GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.87

Vertical separation as a defense against strong suppliers

Noriaki Matsushima and Tomomichi Mizuno

September 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Vertical separation as a defense against strong suppliers∗

Noriaki Matsushima†
Institute of Social and Economic Research, Osaka University
Tomomichi Mizuno
Competition Policy Research Center, Japan Fair Trade Commission
September 10, 2009

Abstract
We provide a simple model to investigate decisions about vertical separation. The
key feature of this model is that more than one input is required for the ﬁnal productof the downstream monopolist. We show that as the bargaining powers of independent
complementary input suppliers grow larger, the downstream monopolist tends to separate from its input units. The results are related to a visible diﬀerence between thevertical structures of Japanese and US auto assemblers.

JEL Classiﬁcation Codes: L13, L22, M11.
Key Words: Multiple inputs; Bargaining; Disintegration; Double marginalization∗
We would like to thank Toshihiro Matsumura, Joji Tokui, and seminar participants at Shinshu University for their helpful comments. Especially, we would like to thank Didier Laussel for his careful andconstructive suggestions. The ﬁrst author gratefully acknowledges ﬁnancial support from a Grant-in-Aid for
Encouragement of Young Scientists from the Japanese Ministry of Education, Science and Culture. Needlessto say, we are responsible for any remaining errors. The views expressed herein are those of the authors andshould not be interpreted as those of the Japan Fair Trade Commission.
†
Corresponding author: Noriaki Matsushima, Institute of Social and Economic Research, Osaka
University, Mihogaoka 6-1, Ibaraki, Osaka 567-0047, Japan.
Phone: +81-6-6879-8571.
E-mail:nmatsush@iser.osaka-u.ac.jp1

1

Introduction

Vertical separation has become a widespread phenomenon in the industrialized world. Examples of industries where vertical separation is a key feature of the organization of production abound: aircraft, cars, computers, audio/video systems, and so on. For example,
in the automobile industry, suppliers have a signiﬁcant role in US, European, and Japanese
auto manufacturing and therefore in the quality of the ﬁnal product (Richardson (1993)).
Japanese assemblers, especially, often spin oﬀ parts development and manufacturing to independently managed yet closely linked suppliers (Ahmadjian and Lincoln (2001)). Moreover,automobiles are developed and manufactured by OEMs and their supplier networks, who
produce as much as 70 percent of the value of a vehicle. Consequently, the cost and qualityof a vehicle are functions of the productivity of a network of ﬁrms working in collaboration(Dyer and Nobeoka (2000)).
The degree of vertical separation (integration) varies between ﬁrms although verticalseparation has become a widespread phenomenon. The automobile industry is a typicalexample. Japanese auto assemblers are known to be substantially less vertically integrated
than their US counterparts (see, for instance, Cusumano and Takeishi (1991) and thereferences therein). Large Japanese auto assemblers such as Toyota and Nissan rely on
suppliers for both design and manufacture of components traditionally produced in-house
by GM and Ford. As summarized in Dyer (1996), there are several explanations that a high(resp. low) degree of vertical integration emerged in the US (resp. Japan). One explanation
is preference for vertical interactions among ﬁrms. The US auto companies tend to eliminate
some negative eﬀects from interactions with their trading partners. For instance, Perry(1989) and Scherer (1980) point out managements’ desire to grow and reduce dependency
on outside suppliers. Moreover, Emerson (1962) and Pfeﬀer and Salancik (1978) mention
that ﬁrms lose power when they increase their dependency on outside suppliers. On theother hand, Japanese cultural norms and values result in a high level of “goodwill trust” in
2Japan, which translates into cooperative interﬁrm relationships (Dore (1983), Sako (1991),
Hill (1995)). Another explanation of the diﬀerences between the US and Japanese in the
degree of vertical integration is based on the lack of an open market for corporate control
in Japan (Sheard (1994)) and the limitations of Japanese ﬁnancial markets (Nishiguchi(1994)).
Although those explanations summarized by Dyer (1996) sound plausible, we provide a
new strategic reason for the diﬀerence between the US and Japan. We think that a simple
key feature to explain those diﬀerences is that more than one input is required for theﬁnal products of those manufacturers. In automobile product development, the degree ofvertical separation (integration) for a single manufacturer is the consequence of hundredsof individual procurement choices, ranging from simple supply contracts for commodity
components to complex arrangements for cutting-edge technology development (Novak andStern (2009)).
We provide a simple model to investigate decisions of vertical separation and show
several results that have not been explained in previous research (we mention the diﬀerence
between this model and those in related previous studies later). The key feature of thismodel is that more than one input is required for the ﬁnal product of the downstream
monopolist.1 This feature is consistent with the examples mentioned above. The model canbe also applied to other industries. For instance, in the aircraft industry two major ﬁrms,
Airbus and Boeing, rely heavily on ﬁrm-speciﬁc inputs (e.g., engines, wings, horizontal
stabilizers) produced by independent manufacturers, and then sell their aircraft to airline
1

