1

 The views expressed in this paper are the author’s, not necessarily those of the Federal

Trade Commission or any individual Commissioner. I would like to thank Denis Breen, David

Reiffen, Michael Vita and two anonymous reviewers for their helpful comments and suggestions.

Any remaining errors are my responsibility.

Complements Integration and Leverage:

 The Case of the Middleman

Christopher Garmon1

Bureau of Economics

Federal Trade Commission

 December 1999

Abstract: In some cases, complementary products are sold to different sets of agents to aid in

transactions between them. In the context of a simplified model, this paper shows that a

monopolist has an incentive to integrate into and foreclose other sellers of a complementary

product used in fixed proportions with the monopolized product, but which is sold to different

consumers. While these latter consumers are made worse off by integration and leverage, output

is expanded and the monopolist’s original consumers are made better-off. The effect of

integration and leverage on overall welfare is uncertain. I illustrate this model with an example

involving trucking fleet cards (sold to trucking companies) and fuel desk point-of-sale systems

(sold to truck stops) that are used in conjunction when diesel fuel is purchased. 
2

 Ordover et al. (1990), Salinger (1988), and Whinston (1990) are also examples of this

new approach to vertical integration and foreclosure. 

3

 For instance, see Tirole (1993) pp. 169-186.

1

1. Introduction

The recent antitrust trial pitting the Department of Justice against Microsoft and the

Telecommunications Act of 1996--which set guidelines for local exchange carrier entry into long

distance telephony--have both sparked a renewed interest in the economic effects of vertical and

complementary products integration. A number of recent articles have investigated the incentive

of a dominant firm to integrate into a complementary market and foreclose rivals and the

associated welfare effects of this foreclosure (e.g., Economides (1998), McAfee (1999), Riordan

(1998), and Sibley and Weisman (1998)). While the results of these studies are mixed, the

general message of the recent literature is that vertical integration can reduce welfare if the

integrating firm is dominant in its original market.2 This contrasts with the traditional view that

vertical integration, with some exceptions (e.g., regulated industries and variable proportions

production), is most likely beneficial if it has any welfare effect at all.3

Despite the wide array of results in the literature, all of the articles analyzing vertical or

complementary product integration have one thing in common. They all assume that both

complementary products are purchased and used in conjunction by a particular consumer (just as

a vertical relationship concerns the inputs and outputs of a particular firm). This seemingly

tautological assumption does not always hold. In some cases, complementary products are sold to

different consumers or firms. For instance, in 1995 Comdata Corporation–the dominant supplier

of fleet card services to long-haul trucking companies–purchased Trendar Corporation–the
4

 Federal Trade Commission (1999)

5

 Denis Breen suggested this latter example.

2

dominant supplier of diesel fuel point-of-sale (POS) devices to truck stops.4 Fleet cards and fuel

desk POS systems are complements that work in conjunction to facilitate the sale of diesel fuel

between truck stops and truckers. Other examples which defy the normal assumption are credit

cards and credit card stripe readers and photographic film and film processing equipment.5 In the

latter case, film processing equipment is sold to retail firms that develop film (e.g., Wal-Mart,

Eckerd, etc.), while film is sold to consumers through a variety of outlets. Although sold to

different agents, the two products are used in conjunction to produce photographs. In these

somewhat unusual cases, the complementary products are used in conjunction to aid transactions

between economic agents. Thus, the firms selling these complementary products and services are

best thought of as middlemen.

