Vertical Mergers and Market Foreclosure

13 Pages·1988·0.395 MB·English

by  Michael A. Salinger

Vertical Mergers and Market Foreclosure
Author(s): Michael A. Salinger
Source: The Quarterly Journal of Economics, Vol. 103, No. 2 (May, 1988), pp. 345-356
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/1885117
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VERTICAL MERGERS AND MARKET FORECLOSURE*
MICHAEL A. SALINGER
The model in this paper illustrates three effects of vertical mergers when both
stages are oligopolistic and vertically integrated and unintegrated producers coexist.
First, the merging firm increases its final good output. Second, the resulting
backward shift in the residual demand curve facing unintegrated final good produc-
ers lowers their demand for the intermediate good. Third, the merged firm
withdraws from the intermediate good market. The increased concentration pushes
the intermediate good price upward. Which effect dominates depends on market
structure. Under some conditions, a vertical merger causes the price of the final good
to increase.
I. INTRODUCTION
In decisions on some antitrust cases, judges have expressed
concern that vertical mergers can result in market foreclosure and,
as a result, be harmful to competition.1 This concern is in distinct
contrast to the view held by many economists (and, apparently,
those currently in charge of antitrust enforcement) that vertical
mergers do not enhance market power and can often lead to a price
reduction for the final good.
The concern about market foreclosure addressed in this paper
is that the merged firm will not participate in the market for the
intermediate good. If it does not, unintegrated final good producers
lose a supplier.2 This concern raises three questions. First, will
vertically integrated producers participate in the intermediate good
market as if they were not integrated? Second, if not, how will a
vertical merger affect the market for the intermediate good? Third,
how will the change in the intermediate good market affect compe-
tition in the final good market?
The two models that are the keystone of a benign view of
vertical mergers do not answer these questions. In the first, an
upstream monopolist sells to a perfectly competitive downstream
*I have received helpful comments from Jean-Pierre Benoit, Alan Fisher,
Geoffrey Heal, Eric Maskin, David Scheffman, L. G. Thomas, three anonymous
referees, and participants in seminars at Colgate, Columbia, the Federal Trade
Commission, GTE Labs, the Justice Department, and Yale. I am, of course,
responsible for any remaining errors.
1. See, for example, A. G. Spalding & Bros., Inc., 56 F.T.C. 1125 [1960]; Brown
Shoe Co., Inc. v. U. S., 370 U. S.294 [1962]; Kennecott Copper Corp. v. U. S.381 U. S.
414 [1965]; and Ford Motor Co. v. U. S., 405 U. S. 562 [1972].
2. Unintegrated intermediate good producers lose a customer. This paper does
not, however, focus on market foreclosure of upstream firms. See footnote 15.
? 1988 by the President and Fellows of Harvard College and the Massachusetts Institute of
Technology.
The Quarterly Journal of Economics, May 1988
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346 QUARTERLY JOURNAL OF ECONOMICS
industry that produces with fixed-coefficients technology. Vertical
integration by the monopolist does not increase its profits or result
in a different final good price. In the second, a merger of successive
monopolists leads to a lower final good price as well as increased
joint profits. Market foreclosure refers to the effect of vertical
integration on unintegrated producers. In these models, however,
no unintegrated firms exist after the vertical merger occurs. Thus,
the view that vertical mergers are not harmful is based on models
that cannot address the primary reason to believe that they are.
Since the early 1970s economists have found cases in which
vertical mergers can lower welfare. The first line of attack was to
relax the assumption of fixed-proportions technology in the produc-
tion of the final good. Vernon and Graham [1971] show that when
there are opportunities for substitution in the production of the
final good, an upstream monopolist has an incentive to monopolize
the downstream stage. Schmalensee [1973], Warren-Boulton
[1974], Mallela and Nahata [1980], and Westfield [1981] show that
these mergers are more likely to raise than to lower the price of the
final good. These models are certainly of theoretical interest.