This setting is related to models with complementary suppliers (Economides and Salop (1992), Nalebuﬀ(2000), Baldwin and Woodard (2007), Casadesus-Masanell et al. (2007), and Maruyama and Minamikawa(2009)). Those papers discuss how mergers among complementary suppliers appear and/or how thosemergers change equilibrium outcomes. Such complementary suppliers provide their products directly to
consumers. This setting is quite diﬀerent from ours. Note that the meaning of the term ‘vertical integration’in these papers is diﬀerent from that in our paper. Although a merger among complementary suppliers iscalled ‘vertical integration’ in these papers, in our model the term indicates a merger between an upstream
and a downstream ﬁrm.

3

companies, which are ﬁnal customers (Beelaerts van Blokland et al. (2008)).
The model structure is as follows. There is a downstream monopolist D that uses two
inputs; A and B. The inputs are produced by an independent upstream supplier A and a
production unit inside the downstream ﬁrm D respectively. The wholesale price of input
A is determined by bargaining between the downstream ﬁrm and the supplier. Under thiscondition, we consider two cases: (1) the downstream ﬁrm produces units of input B, (2)the downstream ﬁrm separates from its input production unit. The separated unit (supplierB) supplies to the downstream ﬁrm D to maximize its own proﬁt.2 We show that as thebargaining power of the independent supplier A increases, the downstream monopolist tends
to separate from its input unit. A corollary of the result is that when the bargaining powerof the independent supplier A is large enough, vertical separation is always proﬁtable forthe downstream monopolist.
Our paper shows that when the number of high-quality input suppliers that tend to havestronger bargaining power is large, assemblers tend to withdraw from design and/or manufacture of other complementary components, as the Japanese assemblers did. Following thediscussion in Clark and Fujimoto (1991) and Clark (1989), we now explain that Japanesesuppliers indeed have strong bargaining power and/or provide high-quality product to auto
assemblers. Clark and Fujimoto (1991) and Clark (1989) examine the impact of “project
scope” in the global auto industry. The impact is a measure of the uniqueness of the partplayed and the extent of development carried out by outside suppliers in project performance. The authors found that 67% of Japanese projects were “black box,” or developedby suppliers, compared with 16% of US vehicles. They argue that the black-box system is
eﬀective because the link between design and manufacturing is strong. They argue that thehigh percentage of unique parts and high supplier involvement contributes to an observed

2

We assume that the downstream ﬁrm cannot merge with supplier A. A more detailed discussion of theassumption is provided in Section 2.

4

Japanese advantage in project lead time and cost.3 This fact is consistent with our result:
As the number of high-quality independent input suppliers, which tend to have stronger
bargaining power, increases the downstream monopolist tends to separate from its input
production units.
Several researchers have investigated how the structure of vertical organizations is determined in competitive environments (Bonanno and Vickers (1988), Gal-Or (1999), Choi
and Yi (2000), Chen (2001, 2005), Lin (2006), Arya et al. (2008), Matsushima (forthcoming)). Although these papers consider downstream competition to derive results for verticalseparation, we show that vertical separation is proﬁtable even with only one downstreamﬁrm. An exception is Laussel (2008) who explicitly incorporates complementary inputs in
an attempt to examine why vertical integration does not occur. Besides several diﬀerencesin the setup (which we will mention later), the present paper diﬀers from Laussel (2008)
as our focus is primarily on the relation between the degree of vertical separation andprocurement conditions.
In a broad sense, since the seminal work by Coase (1937), the problem of vertical
integration/separation has long been discussed by many researchers in the transactioncost-based approach. The related papers mainly deal with well-known hold-up problems
that illustrate the underinvestment hypothesis (e.g., Grout (1984) and Tirole (1986)). Coase(1937) suggested that transaction costs might be avoided or reduced via other organizational
structures, and Klein et al. (1978) and Williamson (1979) suggested vertical integration
as an organizational response. The focus of this approach has been on comparing costs
internal to a transaction, between organizing the transaction within a ﬁrm or through themarket.4 Complementary to the transaction-cost based approach, this paper emphasizes
3