In what cases does a middleman have an incentive to merge with the maker of a

complementary product as Comdata did with Trendar? If an incentive exists, would the merger

increase or reduce social welfare? As with traditional vertical and complementary product

mergers, there are many factors which can determine the answers to these questions. The Federal

Trade Commission recently signed a consent order with Ceridian (the parent company of

Comdata and Trendar) to allow fleet cards access to the Trendar machine and to allow other POS

systems access to ComChek cards. The FTC alleged that the merger of Comdata and Trendar

significantly increased the barriers to entry in fleet cards and fuel desk POS systems since

Comdata/Trendar became a closed network after the merger. In other words, after the merger an

entrant would need to introduce a fleet card and a fuel desk POS system simultaneously since the
3

entrant would not have access to the ComChek cards or the Trendar machine. As in Aghion and

Bolton (1987) and Nalebuff (1999), the increased barriers to entry of a closed system can reduce

welfare by allowing the merged firm the ability to increase price without enticing new entry.

However, if both firms had market power before the merger, their combination may lead to

reduced prices through the elimination of the double margin. 

In order to isolate the effects of a merger of firms making complementary products sold to

different consumers, it is useful to abstract from the many factors that can lead to increases or

decreases in welfare after a complementary products merger. For instance, in this paper I assume

the merger will not result in any cost savings on the margin. In addition, a complementary

products merger is assumed not to heighten or reduce barriers to entry. To abstract from the

reduction of the double margin, it is assumed that one product is supplied monopolistically while

the other is supplied competitively. Finally, to facilitate comparisons with the previous literature

it is assumed that the complementary products are always used together in a one-to-one ratio.

Under these circumstances, it has been shown on numerous occasions that a monopolist of one

product has no incentive to integrate into the sale of the other product if they are both sold to the

same consumer. Even if the monopolist merged with one of the complementary product

producers and foreclosed other producers, the monopolist could not increase its profits since the

consumer only cares about the combined price of the products.

Does this result change if the complementary products are sold to different consumers to

aid in transactions between them? The answer depends on whether the monopolist has the ability

to price discriminate in the previously competitive market. If a uniform price must be charged in

both complementary product markets (e.g., because of arbitrage), then a monopolist of one does
4

not gain by integrating into the other market and foreclosing other producers to gain another

monopoly. The reason is that a price increase on one set of consumers will be passed on to the

other set of consumers via the transactions between them. (For instance, if Comdata were to raise

the price of Trendar services, truck stops would pass this price increase onto truckers through the

fuel price.) However, a monopolist can gain by integrating into the other market and foreclosing

other producers if price discrimination is feasible in the second market (e.g., if Comdata could

charge a price for the Trendar machine that varies non-linearly with its use). With quantitydependent prices, the monopolist can capture rents from the new consumers without reducing the

quantity demanded by the monopolist’s current customers. In fact, the monopolist has an

incentive to lower the price charged to his current customers in order to increase the rents that

can be gained in the complementary market. Thus, the monopolist’s current customers are made

better off when the monopolist integrates and forecloses to gain a monopoly in a complementary

market with different customers. These new customers are obviously made worse off, but the

overall effect on welfare is less clear. In many but not all cases, overall welfare increases after

integration and foreclosure.

At first glance, this result may seem similar to the literature on vertical integration as a

means to effect price discrimination (see, for example, Gould (1977)), but it is actually quite

different. In that literature, it is shown that an input monopolist that serves at least two different

output markets can effect third-degree price discrimination by integrating into the market with

the most elastic demand for the input. In this paper, I show that a monopolist has an incentive to

integrate into and foreclose other producers of a complementary product (sold to different
6

 I am thankful to Mike Vita for pointing out this relationship between my model and the

literature.

5

consumers) in order to gain a monopoly in the complementary product market. This incentive

exists if quantity-dependent prices can be charged when a monopoly is achieved in this market. 

The results of this paper are closely related to the widely known fact that vertical

restraints such as tying and bundling can be profitable for a monopolist facing heterogeneous

consumers since the restraints can mimic the benefits of price discrimination (Adams and Yellen

(1976)). In my model, the monopolist has an incentive to integrate and foreclose even if the

ultimate consumers are homogeneous, as long as the upstream consumers of the complement are

heterogeneous and quantity-dependent prices are feasible.6

Since complements sold to different consumers often exhibit strong network externalities,

the results of this paper are related to the literature on vertical integration and compatibility

choice in network industries (e.g., Church and Gandal (1993)). However, this literature focuses

on compatibility in hardware-software systems where the complements are sold to the same

consumer. To my knowledge, the model in this paper is unique in its exploration of contexts

where the complements are sold to separate consumers.

