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THREE ESSAYS ON SUCCESSIVE VERTICAL
OLIGOPOLIES

presented by

Joon Lim

has been accepted towards fulfillment
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Ph.D. degree in Economics

 

 

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THREE ESSAYS ON SUCCESSIVE VERTICAL OLIGOPOLIES
By

J oon Lim

A DISSERTATION

Submitted to
Michigan State University
in partial fiilfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

2005

 

ABSTRACT
THREE ESSAYS ON SUCCESSIVE VERTICAL OLIGOPOLIES
By
J oon Lim

The first chapter analyzes the anticompetitive effects of vertical mergers in a
composite goods market that has successive vertical structures. In such a market, a group
of firms (the upstream industry) provides the goods they produce to another group of
firms (the downstream industry) that produces complementary goods and then the latter
group sells the composite goods to consumers. We Show that vertical mergers might be
anticompetitive because the integrated firms could increase market power in their own
turfs through foreclosure.

The second chapter examines the strategic motive for specialization in
intermediate good markets. We consider the case where input suppliers have two I
alternatives: either focusing on a specific downstream firm (specialization) or expanding
their businesses and producing inputs for both downstream firms (diversification). Under
these circumstances we show that specialization might be privately and collectively
profitable. In spite of losing the Opportunity to obtain some profits from another
downstream firm, upstream firms choose specialization. The reason is that the choice of
diversification reduces the profits from downstream captive buyers.

The third chapter investigates the profitability of backward integration in the
presence of upstream cost variability. We consider an environment in which idiosyncratic
cost shocks lead to the cost differences between upstream firms. In these circumstances

downstream firms decide whether or not to integrate backwards. We find that the

equilibrium outcomes may result in a Prisoner’s Dilemma: it is privately profitable for
downstream firms to integrate backwards, but not collectively. In our model vertical
integration generates negative externalities between downstream firms by transferring

cost asymmetries from the upstream market to the downstream market.

 

Copyright by
JOON LIM
2005

 

To my Parents for their endless love

 

ACKNOWLEDGMENTS

There are many people whom I should be thanking. First, I would like to express
my thanks to my advisor, Jay Pil Choi. I met him during the most difficult time of my
Ph.D. program. Without his help, I could not have completed my Ph.D. study. He
introduced to me the field of vertical integration, the subject of this dissertation. The
basic models in three essays build on frameworks from the two articles that he
recommended. His comments have further guided my research and helped me make clear
the points of my writing. I also would like to thank my committee members, Anthony
Creane, Carl Davidson, and Steven Wildman for their valuable comments.

During my Ph.D. program, I met another person, Sung Kwan Kim, who also
deserves my thanks. He was my roommate. He talked to me about religion every day.
Owing to his religious lessons, I overcame many difficulties finishing my dissertation.

Eighteen years have passed since I began studying economics. My parents have
helped me continuously during these many years. As for me, eighteen years are a long
time. But those years must have seemed longer to my parents. I heartily thank them for
their endless love and support.

Lastly, I would like to thank God who has made me meet these people.

vi

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES ........................................................................................................... ix
CHAPTER 1. .
FORECLOSURE IN COMPOSITE GOODS MARKETS WITH SUCCESSIVE
VERTICAL STRUCTURES .............................................................................................. 1
1. Introduction ................................................................................................................. 2
2. The Basic Idea ............................................................................................................. 4
' 3. The Basic Model ......................................................................................................... 9
4. Simple F ormalization ................................................................................................ 10
5. Antitrust Analysis of Vertical Mergers ..................................................................... 15
6. Concluding Remarks ................................................................................................. 29
References ..................................................................................................................... 3 1
Appendix ....................................................................................................................... 33
CHAPTER 2.
SPECIALIZATION IN INTERMEDIATE GOOD MARKETS ........ ' ............................. 6O
1. Introduction ............................................................................................................... 61
2. The Basic Idea ........................................................................................................... 66
3. A Simple Model ........................................................................................................ 69
4. Upstream Cost Uncertainty ....................................................................................... 72
5. The Final Product Market ................................................................. 76
6. Endogenous Vertical Structures ................................................................................ 81
7. Concluding Remarks ................................................................................................. 86
References ..................................................................................................................... 87
CHAPTER 3.
A MODEL OF VERTICAL INTEGRATION WITH UPSTREAM COST
VARIABILITY ................................................................................................................. 89
1. Introduction ............................................................................................................... 9O
2. The Basic Idea ........................................................................................................... 94
3. The Basic Model ....................................................................................................... 97
4. The Prisoner’s Dilemma ........................................................................................... 99
5. Antitrust Policy ....................................................................................................... 108
6. Cost Correlation ...................................................................................................... 109
7. Concluding Remarks ............................................................................................... 11 1
References ................................................................................................................... l 13

vii

LIST OF TABLES

Table A-1. Welfare under Non-integration and Full Integration (y = 0.1) ...................... 52
Table 2-1. Upstream and Downstream Profits .................................................................. 71
Table 2-2. Upstream Profits Under Upstream Cost Uncertainty (G , G ) ......................... 74
Table 2-3. Upstream Profits Under Upstream Cost Uncertainty (S l , G ) ........................ 75
Table 2-4. Upstream Profits Under Upstream Cost Uncertainty (S 1 , S 2) ....................... 75
Table 2-5. The Final Product Market (G , G) .................................................................. 77
Table 2-6. The Final Product Market (G , S ) ... ................................................................ 78
Table 2-7. The Final Product Market (S , S) .................................................................... 78
Table 2-8. Profits under Partial Integration ...................................................................... 82
Table 3-1. Profits under Non-integration ........................................................................ 100
Table 3-2. Profits under Partial Integration .................................................................... 101
Table 3-3. Profits under Full Integration ........................................................................ 102
Table 34. The Structure of Input Costs .......................................................................... 111

viii

LIST OF FIGURES

Figure 1-1. Independent upstream and homogeneous downstream (No Foreclosure) ....... 6
Figure 1-2. Independent upstream and homogeneous downstream (Foreclosure) ............. 7
Figure 1-3. Homogeneous upstream and independent downstream (No Foreclosure) ....... 8
Figure 1-4. Payoff Matrix (Independent Upstream and Homogeneous Downstream) ..... 12
Figure 1-5. Payoff Matrix (Homogeneous Upstream and Independent Downstream) ..... 14
Figure 1-6. Vertical Mergers under Upstream Bargaining Power .................................... 20
Figure 1-7. The Profit Function for Ul-Dl ...................................................................... 25
Figure 1-8. Vertical Mergers under Downstream Bargaining Power ............................... 27
Figure A-l. The Graph of 5H5’1_Dl/0”Q21 when y > 7. .................................. 39
Figure A—2. The Profit Function for Ul-Dl under Full Integration ................................. 42
Figure A-3. The Profit Function for Ul-Dl under Partial Integration ............................. 47
Figure A-4. Vertical Mergers under Upstream Bargaining Power (7 = 0.1 ) ................... 49
Figure A-5. Vertical Mergers under Downstream Bargaining Power (7 = 0.1 ) .............. 49
Figure A-6. The Graph of AHI ........................................................................................ 50
Figure A-7. The Graph of AFIZ ........................................................................................ 50
Figure A-8. The Graph of A111 ........................................................................................ 51
Figure A-9. The Graph of A112 ....................................................................................... 51
Figure A-10. The Graph of AW ...... _ ............................................................................ 54
Figure A-l 1. The Graph of AH: ....................................................................................... 54
Figure A-12. The Graph of ac ........................................................................................ 57
Figure A-13. Composite Goods Market under Non-integration ....................................... 59
Figure A-14. Composite Goods Market under Full Integration ....................................... 59
Figure 2-1.’ Initial Situation ............................................................................................... 67
Figure 2-2. Afier Switch ................................................................................................... 68
Figure 2-3. Payoff Matrix for Input Specifications .......................................................... 72
Figure 2—4. Final Product Markets .................................................................................... 80
Figure 2-5. Intermediate Good Markets ............................................................................ 80
Figure 2-6. Payoff Matrix for Input Specifications under Partial Integration .................. 82
Figure 3-1. Non-integration .................. ........................................................................... 96
Figure 3-2. Full Integration ............................................................................................... 97
Figure 3-3. The Prisoner’s Dilemma .............................................................................. 107

ix

 

CHAPTER 1
FORECLOSURE IN COMPOSITE GOODS MARKETS WITH SUCCESSIVE

VERTICAL STRUCTURES

1. Introduction

This paper examines the anticompetitive effects of vertical mergers in a
composite goods market1 that has successive vertical structures. In such a market, one
group of firms (the upstream industry) provides their goods to another group of firms that
produces complementary goods (the downstream industry) and then the latter group sells
a composite of the upstream and downstream goods to consumers. The Korean mobile
telephone system is an example of a composite goods market with successive vertical
structures. 2 Handset manufacturers supply handsets to mobile service operators. The
mobile communication carriers then package handsets and services as composite goods
and sell them to consumers.3

In this paper we analyze the incentives for vertical mergers and foreclosure in the
composite goods market with successive vertical structures. We show that it might be the
profitable strategy to integrate vertically because the integrated firms could increase
market power in their own turfs through foreclosure. We also consider welfare
implications and identify the conditions under which the harmful effects from vertical
mergers outweigh the beneficial ones.

Our article closely relates to the literature on vertical foreclosure. Our results are

similar to Ordover, Saloner, and Salop [1990] in that integrated firms increase prices for

 

' Composite products include hardware and software, VCRs and videotapes, Automatic Teller Machines
(ATMs) and bankcards, etc. For studies on composite goods markets without successive vertical structures,
see Choi [2003], Economides and Salop [1992], and Matutes and Regibeau [1988 and 1992].

2 In Korea, one issue was about whether the mobile operators should be prevented from running businesses
in the handset manufacturing industry. The Ministry of Information and Communication (MIC) considered
a regulation that kept SK Telecom, a Korean dominant mobile operator, from running businesses in the
handset manufacturing industry (Digital Times, September 16, 2004).

3 In Korea, the mobile service operators have control over the distribution channels of mobile handsets. In
contrast, there are many independent dealers selling composite goods in Europe. Handset makers provide
their handsets to independent dealers. The structure of European mobile system is close to complementary
markets (Lee [2004]).

 

their upstream products to raise the downstream rival’s costs. 'We also share some
findings with Church and Gandal [2000]. In their model, vertical foreclosure reduces the
variety of software for a rival hardware technology. Similarly, in our model, foreclosure
decreases the number of the rival’s composite goods. Rey and Tirole [2003] also have
shown results similar to ours. They show that the upstream monopoly with the
downstream duopoly has the incentives to integrate vertically and foreclose in order to
solve the commitment problem.4 In contrast, the downstream monopoly with the
upstream duopoly has no incentive to integrate and foreclose. Our conclusions are
similar to theirs in that the independent upstream with the competitive downstream has
the incentive to foreclose, but the independent downstream with the competitive upstream
does not.

One main difference lies in the equilibrium vertical structure. The previous
literature focuses on partial integration. In contrast, our focus is on the anticompetitive
effects of foreclosure under full integration. The existing literature shows that the
integrated firm under partial integration increases its power in the entire downstream
market through foreclosure. But we show that integrated firms employ foreclosure to
gain monopolistic power in their own turfs of the two grouped downstream markets.
While vertical integration with foreclosure is used as a strategy to monopolize the
downstream market in the previous literature, in our model backward integration with
foreclosure is employed as a device to divide the composite goods market and facilitate

tacit collusion between downstream firms.

 

‘ They assume that the upstream firm can charge two-part tariffs. But we assume that the upstream firms do
not employ two-part tariffs. Therefore, we do not have the commitment problem as in Rey and Tirole
[2003].

 

The organization of this paper is as follows. Section 2 previews the basic idea.
Section 3 presents the model. In Section 4 we illustrate the basic idea formally with a
simple model. Section 5 examines the anticompetitive effects of vertical mergers.

Section 6 concludes.

2. The Basic Idea

In this section we will illustrate the intuition behind our results before presenting
the formal model. Why do the integrated companies have the incentives to' foreclose in
the composite goods market with successive vertical structures? Suppose that there exist
two integrated firms, Ul-Dl and U2-D2. U1 and U2 represent the upstream and D1 and
D2 the downstream divisions of the integrated firms. We will first consider the case in
which the integrated firms provide their upstream products to their rivals. There would
then be four composite goods: UlDl, U1D2, U2D1, and U2D2. If we assume that
upstream products are independent and downstream products are perfect substitutes, we
have the two independent composite good markets categorized by upstream products:
{U1D1, U1D2}, and {U2Dl, U2D2} (see Figure l-l). In each independent composite
goods market, the two composite products are homogeneous. For example, UlDl and
U1D2 are perfect substitutes. In this case the integrated firms face intense competition in
both independent composite goods markets.

Now suppose that the integrated firms foreclose and do not supply their upstream
products to their rivals. There would then exist the two independent composite goods as

in Figure 1-2: UlDl and U2D2. Through vertical foreclosure, the integrated firms expel

their rivals from their own turfs and enjoy monopoly power in one of the two
independent composite good markets.

For comparison, let us consider another extreme case where upstream products
are homogeneous and downstream products are independent. If we assume that the
integrated firms do not foreclose, we have the two independent composite good markets
categorized by downstream products: {U1Dl, U2D1}, and {U1D2, U2D2} (see Figure l-
3). In this case the integrated firms already have monopolistic power in their own turfs.

Therefore, they have no incentive to foreclose.

Figure 1-1. Independent upstream and homogeneous downstream (No Foreclosure)

 

 

U1 U2

 

 

 

 

 

 

 

 

 

 

 

‘i 4/ \A V
D1 D2
UlDl, U1D2 U2Dl, U2D2

 

 

 

 

 

 

 

Figure 1-2. Independent upstream and homogeneous downstream (Foreclosure)

 

 

U1 U2

 

 

 

D1 D2

 

 

 

 

 

 

 

 

 

UlDl U2D2

 

 

 

 

 

 

Figure 1-3. Homogeneous upstream and independent downstream (No Foreclosure)

 

 

U1 U2

 

 

 

 

 

 

 

 

 

 

 

V 4/ g \A i
D1 D2
UlDl, U2Dl U1D2, U2D2

 

 

 

 

 

 

 

3. The Basic Model

As in Section 2, we assume that there exist two upstream and downstream
products: U1, U2, D1, and D2. Then we have four composite goods: UlDl , U1D2, U2D1,
and U2D2. The demand system for the composite goods builds on the framework
developed by Economides and Salop [1992]. 5 We assume the following demand system
in the composite goods market:

511:1- Q11 -aQ12 -bQ21-CQ22,

512 =1- Q12 -0Q11 ’szz — cQ21 ,

521:1— Q21 '0Q22 "bQ11- CQ12,

522 =1-Q22 -0Q21—bQ12 ‘CQ11- (1)

In (1), Si]- and Q9- represent the price and the demanded quantity for the composite good

that consists of U ,- and D j- , respectively.

The substitutability between the composite products is measured by a , b , and c.
The parameter of a (b; c) represents the substitutability between the composite goods
with the same upstream product and the different downstream product (the different
upstream product and the same downstream product; the different upstream. product and
the different downstream product). We assume that 0 S a,b,c s l . For example, if a = 1,
there exists perfect substitutability between the composite goods with the same upstream
product and the different downstream product. But if a = 0, the two composite goods are
independent. For simplicity, we further assume zero marginal costs for all four

components (U1, U2, D1, and D2).

 

5 While they assume Bertrand competition, we assume Cournot competition. The reason is that it is easier
to incorporate perfect substitutability into the Coumot version.

