of incremental margins. Consider two firms

(A and B) selling differentiated products, competing on prices as under Ber-

trand competition, facing linear demand, and having marginal costs that are

constant with respect to output. This setup is illustrated in Figure 1.

Firm A initially sells Q

0A

units of its product at price P

0A

and earns profit of

P

0A

-MC on these Q

0A

units. If Firm A increases price to P

1A

, it earns a higher

profit on those units it continues to sell (shown as Rectangle A), but it loses

the profit it previously earned on those units it no longer sells (shown as

Rectangle B). Assuming firms set prices to maximize profit, Firm A earns

less profit on any price other than the one it actually charges, i.e., at price P

0A

.

Therefore, a stand-alone Firm A finds it unprofitable to increase price, as the

amount of profit it stands to lose from a price increase (as represented by area

B) exceeds the amount of profit it stands to gain from doing so (as represented

by area A). If Firm A were to merge with Firm B, Firm A’s calculation

regarding the impact of a price increase on profitability changes because some

of the lost sales at Firm A would be recovered by Firm B (i.e., Firm B’s

demand curve shifts from D

0

to D

1

), and Firm B would earn profits on these

sales (shown as Rectangle C). Now, a given price increase is profitable for

the merged firm if the sum of areas A and C exceeds area B.

structure. For critical reviews of this literature, see Harold Demsetz, Industry Structure, Market

Rivalry, and Public Policy, 16 J.L. & E

CON

. 1 (1973); Richard Schmalensee, Inter-Industry Stud-

ies of Structure and Performance, in 2 H

ANDBOOK OF

I

NDUSTRIAL

O

RGANIZATION

960 (Richard

Schmalensee & Robert Willig eds., 1989); Michael Salinger, Richard E. Caves & Sam Peltzman,

The Concentration-Margins Relationship Reconsidered, 1990 B

ROOKINGS

P

APERS ON

E

CON

. A

C-

TIVITY

: M

ICROECONOMICS

287.

4

Merger Guidelines, supra note 1, § 6.1 (“A merger between firms selling differentiated

products may diminish competition by enabling the merged firm to profit by unilaterally raising

the price of one or both products above the pre-merger level. Some of the sales lost due to the

price rise will merely be diverted to the product of the merger partner and, depending on relative

margins, capturing such sales loss through merger may make the price increase profitable even

though it would not have been profitable prior to the merger.”).