Nevertheless, as Bork [1978, pp. 230-31] so aptly put it, they
concern "the acquisition of a monopolist of a second vertically-
related monopoly.... [As a result, they] ... have no force in the
broader context of the vertical mergers the law is preventing."
Perry and Groff [1983a,b] show that vertical integration by a
monopolist or oligopolists into a monopolistically competitive
downstream stage can lower welfare. While the consideration of
differentiated products is an important contribution to the theory
of vertical integration, these papers compare no vertical integration
with complete vertical integration. Thus, they also do not address
market foreclosure.
This paper presents a model in which there are both vertically
integrated and vertically unintegrated firms. Section II discusses
conditions under which a vertically integrated firm does not partici-
pate in the intermediate good market. Section III develops a model
in which there is a Cournot-Nash equilibrium at both stages of
production. Section IV contains some concluding comments.
II. VERTICALLY INTEGRATED FIRMS
AND THE INTERMEDIATE GOOD MARKET
One response to the argument that vertical mergers result in
market foreclosure is that nothing prevents a vertically integrated
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VERTICAL MERGERS AND MARKET FORECLOSURE 347
firm from buying or selling the intermediate good. Indeed, many
vertically integrated firms do so. Thus, the argument goes, a vertical
merger should not cause unintegrated producers to lose either a
supplier or a customer. This argument is not persuasive, however,
because sales of the intermediate good by a vertically integrated
firm affect its profits from final good sales. Thus, a vertical merger
may give an intermediate good producer an incentive to restrict its
sales of the intermediate good.3
Throughout this paper I assume that the intermediate and
final goods are homogeneous, that there are constant returns to
scale in the production of both, and that the final good is produced
with fixed-coefficients technology. Let MCI be the marginal (and
average) cost of the intermediate good, MCF be the marginal (and
average) cost of transforming the intermediate good into the final
good, PI be the price of the intermediate good, and PF be the price of
the final good. Note that MCF is net of the cost of the intermediate
good. Thus, a vertically integrated firm's total cost of producing a
unit of the final good is MCI + MCF, while an unintegrated
producer's unit cost is PI + MCF-
In deciding whether to buy or sell the intermediate good, a firm
needs to make some conjecture about the effect of its actions on
both intermediate and final good producers. It cannot make a
Cournot assumption about both. If a firm sells an extra unit of the
intermediate good and assumes that other intermediate good pro-
ducers do not change their outputs, it must also assume that a final
good producer increases its output by one unit. Similarly, if the firm
buys one more unit of the intermediate good, either an intermediate
good producer increases its output or a final good producer
decreases its output by one unit.
The following assumptions are plausible. First, if a vertically
integrated firm sells an extra unit of the intermediate good, it
conjectures that other intermediate good producers maintain their
outputs and that a final good producer increases its output by one
unit. Second, if a vertically integrated firm buys an extra unit of the
intermediate good, it assumes that an intermediate good producer
expands its output by one unit and other final good producers
maintain their output.4 Third, MCI < PI < PF - MCF. The second
3. If the market for the intermediate good is perfectly competitive, then a
vertically integrated firm can maximize profits by running its intermediate good and
final good subsidiaries as if they were independent. In this case, the firm has no
incentive to restrict its sales of the intermediate good because it does not affect the
price of the intermediate good.
4. See Salinger [1987] for a further justification of this pair of assumptions.
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348 QUARTERLYJOURNAL OF ECONOMICS
inequality means that unintegrated final good producers earn
positive profits.
Given these three assumptions, a vertically integrated firm
chooses not to participate in the market for the intermediate good.
Suppose that the firm buys some units of the intermediate good. By
Assumption 2 and the first inequality in Assumption 3, the firm can
increase profits by producing the intermediate good internally.
Thus, buying the intermediate good cannot be profit-maximizing.
Now, suppose that the firm sells X units of the intermediate good.