 

4. Simple Formalization
In this section we illustrate the basic idea about foreclosure with a simple model.
We assume that the vertical structure is firll integration. And also the prices for upstream
products are assumed to be zero when an integrated firm supplies the other integrated
firm. We will relax these restricted assumptions in the next section. The timing of the
simple case is as follows. In the first stage, the integrated firms decide whether or not to

foreclose. In the second stage, the equilibrium for composite goods is determined.

Independent Upstream and Homogeneous Downstream

First, let us consider the case in which the upstream products are independent and the
downstream products are perfect substitutes. Then, in (l), a = l and b = c = 0 . In order
to examine the optimal strategy, we first assume that the integrated firm, U2-D2, does not
foreclose. Now consider the case where the integrated firm, Ul-Dl , decides not to

foreclose. In this case, we obtain the following demand system:
511:1—Q11-Q12,
512 =1-Q12 "Q11,
S21'-‘1—Q21—Q22,
522 =1' Q22 — Q21- (2)
From (2), we can write the integrated firm, Ul-Dl ’s profit maximization problem as:
MaxIIUl_D1= S11Q11+321Q21— (3)

Differentiating with respect to Q11 and Q21,

'—;—=1-2Q11 -Q12 =0,

10

anUl-Dl =

1—2 — =0. 4
§Q21 Q21 Q22 ()

From (4) and the symmetric structure of the model, we obtain
0 o o o 1
Q11=Q12 =Q21-=Q22 =3,
0 o 0 o 1
511:512 =521=522 =3,

E.

o o
nUl—Dl = nUZ—DZ = = 36' (5)

who

Next, consider the case where the integrated firm, Ul-Dl, decides to foreclose.

We have the following demand system for the composite goods:
S11 =1- Q11,
521:1-Q21—Q22,
522 =1- Q22 — Q21- ‘ (6)

In this case, the equilibrium is as follows:

1_1 1__ 1 _l
Q11 2,er Q22 3,
l 1 1 1
S‘_—,s :5 =—,
11 2 21 22 3
1 1 1 l3 1 l 4
H _ =—+—=-——,II _ =—=—. 7
U1 0] 4 9 36 U2 DZ 9 36 _ ()

Now, suppose that the integrated finn, U2-D2, decides to foreclose. When the

integrated firm, U1 -Dl, also forecloses, the demand system is like this:
S11 =1- Q11,
522 =1- Q22- (8)

We obtain the following equilibrium:

ll

(9)

The following matrix summarizes the above discussion. From Figure 1-4, we find

that it is the dominant strategy for the integrated firms to foreclose.

Figure 1-4. Payoff Matrix (Independent Upstream and Homogeneous Downstream)

Ul—Dl

 

 

 

 

(12—02

N F
_8_ _8_ 1 L3.
36’36 36’36
2 :L _9_ 1
36,36 1 36,36

 

 

Homogeneous Upstream and Independent Downstream

The parameters in the demand system of (l) have the following values: a = c = 0 and

b = 1 . First, consider the case in which neither integrated firm forecloses. In this case, we

have the following demand system:

511:1-Q11-Q21,

S12 =1-Q12 *Q22,

12

521:1—Q21—Qna
522 =1-Q22 “Q12-
Next, we can write the integrated firm, Ul -D1 ’5 profits as:

MaxnUI—Dl = 1911er+ S21in-

Substituting (10) into (1 1) and differentiating with respect to Q11 and Q21,

anUl—Dl
———=1-2Q11—2Q21= 0,
5Q“
51101—01
— 1-7-Q21 *2Q11 - 0
0"er

From (12) and the symmetric structure of the model, we obtain

~o ~o ~o ~o 1
Q11+Q21=Q12+Q22=§,
~o_~o_~o_~0_1
11-12- 21- 22-5,

(10)

(11)

(12)

(13)

Next, consider the case where Ul-Dl decides to foreclose, but U2-D2 does not.

We have the following demand system for the composite goods:
S11=1—Q11—Q21,
521:1-Q21-Q11,
522 =1- Q22-

In this case, the equilibrium is as follows:

13

(14)

(15)

Lastly, consider the case where both integrated firms decide to foreclose. In this

case, the equilibrium quantities, prices, and profits are

l

~12=~12:_
Q11 22 2,
~n=~n=1
11 22 2,
~12 ~12 1
I111=1122 =3- (16)

From Figure 1-5, we find that foreclose does not increase the integrated frrms’

profits when the upstream products are perfect substitutes and the downstream products

are independent.

Figure 1-5. Payoff Matrix (Homogeneous Upstream and Independent Downstream)

Ul-Dl

U2—D2

 

M.—
M...
1:11-
M.—

 

4:11-
4:11-
.>|-—
el—

 

 

 

 

l4

5. Antitrust Analysis of Vertical Mergers
In this section, we examine the anticompetitive effects of vertical integration. We
will focus on the case in which upstream products are independent and downstream
products are perfect substitutes.6 We assume that the prices for the upstream goods are

determined by bargaining between sellers and buyers. Let us define P11 (1’12;le ; P22 )

as the upstream price in the transaction between U1 and D1 (U l and D2; U2 and D1; U2
and D2). We assume that no exclusive-dealing contract is allowed. We also assume that
independent upstream firms cannot practice price discrimination. 7 We only consider the
two extreme cases: (1) the upstream firms have all the bargaining power and (2) the
downstream firms have all the bargaining power.8 The timing is as follows. In the first
stage, U1 and D1 decide whether or not to integrate vertically. U2 and D2 simultaneously
make a decision about vertical mergers. In the second stage, the upstream prices are

determined. In the final stage, the equilibrium for composite goods is determined.

Upstream Bargaining Power
The upstream firms make take-it-or-leave—it offers to the downstream firms. And then the

downstream firms either accept or reject the offers.

Non-integration: The upstream firm, U1 (U2), offers P11 ( P21) to the downstream firm,

D1, and P12 (P22 ) to the downstream firm, D2. Since we assume that independent

 

6 We will relax the assumption about upstream differentiation in Appendix.

7 The Robinson-Patman Act prohibits price discrimination in intermediate goods markets. For the welfare
effects of price discrimination in intermediate goods markets, see Degraba [1990], Katz [1987], and
O’Brien and Shaffer [1994].

3 The literature on vertical contracts includes Bolton and Whinston [1993], Chemla [2003], Hart and Tirole
[1990], McAfee and Schwartz [1993], Rey and Tirole [2002], and Salinger [1989].

15

upstream firms cannot practice price discrimination, we can set P1 = P11 = 1’12 and

P2 = P21 = P22 . Given Pl and P2 , the downstream firm, D1, determines the optimal

composite good quantities from the following maximization problem:
M(Drug/i=(511—P1)Q111*(«5'21-1"2)Q21- (17)

Differentiating with respect to Q11 and Q21,

0"le

Di
-——-=1- 2Q11—Q12—1D1=01 (18)
a"Q11
anD’
——=1-2Q21 Q22-1’2:0 (19)
3Q21

Similarly, we can write D2’s maximization problem as:

Maxnglz = (512 —Pl)Q12 +(522 ’P2)Q22- (20)

Differentiating with respect to Q12 and Q22 ,

51102 _

 

 

1- Q11-2Q12-P1=01 (21)

3Q12
=1-Q21—2Q22 — P2 = 0- (22)

3Q22

From (18), (19), (21), and (22),

 

(23)

 

Q2N1I =Qfi’=l’Pz. (24)

In the second stage, the upstream firm, U1, determines the prices for its upstream

products from the following maximization problem:

Maxniili = P1(Q11+Q12)1 (25)

16

Substituting (23) into (25) and differentiating with respect to P1 ,

31151

2
=—1-—2P =0. 26
5P1 3( 1) ( )

From (26) and the assumption of symmetry, the equilibrium upstream prices are

EN] = 172M = g (27)
Substituting (27), we obtain
— — — — l
Qlli” - Q12” = Qzli” - Q22” = 6' (7-8)
—‘N1 —N1 1 6 --NI —NI 2
II = H = — = -—— , II = II = —-. 29
U1 U2 6 36 01 02 36 ( )

Partial htgration: Suppose that U1 and D1 integrate vertically, but U2 and D2 remain

the independent firms. The upstream division of the integrated firm, Ul-Dl, offers P12 to
the independent downstream firm, D2. The independent upstream firm, U2, offers P21 to
the downstream division of Ul-Dl and P22 to D2. By the assumption of no price

discrimination, we can set P2 = P21 = P22 . And also we let Pl = P12 . Given P1 and P2 ,

the integrated firm, U1 -D1, determines the optimal quantities from the following

maximization problem:

Marla—01 = S11Q11+(521— P2)Q21+ P1Q12- (30)

Differentiating with respect to Q11 and Q21,

P1
511U1-D1

=1—2 — =0, 31
5Q“ Q11 Q12 ( )

l7

P1
511U1—Dr

=l—2 - —P =0. 32
5Q21 Q21 Q22 2 ( )

Next, we can write D2’s maximization problem as:

MaxIIZ’z =(512 —Pi)Q12 +(522 -P2)Q221 (33)

Differentiating with respect to Q12 and Q22 ,

311512

 

 

=1-Q11-2Q12-P1=01 (34)
3Q12

=1-Q21—2Q22—P2 =0 (35)
3Q22

From (31), (32), (34), and (35),

 

 

 

1+ P 1— 2P
QIIII=311QIIEI= 1 9
3
l— P

Q21 =Q221‘ - 3 2 - (36)
Substituting (36) into (30), and differentiating with respect to P1 ,

an Pl

M=§(1-2pl)=o, (37)

6P1 9

From (37), we obtain

fi”=%. (n)

Next, the independent upstream firm, U2, solves the following maximization problem:

Maxniilz = 1D2(Q21 + Q22)1 (39)

Substituting (36) into (39) and differentiating with respect to P2 , we obtain

= —. (40)

18

Substituting (38) and (40), the equilibrium quantities and profits are given by

—P1 1 —P1 —P1 —P1 1
Q11 =—1 12 =01 21 = 22 =—- (41)

2 6

—P1 10 —P1 6 —p1 1
_ _—,11 _——,11 =——. 42
U1 01 36 U2 36 DZ 36 ( )

Full Integration: The upstream division of the integrated firm, Ul-Dl (U2-D2) offers P12

(P21) to the downstream division of the other integrated firm, U2-D2 (U l-Dl). Let

P1 = 1’12 and P2 = P21. Given Pl and P2 , Ul-Dl determines the optimal quantities

from the following maximization problem:
M011151—01=Sr1Q11+(521‘1’2)Q21+P1Q12- (43)

Differentiating with respect to Q11 and Q21,

511511-01 '
———-=1-2Q11-Q12=01 (44)
5Q“
Fl
m=1-2Q21’Q22-P2=0- (45)
5Q21

Similarly, U2-D2 solves
Maxnijlz—Dz = (512 - P1)Q12 + 522sz + P2Q21~ (46)
Differentiating with respect to Q12 and Q22 ,

an F1

U2-D2 ' -

-—-——=1-2Q12-Q11-P1=0, (47)
5Q12

511152—02

———-=1-2Q22—Q21=0- (48)
5Q22

From (44), (45), (47), and (48), we have

19

 

 

 

 

l+P l—2P
Q111=311Q121= l1
3
—2P_1+P
QzFrl= 2 ,fz’Q 32. (49)

Substituting (49) into (43), differentiating with respect to P1 and using the symmetric

structure of the model, we obtain

2
Substituting (50), the equilibrium quantities and profits are given by
F 1 —-F —FI
Q11 =Q221=-2-1Q121==Q21 =0- (51)
_—F1 1 9
HF -II _ = — = —. 52
Ui- 01- U2 DZ 4 36 ( )

The above results can be summarized in Figure 1-6. The profits in each cell
represent the sum of the upstream and downstream profits. We find that it is the dominant

strategy to integrate vertically.

, Figure 1-6. Vertical Mergers under Upstream Bargaining Power

 

 

U2&D2
N V
8 8 7 10
N _9_ —
36 36 36 36
U1&Dl
V .12 _7__ 2 2
36’36 36’36

 

 

 

 

20

Downstream Bargaining Power
The downstream firms make take-it-or-leave-it offers to the upstream firms. And then the

upstream firms either accept or reject the offers.

Non-integration: The downstream firm, D1 (D2), offers P11 (P12 ) to the upstream firm,
U1, and P21 (P22 ) to the upstream firm, U2.9 Given P11 , 1’12 , P21, and P22 , the

downstream firm, D1, determines the optimal quantities from the following maximization

problem:

Mfungi=(511‘11’11)Q11+(521*1021)Q21- (53)

Differentiating with respect to Q11 and Q21,

51151
-——-=1-2Q11-Q12-P11=01 (54)
5'Q11

511E
—=1-2Q21—Q22-P21=0- (55)
5Q21

Similarly, we can write D2’s maximization problem as:
Mani)”; = (512 'P12)Q12 +(522 ‘P22)Q22- (56)

Differentiating with respect to Q12 and Q22 ,

arr ’3’2
5Q12

 

=1-Q11—2Q12—P12=01 (57)

 

9 Unlike upstream bargaining power, we allow downstream firms to make different offers to upstream
fn'ms. Why the asymmetric assumption? When the upstream firms have all the bargaining power, upstream
firms should make same offers to both downstream firms because they sell same products. In contrast,

downstream firms may offer different prices to different upstream firms because they purchase different
products.

21

an 155. _
§Q22

 

From (54), (55), (57), and (58),

 

Q1111” =1-2P11+P12 Q1112” = 1+P11 "2112
3 9
N1
Q21 =

 

3

Substituting (59) into (53) and rearranging,

—1-Q21—2Q22 —P22 =01

 

I-2P21+P22 Q£I=1+le-2P22 .