The model is described in section 2. The results are discussed in more detail in section 3.

Section 4 concludes with a discussion of possible extensions. 
7

 In the short-run, this assumption also probably fits in the fleet card case as the amount

purchased per diesel fueling transaction does not vary much. However, the assumption may be

violated in the long-run as trucking companies could use larger fuel tanks if fleet card transaction

6

2. The Model:

In this model, there are three goods (A,B, and X) and three classes of economic agents. I

will refer to the agents as "the middlemen," "the producers," and "the consumers." A is sold by

the middlemen to the consumers and is necessary for the consumers to purchase X. B is used by

the producers as a necessary input to produce good X. Good X is sold by the producers to the

consumers. Figure 1 illustrates the relationship between the three sets of agents. Table 1

summarizes two of the previously mentioned examples that fit this scenario.

Table 1

Trucking Film Processing

Good Sold to

(examples)

Good Sold to

(examples)

A Fleet card

services (data

capture &

transaction

authorization)

Trucking

companies

(Schneider, J.B.

Hunt, Swift,

etc.)

Camera film consumers

B Fuel desk

automation

systems (e.g.,

Trendar)

Truck Stops

(TA, Flying-J,

etc.)

Film developing

equipment

Retail stores

(Wal-Mart,

Eckerd, Moto

Photo, etc.)

X Diesel fuel Film developing

It is assumed that A and X are perfect complements always consumed in a one-to-one

ratio (e.g., for every roll of film you buy, you use one unit of "film developing").7 Thus, A = X
fees increase. Again, this assumption is included primarily to help promote comparisons between

the results of this model and those of the previous literature on vertical integration.

8

 If the production processes were instead constant returns to scale, then only one type of

producer would exist in equilibrium, the lowest cost producer. Furthermore, this type of producer

would earn no rents in equilibrium, so a middleman monopolist of A would have no incentive to

integrate into B and foreclose other makers of B, since no rents can be captured through the sale

of B.

7

A'X'D(pa%px)

and the demand for A and/or X is a function of the sum of their prices (pa+px). The aggregate

demand for A and/or X is given by:

where DN < 0. 

Producers are characterized by the cost function C(?,x) where x is the amount produced

and ? is a productivity factor. Cx and Cxx are both strictly positive, implying diminishing returns

to scale.8 Higher values of ? imply lower costs and lower marginal costs (C? < 0, Cx? < 0, Cxx? <

0). Producers exist in two types: high cost producers with ? = ?1 and low cost producers with ? =

?2 (?2 > ?1). There are ?1 high cost producers and ?2 low cost producers. To simplify notation, let

C(?i,x)/C

i

(x) for i = 1,2. In addition, producers need B to produce their output, x. As with A, it is

assumed that B and x are perfect complements in production and always used in a one-to-one

ratio. In the examples listed above, this is not the case. However, this assumption is made to

facilitate comparisons between the results of this model and those in the existing literature in

which the fixed proportions assumption is common. 

Middlemen can sell to consumers or producers or sell to both. It is assumed that they can

produce A at a constant marginal cost of c and can produce B at a constant marginal cost of d. 
8

MaxxVi'(px&pb)x&C

i

(PP) (x) for i'1,2

px&pb'C

i

x

(x) for i'1,2 (1)

D(pa%px)'?1x1(px,pb)%?2x2(px,pb) (2)

Max

pa

(pa&c)D(pa%px(pa,d))

(MP1)

D%D

)

(pa&c) 1%

dpx

dpa

'0 (3)