Consider reducing sales of the intermediate good to 0 and increasing
final good production by X. By the first assumption, the reduced
sales of the intermediate good cause final good producers to reduce
output by X. This exactly offsets the vertically integrated firm's
increased output of the final good. The market output and, there-
fore, the price of the final good and revenues from inframarginal
sales are not affected. The change in profits is, therefore,
Ar = (PF - MCF) X - PIX.
By the second inequality in the third assumption, zAir is positive.
It may be surprising that the firm does not sell any of the
intermediate good even if PI > MCI. The firm recognizes, however,
that its sales of the intermediate good ultimately compete with its
own final goods. Provided that PI and PF are such that it makes
more money from final good sales than from intermediate good
sales, it should use all of its intermediate good output internally.
The second assumption rules out the possibility that the
merged firm will try to buy up existing supplies of the intermediate
good to raise the costs of its unintegrated rivals. This strategy might
make sense when the supply of the intermediate good is inelastic.5
With constant returns to scale in producing the intermediate good,
however, the assumption that it would result in increased produc-
tion of the intermediate good seems more sensible.
There are, of course, reasons why firms might either buy or sell
the intermediate good. For example, diminishing returns in the
production of the final good could cause a vertically integrated firm
to sell the intermediate good,6 while diminishing returns in the
production of the intermediate good could cause a vertically inte-
grated firm to purchase the intermediate good. If the intermediate
5. Salop and Scheffman [1984] show that a dominant downstream firm facing a
competitive fringe might try to buy up supplies of an intermediate good for which the
supply is not perfectly elastic.
6. See Quirmbach [1986].
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VERTICAL MERGERS AND MARKET FORECLOSURE 349
or final good is a differentiated product, then a vertically integrated
firm might buy or sell the intermediate good.7 A vertically inte-
grated firm might purchase the intermediate good to force its
intermediate good subsidiary to be competitive. All of these reasons
fall, however, outside the basic assumptions of the model in this
paper. Throughout the rest of the paper, therefore, I assume that
vertically integrated firms do not participate in the intermediate
good market.
III. COURNOT EQUILIBRIUM AT EACH STAGE OF PRODUCTION
This section presents a model of an industry in which there is
oligopoly at two successive stages of production. The equilibrium in
the final good market is Cournot. Unintegrated final good produc-
ers are assumed to take the price of the intermediate good as given.
Thus, the output and price of the final good are functions of the
intermediate good price. The relationship between the price of the
intermediate good and the equilibrium output of the unintegrated
final good producers is the demand curve faced by the unintegrated
intermediate good producers. The intermediate good market equi-
librium is Cournot and is based on that demand curve. The
assumption that the intermediate good market equilibrium is based
on the true demand curve is standard, but not trivial. As Lewis,
Lindsey, and Ware [1986] point out, it amounts to assuming that
the unintegrated upstream producers move first and that the final
good (both unintegrated and integrated) producers move second.8
I make the additional restrictive assumption that the demand
for the final good is linear. Elsewhere [Salinger, 1987], I allow for
general demand curves and conjectures between stages. The advan-
tage of linear demand curves is that the model can be solved in
closed form; whereas the results in the general case rest on the
implicit function theorem. The solution of this special case suggests
intuitive explanations of the results that are less transparent (but
present) in the more general model. Moreover, the key result of this
model is that the effect of vertical mergers on the final good price is
indeterminate. A vertical merger eliminates the successive markup
7. See Salinger [1986] for an analysis of the case with a differentiated upstream
good.
8. The equilibrium in this model when there is only one unintegrated upstream
producer and an infinite number of unintegrated downstream producers is identical
to a Stackelberg equilibrium in which the unintegrated upstream producer is the
leader and the vertically integrated firms are followers.
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350 QUARTERLY JOURNAL OF ECONOMICS
for the merging firms. In addition, however, it eliminates an
independent supplier of the intermediate good and, as a result, can
cause the intermediate good price to increase. If it does, the
remaining unintegrated producers become less competitive, which,
other things equal, causes the price of the final good to increase.
Even under the restrictive assumptions of this model, either effect
can dominate. Obviously, if the price can go either up or down in a
special case, it can also go either way under more general assump-
tions.