 

1-21’11+P12 1-2P21+P22

 

NI
HD1(Pll1P21)=( 3

Differentiating (60) with respect to P11 [and P21 ,

N!
51101 4 N1 <

=__ _0,
0,1,“ 3Q11
NI
fl=_£QZA{I _<_0_

Equation (61) implies that

Similarly, we obtain

NI NI
£12 = £22 = 0-

 

(53)

(59)

(60)

(61)

(62)

(63)

Substituting (62) and (63), we obtain the following equilibrium quantities and profits:

(64)

(65)

Partial Integration: The downstream division of the integrated firm, Ul-Dl, offers P21 to
the independent upstream firm, U2. The independent downstream firm, D2, offers 1’12 to
the upstream division of Ul-Dl and P22 to U2. Given P12 , P21, and P22 , the integrated

firm, Ul-Dl, determines the optimal quantities from the following maximization

problem:

Maxwell-01=511Q11+(521-P21)Q21+P12Q12- (66)

Differentiating with respect to Q11 and Q21,

511511—01
——-=1-2Q11—Q12=01 (67)
5Q11 .
PI
m=1_2Q21_Q22.—1921=0, (68)
5Q21

Next, we can write D2’s maximization problem as:

444111111312 = (512 ‘52)Q12 +(522 —P22)Q22- (69)

Differentiating with respect to Q12 and Q22 ,

31151,
5Q12

 

=1-Q11-’2Q12“P12=01 (70)

511512
5Q22

 

=1—Q21—2Q22—P22 =0. (71)

From (67), (68), (70), and (71),

 

 

p] 1+P p] l-ZP
Q11 =-——12 1 Q12 =——121
3 3
Q2111=1—2P21+P22,Q£I=1+P21—2P22. (72)

3 3

Substituting (72) into (66) and rearranging,

23

 

 

 

2 2
l+P l—2P +P l—2P
“(Iii-01(P21)=( 312) +( 23] 22) +P12[ 312) (73)

Differentiating (73) with respect to P21,

Pl
gum—01 = _ 4

— P’ s 0. 74
5P21 3 Q“ ( )
From (74), we find that
£5? = 01 (75)

Substituting (72) into (69) and rearranging,

 

 

2 2
l—ZP 1+P —2P
I111312(1D1211"22)=[ 312) +( 213 22) - (76)

Differentiating (76) with respect to P22 ,

Pl
51102 =..51_ 75’ so. (77)
5P2) 3

 

Equation (77) implies that
353’ = 0. ' (78)

Similarly, can we conclude that £51 , the price that the independent downstream
firm, D2, offers to the upstream division of the integrated firm, Ul-Dl, will also be equal
to zero? In order to answer this question, we first construct the profit function for Ul-Dl

(see Figure 1-7). Differentiating (73) with respect to P12 ,

PI
m=§(1_2plz). (79)
071312 9

Equation (79) implies that 11511-01 is an increasing function of P12 when P12 is less

than 1/2. If P12 2 1/2 , Q12 = 0 from (72) and equation (70) is not binding. From (67),

24

(68), and (71), we find that the equilibrium quantities and profits do not depend on P12
when P12 2 1/2 . As Shown in Figure 1-7, the integrated firm, Ul-Dl , can obtain the
status quo profits of E16, when there is no transaction. In this case, D2 should offer at

least 1/2 as a price for the U1 -D1 ’3 upstream products. Otherwise Ul-Dl will reject D2’S

 

 

 

 

 

offer.
1
£g=_, mm
2
Figure 1-7. The Profit Function for Ul-Dl
PI
11 U1 — Dl
Q12 = 0(No Transaction)
D
77111 """"""" |
I
I
I
I
I
I
l
I
I
I
0 1/2 P12

25

Substituting (75), (78), and (80), we obtain

Pl_1 PI_ PI_ Pl_1

Q11 ”5’ 912 ‘0’ 221-222 ‘5' (31)
p] 13 4

HUI—DI ‘ 3—6’ 1HU2 - 01302 - -3_6 (82)

Full Integration: The downstream division of the integrated firm, Ul-Dl (U2-D2) offers
P21 (P12) to the upstream division of the other integrated firm, U2-D2 (U l-Dl). In this
case, the profit fimctions for the integrated firms, Ul-Dl and U2-D2, have the similar
shape as in Figure l-7. Therefore, the downstream division of Ul-Dl (UZ-DZ) should

offer 1/ 2 at least to the upstream division of U2-D2 (U 1-D1).

1
P3 = p51 :5. (83)

Since we have the same upstream prices as in the case of upstream bargaining power, we

also have the same equilibrium quantities and profits.

FI_ F1_1 Fl_ FI__

211—922 "2’ 212 ’921_O° (34)
l 9

HUI- 01=I1U2- 02=Z=§g- (85)

Figure 1-8 summarizes the above discussion. We find that it is the dominant strategy to

integrate vertically as in the case of upstream bargaining power.

26

Figure 1-8. Vertical Mergers under Downstream Bargaining Power

 

 

U2&D2
N V
8 8 4 13
N —9— —s_
36 36 36 36
U1&Dl
1 2 2 2 2
36’36 36’36

 

 

 

 

From Figure 1-6 and Figure 1-8, we find that it is the dominant strategy to

integrate vertically regardless of who has bargaining power.

Proposition 1. When upstream products are independent and downstream products are
perfect substitutes, the equilibrium vertical structure is full integration in both cases:

upstream bargaining power and downstream bargaining power.

Welfare Implications

The demand system in (2) can be derived from the following utility function:10

U ={(Q11+ Q12)--;-(Q11+ Q12)2}+{(Q21+ Q22)-%(Q21+ Q22)2}- (86)

Since we assume that the marginal costs are zero, the welfare function has the following

form:

 

'° See Singh and Vives [1984].

27

W ={(Q11+ Q12)-%(Q11+ Q12)2}+{(Q21+ Q22)-%(Q21+ Q22)2}- (87)

When Q=Q11+Q12 =Q21+Q221

a—W=2(1—Q)>0,for Q<1.

5Q

From the equilibrium quantities, we find that

—M —M —M —M —M 1
Q=11+12=21+22=§1
—F1 —F1 —F1 —F1 —F1 1
Q=11+12=21+22=§1

N1_ N1 N1_ N1 Nl__
Q “211+Q12‘Qz1+Q22’ ’

FI_ Fl F1_ F1 Fl__1_
Q “211+212‘921+222'2‘

From (89) to (92),

EN] < @‘Fl = _Q_Fl < QNI .

From (88) and (93), we could obtain the following proposition 2:

(88)

(89)

(90)

(91)

(92)

(93)

Proposition 2. When upstream products are independent and downstream products are

perfect substitutes, the welfare effects of vertical integration depend on who has

bargaining power. Vertical mergers increase (decrease) welfare when the upstream

(downstream) firms have all the bargaining power.

The intuition for Proposition 2 can be explained as follows. Vertical mergers have two

contradictory welfare effects: foreclosure and elimination of double marginalization.

28

While vertical mergers decrease welfare through foreclosure, they increase welfare by
eliminating double marginalization. When the downstream firms have bargaining power,
the equilibrium upstream prices will not be high under non-integration and thus the
positive welfare effects of elimination of double marginalization will not be great. As the
downstream firms have more bargaining power, the negative effects are more likely to

outweigh the beneficial ones.

6. Concluding Remarks

We have found that in the composite goods market with successive vertical
structures, vertical mergers are more likely to be anticompetitive under the following two
conditions: as upstream products are more differentiated and as the downstream firms
have more bargaining power. Under the former condition, the integrated companies
obtain more market power through foreclosure. Under the latter condition, the beneficial
welfare effects of elimination of double marginalization will be less.

We conclude by making some remarks about the limitations of our model and
further studies. First, we have asSumed that downstream products are perfect substitutes.
But if mobile operators provide data, video as well as voice services, downstream mobile
services can be highly differentiated. A future study might relax the assumption about

downstream product differentiation.ll

 

" We can set c = a x b in the demand system of (1). In this case we have the two parameters. We might
use specific numbers to simulate this numerically even though we could not solve the model algebraically.

29

Second, we have only considered the case in which the downstream firms have
symmetric structures. It would also be worthwhile to analyze the asymmetric case.‘2

Third, in order to apply our framework to the real cases, we need to conduct
additional empirical studies measuring upstream and downstream product differentiation.
We also have to obtain information about the margin rates for the upstream products in
the transactions between upstream and downstream firms.

Lastly, it would be interesting to introduce network extemalities into composite
goods markets. For example, mobile services seem to have network extemalities, but
handsets do not. In this case, we could consider a model of composite goods markets
with one-sided network extemality. Such a model might be helpful in examining issues
about handset subsidies13 and the effects of vertical mergers on tipping in the mobile

service industry.

 

'2 In Korea, there exist three mobile operators. But SK Telecom has about 50% rrrarket share of the mobile
service industry. The handset manufacturing industry also has the asymmetric structure. Samsung
Electronics Company is a dominant firm among handset makers.

'3 Handset subsidies are meant by the following marketing strategy: mobile operators provide handsets to
consumers at the prices that are lower than ones at which they purchase handsets from handset makers. In
Korea, one issue is whether handset subsidies could be used as a predatory strategy.

30

 

References

Bolton, P. and Whinston, M. [1993] “Incomplete Contracts, Vertical Integration, and
Supply Assurance.” Review of Economic Studies, 60, pp. 121-148.

Chemla, G. [2003] “ Downstream Competition, Foreclosure, and Vertical Integration.”
Journal of Economics and Management Strategy, 12 (2), pp. 261-289.

Choi, J .P. [2003] “Antitrust Analysis of Mergers with Bundling in Complementary
Markets: Implications for Pricing, Innovation, and Compatibility Choice.”
Available at http://www.msu.edu/~choij ay/Merger.pdf.

Church, J. and Gandal, N. [2000] “Systems Competition, Vertical Mergers, and
Foreclosure.” Journal of Economics and Management Strategy, 9(1), pp. 25-51.

Degraba, P. [1990] “Input Market Price Discrimination and the Choice of Technology.”
American Economic Review, 80 (5), pp. 1246-1253.

Digital Times, September 16, 2004, (in Korean).

Economides, N. and Salop, SC. [1992] “Competition and Integration among
Complements, and Network Market Structure.” Journal of Industrial Economics,
XL (1), pp. 105-123.

Hart, 0. and Tirole, J. [1990] “Vertical Integration and Market Foreclosure.” Brookings
Papers on Economic Activity, pp. 205-276.

Katz, M. [1987] “The Welfare Effects of Third-Degree Price Discrimination in
Intermediate Good Markets.” American Economic Review, 77 (1), pp. 154-167.

Lee, YJ. [2004] “The Distribution Channels of Handsets and Handset Subsidies in
Foreign Mobile Service Markets.” Korea Information Strategy Development
Institute, (in Korean).

Matutes, C. and Regibeau, P. [1988] “Mix and Match: Product Compatibility without
Network Externalities.” Rand Journal of Economics, 29(2), pp. 221-234.

Matutes, C. and Regibeau, P. [1992] “Compatibility and Bundling of Complementary
Goods in a Duopoly.” Journal of Industrial Economics, XL (1), pp. 37-54.

McAfee, RP. and Schwartz, M. [1993] “Opportunism in Multilateral Vertical

Contracting: Nondiscrimination, Exclusivity and Uniformity.” American
Economic Review, 84, pp. 210-230.

31

O’Brien, DP. and Shaffer, G. [1994] “The Welfare Effects of Forbidding Discriminatory
Discounts: A Secondary Line Analysis of Robinson-Patman.” Journal of Law,
Economics, and Organization, 10(2), pp. 296-318.

Ordover, J.A., Saloner, G., and Salop, SC. [1990] “Equilibrium Vertical Foreclosure.”
American Economic Review, 80, pp. 127-142.

Rey, P. and Tirole, J. [2003] “ A Primer on Foreclosure.” mimeo.
Salinger, MA. [1989] “The Meaning of “Upstream” and “Downstream” and the
Implications for Modeling Vertical Mergers.” Journal of Industrial Economics,

xxxvrr (4), pp. 373-387.

Singh, N. and Vives, X. [1984] “Price and Quantity Competition in a Differentiated
Duopoly.” Rand Journal of Economics, 15 (4), pp. 546-554.

32

Appendix

In the Appendix, we relax the assumption about upstream product differentiation.
We assume that upstream products are imperfect substitutes and downstream products are

perfect substitutes. In this case, we have the following demand system:
S11=1—Q11—Q12 *7Q21-7Q22,
S12 =1-Q12 -Q11-}’Q22 —7Q21,
521:1-Q21-Q22 -7Q11—7Q121

522=1-Q22-Q21—7Q12—7Q111Where 0<7<1. (A-l)

Upstream Bargaining Power
Non-integration: Since we assume that independent upstream firms cannot practice price
discrimination, we can set P11 2 Plz = P1 and P21 = P22 = P2 as in Section 5.

Substituting (A-l) into (1 7) and (20) and differentiating with respect to quantities,

51151
3Q1 1

 

=1-2Q11-Q12"2}’Q21—J’Q22"1[’1=01 (A‘Z)

_an’l‘fi
5Q21

 

=1-2Q21-Q22-2rQ11-7Q12-P2=01 (A'3)

an gs
5Q12

 

=1-2Q12-Q11—27Q22-7Q21‘P1=01 (A-4)

N]
031102

=1-2Q22-Q21—27Q12-7Q11-P2=0- (A-5)
§Q22

Solving four equations (A-2), (A-3), (A-4) and (A-5) simultaneously,

33

_1-7-1’1 +7’P2

 

 

30—12)
1— + P—P
Q2111_QN1= 7 712 2. (A-6)
3(1-7)

Substituting Q1111” and Q1112” in (A-6) into (25) and differentiating with respect to Pl ,

61151 _2(1-7-2P1+7P2)_
5P1 311-12)

 

 

o. (A-7)

From (A-7) and the assumption of symmetry, the equilibrium upstream prices are

171”] = 1'32”] :1. (A_g)

Substituting (A-8), we obtain

 

 

-— —— — 1 --N1 1 1
Q1111] = Q12” = Qzli, = Q22 = ° (A'g)
3(1+7)(2—7)

__ ._ _ -— 4-37 1

5111” = 112” = 241” = £1 = . (141-10)
3(2-r)

—-N1 --N1 6(1- )

“U1 = r1U2 = 7

 

9(1 +7)(2 — 112 ’

2

 

8—6y

. A-ll
901410-112 ( )

 

Partial Integration: Let us set P12 2 Pl and P21 = P22 = P2 . Substituting (A-l) into (30)

 

and (33) and differentiating with respect to quantities,

34

Pl
511U1~Dr

 

=1-7-Q11—Q12 ‘27Q21-7Q22 =01 (A-12)
5er
01.1—11’1_ .
———U1 D] =1-2Q21-Q22‘27Q11—7Q12—P2=01 (A'13)
3Q21
3UP .
D—-—2- =1- 2Q12 Q11-27Q22 7Q21—P1=01(A'14)
3Q12
51—11)
02 =1- 2Q22-Q21-27Q12'“7Q11—P2=0 (A'ls)
3Q22

Solving four equations (A-12), (A-13), (A-14) and (A-15) simultaneously,

 

 

 

 

 

 

 

 

QP1_1-7+P1+7P2
II - 2
3(1-7)
QPI_1"7"2PI+7’P2
12 — 2 9
3(1-7)
QP1_1-7-7P1-P2
21 - 2 ,
3(1-7)
1— +2 P-P
szzl= 7 72‘ 2. (A-16)
3(1-7)
Substituting (A- l 6) into (A- 1 ),
p1 p] 1+P 1-2P
511=S1z= 311511-1’1=S121—1 = 311
l 2P21—P
Sf1’=s£’= +32 ,sf{—Pz=s{3’—Pz= 32. (A-17)

Substituting (A-16) and (A-17) into (30) and (39) and differentiating with respect to

prices,

511511—01 = 5(1-7-21’1 +7P2)

= 0. (A-l8)
5P1 9(1-12)

 

35

 

41155 _(2-27+rP1-4P2) _

2 0.
4P2 3(1—7 )

From (A-18) and (A-l9), the equilibrium upstream prices are

 

FF] _ 4‘27"272
1 _ 2
8-7

— 111 _ 4 - 37 — 72
P2 —- ——2__ .
8 - 7
Substituting (A-20), we have

~10: _, 12 -6r-6r2
3(1-12x8—72)

 

 

—p[ 4—9y+272-l-3y3
l = 1
3(1-72)(8-72)

 

—111 11.131-412-313
3(1-7 )(8-7)

 

 

-PI —PI -P1 —P1
11=12= 2 181-3 =fi2-fi =
3(8-7 )
2
—P1 -P1 16-6 -3 - —m --P -—
521 52 7 7 152111—102 =5221—P2PI=

__ 160—1207-11572 +4873 +2774
9(1-72)(8-72)2

 

9

-—p[ 96—1447 +672 4- 3673 +674
“”2 = 2 2 2
9(1-7 )(8-7 )

 

36

(A-19)
(A-20)
(A-21)

47 + 372

3(8 - 72) ’

4412—. (A-22)

3(8 - r )

fip, _16+247—772 —2473 —9y4
9(1-72)(8-72)2

 

2 3 4
—p[ .—p[ 112-1207-7 +127 -3)/
I_IU21’1102= 2 2 2 -
9(1—}’ )(8‘7)

 

(A-23)

The above solutions under partial integration are justified only when 7 is not
large. If y is greater than 7* a (—5 + 4/73 )/ 6 z 059 , the value of @211), in (A-21) is
negative. When 7 > 7‘ , we should solve the model in another way. We can use a trick.