Since there are numerous consumers and numerous producers, the market for X between

them can be characterized as perfectly competitive. In addition, it is assumed that the producers

and consumers observe the prices offered by the middlemen before purchasing A or B and

trading X between themselves. Consider the following scenarios:

Case 1:

Suppose one middleman has a monopoly on the sale of A while B is supplied

competitively. Consider first the market for X between the producers and the consumers. The

producers, in general, solve the following problem:

where pb is the price of B. The solution to this problem, denoted as xi(px,pb) for i=1,2, is

implicitly described by the following condition:

The equilibrium price of X, px(pa,pb), is that which equates supply and demand in the market

between the producers and consumers. This is implicitly given as the px which solves:

Since B is competitively provided, pb = d. Thus, the monopolist producing A solves:

Therefore, the monopolist chooses pa to satisfy:
9

Max

pa,pb

(pa&c)D(pa%px(pa,pb))%(pb&d)(?1x1%?2x2)

(MP2)

Max

pa,pb

[(pa%pb)&(c%d)]D(pa%px(pa,pb))

(MP2N)

pa%pb'&

D

D

)

1%

dpx

dpa

%c%d

(5)

dpx

dpa

'

&D

)

D

)&

?1

C

1

xx

&

?2

C

2

xx

0(&1,0)

(4)

where:

by the implicit function rule. Denote the solution to (1) and (MP1) as (p ̃a, p ̃x, x ̃1, x ̃2).

Case 2:

Now suppose the monopolist of A vertically integrates into the sale of B and forecloses

other sellers of B until they exit. This could be accomplished by making A only compatible with

the B sold by the monopolist, as long as there are sufficient barriers restricting the successful

introduction of competing A’s that are compatible with the foreclosed B’s. If price discrimination

is not feasible in the market for B (e.g., because of arbitrage), then the monopolist’s solves:

after integration and foreclosure. Using (2), this simplifies to:

In this case, the pa chosen by the monopolist may be different from that chosen in case 1.

However, it is clear from a comparison of (MP1) and (MP2N) that pa+pb will be the same as it

was in case 1. That is:
10

in both case 1 and case 2. It follows that the monopolist’s profits in this case are the same as in

case 1. Therefore, if the monopolist cannot price discriminate in the market for B, then the

monopolist has no incentive to foreclose other sellers of B. Without the ability to price

discriminate, the incentive (or lack thereof) for integration and foreclosure when complements

are sold to separate sets of agents is the same as that when complements are both sold to the

same agent. As in the standard case with fixed proportions, an increase in the price of one

complement causes the profit maximizing price of the other to drop by an exactly off-setting

amount. In this case, there is a slightly different mechanism, but the overall effect is the same. An

increase in the price of B, for instance, causes the equilibrium price of X to rise, reducing the

amount demanded of X and thus reducing the demand for A. An increase in the price of A has

the same effect on the demand for B. Thus, nothing can be gained by monopolizing B if A is

already monopolized, and vice versa. 

Case 3:

Now suppose the monopolist of A vertically integrates and forecloses other sellers of B,

but, in this case, price discrimination is feasible. To be specific, the newly created monopolist of

B can sell B at quantity-dependent prices. However, the monopolist cannot offer type-dependent

prices. This is consistent with cases in which the monopolist cannot directly observe whether a

producer is a low-cost or high-cost producer. Even if the monopolist can observe the producer’s

type, he may not be able to verify it in a way that can be the basis of a contract. If it is profitable

to price discriminate, the monopolist will offer a menu of contracts {(s1,x1),(s2,x2)} in which si is
9

 This assumes that ?1 is sufficiently close to ?2 so that the monopolist profits by serving

the high cost producer. Otherwise, the problem is essentially equivalent to (MP2) with ?1 = 0.