The following notation is used.
N. = number of intermediate good producers
NF = number of final good producers
n = number of vertically integrated firms9
QF = total output of the final good
Qu= total output of unintegrated final good (and, therefore,
intermediate good) producers
QvI = total output of vertically integrated firms
qj = output of firm i
Ri = output of all final good producers other than firm i.
The inverse demand curve for the final good is
(1) PF = a - bQF-
Given the output of all other firms and PI, the output of each
final good producer is given by
(2 ) a - MCI,-MCF - bRi (
(2b) qj = a-PI -MCF - bRj (j E n + 1, ... *NF
2b
where the vertically integrated firms are indexed 1 to n.
Equations (2a) and (2b) are a set of NF simultaneous equations,
which can be solved for the output of each firm as a function of PI
and the exogenous parameters of the model:
(3a) qj = b [N + I (a - MCI - MCF) +- N I (P- - MCI)(
i (1, ... ., n)
(3b) qj = b[N 1 (a - PI - MC) + N (MCI - PI)]
i E (n + 1, . .. , NF).
9. Note that there are N1 - n unintegrated intermediate good producers and
NF - n unintegrated final good producers.
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VERTICAL MERGERS AND MARKET FORECLOSURE 351
Aggregating (3b) and rearranging gives an inverse demand
curve for the intermediate good:
(4) P a - MCF- nMCI _ NF l+ 1 bQ
n?1 (NF- n)(n +l)QU
The Cournot price of the intermediate good is
(5) PI=MI+ a- MCI - MCF
( ) I I ~~~(NI - n + 1 ) (n +1 )
Substituting (5) into (3a) and (3b) yields the output of each final
good producer in terms of the given parameters:
(6a) q I +I (a - MCI - MCF) I(1 + -N+ n+1))
(6a) '~b (NF + 1) (NI ? -(N1-n 1)(n?+ 1))
iG (l. n)
(6b) 1 1) (a-MCI - MC') (1 N 1 )
iG(n?+,...,NF)-
The Cournot market output and price of the final good are
(7) QF= F (a-MCI - MCF)
b (NF + 1) (i N (N J)( ?
I1 NF- n
NF(NI - n + 1 )(n + 1 )
a - MCI MCF
(8) PF= MC + MCF + N ? 1
x 1+ NF- n )
+(N1 - n- 1)(n + 1
To see the effect of vertical mergers on the final good price,
differentiate (8) with respect to n:10
dPF a - MC, - MCF 2nNF- n' - NI - NINF -
dn NF+ I [(NI - n+ 1)(n + 1
10. I model vertical mergers as occurring between one intermediate good
producer and one final good producer regardless of the relative sizes of the two types
of firms. A natural alternative would be to assume that if, for example, unintegrated
intermediate good producers are twice as large as unintegrated final good producers,
then an intermediate good producer merges with two final good producers. Under
the alternative assumption, vertical mergers have the effect of reducing the number
of firms at one stage of production. Thus, the alternative would push the model in
the direction of finding that vertical mergers result in higher prices.
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352 QUARTERLY JOURNAL OF ECONOMICS
The sign of dPF/dn is determined by the sign of
(10) Z= 2nNF- n2 - NI - NINF- 1.
Z can be either positive or negative, which means that vertical
mergers can lead either to an increase or a decrease in the price of
the final good. If n < N,/2, then Z is negative because (2nNF -
NFNI) is negative and the remaining terms are all negative. It is also
easy to show that NF < N + 1 is sufficient for Z to be negative." On
the other hand, if n > N,/2 and NF is sufficiently larger than N., Z is
positive.12
Because the assumptions of linear demand and Cournot-Nash
equilibrium are so specialized, it would be a mistake to make too
much of the precise structural conditions under which vertical
mergers raise or lower prices. A closer examination of the model,
however, reveals how this model differs from the successive monop-
oly model.