First, we set @211), = 0. Second, since equation (A-13) is not binding, we solve the model
using only three equations, (A-12), (A-14), and (A-15). And then we substitute the
equilibrium quantities into (A-l3) and check whether the partial derivative in (A-13) has

a negative value. From (A-12), (A-14), and (A-15),

 

 

 

 

[)1 1+ P
Q11 = 3 l 1
Q1131 = (2-37+72)-(4-72)P1 +3er
60—72)
1— + P —P
2(1-7 )
Calculating the upstream prices, we obtain
—p1 20--9;1--11;12
P1 = 2 3
40—13y
—p] 20—10}’-11}/2+73
P2 = . (A-25)

 

40—1372

Substituting (A-25) into (A-24),

37

—p] 40+34y--22y2 —1673
l :
2(1+ ”(404372)

 

—p1 -8r+872 +773
2 = ’
2(l+7)(4O—l372)

 

—PI
Q21 =0,

-—-p] 20+107-72
2 = '
2(1+7)(40—1372)

 

(A-26)

The upstream and downstream firms’ profits are given by

fil’fi m = 800+ 400y ~63072 — 370y3 + 7374 +5175
2(1+7)(4O—1372)2

 

9

fip, 400— 340;!2 -8073 + 2174 — 75
U2 =
2(1 + 7)(40— 1372)2

 

9

400—19672 + 20873 +201y4 + 3575

fiPI _
DZ _ 2 2
4(1+y)(40-137 )

 

9

-—p] _ 3(400—292y2 +1673 +8174 +1175)
+1102 — .

1155
4(1+ y)(40-1372)2

 

(A—27)

Lastly, we have to show that the value of é’HSL D1/8Q21 , evaluated at the
equilibrium prices and quantities, is negative. Substituting (A-25) and (A-26) into (A-13)
and doing numerical calculation, we obtain Figure A-l. From the figure, we find that
51-1511—01 /§Q21 has a negative value for 7 > 7*. As an example, é’fl5’1_ DI /o"Q21 is

—0.055 when 7 is 0.7.

38

Figure A-l. The Graph of 6H511_Dl/0”Q21 when y > y!“

(1,0)

 

 

 

PI
gum—01
Q21

Full Integration: We set P12 = P1 and P21 = P2. Substituting (A-l) into (43) and (46)

and differentiating with respect to quantities,

an”-
--—-—--Ul DI =1-2Q11-Q12 -2}’Q21-7sz =0, (A-28)
5Q“
an”-
——U' DI=1-2Q21-Q22—27Q11‘rle-Pz=0: (A’29)
0”Q21
61‘1”_ .
-—-—-0,,UQ2 Dz =1-2Q12—Qn‘27Q22-7Q21—P1=0, (A'30)
12

39

311p
#2421: 1-2sz -Q21-2rQ12-7Qn =0 (A-31)
0"sz

Solving four equations (A-28), (A-29), (A-30) and (A-31) simultaneously,

Fl l-7+P1+27P2
Q11: 2 ,
3(1-7)

 

 

F1_1-7-2P1-7P2
Q12 - 2 ,
3(1-7)
F1_1-}’-7P1 2P2
Q21—
3(1- r2)

 

1— +2 P+P
Qfll— 7 721 2 (A-32)

3(1-1'2)

 

Substituting (A-32) into (A- 1 ),

 

 

F] F] 1+P l-2P
511:512 = 31 511—P1=512 -P1= 31,

1—2102
3 .

 

1+ P
55] = 551:3 -—2 521 — P2 - 522 *P2 = _(A-33)

Substituting (A-32) and (A-33) into (43) and (46) and differentiating with respect to

prices,

aHLF/ll—Dl = 5’57-101’1 +7P2

 

(A-34)
51% 9(1 -72)
5H5’2-132_ 5 57+7P12—10P2 (A-35)

 

 

5P2 9(1- 72)

In order to derive the equilibrium upstream prices, we construct the profit

function for the integrated company, Ul-Dl. First, let us define P; as

40

-7-2P1-7P2

 

.. 1 .
Q5] (P1 = P1 )= 2 = O,g1ven P2. (A-36)
3(1-7 )
From (A-36),
pl" = Elli, (A-37)

2

* . . . .
When P1 3 P1 , “(171—01 15 1ncreas1ng in P1 because

 

 

anflLDl = 5—57—101’] +7102 2 5—5;z—10P,"'+y102 >
6P1 9(1-72) 9(1-72)

0. (A-38)
If P1 > Pf. QS’ = 0 and (A-30) is not binding. This implies that the equilibrium
quantities and profits do not depend on P1. From Figure A-2, we find that the profits for

Ul-Dl are maximized when P1 2 P; , given P2 . From (A-37) and the assumption of

symmetry, we obtain

 

P“ = P," = P; = :1: . (A-39)

The equilibrium upstream prices are given by

 

Pl" =13” .21)“ = 1‘7 . (A-40)
2+7

Substituting (A-39), we have

 

 

_ _ 1 . _ _
Q17] = Q2127 = , Q1127 = Q2]? = 0- (A41)
2 +9!
—F1 -F1 1
= S - A-42
11 22 2 +7 ( )
1 2
—F1 —F1
nUl—Dl = nUZ—DZ = {—2 ] - (A-43)
+7

41

Figure A-2. The Profit Function for Ul-Dl under Full Integration

Fl
nUl-Dl

Q12 =0

 

 

EFF] 1' ------------

 

 

 

Downstream Bargaining Power
Non-integr_ation: Substituting (A-l) into (53) and (56) and differentiating with respect to

quantities given P”, P12 , P21, and P22 ,

3111‘,

—-D—{ =1- 2Q11-Q12-27in }’Q22"1"11=O (A-44)
5Q”
é’HN

_Q_1 =1-2Q21 sz '27Q11-7Q12 — P21: 0 (A-45)
5Q21
fil’IN

D——2 =1-2Q12 -Q11-2)’Q22 7in P12 =0 (A-46)
0"le

42

ambit _

———1-2Q22 ‘Q21-27Q12-YQ11—P22 =0-

0”sz

From (A-44) to (A—47),

NI _1-7-21’11+1’12+27P21-7P22

 

 

 

Q11 — 2
3(1-7)
glitz/1:1-7-2P12 +P11+27P22-7P21
3(1-72)
QZAIII=1-7-2P21+P22+27P11-7P12
30—72)
Q2115!=1-7-2P22+P21+27P12-7P11.

 

3(1 — r2)
Substituting (A-48) into (A-l ),

_l+fil+52
' 3

 

 

N1 N1 1+P +1022 N]
S 522 = 213 , 521

1‘21’111‘1‘12

 

NI
, 511-1311:

 

'P21=

(A-47)

(A—48)

(A-49)

Substituting (A-48) and (A-49) into (53) and differentiating with respect to PM and P21,

51111311 =_fl 111/1 so
am 3 ’
Lug =—1Q2"{’ so.
5P2] 3

From (A-SO), we can conclude
N] N]
£11 = £21 = 0-

Similarly, we have

43

(A-SO)

(A-Sl)

(A-52)

Substituting (A-51) and (A-52), the equilibrium quantities, prices, and profits are

 

N1_ N1_ N1_ NI_ 1
211 _le ‘221 ’222 — 3(1+}’). (A-53)
1 .
sit =§i”2’ =§$V{ 451’ =3. (21-54)
2

(A-SS)

 

Eagial Integration: Substituting (A-l) into (66) and (69) and differentiating with respect

 

to quantities given P12 , P21, and P22 ,

PI
aHUFDl

=1-2Q11-Q12-27Q21—7Q22 =0, (A-56)
5Q“

P]
aHUl-Dl

=1-2Q21‘Q22-27Q11-7Q12-P21=0, (A'57)
§Q21

51155
5Q12

 

=l—2Q12‘Qll‘27Q22"7Q21‘P12=0, (A'58)

an” '
-—Dz-=1-2Q22-Q21‘27Q12-7Q11—P22=0- (A'59)
5sz

From (A-56) to (A-59),

Pl _1-7+P12 +27P21-7P22
Qll — 2
3(1-7)

 

9

=1-7-2P12 *7P21+27P22
3(1-72)

 

Pl
Q12

PI _1-7-71’12 -2P21+P22
Q21 — 2
3(1-7)

 

9

44

 

_1-7+27P12 +P21—7-P22

 

Q2P2’ — 2 (At-60)
3(1- r )
Substituting (A-60) into (A- 1 ),
PI PI 1+ P
511 = S 12 = —3—12’
1+ P + P
52’? = 55’ = 2‘3 22 . (A-61)
Substituting (A-60) and (A-6l) into (66) and differentiating with respect to P21,
511511 01 4 P] r P12
— : ——Q21 - 2 SO. (A-62)
0"sz 3 3(1-7 )
From (A-62), we find that
551’ = o. (A-63)

Similarly, substituting (A-60) and (A-6l) into (69) and differentiating with respect to
1"22 ,

mg],

= _ggfil s 0. (A454)
Equation (A-64) implies that

322’ =1 . (A-65)
Will P21, the price that the independent downstream firm, D2, offers to the upstream
division of the integrated firm, Ul-Dl, be equal to zero as P22 ? In order to answer this
question, we first derive the profit function for the integrated firm, Ul-Dl . Given

£201] :32); =O,let us define 1312 as

~7-2fizz

Pl 1 ~ 1
Q12(P12=P12)= 2
3(1-7 )

 

0 . (A-66)

45

From (A-66),

~ 1-
P12 = 71 (A-67)

We can easily prove that when [’12 S P12 ,

311511—01 : 5(1-7-21’12)2 5(1-7-7-1512) =
”12 9(1-72) 9(1-72)

 

 

 

0 . (A-68)

This implies that the profit for the integrated firm is increasing in P12 when PIZ 3 i512. If
P12 is greater than 7’12 , the profit for Ul-Dl does not depend on P12 . The reason is that
Q1121 = O and (A-58) is not binding. From Figure A-3, we find that Ul-Dl obtains the

status-qua profits of '7? P] when there is no transaction. Therefore, D2 should offer 1312 at

least to Ul-Dl.

 

£1131 = 1:1 (A-69)
2
Substituting (A-63), (A-65), and (A-69), we have
Q”: 1 Qplzo QP’=_2___7_ QP’zl. (A170)
—11 2(1+7)’ ——12 ’ —21 60 +7) ’ —22 3
3— 1
sfi’ = £3 =-- _l, .515? = s5”; = —. (MI)
6 3
13-57 PI PI 1
HP’ =————,n =o,r1 =—. A-72
-—Ul-Dl 360+?) ——U2 -02 9 ( )

46

Figure A-3. The Profit Function for Ul-Dl under Partial Integration

 

 

 

 

 

P]
H U1— 0]
Q12 = 0(N0 Transaction)
»
a: P1 P ------------ I
I
1
1
l
1
I
I
I
l
I
0 17‘12 P12

Full Integration: The downstream division of the integrated firm, U2-D2 (U l-Dl), offers

P12 (P21) to the upstream division of the other integrated firm, Ul-Dl (UZ-DZ). From

Figure A-2, we see that the Ul-Dl obtains the status-qua profits of fi Fl without

transaction. Therefore, U2-D2 should offer P1. = P]. at least to Ul-Dl. For the similar

reason, Ul-Dl should offer Pt to U2-D2. Therefore, the equilibrium upstream prices are

 

£3 =£2Fi =P" =1”. (A-73)
2+y

We have the same equilibrium as in the case of upstream bargaining power.

 

1
Qg=z+7,Qg.—.Q§l’=o. (A-74)

NO

Fl
ll

47

 

§Fl _ SF] 1 (A-75)

 

:- 2+7.
1 2
F] F]
Hal-Di =EU2—Dz {2+7} - (A-76)

Vertical Mergers
Now we examine the incentives to integrate vertically. Figure A-4 and Figure A-S show

the case in which 7 is 0.1. From those figures, we find that vertical integration is the

dominant strategy in both cases: upstream bargaining power and downstream bargaining
power. We can also show that it is the dominant strategy to integrate vertically for all

0 < 7 < l . First let us define the following notations:
, Afil a “511-01 — (HM + II 9%) under upstream bargaining power,
Afiz a 11512—02 — (II 512 + H512) under upstream bargaining power,
Ag] 5 [1511431 — (II (1% + 1'1 50 under downstream bargaining power,
A_I_I_2 a 11512—02 - ([1512 + [155) under downstream bargaining power. (A-77)
From Figure A-6 to Figure A—9, we see that Afil , Afiz , Afll , and A32 are always

positive for all 0 < 7 < l .‘4 This implies the following proposition:

Proposition A-l. When upstream products are imperfect substitutes and downstream
products are perfect substitutes, it is the dominant strategy to integrate vertically

regardless of who has bargaining power.

 

'4 In Figure A-6 and Figure A-7, the graph is discontinuous at 7 = 7*.

48

Figure A-4. Vertical Mergers under Upstream Bargaining Power (7 = 0.1 )

 

 

U 2& D2
N V
N 0.207, 0.207 0.176, 0.258
U1& Dl
V 0.258, 0.176 0.227, 0.227

 

 

 

 

Figure A-S. Vertical Mergers under Downstream Bargaining Power (7 = 0.1)

 

 

U 2& D2
N V
l
N 1 0.202, 0.202 0.111, 0.316
U 1& D]
V 0.316, 0.111 0.227, 0.227

 

 

 

 

49

Figure A-6. The Graph of Afil

0.03

0.02

0.01

 

 

 

(0,0)

Figure A-7. The Graph of AFB

Afi2

0.05
0.04
0.03

0.02

0.01

#

 

 

(0,0) 0.2 0.4 0.6 0.8 1

50

0.12

0.1
0.08
0.06
0.042

0.02

Figure A-8. The Graph of All]

 

(0,0)

Afl2

0.14
0.12

0.1
0.08
0.06
0.04
0.02

(0,0)

 

 

 

Figure A-9. The Graph of Afl2

 

 

5l

Welfare Implications
Following Singh and Vives [1984], we can derive the following welfare function

associated with the demand system in (A-l ):

1 .
W=(Q11+Q12 +Q21+Q22)-§(Q121+Q122 +Q221+Q222) . (Mg)
-(Q11Q12 +7Q11Q21+7Q11Q22 +7Q12Q21+7Q12Q22 +Q21Q22)

. Table A-1 compares social welfare under non-integration with social welfare under full

integration when 7 is 0.1. From Table A-1 , we find that vertical integration increases

(decreases) welfare when the upstream (downstream) firms have all the bargaining power.

Table A-1. Welfare under Non-integration and Full Integration (7 = 0.1)

 

 

Bargaining Power Non-integration Full Integration
Upstream 0.526 0.703
Downstream 0.808 0.703

 

 

We can show that the above result holds for all 0 < 7 < 1 . First, let us define the
following notations:

AWEWH-WM

AZEKM—Wn. (AW)
In (A-79), W M (K M ) represents the welfare under non-integration when the upstream

(downstream) firms have all the bargaining power. The welfare under full integration can

52

be represented by only one notation, W F] because it is identical in both cases. From
Figure A-10 and Figure A-l 1, we see that AW and AH: are always positive for all

0 < 7 < l . This implies the following Proposition A-2:

Proposition A-2. When upstream products are imperfect substitutes and downstream
products are perfect substitutes, vertical mergers decrease (increase) welfare when the

downstream (upstream) firms have all the bargaining power.

As explained in Section 5, the intuition for Proposition A-2 is that the equilibrium
upstream prices will not be high under non-integration and thus the beneficial effects
from vertical mergers, elimination of double marginalization, will not be great when the

downstream firms have all the bargaining power.