11

Max

pa,px,s

1

,s

2

,x1,x2

(pa&c)D(pa,px)%?1(s

1

&dx1)%?2(s

2

&dx2)

s.t. (P1) pxx1&s

1

&C

1

(x1)$0

(P2) pxx2&s

2

&C

2

(x2)$0

(IC1) pxx1&s

1

&C

1

(x1)$pxx2&s

2

&C

1

(x2)

(IC2) pxx2&s

2

&C

2

(x2)$pxx1&s

1

&C

2

(x1)

(SD) D(pa%px)'?1x1%?2x2

(MP3)

the payment required for buying xi of B. After integration and foreclosure, the monopolist

solves:9

 The first two constraints in (MP3) are participation constraints which insure that the menu item

intended for each type of producer gives the producer its reservation profit level (normalized to

zero). The second two constraints in (MP3) are incentive compatibility constraints which insure

that the menu item intended for each type of producer will be selected over that item intended for

the other producer. The fifth constraint is simply the equilibrium condition that supply equals

demand in the market for X. 

(MP3) can be simplified considerably. First, notice that (IC2) and (P1), plus the fact that

C

1

(x) > C2(x) for all x, imply that (P2) will not bind at the solution to (MP3). In other words, the

low-cost producer will earn a premium over its reservation profit level when the middleman

monopolist price discriminates. If (P2) does not bind, then (IC2) must bind at the solution since

s2 could be increased slightly, improving the monopolist’s profits, if both (IC2) and (P2) did not
10 That is, as long as x1 ... x2

. If they are equal, then the constraints imply s1 = s2 and the

monopolist is no longer price discriminating. The monopolist’s problem then essentially reverts

back to case 2. 

12

Max

p,x1,x2

(p&c&d)D(p)&?1C

1

(x1)&?2C

2

(x2)&?2[C

1

(x1)&C

2

(x1)]

s.t. D(p)'?1x1%?2x2

(MP3O)

Max

pa,px,x1,x2

(pa&c)D(pa%px)%?1[(px&d)x1&C

1

(x1)]

%?2[(px&d)x2&C

2

(x2)]&?2[C

1

(x1)&C

2

(x1)]

s.t. D(pa%px)'?1x1%?2x2

(MP3N)

bind. This, in turn, implies that (IC1) does not bind since Cx? < 0.10 Finally, this implies that (P1)

binds, since s1 could be increased slightly if it did not.

Using these facts, (MP3) can be simplified to:

Essentially, (MP3N) mirrors the standard discrete-type adverse selection problem. The monopolist

wants to capture all of the producers’ surplus, but cannot because he must give the low-cost

producers enough rent to make them indifferent between choosing the bundle intended for them

and the bundle intended for the high-cost producers. The magnitude of this premium for each low

cost producer is [C1(x1)-C2(x1)](i.e., their cost advantage over the high-cost producers at the highcost production level). The monopolist can lower the premium required by the low-cost

producers by making the high-cost producers’ bundle less attractive. This entails less production

from the high-cost producers than the monopolist would prefer under full information. 

Notice, also, that (MP3') can be rewritten as:

where p = pa + px. Denote the solution to (MP3) (as well as (MP3N) and (MP3O)) as (p ̄, x ̄1, x ̄2). In

other words, any pa and px in which pa + px = p ̄ is a partial solution to (MP3).
11 The proof of this and other results is found in the Appendix.

13

3. The Results:

A comparison between case 1, in which the middleman only has a monopoly over A, and

case 3, in which the middleman has also monopolized B through integration and foreclosure,

reveals the following:

Result 1: If price discrimination is feasible when selling B, then a monopolist of A can profit by

integrating into the market for B and foreclosing other sellers of B to force their exit.11

With price discrimination, the tradeoff between profits from A and profits from B

illustrated in case 2 is no longer present. A monopolist of A can integrate into (and foreclose

other sellers of ) B to capture producers’ rents without necessarily sacrificing profits from the

sale of A. In particular, with quantity dependent prices, the monopolist can capture at least a

portion of the producers’ rents without necessarily reducing the amount of X sold, and thus

without reducing his profits from the sale of A.