To understand more completely how vertical mergers affect
PF, consider their effect on the price of the intermediate good:
(11) dPI (a - MCI - MCF) (NI - 2n)
dn [(N.-n + 1)(n + 1)]2
which is negative if and only if less than half the intermediate good
producers are vertically integrated (n < N1/2).
A vertical merger has two effects on the market for the
intermediate good. First, it lowers the number of suppliers which,
other things equal, causes PI to increase. Second, the merged firm
produces more of the final good than the previously unintegrated
final good producer. This increase in output causes the residual
demand curve facing the remaining unintegrated final good produc-
ers and, accordingly, their demand for the intermediate good to
shift back. With linear demand curves, this shift causes a reduction
in PI. Equation (11) gives the condition under which each of the
opposing effects dominates.'3
An increase in PI is an economically meaningful definition of
11. Z can be written as [-(n - NF)z - NF(NI - NF) - N1 - 1]. It is clearly
negative for N1 2 NF. For NF = N1 + 1, Z = - (n - NF)2, which is also negative.
12. The precise condition for Z to be positive (given n > N1/2) is NF > N1 +
1 + (NI - n + 1)2/(2n - Ni).
13. The elimination of the merging final good producer as a purchaser of the
intermediate good causes the demand curve for the intermediate good to pivot
downward around the price intercept. Given constant marginal costs, the Cournot
price depends on the price intercept but not the slope of a linear demand curve.
Because this shift does not change the price intercept, it does not affect the price of
the intermediate good.
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VERTICAL MERGERS AND MARKET FORECLOSURE 353
market foreclosure of downstream firms.'4 One might define fore-
closure as the inability to transact with a particular firm. Even if the
unintegrated downstream producers cannot buy the intermediate
good from the merged firm, however, they are not foreclosed in any
meaningful sense if they can purchase the intermediate good
elsewhere for less than the pre-merger price. Similarly, foreclosure
is sometimes loosely used to refer to any harm to firms due to
vertical integration or restraints by other firms. This definition is
also inadequate, though, since an increase in competition harms
rivals. An increase in PI is a useful definition of foreclosure, since it
captures only the harm to unintegrated downstream firms due to a
reduction in competition."
Note that the condition in (11) for a vertical merger to result in
market foreclosure is a necessary but not a sufficient condition for
the price of the final good to increase. This condition is easy to
interpret. The Cournot price can be written as a function of the
number of producers and their average marginal cost. A vertical
merger does not affect the number of final good producers. The
marginal cost of the merged firm, which produces the intermediate
good for MCI, is lower than the marginal cost of the previously
unintegrated final good producer, which had to purchase the
intermediate good for PI. In addition, insofar as the merger affects
PI, it changes the marginal cost of the remaining unintegrated final
good producers. If it causes P1 to drop, average marginal cost and,
therefore, PF must drop. If P1 increases, then the change of PF
depends on which effect dominates: the reduced costs of the merged
firm, or the increased costs of the unintegrated producers.'6
Mergers in this model do not necessarily increase the joint
profits of the merging firms. This result seems odd, since the
merged firm has the option of operating exactly as the unmerged
14. See Krattenmaker and Salop [1986] for a lucid discussion of discredited and
valid theories of foreclosure. The model in this paper supports their argument that
the legality of exclusionary rights should turn on how they affect rivals' costs.
15. Market foreclosure of upstream firms can usefully be defined as an increase
in PF - P1. Under the special assumptions of this model, such foreclosure never
occurs. See Salinger [1987] for a more complete discussion of why this definition is
appropriate and a demonstration that it can occur under more general conditions.
See Salinger [1986] for a model of differentiated products in which market foreclo-
sure of upstream firms can occur.
16. Greenhut and Ohta [1979] use a model similar to the one in this paper to
argue that when there is oligopoly at both stages of production, vertical mergers
always cause the price of the final good to drop. They arrive at a fundamentally
different conclusion from the one in this paper because they compare no vertical
integration with complete vertical integration. That comparison ignores the effect of
a vertical merger on the intermediate good price and, in turn, the unintegrated
producers.
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