53

Figure A—lO. The Graph of AW

0.15

0.1

0.05

 

 

 

(0.0)

Figure A-l l. The Graph of AZ

0.14
0.12

0.1
0.08
0.06
0.04

0.02

 

 

 

(0,0)

54

Now we calculate the critical bargaining power at which social welfare under
non-integration (W N] ) is equal to social welfare under full integration (WF1 )1 We first
identify the condition under which W M = W” . From (A-9) and (A-53), we find that
four equilibrium quantities are identical under non-integration. Therefore, we let

0” = Q11 = Q12 = Q21 = on. (A-SO)
Substituting (A-80) into (A-78),

W” = 40"” —4(1+r)(Q"’)2. (A-81)

From (A-41) and (A-74), we see that the equilibrium quantities under full integration

have the following pattern:
Fl _ _ _ _
Q - Q11- Q22 , Q12 - Q21- 0- (A432)
Substituting (A-82) into (A-78),
W” = 20” — (I + mo”)? (A-83)
We can easily prove that W” = WM , if

Qn ___ ‘2sz. (A-84)

Next, we derive the upstream prices under non-integration at which (A-84) is
satisfied. Let us define PIC and P2C as
Q” =2Q”’(IiC.P2C). (A-85)

We restrict our attention to the symmetric case and assume that

PC = PIC = P2C . (A-86)

Substituting (A-86) into (A-6), we obtain

55

NI _ l-PC

 

 

_ . A-87
Q 3(1 + 7) ( )
Substituting (A—41) (or (A—74)) and (A-87) into (A-85) and rearranging,
PC 1" 7 (A-88)

= 2(2+7)'

Lastly, let us define a representing bargaining power. If the upstream firms have

all the bargaining power, a is equal to 1. If the downstream firms have all the bargaining

power, a is equal to 0. Then, we can define ac as

aCxPM+(l——ac)x£NI=PC. (A-89)
In (A-89), P N] ( f N] ) represents the equilibrium upstream prices under non-integration

when the upstream (downstream) firms have all the bargaining power. From (A-8), (A-

51), and (A-52),

erzl-r
2 - r
13"” = 0. (A-90)

Substituting (A-88) and (A-90) into (A-89), we have

 

do 2-7

= 2(2+}/), for7¢l. (A'91)

From Figure A-12, we find that ac is decreasing in 7 . This implies the following

Proposition A-3:

56

 

Proposition A-3. As upstream products are more differentiated (as 7 decreases), vertical

mergers are more likely to be anticompetitive.

Figure A-12. The Graph of aC

 

 

 

 

a
I
ace)
Pro-competitive
l A /
2 \
\ ~
~ ~
~
~ ~ ~ ~ ~ 4 .1.
Anti-competitive 6
0 7

The intuition for Proposition A-3 can be “explained as follows. Let us define
market power, a), as follows:

a) E l— 7. (A'92)
In (A-92), 7 represents the substitutability between products. If rival firms sell perfect

substitutes (7 = 1), the market power of a firm is equal to zero. But if there is no

57

 

substitute (7 = 0), a) is equal to one. First, consider non-integration under which there is

no foreclosure (see Figure A-13). The downstream firm, D1 (D2), sells UlDl and U2D1
(U 1D2 and U2D2). Since we assume that downstream products are perfect substitutes,
UlDl and U1D2 are perfect substitutes. Similarly, U2D1 and U2D2 are also perfect

substitutes. Therefore, in this case, the market power of the downstream firms is given by

N1 = 0_ (A-93)

Next let us consider full integration under which the integrated firms foreclose (see
Figure A-14). There exist two composite goods, UlDl and U2D2. The substitutability
between the two products is determined by upstream product differentiation (7). In this

case, the market power of the integrated firms can be determined by

F]

a) 1— 7. ' (A-94)

From (A-93) and (A-94),

AwEwFI-lezl—7. (A-9S)
This implies that the integrated companies could obtain more additional market power

through foreclose as upstream products are more differentiated (as 7 decreases).

58

 

Figure A-13. Composite Goods Market under Non-integration

 

UlDl, U1D2 U2Dl, U2D2

 

 

 

Figure A-l4. Composite Goods Market under Full Integration

 

UlDl U202

e—-—-d

 

 

 

59

CHAPTER 2

SPECIALIZATION IN INTERMEDIATE GOOD MARKETS

6O

1. Introduction

This paper examines the strategic motive for specialization in successive vertical
oligopolies. We may define specialization as focusing on a specific group of customers
(or a specific market). The opposite concept, diversification, can be defined as serving
several groups of customers (or entering many different markets). In this paper we
analyze the strategic choice of specialization versus diversification in the intermediate
good market and show that specialization may facilitate upstream tacit collusion. Despite
losing the opportunity to obtain some profits from additional downstream firms, upstream
firms stick to specialization because the choiCe of diversification actually reduces the
profits from captive downstream buyers.

The strategic choice of specialization versus diversification can be expressed in
many ways: specialized versus generalized inputs, designated versus flexible
technologies, and R&D investment on specific technologies versus on basic technologies.
In this paper we use the framework developed by Choi and Yi [2000]. Upstream input
suppliers can choose the degree of specificity of the inputs they produce for downstream
buyers. They have two options: a generalized input that can be used by all downstream
firms and a specialized input that is dedicated to a particular downstream firm.15 We
show that the choice of specialized inputs can be privately and collectively profitable.

We also show that the strategic choice of specialization versus diversification
might be different between the market for consumers (final goods markets) and the
market for businesses (intermediate goods markets). Let us consider the following cases

in which two products are not substitutable. First, suppose that there exist two final

 

'5 For example, a software firm may develop a program for a particular customer or may design it for the
mass market as packaged software (Baba, Takai, and Mizuta [1995]).

61

products for consumers: men’s clothing and women’s clothing. Two apparel companies
are considering whether to produce both products or specialize in the production of a
specific product. Next, we can think of the vertical structure that has upstream electronics
and downstream communication industries. A cable company enters the
telecommunication industry with VoIP (Voice over Internet Protocol) and competes with
a telephone company for the communication business. Both companies employ different
kinds of equipments. The two electronics companies are considering whether to produce
two kinds of equipments and provide both downstream firms with those equipments or
specialize and supply to a specific downstream firm. According to our model,
specialization is more likely to be profitable in the latter case than in the former case. The
reason is as follows. When two products are not substitutable in the final goods market,
the markets for the two final products are independent and thus the choice of
diversification has no negative effect on the profits from captive downstream buyers. But
the markets for the two intermediate goods might be dependent through the downstream
market even though the intermediate goods are not substitutable. Such dependence may
make the choice of diversification lead to negative effects on the profits from captive
downstream buyers.

It is interesting to compare our article with Roller and Tombak [1990]. They
analyze the choice between flexible and designated manufacturing technologies“. There
are two differentiated products in their model. A firm can produce both products if it
chooses a flexible technology. But only one product can be produced if a designated

technology is chosen. In each market, two firms engage in Coumot competition. Under

 

'6 For other issues on flexible manufacturing technologies, see Chang [1993], Eaton and Schmitt [1994],
Mansfield [1993], Milgrom and Roberts [1990], and Norman and Thisse [1999].

62

these circumstances, they show that when the two products are highly differentiated, the
industry is driven to adopt flexible technologies. Their model relates to ours in that they
also examine the strategic choice of specialization versus diversification in a broad sense.
In fact, generalized inputs in our model are matched to flexible technologies and
specialized inputs to designated technologies. But both articles have the following
difference: while they focus on the effects of product differentiation, we investigate the
effects of upstream cost structures.

It is worthwhile to compare our article with the literature on horizontal
differentiation. One of the classic models of horizontal differentiation is the so-called
location or Hotelling model. In this model, the distance between two firms’ locations is
directly related to the degree of differentiation between their products. The closer two
firms are located to each other, the more substitutable their products become. If they are
located at the same point, their products become perfect substitutes. D’Aspremont,
Gabszewicz, and Tisse [1979] endogenize the firms’ locations, which are fixed in the
Hotelling model. In their model, two firms choose their locations in the first stage and
choose their prices in the second stage. This model shows that the two firms will locate at
the two most extreme points. Each firm locates as far from its rival as possible. The logic
behind this result is as follows. When a firm moves toward the center, two contradictory
effects occur. The first is to increase the finn’s market share, the market-share effect. But
this also decreases the distance between the two firms and makes their products more
substitutable, fostering more intense competition, the strategic effect. The strategic effect
dominates the market-share effect in their model. Our conclusion is very similar to

d’Aspremont at al. [1979], but the logic behind our result is markedly different. The main

63

difference lies in the mechanism through which the firm’s product choice can lead to a
negative effect on its profits. In their model, a firm’s movement toward the center
decreases its profits by triggering intense price competition. But our model shows that the
choice of generalized inputs has a harmful effect on a firrn’s profits by decreasing sales in
its own turf.

Our article relates to Choi and Yi [2000] because they also study the strategic use
of specialized inputs in successive vertical oligopolies. But in their model, the integrated
firm uses specialized inputs strategically as a commitment device to foreclose. Suppose
that the upstream division of the integrated firm chooses a specialized input that is
dedicated to its downstream division. The independent upstream firm then remains the
only input supplier to the independent downstream firm. This will cause the independent
upstream firm to enjoy monopoly power and thus maintain its ability to charge a higher
input price to the independent downstream firm. The choice of a specialized input thereby
allows the integrated firm to raise its downstream rival’s costs.

Our article also relates to the literature on upstream collusive behavior. The 1984
Non-Horizontal Merger Guidelines envisage, for instance, that vertical mergers may
facilitate upstream collusion through the acquisition of disruptive downstream firms. The
idea laid out in the Guidelines has been formalized and refined by Nocke and White
[2003]. Franchise fees and intrabrand exclusive territories also have been regarded as
candidates for upstream collusive devices. According to Bonanno and Vickers [1988],
upstream firms can relax downstream competition by charging higher wholesale prices
and extract downstream rents through franchise fees. Rey and Sti glitz [1995] have shown

that manufacturers can sofien interbrand competition with intrabrand exclusive territories.

64

While the previous literature has mainly focused on vertical restraints as upstream
collusive devices in the context of manufacturers and retailers, our article concentrates on
Specialized inputs in the relationship between input suppliers and manufacturers.

Although his model is not about upstream collusion, Chen [2001] also deals with
collusive behavior in the vertically related industries. His focus is on tacit collusion
between the integrated firm and its downstream rivals. The independent downstream
firms in his model are assumed to be strategic buyers in the input market. He shows that
they have incentives to choose the integrated firm as an input supplier when they choose
input suppliers strategically. The reasoning is as follows. The integrated firm is not likely
to cut its prices in the downstream market when independent downstream firms are
purchasing inputs from it. Doing so would reduce the independent downstream firms’
sales, leading to a reduction in their demand for inputs and a corresponding reduction in
the integrated firm’s own profits. The integrated firm can maintain a higher price to the
independent downstream firms due to their incentives for strategic purchases. This makes
the integrated firm supply to its downstream rivals instead of foreclosing them.

The rest of the paper is organized as follows. Section 2 previews the basic

intuition. We illustrate the basic idea formally with a simple benchmark model in Section

asymmetries on input specifications. Section 5 compares our result in the intermediate

3. Section 4 introduces upstream cost uncertainty and analyzes the effects of ex post cost
good market with that in the final good market. We allow for endogenous decisions of
I

vertical integration in Section 6. And we conclude in section 7.

65

2. The Basic Idea

In this section we will illustrate the intuition behind our results before presenting
the formal model. Suppose that there exist two upstream firms, U1 and U2 , and two
downstream firms, D1 and D2. We assume that upstream firms engage in Bertrand
competition. Upstream firms, U1 and U2 , are initially assumed to choose the specialized
inputs designed for downstream firms, D1 and D2 , respectively, as in Figure 2-1.

Let us consider what happens if U1 switches its input specification to a
generalized input as in Figure 2-2. U1 can then sell to D2 as well as Dl. Since upstream
firms engage in Bertrand competition, the equilibrium price of the inputs for D2 will be
driven down to the marginal cost. As a result, U1 will gain no profit from the new market.
This seems to imply that the switch to a generalized input is neither beneficial nor
harmful to U1 .

But this answer is illusory. If we consider the effect on U1 ’8 own turf as well as
on U2 ’5 turf, we reach a different conclusion. The key logic here lies in the changes in
downstream market share. When both upstream firms chose a specialized input, each
charges a monopoly price to its respective captive downstream firm. Thus, the two
downstream firms have the same market share. But if U1 switches to a generalized input,
the price of inputs for D2 decreases due to competition while the price of input for D1
remains as high as before. D1 ’5 market share will then decrease in the downstream

market and U1 ’3 profits from its captive buyer, D1, will also decrease.

66

Figure 2-1. Initial Situation

 

 

U1

 

 

 

U2

 

 

 

 

 

 

 

Dl

 

 

D2

 

 

67

 

 

Figure 2-2. After Switch

 

 

 

U1

 

 

 

U2

 

 

 

D1

 

 

 

 

D2

 

 

68

 

 

3. A Simple Model
In order to formalize the basic idea in Section 2, we construct a simple model
based on the framework developed by Choi and Yi [2000]. We consider a model in which
there exist more than two upstream firms engaging in Bertrand competition. We assume
that two of the upstream firms, U1 and U2 , are more efficient than the others in the
sense that their marginal cost of production is lower. The two upstream firrns’ constant

marginal cost is assumed, for simplicity, to be zero. The others’ cost is c(> 0). The less

efficient firms can be considered the competitive fringes.l7 Upstream firms can choose to
produce generalized or specialized inputs. The choice of generalized inputs allows them
to supply any downstream firm. But if they choose specialized inputs, they can supply
only certain doWnstream firms.

In the downstream market there exist two firms, D1 and D2. They transform one
unit of the intermediate goods into one unit of the final goods and incur no other costs
except the input prices. The downstream equilibrium output and profit can then be
expressed simply as functions of the input prices paid to the upstream firms. We need
only the equilibrium output and profit for one representative downstream firm because

the two downstream firms are symmetric. For exposition, let us denote q(x, y) and
7r(x, y) the equilibrium output and profit respectively, where the first component (x)
refers to its own input costs and the second component (y) refers to the rival firm’s input

costs. We will not assume any specific downstream competition until we derive

equilibrium vertical structures.

 

'7 We can also assume that there exist inferior substitutes instead of competitive fringes.

69

We assume that c is not too large in order to avoid complexities in the efficient
upstream firm’s optimal pricing strategies. Let us consider a situation in which an
upstream firm has a captive downstream firm. If the upstream firm sets the input price at

x , its profits will be given by xq(x, y) where y is the other downstream firm’s input

cost. We assume that this upstream firm’s profit expression is a well-behaved concave

firnction. There then exists 2:: (y) that maximizes xq(x, y) for y 2 0. The Optimal input

price will be always c if c < x*(y) , for y 2 0.

We firrther assume that the vertical structure is not integrated. We will allow for
endogenous decision of vertical integration in Section 6. The timing of our simple
benchmark model is as follows. Upstream firms choose input specifications in the first
stage. We assume that if U1 (U2) chooses a specialized input, it is for D1 (D2 ). Input
prices are detemrined in the second stage. Finally in the third stage, downstream

equilibrium is determined.

Input Specification
Suppose that both U1 and U2 choose generalized inputs. Let us consider the input
market for BI (D2 ). The equilibrium price of inputs for D1 (D2) will be zero because
both U1 and U2 can supply to D1 (D2) and both engage in Bertrand competition. Then
both upstream firms will obtain no profit in the input market for Dl (D2 ).

Next let us consider the case in which U1 chooses a generalized input suitable for
both D1 and D2 but U2 chooses a specialized input suitable only for D2. In the input
market for D1 there then exists only one input supplier, U1 . U1 can, as a result, enjoy

monopoly power and charge c as an input price. Due to the existence of the competitive

7O

fringes, U1 cannot charge the prices above c. The equilibrium price of inputs for D2
will be equal to zero since both U1 and U2 can supply to DZ. In this case, U1 ’5 profit

is £5 = c x q(c,0) while U2 ’3 profit is zero.