Result 2: After integration and foreclosure, the total price paid by consumers (pa + px) is less than

before. Thus, the equilibrium quantities of X, A, and B are greater than before and

consumers’ surplus is greater than before.

If price discrimination is feasible in the market for B, not only does the monopolist profit

by using integration and foreclosure to gain a monopoly in B, but the monopoly in B is more
12 One can think of this as an efficiency rationale for integration, but it is distinct from

other common vertical efficiencies such as marginal cost reduction and the elimination of the

double margin.

14

profitable on the margin than that in A. The monopolist has an incentive to lower the total price

of A (pa + px) from its stand-alone profit maximizing level so that more X, A, and, in particular,

B are produced. Essentially the monopolist has an incentive to subsidize the production of B by

lowering the price of X and A, since the monopolist captures a greater portion of the producers’

surplus through price discrimination in B than he is able to capture in the market for A. This, of

course, makes consumers of X and A better off and leads to larger amounts of X, A, and B in

equilibrium.12

An alternative rationale for the lower total price after integration and leverage relates to

the relative movements of pa and px. Before integration, the monopolist only cares about the

market for A. If he increases the price of A, demand for A will decrease, but this is ameliorated

somewhat by a decrease in the equilibrium price of X. Thus, the impact of a price increase on the

monopolist’s profits is lessened by the effect of the price increase on the equilibrium price of X.

However, after integration and leverage, this reduction in the price of X will lower the rents that

the monopolist can capture through price discrimination in the market for B. Therefore, the

monopolist is better off reducing the price of A after gaining a monopoly over B. 

Result 3: After integration and foreclosure, the production of the low-cost producers (x2) 

increases and the difference between low-cost production and high-cost production (x2 -

x1) also increases.
15

Since the combined price of A and X will fall and the amount of A and X demanded will

increase after integration and foreclosure, the amount of X and B produced will also increase.

However, since the monopolist wants to minimize the premium he pays to the low cost

producers, the high cost producers’ production will not increase by as much as that of the low

cost producers, if it increases at all. In many cases, the high cost producers will produce less after

integration and foreclosure.

Result 4: After integration and foreclosure, producers’ surplus is reduced. 

This simply comes about because the monopolist can now capture most of the producers’

rents through price discrimination. This reduction in producers’ surplus is also enhanced by an

inefficient level of production from high-cost producers. After integration and foreclosure, these

producers produce too little so that low-cost producers do not choose the high-cost option when

buying B.

If price discrimination is feasible, integration and foreclosure by a monopolist of A to

create a monopoly of B is profitable for the monopolist, beneficial to the consumers, and harmful

to the producers. Overall welfare could increase or decrease as a result of integration and

foreclosure. This is because foreclosure has two opposing effects on welfare. As described in

Result 2, welfare increases because the monopolist has an incentive to see increased production

after gaining a monopoly over B if price discrimination is possible. However, to sustain price

discrimination, the monopolist must offer the high-cost producers a relatively unfavorable menu
16

option specifying too little production. This latter inefficiency could outweigh the former

efficiency and cause welfare to decline after integration and foreclosure.

To illustrate these two opposing effects and their overall effect on welfare, a simulation of

the model is useful. Suppose D(pa+px) = a - ß(pa+px) and C(?,x) = (x2)/?. In addition, let ?1 = 2, ?2

= 4, a = 10, c = d = 1, and ?1 = ?2 = 1⁄2. Table 1 gives changes in various measures resulting from

integration and foreclosure as ß becomes smaller (i.e., as the demand for X and A becomes less

responsive to price). Notice that the simulation confirms the conclusions stated above in Results

