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Quantitative Applicationof the
Hypothetical Monopolist Paradigm
Gregory J. Werden
Senior Economic CounselAntitrust Division
U.S. Department of Justice*
*The views expressed herein are not purported toreflect those of the U.S. Department of Justice.
The Hypothetical Monopolist Test in theU.S. Horizontal Merger Guidelines
A market is defined as a product or group of products and
a geographic area in which it is produced or sold such
that a hypothetical profit-maximizing firm, not subject to
price regulation, that was the only present and future
producer or seller of those products in that area likely
would impose at least a “small but significant and
nontransitory” increase in price, assuming the terms of
sale of all other products are held constant.
The Hypothetical Monopolist Test in theOFT’s Market Definition
One way to look at this problem is to consider an
undertaking that was the only supplier of the products (or
group of products) at the centre of the investigation and
use the conceptual framework of whether a hypothetical
monopolist of these products would maximise its profits
by consistently charging higher prices than it would if it
faced competition.
The Hypothetical Monopolist Test in theOFT’s Mergers: substantive assessment
[A] market is defined by asking whether it would be
profitable for a hypothetical monopolist to impose a small,
but significant (five to ten per cent), non-transitory increase
in price (the SSNIP test) on a given product or group of
products. Starting from the product or products immed-
iately affected by the merger, further products are added to
the group until a price increase of five to ten percent would
be profitable because customers would not switch away
from the postulated group in sufficient numbers.
Merger and Non-Merger Scenarios
! The hypothetical monopolist test is designed to address
whether proposed conduct would create market power.
! That is the issue when the conduct under review (e.g.,
a proposed merger or new business practice) has not
fulfilled any potential to create market power.
! The hypothetical monopolist test is not well suited for
addressing whether a firm is exercising significant
market power (i.e., whether it is dominant).
Application vs. Full Implementationof the Hypothetical Monopolist Test
Mere application of the hypothetical monopolist test asks
whether a profit-maximizing monopolist over a given set
of goods would increase price significantly.
Full implementation of the test applies it only to a
sequence of “candidate markets,” starting with a “focal
good” produced by a merging firm, and constructed by
adding the best substitute for the focal good, and so on.
Standard Formulae for Applying theHypothetical Monopolist Test
Critical Elasticity of Demand Analysis
Profit-Maximization Calculation
Breakeven Calculation
Critical Sales Loss Analysis
Profit-Maximization Calculation
Breakeven Calculation
Critical Elasticity of Demand Analysis
Profit-Maximization Calculation:
The maximum elasticity of demand a profit-maximizing
monopolist could face at pre-merger prices and still want to
increase price by some significance threshold, e.g., 5%
Breakeven Calculation:
The maximum elasticity of demand a monopolist could face
at pre-merger prices and still not experience a net reduction
in profits from a given price increase, e.g., 5%
Critical Sales Loss Analysis
Profit-Maximization Calculation:
The maximum reduction a hypothetical, profit-maximizing
monopolist would be willing to tolerate in its quantity sold
to sustain a given price increase, e.g., 5%
Breakeven Calculation:
The maximum reduction a monopolist could experience in
its quantity sold and still not experience a net reduction in
its profits from a given price increase, e.g., 5%
Profit-Maximization vs. Breakeven
Profit-Maximization Calculations:
These calculations implement the HMGs’ hypothetical
monopolist test but are sensitive to the unknown shape of
the hypothetical monopolist’s demand curve.
Breakeven Calculations:
These are close to profit-maximization calculations for
small price increases and high margins, and critical sales
loss is independent of the shape of the demand curve.
Critical Elasticities of Demandfor Market Delineation
DemandCurve
ProfitMaximization
Break-Even
Linear1 1
m + 2t m + t
Isoelastic1 + t log(m + t) – log(m)
m + t log(1 + t)
m = price-cost margin t = price increase significance level
Critical Elasticities of Demandfor a 5% Price Increase
DemandCurve
Premerger Price-Cost Margin
0% 40% 50% 60% 70% 100%
Profit Maximization
Linear 10 2.00 1.67 1.43 1.25 0.91
Isoelastic 21 2.33 1.91 1.62 1.40 1
Break-Even Linear 20 2.22 1.82 1.54 1.33 0.95
Isoelastic 4 2.41 1.95 1.64 1.41 1
Critical Sales Lossfor Market Delineation
DemandCurve
ProfitMaximization
Break-Even
Lineart t
m + 2t m + t
Isoelastict
1– (1+ t)
–1– t
m+ t m + t
m = price-cost margin t = price increase significance level
Percentage Critical Sales Lossfor a 5% Price Increase
DemandCurve
Premerger Price-Cost Margin
0% 40% 50% 60% 70% 100%
ProfitMaximization
Linear 50.0 10.0 8.3 7.1 6.3 4.5
Isoelastic 64.1 10.8 8.9 7.6 6.6 4.8
Break-Even Any 100 11.1 9.1 7.7 6.7 4.8
FTC v. Tenet Health Care Corp.17 F. Supp. 2d 937 (E.D. Mo. 1998),rev’d, 186 F.2d 1045 (8th Cir. 1999)
! The district court accepted the FTC’s contention that the
geographic scope of the relevant market was a 50-mile radius
around Poplar Bluff, Missouri.
! On appeal, the defendant argued that its critical loss analysis
demonstrated that the FTC’s market was too narrow.
! The Eighth Circuit held that the FTC failed to show that
hospitals outside its alleged market were not “practical
alternatives for many Poplar Bluff consumers.”
United States v. Mercy Health Services902 F. Supp. 968 (N.D. Iowa 1995),
vacated as moot, 107 F.3d 632 (8th Cir. 1997)
! Relying on defendant’s breakeven critical loss of 8%, the court
found sufficient switching would occur “in the event of a 5%
price rise” “to make the price rise unprofitable.”