Finally, consider the case in which U l chooses a specialized input for D1 and
U2 chooses a specialized input for D2 . Then there exists only one input supplier in the
input market for each downstream firm. Consequently U1 and U2 can charge the

monopoly price, c , to D1 and D2 , respectively. Thus they obtain the profit,

 

 

 

J = c x q(c,c).
Table 2-1. Upstream and Downstream Profits
In ut In ut
p p Profits
Specification Prices
U1 U2 D1 D2 U l U 2 Dl D2
G G O O 0 0 ”(0,0) n(0,0)
G S2 c 0 g1 0 7r(c,0) 7r(0, c)
S1 G 0 c 0 £1 7t(0, c) 7r(c,0)
S1 S2 c c J J 7r(c, c) n'(cs 0)

 

 

 

From Table 2-1, we can construct the payoff matrix for the choice of input
specifications (see Figure 2-3). The first and second element in each cell of the payoff

matrix represent the profit for U1 and U2 , respectively. As shown in Figure 2—3, the

71

generalized input is weakly dominated because 3 >9. Summarizing the above

discussion, we can draw the following proposition:

Proposition 1. The dominant strategy equilibrium is (S l , S 2) in the choice of input

specification, and the equilibrium profits are given by

NI N "
rIU1 =11U’2 =¢,and mg] =qu =7r(c,c). (1)

Figure 2-3. Payoff Matrix for Input Specifications

 

 

U2
G 52
a 0,0 {.0
U1
S1 0,11 17,5

 

 

 

 

4. Upstream Cost Uncertainty
In this section we introduce upstream cost uncertainty as an extension to our
simple model. It may be more natural in this case to reinterpret our model in terms of
R&D investment to improve inputs. For comparison with the final product market, we
will Change the setup of the basic model slightly. Suppose that the downstream firms, D1

and D2 employ different kinds of inputs which are not substitutable. With current

72

technologies, U1 and U2 can produce both kinds of inputs at the production cost of c.
Now upstream firms are considering whether to pursue alternative G (generalized
project) or alternative S (specialized project), where G represents an R&D investment
on basic technology to improve both kinds of inputs and S represents an R&D
investment on a specific technology to improve a specific kind of inputs. We assume that
the two projects incur the same costs.18

If the upstream firms succeed in a generalized project, they can produce both
kinds of inputs at a lower cost of 0. But if they succeed in a specialized project, they can
produce a specific kind of inputs at the cost of 0. The cost of production for the two
upstream firms takes two values, 0 and c , where c > 0. We have the following four
outcomes of cost realizations: ‘( c , c ), (c , O), (0, c ), and (0, 0). The probability

distribution is given by19

Pr(c,c) = Pr (0,0) = LEE, and

Pr(0,c) = Pr(c,0) = li—e,where O<p <1.

The parameter p represents the degree of cost correlation. Higher p implies a more
symmetric ex post cost structure. We further assume that p is not affected by the choice
of input specification.

The timing of our model with upstream cost uncertainty is as follows. Upstream
firms choose input specifications (or R&D projects) in the first stage. Input costs are

realized and observed publicly in the second stage. Given the cost realizations, input

 

lg . . . .
Thrs rs a conservatrve assumption.

'9 We introduce cost correlation in order to construct a more generalized distribution than the simple one
with equal probabilities.

73

 

prices for the downstream firms are then determined. Based on the given input prices, the

downstream equilibrium is determined in the final stage.

Input Specification

From Table 2-2 to Table 2-4, the upstream profits are given by

115% (G, G) = 1151, (G, G) = (Bijou?) (2)
nl’fi (51, G) = n 512(G,sz) = [1:43]; . (3)
ng{(G,sz) = ngg(s1,c)=(1-TP)(2J)+(1¥)2. (4)
1131 (51, S2) = n 2",”2 (s1, 52) = (30¢?) . (5)

Table 2-2. Upstream Profits Under Upstream Cost Uncertainty (G , G )

 

 

 

Cost Input
Profits
Realization Prices
U1 U2 D1 D2 U 1 U2
(1+ p)/ 4 c - c c c 0 0
(l — p) / 4 O c c c 2(3- 0
(1 — p)/4 c 0 c c 0 26
(1+ p)/4 0 O O 0 0 0

 

 

 

 

74

 

 

Table 2-3. Upstream Profits Under Upstream Cost Uncertainty ( S l , G )

 

 

 

Cost Input
Profits
Realization Prices
U1 U2 D1 D2 U1 U 2
(1 + p)/4 c c c c 0 0
(1 __ p) /4 0 c c c (if 0
(1 _ p)/4 c O c c O 247
(1 + p) /4 O 0 0 c 0 £5

 

 

 

 

Table 2-4. Upstream Profits Under Upstream Cost Uncertainty (S l , S 2)

 

 

 

Cost Input
. . . Profits
Realization Pnces
U l U 2 D1 D2 U l U 2
(1 + p) /4 c c c c O 0
(1 _ p) /4 0 c c c (17 0
(1 _ )0)/4 c 0 c c O J
(1 + p) /4 O 0 c c 4.1- W

 

 

 

 

Let us find equilibrium input specifications. We begin by assuming that the rival
firm’s choice is G . From (2) and (3), we find that it is always optimal to choose G

regardless of p. In this case, the choice of input specification does not depend on p.

75

 

But suppose that the other firm chooses a specialized input. The choice of input
specification does, in this case, rely on p. Comparing (4) and (5), we find that it is
optimal to choose a specialized input if

.. ¢
2 _— . 6
p>p (2%?) ()

 

We can easily prove that 0 < p* < l . From (2) and (5), we find that (Sl , S2) is pareto-

superior to (G , G) for both upstream firms.

Proposition 2. If p < p‘ , then (G , G) is the unique equilibrium input specification,

otherwise we have two Nash equilibria, (G , G ) and (S l , S 2 ).

The optimal choice of input specification actually depends on cost structures. If
two upstream firms have symmetric cost structures, it may be optimal to choose
specialized inputs. But when an upstream firm has cost advantages over the rival firm, it
is advantageous for the more efficient firm to choose generalized inputs. Since lower p
implies more asymmetric ex post cost structures, generalized inputs will be optimal when

p is low. But in the case of high p , specialized inputs will be more profitable.

5. The Final Product Market
In this section we will examine the strategic choice of R&D projects in the final
product market and compare the results with those in Section 4. Suppose that there exist

two final products, F l and F2 , that are not substitutable. In each market there are (0

persons, each of whom demands one unit. There exist two firms, A and B , which

76

 

compete on prices. With current technologies, they can produce both final products, F l
and F2 , at the production cost of c. In order to improve the production technologies, the
two firms are considering whether to make an R&D investment on a specialized project
(S ) or a generalized project (G). If the firms succeed in S , they can produce a specific
kind of final products at a lower cost of 0. But if they succeed in G , they can produce
both kinds of products at the lower cost of 0. We assume that the investment costs are
same for the two projects. We also assume that if A (B) chooses S , it is for the market
F 1 (F2 ). The distribution of cost realizations is assumed to be the same as in Section 4.

The timing is as follows. The two firms make choices about R&D projects in the
first stage. The outcomes of R&D are realized and production costs observed publicly in
the second stage. And the equilibrium prices for the final product markets are determined
in the final stage.

By backward induction we first derive the equilibrium prices and profits given

 

 

 

R&D projects.
Table 2-5. The Final Product Market (G , G)
Cost
2 2 Price Profit
Realrzatron

A B F1 F2 A B
(1 + p) /4 c c c c 0 O
(1- p) /4 0 c c c 2c¢ _ O
(1... p) /4 c 0 c c 0 2c¢
(1 + p)/4 0 0 0 O 0 O

 

 

 

 

77

Table 2-6. The Final Product Market (G , S )

 

 

 

Cost
. . Price . Profit
Realrzatron
A B F1 F2 - A B
(1 .1. p) /4 c c c c O 0
(1.. ,0)/4 0 c c C 26¢ 0
(1 _ p)/4 c 0 c c 0 c¢
(1 + p) /4 0 O c 0 C¢ O

 

 

 

 

 

Table 2-7. The Final Product Market (S , S )

 

 

 

Cost 1
1 . Price Profit
Realrzatron
A B F1 F2 A B
(1 + ,0) /4 c c c c 0 0
(1 _ p)/4 0 c c c C¢ O
(1 _ p) /4 c 0 c c 0 c¢
(1 ... p) /4 0 0 c c c¢ c¢

 

 

 

 

From Table 2-5 to Table 2-7, the firms’ profits are given by

HA(G.G) = new. G) = (ifltzcm. (7)

78

 

HA(S,G)=HB(GsS)=(1;p)(C¢)- (8)

 

r1A(G.S)= 11309.0) = (FTPJQCPW flees). (9)

HA(S,S) =HB(S,S) =G)(ZC¢). (10)

From (7) to (10), we could obtain the following Proposition 3:

Proposition 3. When the two final product markets are not substitutable, the dominant

strategy is to choose the generalized project (G) regardless of p.

Why the different conclusion between the intermediate good market (Proposition
2) and the final product market (Proposition 3)? The reason is as follows. If the two final
products are not substitutable, the markets for the two final products are independent and
thus a firm’s choice of generalized projects has no negative effects on the profits in its
own turf (see Figure 2-4). In the intermediate good market, however, even if the two
products are not substitutable, the two intermediate goods markets might be dependent
through the downstream final product market (see Figure 2-5). In this case, the choice of
generalized projects lead to the decreases in the profits from the captive downstream

buyers.

'79

Figure 2-4. Final Product Markets

 

 

 

F1 F2

 

 

 

 

 

 

Figure 2-5. Intermediate Good Markets

 

 

 

ll 12

 

 

 

 

 

 

 

 

 

 

 

 

80

 

6. Endogenous Vertical Structures

In this section we introduce vertical integration decisions into the simple model
from Section 3. The timing is as follows. In the first stage, U1 and D1 decide whether or
not to merge. U2 and DZ simultaneously make a decision about merging. Upstream
firms choose input specifications in the second stage. Input prices are determined in the
third stage. And downstream equilibrium is determined in the fourth and final stage.

The equilibrium input specifications are first derived by backward induction given
the vertical structures. Since we have examined input specifications under non-
integration in Section 3, let us deal with partial integration and full integration in this

section.

Partial Integration
Consider the situation in which U1 and D1 integrate vertically while U2 and D2
remain independent firms. Suppose that the integrated firm U1 — D1 chooses a
specialized input. The independent upstream firm, U2 , then becomes the only input
supplier to the independent downstream firm, D2 . This will allow U2 to enjoy
monopoly power and enable it to charge a monopoly price to D2. Thus the choice of a
specialized input by the integrated firm can foreclose its downstream rival and raise its
costs (see Table 2-8). 1

As shown in Figure 2-6, the choice of a specialized input is the dominant strategy
for the integrated firm, U1 — Dl. The choice of input specifications for U2 actually
becomes irrelevant if the integrated firm chooses a specialized input. Under partial

integration the equilibrium profits are given by

81

 

 

 

 

HELD] =7r(0,c), r1{}’2 =Q,and 115’2 =7r(c,0). (11)
Table 2-8. Profits under Partial Integration
In ut In ut
. p 1 p Profits
Specrficatron Pnces
U1 - U2 D1 D2 Ul—Dl U2 D2
G G O O 7r(O,O) O ”(0.0)
G S2 0 0 7r(0,0) 0 ”(0,0)
S l G 0 c 7r(0,c) (if 7r(c,0)
S 1 S2 0 c It(0,c) Q n(c,0)

 

 

 

Figure 2-6. Payoff Matrix for Input Specifications under Partial Integration

Ul-Dl

 

 

U 2
G S2
G ”(0.0) ,0 no.0) .o
51 Me) .g n(0.c) .g

 

 

 

 

82

 

Full Integration

Under full integration, the upstream divisions of the two integrated firms supply to their
downstream divisions at the internal transfer price equal to the marginal cost. The input
prices for D1 and D2 are then always equal to zero and the two integrated firms,

U1 — D1 and U2 — D2 , obtain the same profits of 7t(0,0) regardless of their choices of
input specifications. This implies that the choice of input specifications becomes

irrelevant to the integrated firms under full integration. The equilibrium profits under full

integration are given by

r111311—131 = 1752—02 = ”(0,0). (12)
Hotelling Competition

In order to derive the equilibrium vertical structures, we will specify downstream
competition. We assume that downstream firms engage in Hotelling competition. We

first express the downstream equilibrir'un quantities and profits as a function of c,- and

cj , where ci is the downstream firm’s own cost and cj is its rival’s cost.

(6} ‘00
6t

9

l
q(Ci,Cj) =54-

 

2
t +(cj-ci)+(cj"ci) .

7: ~, - =— 13
(610,) 2 3 18’ ( )

In (13), the parameter of t represents the transportation costs.
We have assumed in the previous section that c is not too large in order to
simplify the equilibrium input prices. As the next step, we specify the range of c.

Upstream firms will charge c as an input price to their captive downstream firms if

83

c<%. (14)

From (13) and (14), we can obtain the following profits:

2 2
I t C C t C C
7rc,c =7r 0.0 =—. 7r ,0 =———+——, n0,c =—+—+——,
()()Z(C)2318t()2318t
975-5 audit-3mg?- (15)
2’ — 2. 61'

Now let us examine the incentive to integrate. We will show that it is the

dominant strategy not to integrate vertically. First, suppose that U2 and DZ do not

merge. U1 and D1 will then decide whether to merge or not by comparing I151 + Hg:

with “(171—01 . From (1), (11), and (15),

- l C
1151 +11% =¢ +7r(c,c)=E+-2—. (16)
n” —7r(0c)——’—+3+-c—2— (17)
UH” ’ 2 3 181'

Comparing (16) and (17), we find that
mg; .1151 > n51,_,,,, for c g (18)

Next consider the case where U 2 and D2 merge. U1 and D1 will then decide whether

to merge or not by comparing 1151 + 11511 with “51—01 . From (1 l), (12), and (15), we

reach
PI PI PI P] t c 2c2
- 2 6 181
t
“51-01 = ”(0,0) = 2' (20)

84

Comparing (19) and (20), we can see that
my, .1151, > 115101;... “22: (20

Equations (18) and (21) imply Proposition 4.

Proposition 4. The equilibrium vertical structure is non-integration when the

downstream firms engage in Hotelling competition.

The intuitive explanation for Proposition 4 is as follows. One of the roles of
vertical integration is to lower the integrated firm’s own downstream costs by eliminating
double marginalization. The integrated firm’s lower cost leads to its lower downstream
price. Since prices constitute strategic complements (Bulow, Geanakoplos, and
Klemperer [1985]), the downstream rival also decreases its price, which, in turn, causes a
negative effect on the integrated firm’s downstream profits. This strategic complement

effect compels downstream firms not to integrate backwards.20

Consumer Welfare

When upstream firms choose specialized inputs under non-integration, the equilibrium
input price and consumer price will be c and t + c , respectively. But if upstream firms
choose generalized inputs, the equilibrium input price and consumer price will be zero
and t , respectively. The choice of specialized inputs causes an increase in consumer

prices and decreases consumer welfare.

 

2° In contrast, Coumot quantity competition has the strategic substitute effect. This effect makes the
vertical structure fully integrated. In this case the choice of input specifications becomes irrelevant.

85

 

 

An interesting conclusion from our model is that double marginalization is not
caused by non-integration but by the choice of specialized inputs. If upstream firms
choose generalized inputs, the equilibrium input price will be equal to marginal costs

even. under non-integration.