1 through 4. The combined price of A and X falls while overall production of X, A, and B, and

consumers’ surplus, increases. Low-cost producers produce more than before, while high cost

producers produce less than before. The middleman monopolist’s profits increase and producers’

surplus falls. The change in total welfare depends on the size of the increase in consumers’

surplus and the degree to which high-cost production is reduced. As seen in Table 2, when ß is

relatively large, the increase in consumers’ surplus associated with integration and leverage is

large while the reduction in high-cost production necessary to sustain price discrimination is

relatively small. In these cases, overall welfare increases after integration and foreclosure. When

ß is relatively small, the decrease in price causes a small increase in consumers’ surplus while a

relatively large reduction in high-cost production is needed to sustain price discrimination. In

these cases, integration and foreclosure can cause overall welfare to decline. 

Table 2

Measure ß=1 ß=1/2 ß=1/4 ß=1/16 ß=1/32 ß=1/64

? Price -0.51 -0.83 -1.09 -1.35 -1.40 -1.43

? X 0.51 0.41 0.27 0.08 0.04 0.02
Measure ß=1 ß=1/2 ß=1/4 ß=1/16 ß=1/32 ß=1/64

17

? x1-0.15 -0.36 -0.54 -0.75 -0.79 -0.81

? x2 1.16 1.18 1.09 0.92 0.88 0.86

? Consumers’ Surplus 1.35 0.90 0.50 0.13 0.06 0.03

? Monopolist’s Profit 2.04 3.73 5.16 6.67 6.97 7.13

? Producers’ Surplus -1.66 -3.35 -4.94 -6.76 -7.14 -7.34

? Welfare 1.73 1.28 0.72 0.04 -0.11 -0.18

Conclusion and Extensions:

When complements are sold to different groups of consumers or producers to aid in

transactions between them, it is possible for vertical integration and leverage to reduce welfare.

However, any reduction in welfare comes about despite an increase in output. The possible

inefficiency of integration and leverage in this case comes about because the high-cost producers

produce too little, even though overall production increases. If this production inefficiency is

small, the benefit of increased output may lead to greater overall welfare. 

While illustrating the effects of integration when complements are sold to different

consumers, these results do not account for other potentially important factors such as variable

proportions production, strategic behavior, innovation, and entry. In particular, the incorporation

of entry into the model may indicate that vertical integration and leverage is more harmful (or

less beneficial) in cases where complements are sold to different consumers. For instance, entry

might be more difficult after a middleman monopolist forecloses other producers of a

complementary product since a potential entrant would need to develop and market both

complementary products simultaneously. This entry barrier might be heightened by the fact that
18

an entrant would have to sell the two products to different consumers. It is also possible that the

increased profits from integration could spur more research and development from potential

entrants wishing to capture this profit, ultimately increasing welfare. 

References:

Adams, W.J. and Yellen, J.L. (1976), “Commodity Bundling and the Burden of Monopoly,”

Quarterly Journal of Economics, 90, 475-98.

Aghion, P., and Bolton, P. (1987), “Contracts as a Barrier to Entry,” American Economic Review,

77(3), 388-401.

Church, Jeffrey and Gandal, Neil (1993), “Equilibrium Foreclosure and Complementary

Products,” Tel Aviv Sackler Institute of Economic Studies Working Paper 3/93.

Economides, N. (1998), “The Incentive for Non-Price Discrimination by an Input Monopolist,”

International Journal of Industrial Organization, 16, 271-84.

Federal Trade Commission (1999), “Ceridian Corporation - Analysis of Proposed Consent Order

to Aid Public Comment,” 9/30/99, http://www.ftc.gov/os/1999/9909/ceridiananalysis.htm

Gould, J.R. (1977), “Price Discrimination and Vertical Control: A Note,” Journal of Political

Economy, 85, 1063-1071.

McAfee, Preston (1999), “The Effects of Vertical Integration on Competing Input Suppliers,”

Federal Reserve Bank of Cleveland Economic Review, 35, 2-8.

Nalebuff, B. (1999), “Bundling,” Mimeo, Yale University.