! The government predicted the total elimination of managed care
discounts—a far larger price increase, so the court also
considered a larger (albeit not large enough) price increase.
! The court reckoned the critical loss at 20–35%, although it was
actually about 46%.
California v. Sutter Health System84 F. Supp. 2d 1057 (N.D. Cal. 2000), aff’d, 217 F.3d 846 (9th
Cir. 2000), amended by 130 F. Supp. 2d 1109 (N.D. Cal. 2001)
! A major point of contention was whether the critical loss
analysis should consider only a 5% price increase.
! Purporting to follow the Horizontal Merger Guidelines, the court
held that only 5% should be used.
! This may be the most clear-cut and serious error ever made by
a court in applying the hypothetical monopolist paradigm.
! Although a 5% price increase is unprofitable, a far greater price
increase still could be profit maximizing.
FTC v. Swedish Match131 F. Supp. 2d 151 (D.D.C. 2001)
! Both sides’ experts relied on critical elasticity analyses, which
differed as to both on the critical and actual elasticity.
! Although the court discussed these analyses in detail, it found
neither expert’s evidence “persuasive.”
! The court, however, applied its own critical loss analysis,
finding that “it cannot be unprofitable for the hypothetical
monopolist to raise price . . . because the hypothetical
monopolist would lose only a small amount of business.”
United States v. SunGard Data Sys., Inc.172 F. Supp. 2d. 172 (D.D.C. 2001)
! The court noted defendants’ contention that margins exceeded
90% so the critical loss was very low.
! The government and its expert said nothing about this analysis.
! The court held that the government had failed to show that the
customers who would not switch in the face of a price increase
were “substantial enough that a hypothetical monopolist would
find it profitable to impose such an increase in price.”
Assessing Price-Cost Margins: Theory
! The relevant cost concept is avoidable cost, and which costs are
avoidable depends on
the magnitude of the change in output and
the time period considered.
! The relevant change in output depends on how much price
actually would be increased and on the elasticity of demand.
! Sales contracts and other institutional details may affect which
costs are avoidable.
Assessing Price-Cost Margins: Practice
! Never simply use whatever the parties call their margins; rather,
get data from which margins can be computed.
! Get disaggregated revenue and cost data supporting a range of
options as to which costs and which products are included.
! Find out from the parties exactly how the data were complied.
! Treat the determination of margins as a central task of the
investigation and anticipate the parties’ arguments.
! Premerger margins should be explainable as the product of an
equilibrium of the premerger game.
Assessing Price-Cost Margins: Issues
! Could shutting some capacity down avoid fixed any costs?
! Does some capacity entail higher-than-average marginal cost?
! Could capacity be diverted to other profitable uses?
! Do sellers price discriminate, and if so, would the margins on
the lost sales be above or below average?
! How would the hypothetical monopolist and actual competitors
raise price and reduce output?
The Paradox of High Price-Cost Margins
! A high pre-merger margin implies a low critical elasticity and
critical sales loss, perhaps suggesting a broad market.
! In equilibrium, however, a high margin tends to imply a low
actual demand elasticity and actual sales loss.
! In standard oligopoly models, higher pre-merger margins imply
larger unilateral price effects from mergers.
! Small differences in demand elasticities are important when they
are nearly unitary as with very high margins, and it may be
difficult to measure them precisely enough to be useful.
Pitfalls In Applying Standard Formulae
! While typical applications posit small price increases, the profit-
maximizing monopoly price increase, and even that from the
merger, may be large.
! While standard formulae presume constant marginal cost and no
avoidable fixed costs, actual cost functions may be quite
different.
! While standard formulae implicitly increase all prices
proportionately, profit-maximization often implies highly
disproportionate price increases.
Modeling the Hypothetical Monopolist
! The demand and cost assumptions of critical loss and critical
elasticity analysis can be relaxed.
• On the demand side, it is possible to have distinct customer
types with different demands.
• On the cost side, many things are possible.
• Information needed to calibrate more flexible demand and
cost functions commonly is available.
! The implicit assumption that the hypothetical monopolist
increases prices proportionately can be dropped.
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Full Implementation of the
Hypothetical Monopolist Test
! The hypothetical monopolist test is applied only to candidate
markets built up through an iterative process.
! The process begins with a focal good sold by one of the merging
firms, and the next-best substitute added at each iteration.
! The process generally stops when a hypothetical monopolist over
a candidate market would raise price significantly.
The Candidate Market Sequence
! Goods are ranked on the basis of closeness to the focal good,
normally using a metric based on cross elasticities of demand.
! The first candidate market is just the focal good; the second is the
focal good and its closest substitute; and so on.
! The hypothetical monopolist test is applied to each candidate
market and only to each candidate market.
The Hypothetical Monopolist Test
! The hypothetical monopolist selects prices for all goods in a
candidate market so as to maximize its profits.
! Prices of goods outside a candidate market generally are assumed
to be held constant.
! The hypothetical monopolist’s many prices are combined (e.g.,
by averaging) to form a price-increase norm.
! Every candidate market is a market if the price increase norm
exceeds the price increase significance threshold (e.g., 0.05).
The Relevant Market Rule and Property
! From the many markets, a single relevant market is selected,
using a relevant market rule, e.g., the smallest market principle,
which holds that the relevant market is the smallest one.
! The relevant market actually alleged is the relevant market
property, which distinguishes goods in the relevant market from
all others on the basis of traits.
! The relevant market property may employ natural market
boundaries, which are groupings recognized in the industry or by
data compilers and national or other political boundaries.