7. Concluding Remarks

In this paper we have shown that it may be privately and collectively profitable
for upstream firms to specialize in successive vertical oligopolies. These results,
however, rely on two assumptions. First, we have assumed that cost correlation is
independent of input specifications. Otherwise it may not be an equilibrium input
specification for both upstream firms to choose specialized inputs. 2‘ Second, downstream
product differentiation is assumed to be exogenous. But if we allow for an endogenous
choice of downstream product differentiation as in Belleflamme and Toulemonde [2002],

we might have different results. 22

 

2’ A case can be found in Choi and Yi [2000].

22 Belleflamme and Toulemonde [2002] examine downstream product differentiation in successive vertical
oligopolies. They have shown that downstream firms select a particular variety of product, and upstream
firms specialize in the production of one input designed for that variety. In spite of some loss of profits
from intensified competition, downstream firms choose less differentiated products because they can obtain
inputs at lower prices.

86

References

Baba, Y., Takai, S., and Mizuta, Y. [1995] “The Japanese Sofiware Industry: The ‘Hub
Structure’ Approach.” Research Policy, 24, pp. 473-486.

Belleflamme, P. and Toulemonde, E. [2002] “Product Differentiation in Successive
Vertical Oligopolies.” mimeo.

Bonanno, G. and Vickers, J. [1988] “Vertical Separation.” Journal of Industrial
Economics, 36, pp. 257-265.

Bulow, J.I., Geanakoplos, J.D., and Klemperer, PD. [1985] “Multimarket Oligopoly:
Strategic Substitutes and Complements.” Journal of Political Economy, 93, pp.
488-511.

Chang, M.H. [1993] “Flexible Manufacturing, Uncertain Consumer Tastes, and Strategic
Entry Deterrence.” Journal of Industrial Economics, 41, pp. 77-90.

Chen, Y. [2001] “On Vertical Mergers and Their Competitive Effects.” Rand Journal of
Economics, 32, pp. 667-685.

Choi, J .P. and Yi, S-S. [2000] “Vertical Foreclosure with the Choice of Input
Specifications.” Rand Journal of Economics, 31, pp. 717-743.

d’Aspremont, C., Gabszewicz, J ., and Tisse, J.-F. [1979] “On Hotelling’s Stability in
Competition.” Econometrica, 17, pp. 1 145-1151.

Eaton, BC. and Schmitt, N. [1994] “Flexible Manufacturing and Market Structure.”
American Economic Review, 84, pp. 875-888.

Mansfield, E. [1993] “The Diffusion of Flexible Manufacturing Techniques in Japan,
Europe and the United States.” Management Science, 39, pp. 149-159. .

Nocke, V. and White, L. [2003] “Do Vertical Mergers Facilitate Upstream Collusion?”
mimeo.

Norman, G. and Thisse, J.-F. [1999] “Technology Choice and Market Structure: Strategic
Aspects of Flexible Manufacturing.” Journal of Industrial Economics, 47, pp.
345-372.

Rey, P. and Stiglitz, J. [1995] “The Role of Exclusive Territories in Producers’
' Competition.” Rand Journal of Economics, 26, pp. 431-451.

87

 

Roller, L-H. and Tombak, M.M. [1990] “Strategic Choice of Flexible Production
Technologies and Welfare Implications.” Journal of Industrial Economics, 38, pp.
417-431. .

88

CHAPTER 3

A MODEL OF VERTICAL INTEGRATION WITH UPSTREAM COST

VARIABILITY

89

 

 

1. Introduction

One issue in the literature on vertical integration is whether vertical mergers will
be profitable. This paper examines this issue in the presence of upstream cost variability.
We consider an environment in which idiosyncratic cost shocks lead to cost differences
between upstream firms. Idiosyncratic cost shocks are produced by innovation, for
example. Suppose that the upstream industry is highly innovative.23 In this case it will not
be uncommon that upstream firms have different production costs. We will examine the
issue of private versus collective profitability of backward integration under these
circumstances.

An interesting conclusion in our paper is that equilibrium outcomes may result in
a Prisoner’s Dilemma: it is privately profitable for downstream firms to integrate
backwards, but not collectively. The Prisoner’s Dilemma usually occurs because a
player’s behavior has external negative effects on the rival. In our model, backward
integration generates negative extemalities between downstream firms by transferring
cost asymmetries from the upstream industry to the downstream industry.24 A
downstream firm has the private incentive to integrate backwards because it is able to
lower its costs and thus gains cost advantages in the downstream market. The fact that a
firm has cost advantages implies that a rival firm has cost disadvantages. Even though
backward integration does not affect the rival’s costs, it may have negative effects on the

rival’s profits by making asymmetric the cost structure in the doWnstream market.

 

’3 The biotechnology industry is an example of a highly innovative upstream industry. Many
biotechnology specialty firms were founded in the 19705 and 19805. They have provided new
biotechnologies for established chemical and pharmaceutical firms (Pisano [1991]).

2‘ Spengler [1950] has shown that in successive monopolies, vertical integration can eliminate the
extemalities, e. g., double marginalization, between the upstream firm and the downstream firm.

90

 

 

Our article relates to Ordover, Saloner, and Salop [1990] in that backward
integration leads to a Prisoner’s Dilemma.25 In their model, the independent downstream
firm suffers because the integrated firm forecloses and raises its input cost. But the
foreclosing downstream firm also suffers. Although its gross profits are increased as a
result of the merger, its net- acquisition-cost-profits are lower than they would be without
vertical merger. This is because the fear of being foreclosed drives the acquisition price
up until the foreclosing downstream firm’s net profits are exactly equal to the foreclosed
downstream firm’s. Even though our article shares the conclusion that vertical mergers
display characteristics of the Prisoner’s Dilemma, our study differs in two areas. The first
difference lies in the type of equilibrium vertical structure in which the Prisoner’s
Dilemma occurs. While their equilibrium vertical structure is under partial integration,
where only one downstream firm acquires an upstream firm, ours is under full integration,
in which both downstream firms integrate backwards. The second and more important
difference lies in the reason for the existence of the Prisoner’s Dilemma. In their model,
the Prisoner’s Dilemma occurs because the fear of being foreclosed increases the
acquisition price. But in our model, the Prisoner’s Dilemma occurs because backward

integration creates negative extemalities by transferring cost asymmetries.

 

2’ Some other authors show that a different type of Prisoner’s Dilemma may arise in successive vertical
oligopolies (Greenhut and Ohta [1979], Lin [1988], Salinger [1988], Gaudet and van Long [1996], and
Abiru et al. [1998]). In their models, a Prisoner’s Dilemma means that vertical mergers may reduce the
joint profits of the merging firms. While they focus on the effects of vertical mergers on joint profitability,
we concentrate on the impact of backward integration on downstream firms’ net profitability. Another
difference lies in the types of competition. They assume that upstream and downstream firms engage in
quantity competition. In our model and in Ordover, Saloner, and Salop [1990], however, price competition
is assumed.

91

 

Our article also relates to the model of vertical integration with upstream cost
uncertainty developed by Choi [1998].26 Vertical integration in his model changes the

information structure available to the downstream competition. Under non-integration,

 

downstream firms compete With perfect information about their rival’s costs because
inputs are openly traded in the market and both downstream firms’ input costs are thus
publicly observed. But when the integrated firm trades internally, its input costs become
private information. The latter case becomes a Bayesian game with imperfect information.

We assume in this paper, however, that after the upstream costs are realized, both

 

a
V~

downstream firms’ input costs are publicly observed even under vertical integration.
Based on that assumption, we focus on another role of vertical integration. Vertical

integration in our model changes the cost structure in downstream competition. Both

 

downstream firms’ ex post cost structures under non-integration are always symmetric
since the efficient upstream firm sells inputs to the downstream firms at the market price.
‘ But under vertical integration, the cost structure in downstream competition may become
asymmetric.

We also consider the implications for antitrust policy. Suppose that two firms
decide sequentially whether or not to enter the downstream industry. We can think of the
two alternate policy regimes: one allows vertical integration and the other prevents it.
How many firms will enter the downstream industry in each regime? When there exists a
Prisoner’s Dilemma, it might be possible that the second firm enters in the prevention
regime while it does not in the allowance regime. The reason is that downstream net

profits are higher under non-integration than under firll integration.

 

2‘ Carlton [1979] also examines the incentives for vertical integration under uncertainty. But in his model
there exists downstream demand uncertainty. He shows that supply assurance can be a strategic motive for
vertical integration.

92

Our article relates to the foreclosure literature in terms of antitrust policy
implications. In the first category of the foreclosure theory, there is no upstream, non-
integrated supplier. If the integrated firm limits its supply, a downstream entrant has to
establish an upstream firm in order to obtain the necessary inputs. This will raise the
amount of capital required for entry and thus increase the difficulty of entry (Comanor
[1967]). The second category of foreclosure theory introduces an independent upstream
supplier into the model. In this case, if the integrated firm does not supply its inputs to a
downstream entrant, the independent upstream firm becomes the unique supplier to the
downstream entrant. The independent supplier can then enjoy monopoly power and raise
the price of essential inputs (Ordover, Saloner, and Salop [1990], Choi and Yi [2000]).
Vertical integration can deter entry by raising the costs obtaining necessary inputs (Sa10p
and Scheffrnan [1983]).27 We find from the foreclosure literature that when the
possibility of vertical foreclosure exists, divestiture can be pro-competitive by
encouraging entry. The difference between our article and the foreclosure literature lies in
the mechanism through which antitrust enforcement encourages entry. Prohibition of
vertical integration as cited in the foreclosure literature facilitates the potential entrant’s
access to essential inputs. But in our model, divesting the integrated firm eliminates the
negative extemalities between downstream firms caused by backward integration.

It is interesting to compare our article with Kuhn and Vives [1999]. While our

article and the foreclosure literature focus on the case in which divestiture may enhance

 

27 McAfee [1999] has shown that vertical integration can lower rival’s costs. A key assumption in his
model is that the intermediate goods are imperfect substitutes. Now suppose that a downstream firm
integrates backwards. The downstream division of the integrated firm then increases demand for the inputs
provided by its upstream division due to easier access to those inputs. This reduces demand for conrpeting
inputs produced by the independent upstream supplier. A decrease in demand for competing inputs tends to
lower their prices and in response, the integrated firm also lowers the price for its inputs. The prices of all
inputs are decreased as a result.

93

welfare, Kiihn and Vives [1999] concentrate on the case in which the prohibition of
vertical integration may reduce welfare. They analyze the welfare effects of vertical
integration when the downstream industry is monopolistically competitive. Vertical
integration in their model has two effects: output and variety. Vertical integration tends to
increase output due to the elimination of double marginalization. But the integrated firm
generates less variety than disintegrated downstream. In their model as in our model,
vertical integration also restricts downstream entry. But they show that the reduction in
variety can enhance welfare. They identify the consumer preference conditions under
which the variety provided by disintegrated downstream is excessive in terms of welfare.
Vertical integration can eliminate excess entry under these conditions and thus enhance
welfare.

The remainder of this paper is organized as follows. Section 2 previews the basic
idea and Section 3 sets up the basic model. We derive the market equilibrium and prove
the existence of the Prisoner’s Dilemma in Section 4. We transform the basic model into
an incumbent-entrant framework in Section 5 and analyze the effects of divestiture on
downstream entry. In Section 6, we introduce cost correlations into the basic model.

Section 7 concludes.

2. The Basic Idea
We illustrate the basic idea in this section before presenting the formal model.
Suppose that there exist two upstream firms, U1 and U2 , and two downstream firms,

D1 and D2. Let us see what benefits and costs downstream firms have when they

94

integrate backwards. When a downstream firm, D1, acquires an upstream firm, U1, D1
has two benefits. Those benefits occur when U1 is ex post more efficient than the
competing upstream firm, U 2 . Since D1 obtains inputs from U1 at the internal transfer
price, D1 has a cost advantage over D2 in the downstream competition. And when

U1 ’s realized cost is lower than U2 ’s, 01 can obtain additional upstream profits by
selling U1 ’8 inputs to its downstream rival, DZ. If the value of these two benefits
exceeds the acquisition cost, the downstream firm has the private incentive to acquire an
upstream firm.

But both downstream firms’ backward integration may not be collectively
profitable even though the two benefits exceed the acquisition costs. This is because a
factor exists that does not affect the private incentive to integrate backwards but does
have negative effects on collective profitability. Backward integration creates negative
extemalities between the downstream firms. What type of negative extemalities exists in
our model? Suppose that U1 succeeds in R&D and has a lower cost while U2 fails in
R&D and has a higher cost. The efficient upstream firm, U1, will sell inputs to both
downstream firms at the price of E under non-integration (see Figure 3-1). Both
downstream firms will have symmetric cost structures in downstream competition. But
under full integration they have the asymmetric cost structures shown in Figure 3-2. The
reason is that U l supplies D1 at the internal transfer price but provides to D2 at the
market price. In this case, DZ has a cost disadvantage in downstream competition. But
DZ does not have such disadvantage under non-integration.

A downstream firm’s backward integration does not decrease the rival firm’s

profits by raising the rival’s costs but rather by lowering its own costs and thus

95

 

generating cost asymmetries. This implies that we do not have negative extemalities

when the two downstream products are independent.

Figure 3-1. Non-integration

 

 

 

 

 

 

 

 

 

U1 U2
(9) (E)
‘7

D1 D2
(E) (E)

 

 

 

 

 

 

96

 

Figure 3-2. Full Integration

 

 

U1 . U2
(9) (E)

 

 

 

 

 

 

 

3. The Basic Model

There are two upstream firms, U l and U 2 . They produce homogenous inputs
and engage in price competition. We assume that upstream firms’ production costs are
uncertain. For instance, upstream cost uncertainty can be generated when upstream firms
undertake uncertain R&D. To simplify the analysis, let us assume that the cost of
production takes only two values, 0 and c , where c > 0. Then four outcomes of cost
realizations are possible: (c , c ), (c , 0), (0, c ), and (0, 0). For simplicity we further
assume that each outcome is realized with an equal probability.

The upstream firms supply homogenous inputs to downstream firms, D1 and D2.

The downstream firms produce differentiated products and use prices as their strategic

97

variables. Both downstream firms transform one unit of the intermediate good into one
unit of the final good, and they are assumed to incur no costs other than the input prices
they pay to the upstream suppliers. Then the equilibrium output and profit can be
expressed as functions of input prices they pay to the upstream firms. Since the two
downstream firms are symmetric, we need only the equilibrium output and profit for a

representative downstream firm. For exposition, let us denote q(x, y) and 7t(x, y) the
equilibrium output and profit, respectively, where the first component (x) refers to its

own input costs and the second component (y) refers to the rival firm’s input costs.

 

We assume that the cost differential, c , is not too large in order to simplify the
monopolistic input supplier’s optimal pricing strategy. Consider a situation in which
U1 ’5 realized cost is 0 but U 2 ’s is c under non-integration. Then since U1 is more
efficient, it will sell inputs to both downstream firms. If U1 set the price of the input at x ,

U1 ’5 profit is given by Z(x — 0)q(x, x). We assume that this profit function is thewell-

behaved concave function. Then there exists x* that maximizes 2(x — 0)q(x, x) . Next,

suppose that U1 and D1 integrate vertically. Then when U1 ’3 realized cost is O and
U 2 ’s is c , the upstream division of the integrated firm, U1, supplies inputs to its
downstream division, D1, at the internal price, 0, and sells inputs to D2. If U1 — D1 sets

the selling price at x , its profit is given by 7I(0, x) + (x — 0)q(x,0). We also assume that
this profit function is concave. Then we have x“ that maximizes 7r(0, x) + (x —- 0)q(x,0) .

Let us restrict our attention on the case in which c < min {x* , xn} . The input price will

then be always set at c when the upstream cost structure is asymmetric.