Ordover, J., Saloner, G., and Salop, S. (1990), “Equilibrium Vertical Foreclosure,” American

Economic Review, 80, 127-142.

Riordan, M.. (1998), “Anticompetitive Vertical Integration by a Dominant Firm,” American

Economic Review, 88, 1232-1248.

Salinger, M. (1988), “Vertical Mergers and Market Foreclosure,” Quarterly Journal of

Economics, 77, 345-356.
19

D(pa%px)%D

)

(pa%px)[pa&c](1%

dpx

dpa

)'0 (P2.1)

D(pa%px)%D

)

(pa%px)[pa&c]'0 (P2.3)

D(pa%px)%D

)

(pa%px)[(pa%px)&c&d&C

2

x

]'0 (P2.2)

PS ̃ '?1[(p ̃

x

&d)x ̃

1

&C

1

(x ̃

1

)]%?2[(p ̃

x

&d)x ̃

2

&C

2

(x ̃

2

)] (P4.1)

C

2

x

(x2)&C

1

x

(x1)'

?1

?2

[C

1

x

(x1)&C

2

x

(x1)]

Sibley, David S. and Weisman, Dennis L. (1998), “Raising Rivals’ Costs: The Entry of an

Upstream Monopolist into Downstream Markets,” Information Economics and Policy,

10, 451-470.

Tirole, Jean (1993), The Theory of Industrial Organization, Cambridge, MA: MIT Press.

Whinston, M.(1990), “Tying, Foreclosure, and Exclusion,” American Economic Review, 80, 837-

859.

Appendix

Proof of Result 1: I will prove this result by showing that there exists an outcome that is feasible

under the constraints of (MP3) that results in more profit for the monopolist than in (MP1). Since

x ̃i = argmax Vi(p:x,d) for i = 1,2, and since C1

(x) ... C2(x) for all x, there exists an e > 0 such that

{pa,px,(s1,x1),(s2,x2)}= {p:a,p:x,(e,x ̃1),(e,x ̃2)} satisfies the constraints of (MP3). This outcome results

in e(?1+ ?2) more profit for the monopolist than is possible in (MP1). €

Proof of Result 2: Expression (3) which characterizes pa + px before integration and leverage can

be expressed as:

The first order condition that characterizes the pa + px which solves (MP3') can be expressed as:

Notice from (MP3') that, given px, x2 will be chosen by the monopolist so that px-d-C2

x=0. Then

(P2.2) becomes:

Since dpx/dpa 0 (-1,0), the pa + px characterized by (P2.2) and (P2.3) is less than that

characterized by (P2.1). €

Proof of Result 3: The first order conditions of (MP3') with respect to x1 and x2 imply:

which implies that C2

x

(x2) > C1

x

(x1). Before integration and leverage, C2

x

(x2) = C1

x

(x1) = px -d.

Therefore, since Cxx? < 0, this implies that x2 - x1 is greater after integration and leverage. This,

along with result 2, implies that x2 is greater than before integration and leverage.€

Proof of Result 4: Under (MP1), producers’ surplus is:
20

PS ̄ '?2[C

1

(x ̄1)&C

2

(x ̄1)] (P4.2)

C

1

(x ̄1)&C

2

(x ̄1)>(p ̃

x

&d)x ̃

2

&C

2

(x ̃

2

) (P4.3)

(p ̄x&d)x ̄1&C

2

(x ̄1)>(p ̃

x

&d)x ̃

2

&C

2

(x ̃

2

) (P4.4)

Under (MP3), producers’ surplus is:

Suppose, producers’ surplus is greater after integration and foreclosure. This implies:

This implies:

Since p2x can take on any value as long as pa + px = p ̄ without changing profit, producers’ surplus,

or consumers’ surplus, there exists a solution to (MP3) with p2x = p:x. However, this solution along

with (P4.4) contradicts the fact that x ̃2 = Argmax V2 for pb = d. €