98

The timing of the basic model is as follows. In the first stage, D1 decides whether
or not to acquire U1, and D2 simultaneously decides whether or not to acquire U 2 . In
the second stage, input costs are realized and observed publicly. Given cost realizations
and the industry structure, input prices for the downstream firms are determined. In the

final stage, the downstream equilibrium is determined given input prices.

4. The Prisoner’s Dilemma
In this section we derive the market equilibrium of the basic model and show that
the game has a structure similar to the Prisoner’s Dilemma. We prove the existence of the
Prisoner’s Dilemma with the assumption of linear demand in the final product market.
But before that, we first analyze using general expressions without making a specific
assumption about the final demand functions. This will help us to understand why the

Prisoner’s Dilemma situation can occur.

General Expressions
By backward induction we first derive the equilibrium prices and profits given the

vertical structure before examining the incentive to integrate vertically. .

Non-integgrtion: When the outcome of cost realization is symmetric (( c , c) or (0,0)), the
equilibrium input will be equal to the marginal cost because two upstream firms engage
in Bertrand competition. In this case the upstream firms’ profits are zero. But when the ex
post cost structure is asymmetric, the efficient upstream firm sells inputs to the

downstream firms and obtains positive profits. For instance, consider the case in which

99

U1 ’5 realized cost is 0 and U 2 ’s is c. Under the assumption of c < min {x*,x“} , U1

will set the input price at c and has the profit of 2(3 = Zcq(c,c). From Table 3-1, we can

calculate the expected profits for the upstream and downstream firms under non-

 

 

 

 

 

 

 

integration.
1 _
r131 41372 =Z[2¢]. (1)
1
11% = my, = Z[37:(c,c) + ”(0,0)1. (2)
Table 3-1. Profits under Non-integration
Cost Input
Profit
Realization Cost
U1 U2 D1 D2 U1 U2 D1 D2
1/4 c c c c 0 O 7t(c,c) 7r(c,c)
1/4 0 c c c 23* 0 ”(c, c) fl'(C, c)
1/4 c 0 c c 0 23* rt(c, c) 7t(c, c)
1/4 0 0 0 0 0 0 7t(0,0) 7r(0,0)
* 47 = cq(c.c).

Partial integration: Consider a case where U1 and D1 integrate vertically while U 2 and
D2 remain as the independent firms. Comparing with non-integration, we can find that
there exists a difference in the downstream cost structure when the upstream division of

the integrated firm is ex post more efficient than the other upstream firm. This case is

100

matched to the outcome of cost realization where U1 ’5 realized cost is 0 and U 2 ’s is c

in Table 3-2. Since U1 supplies inputs to D1 at the internal transfer price, D] ’5 input

cost is 0. Meanwhile, U1 — D1 also sells inputs to D2 because U I has a cost advantage

over U 2 . Under the assumption of c < min {x* , xfl} , U1 - D1 will set the selling price

at c. From Table 3-2, we can derive the profits for each firm under partial integration.

 

 

 

115L121 = :11-[71'(c,c) + 7t(0,c) + 21+ 7r(c,c) + n(0,0)] . (3)
1 _
1153 = 212151. (4)
PI 1
IT DZ = Z[7r(c, c) + 7r(c,0) + 7t(c,c) + 7t(0,0)] . (5)
Table 3-2. Profits under Partial Integration
Cost Input
Profit
Realization Cost
U1 U2 D1 DZ Ul—Dl U2 DZ
1/4 c c c c 7t(c,c) O 7r(c,c)
1/4 0 c 0 c ”(0, c) + £1” 0 7:(c,0)
1/4 c 0 c c ”(6, C) 23 ”(6.6)
1/4 0 0 O 0 7r(0,0) 0 ”(0,0)

 

 

 

 

** £5 = cq(c,0).

101

 

Full integration: From Table 3-3, the expected profits for the integrated firms under full

integration are given by

1
HELD, = 1152,22 = Z[7r(c,c) + 7r(0,c) + g + 7t(c,0) + n(0,0)] . (6)

Table 3-3. Profits under Full Integration

 

 

 

Cost Input
_ _ Profit

Realrzatron Cost

U1 U2 D1 D2 Ul—Dl UZ—DZ
1/4 c c c c 7r(c,c) 7r(c,c)
1/4 0 c 0 c 7r(0, c) +£ 7r(c,0)
1/4 c 0 c o 7t(c,0) ”(0.c) +13
1/4 0 0 0 ' 0 7r(0,0) 7r(0,0)

 

 

 

 

Now let us examine the indentives to integrate vertically. We first analyze D1 ’5

incentives. Suppose that U 2 and D2 does not integrate. Then U1 and D1 will merge if
n5’1_m> r151 +1131. (7)
Next suppose that U 2 and D2 integrate. Then U1 and D1 will merge if

1151-01 >Ht’7t +1151. (8)

102

Using H511 = H512 and [1511 = H512 from the symmetries of the firms, substituting (1) ~

(6) into (7) and (8), and rearranging, we find that U1 and D1 will merge regardless of

U 2 and D2 ’s merging decision if

1 1 1 _
2[”(0,C)-”(C,C)l+zé>212¢l~ (9)

When (9) is satisfied, it is the dominant strategy for U l and D1 to integrate
vertically. Equation (9) can be interpreted as follows. In (9), the left-hand side means the
two benefits that the downstream firm can obtain from the acquisition of an upstream
firm. Those benefits occur when U1 is ex post more efficient than U 2 . Since U1
supplies inputs to D1 at the internal transfer price, D1 has a cost advantage over DZ.

This downstream gain is reflected in the first bracket term, [7r(0, c) — 7t(c, c)]. And also
the integrated firm obtains the profit of Q through selling inputs to the other downstream

firm. This upstream business gain is the second benefit. Since the independent upstream
firm’s expected profits are (l/4)[Z$] , the downstream firms should pay that amount in

order to acquire an upstream firm. Therefore, the right-hand side in (9) means the
acquisition costs. Since the firms are symmetric, it is also the dominant strategy for U2
and D2 to integrate vertically when (9) is satisfied.

Now let us compare the net expected profits for the downstream firms under full
integration with those under non-integration. Under full integration the net expected

profits for the downstream firms are given by

HELDI em?) = 11mm) + 7r(0,c) + 21+ 7r(c,0) + ”(0,0) — 261. (10)

103

Comparing (Z) and (10), we find that the net expected profits for the downstream firms

are lower under full integration than under non-integration if
1 1 1 — 1
2171(0, 6) - 71(6.6)] + if“ KIM] + 3046.6) - ”(0.0)]- (11)

In equation (11) all terms except the last term exist in equation (9). The last term
represents a decrease in a downstream firm’s profits caused by the other downstream
firrn’s backward integration. In our model vertical mergers generate the negative
extemalities between the downstream fums. Equation (11) implies that if the negative
extemality and acquisition costs are greater than the two benefits from vertical
acquisitions, the net expected profits for the downstream firms under full integration are
less than under non-integration.

When both (9) and (11) are satisfied, the game has a Prisoner’s Dilemma structure.
In order to prove the existence of the Prisoner’s Dilemma, we will assume linear demand

in the final product market.

Linear Demand
We assume that the demand functions in the final product market are given by

qi=1—p,—+bpj,wherei,j=1,2,j¢i,and O<b<1. (12)

By backward induction we first derive the downstream equilibrium given the input prices.
Since the downstream firms are symmetric, we can write the equilibrium downstream
prices and outputs as follows:

(2+b)+2a+b,6

p(a.fl) = 2
4—b

 

9

104

 

(2+b)-(Z-b2)a+b,B
4—b2

 

q(a./3) =

, where a is a downstream firm’s

own input cost and ,B is its rival’s input cost. (13)

Next, we calculate x* and x“ in order to simplify ”the monopolistic input

supplier’s optimal pricing strategy. Suppose that the input supplier sets the input price at

x. Then we can derive x: and x“ from the following equations, respectively:

 

 

 

312xq(x.x)1=0. (14)
6x
a
—[7r(0, x) + xq(X.0)] = 0- (15)
0x
Solving (14) and (15),
... I
x = , (16)
Z(l—b)
_ 3
x : 8+8b2 b 4 . (17)
2(8—7b +b )
Comparing (16) and (17), we find that
_ 3
“8be 4 s 1 ,where0<b<1. (18)
2(8—7b +b ) 2(1-b)
From (18), we assume that
8+8b—b3
(19)

 

C_ .
2(8—7b2+b4)

When (19) is satisfied, the monopolistic input supplier will set the input price at c.

105

Under the assumption that cost differentials are not too large, the upstream and

downstream profits are given by

 

Z
”(6,6):[(2+b)—(Z+b)(1—b)c] ,

 

 

 

 

4—b2
2
,(0,,)-[12_~;0:2121,
4—b
2 Z
”(C,O)=[(2+b)—(2—b )c] ,
4—b2
2
7r(0,0)=[(2+b)] ,
4—b2
J = (Z+b)c—(Z+b)(1—b)c2
4—b2 ’
2 2
£=(Z+bk-(Z—b)c . (flD

4—b2

Substituting (20) into (9) and rearranging, we can find the following condition

under which it is the dominant strategy for a downstream firm to integrate backwards:

2 3
c> 2b +b (2])

—4—4b—2b2 7

 

Substituting (20) into (11) and rearranging,

4b+4b2+b3
c<

_ . (2»
4—31;2 -2b3

 

When (22) is satisfied, the downstream firm’s net profits are lower under full integration

than under non-integration.

106

Calculating the parameter regions that satisfy (19), (21), and (22), we could obtain

the following proposition:

Proposition 1. The game has a Prisoner’s Dilemma structure if

2 3 2 3
2b +b Scs 4b+4b +b

4—4b—sz 4b—3b2—Zb3,

 

 

for OSbSO.46,

2b2+b3 (C 8+8b—b3
4-4b—Zb2— —Z(8—7b2+b4)

/\

, for 0.46 S b S 0.6.

 

 

In Figure 3-3, the region of A represents the area in which the Prisoner’s Dilemma occurs.

Figure 3-3. The Prisoner’s Dilemma

1.5

1.25

0.75

0.5

0.25

 

 

 

107

5. Antitrust Policy

In this section we modify the basic model to show a case where divestiture can
encourage entry. There exist an integrated firm, U1 — D1, and an independent upstream
firm, U 2 in the modified model. A potential entrant, DZ , considers whether or not to
enter the downstream industry. When DZ enters the market, it incurs a fixed cost, K .
The timing of the modified model is as follows: In the first stage, the potential entrant,
DZ , decides whether or not to enter. If DZ enters the downstream market, D2 decides
whether or not to acquire U 2 . In the second stage, input costs are realized and observed
publicly. Given cost realizations and the industry structure, input prices for the
downstream firms are determined. In the final stage, the downstream equilibrium is
determined given input prices.

Let us restrict our attention to the parameter region where the Prisoner’s Dilemma
occurs in the basic model. If the game has a Prisoner’s Dilemma structure, downstream

firm’s net profits under full integration are less than those under non-integration
(Hf/724” - (1/4)[2¢I] < mg], ). Now suppose that 115202 - (1/4)[2$1 < K < nfi’z.

Under this assumption we examine the effects of divestiture on downstream entry. First,

consider the regime in which vertical integration is allowed. If D2 enters, it will

integrate backwards and obtain the net profits of 11512432 — (l/4)[Z¢T] . Since its net

profits are less than the fixed entry cost, D2 will not enter in the allowance regime. Next,

suppose that divestiture is implemented and vertical integration is prevented. In this

prevention regime, if DZ enters, it will obtain Egg. Since K < IT 19%. , D2 will enter.

108

6. Cost Correlation
In the basic model, we have assumed that each outcome of cost realizations has an
equal probability. But in some industries the cost of production may have high
correlations between firms. For instance, if production costs mainly depend on the price
of raw materials, their correlations will be high. In this section we assume the distribution

of cost realizations as follows:

Probability of (c,c) = Probability of. (0,0) = l—Z—P— , and

Probability of (0,c) = Probability of (c,0) = 1&8,

where 0<c and 0<p<1.
Now let us examine the incentives to integrate. First, suppose that U 2 and D2 do

not merge. In this case U1 and D1 decide whether to merge or not by comparing

N1 N] P]
HUI +HDI and nu1_D1.

 

, 1— — 3— 1+
“51 +1151 LIP—[2111+ 4" ”(c,c)-«711M001. (23)
2 1 — 1+
115101 = 2m, mar—231nm, c) +g1+7£n(0,0). (24)
From (23) and (Z4),
1.. _
1151 +1151 -—rr{;’l_Dl =7312¢ +7t(c,c)—7r(0,c)-Q]. _ (25)

Next suppose that U 2 and DZ merge. U1 and D1 decide whether to merge or

not by comparing H511+IISII (=H5’2 +I'IEIZ ) and “flit—Dr-

109

11171 + 115’1 = 1313-1221 + i—rflc, c) + :43 7r(c,0) + if—n(0,0) . (26)

l_1U11—Dlz 1L4-7I(C,C)+l—4-—[7I(O,C)+¢]+-1—4—7[fl(c,1—-+—-0)+ 4 p,7t(0 0). (27)
From (26) and (27),

[11‘7”an 115101: —1 ——p4[2¢+7t(c,—c) 7r(0,c)— p]. (28)

We can find that equation (28) is exactly same as equation (25). But the sign of

both equations do not depend on p. As a result, we can draw the conclusion that the
incentive to merge does not depend on p.

Table 3-4 shows the struCture of input costs given the vertical structures. When
the outcome of cost realizations is (c,c) or (0,0) , the three different vertical structures
have the same input cost structures. This implies that the three vertical structures have the
same industry profits in the cases of (c,c) and (0,0) . That’s the reason why p does not

affect the incentive to merge. This result, however, depends on the fact that our model
does not have foreclosure. If there is foreclosure in the model, we can obtain the different

results. Let us consider the case where the outcome of cost realizations is (0,0) . If there

is foreclosure, the input cost for the foreclosed firm, DZ , will be c unlike zero in our
model. Then partial integration has the different structure of input costs from non-

integration and thus p may affect the incentive to merge.

110

Table 3-4. The Structure of Input Costs

 

 

 

Probability Cost NI PI PI
Realizations (U l - D1)
U1 U2 D1 D2 D1 D2 D1 D2
(1 + p)/4 c c c c c c , c 2 c
(1 — p) /4 0 c c c O c 0 c
(1 — p) /4 c O c c c c c 0
(1+p)/4 . 0 , 0 (,1 O 0}, _0 t 0 * . .0 0

 

 

 

 

 

7. Concluding Remarks

We have investigated the profitability of backward integration in the presence of
upstream cost variability in this paper and we have proven the existence of a Prisoner’s
Dilemma. We also have shown that divestiture may encourage downstream entry when
there exists a Prisoner’s Dilemma. We have not, hoWever, examined the welfare effects
of antitrust policy. Will divestiture increase consumer and total welfare? This is not
trivial because antitrust enforcement has two contradictory effects. While antitrust
enforcement increases the number of firms entering downstream industry and fosters
competition in the downstream market, it also forces a non-integrated vertical structure
and causes double marginalization. A further study might calculate the welfare effects of
preventing vertical integration.

A natural reinterpretation of our model might be that upstream cost variability is
created when upstream firms undertake R&D. When we reinterpret our model in this way,

one limitation of our model is that upstream R&D decisions are exogenous. Interesting

lll

conclusions might be reached by allowing for endogenous innovation. Suppose, for
instance, that two upstream firms undertake R&D. They will compete in R&D with
upstream product competition if they do not integrate vertically. But with vertical
integration they could engage in R&D competition with downstream product competition
because vertical mergers transfer cost asymmetries from the upStream market to the
downstream market. The different characteristics between upstream and downstream
product markets might have different effects on upstream R&D competition. An

interesting hypothesis might be that forward integration could be used as a device to relax

upstream R&D competition.

llZ

 

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