Many researchers also point out that Japanese suppliers have superior technology, which contributes

to better performance by Japanese automakers (see Hemmert (1999) and the references therein).
4

Using the property rights approach to address the question of whether vertical integration can escapethe hold-up problem, Grossman and Hart (1986) and Hart and Moore (1990) considered how a particular5

the importance of incorporating multiple inputs into the standard models with vertical
relations.
The model setup is somewhat similar to those in the literature on patent pools although
the motivations of these papers are quite diﬀerent from ours (Lerner and Tirole (2004),
Kim (2004), and Schmidt (2008)). These papers discuss how vertical integration and/or
patent pools (alliances among patent holders) alter the prices of patented inputs. However,
the incentives for vertical integration between upstream and downstream ﬁrms are notdiscussed.
The remainder of this paper is organized as follows. Section 2 formulates the model.
Section 3 presents the results. Section 4 extends the basic model. Section 5 brieﬂy discusses
the relation between our results and the diﬀerences between US and Japanese automakers.
Section 6 concludes the paper.

2

The model

Consider a downstream monopolist D that uses two inputs, A and B. The inputs are produced by an independent upstream supplier A and a production unit inside the downstreamﬁrm D, respectively. The wholesale price of input A is determined by bargaining between
the downstream ﬁrm and the supplier.
The demand for the product is linear:p = 1 − Q,(1)where p is the market price and Q is the output supplied by the downstream ﬁrm. A unit
ownership structure aﬀects the parties’ exposure to hold-ups. Che and Sákovics (2008) provided an excellent
brief survey of the hold-up problem. The topic of vertical foreclosure is also related to the problem of vertical
integration. The vertical foreclosure issue primarily concerns the relation between vertical integration andthe competitiveness of downstream ﬁrms (e.g., Ordover et al. (1990) and Hart and Tirole (1990)). See also
O’Brien and Shaﬀer (1992), McAfee and Schwartz (1994), Gaudet and Long (1996), Ma (1997), Riordan(1998), and Choi and Yi (2000). Rey and Tirole (2007) provide an excellent survey of the literature.

6

of ﬁnal product is made with one unit of input A and one unit of input B:
Q = min{qA , qB },where qi is the amount of input i (i = A, B). That is, the downstream ﬁrm uses Leontief
production technology. The ﬁrms incur no marginal cost for units of product.
In this paper, we consider two cases: (1) the downstream ﬁrm produces units of input
B, (2) the downstream ﬁrm separates from its input production unit. The separated unit
(supplier B) supplies to the downstream ﬁrm D to maximize its own proﬁt (see Figure 1).
[Figure 1 here]
We now discuss two reasons for our assumption that the downstream ﬁrm cannot merge
with ﬁrm A. First, when ﬁrm A is an essential input supplier, vertical integration between
ﬁrm A and a downstream ﬁrm tends to be prohibited by antitrust authorities. In general,
downstream ﬁrms compete, and they usually procure their inputs from common suppliers(Ahmadjian and Lincoln (2001)), although we use a model with a downstream monopolist
to simplify the analysis. The common supplier in our model is ﬁrm A, which supplies
essential inputs for the industry. In this situation, a vertical merger between ﬁrm A and adownstream ﬁrm is generally prohibited by antitrust authorities because of the foreclosure
problem (Rey and Tirole (2007)). Second, we can regard ﬁrm A as a labor union in
the downstream ﬁrm. In standard oligopoly models with labor unions, each downstream
ﬁrm negotiates with its labor union, which maximizes the product of its wage level andnumber of employees (see, for instance, Horn and Wolinsky (1988a,1988b), Davidson (1988),
Dowrick (1989), Mumford and Dowrick (1994), Naylor (2002), Lommerud et al. (2003),
and Lommerud et al. (2009)). The setting employed here is the standard one concerning
the objective function of labor union.55The second explanation seems unsuitable in the case of US and Japanese auto assemblers discussed

in Section 5 because it is often recognized that US labor unions have stronger bargaining power than7

We assume that the input prices are determined through Nash bargaining. The solution
is input prices wA and wB such that wi is the Nash solution to the bargaining problem
between supplier i and the downstream ﬁrm, given that both expect to agree upon the pricewj . That is, given wj , the bargaining problem between supplier i and the downstream ﬁrm
is described by the payoﬀ pairs BiI = {[wi qi , πD ]|wi ≥ 0} and the disagreement point (0, 0),
where πD is the proﬁt of the downstream ﬁrm. The solution is given by:
wi = arg max αi log[wi qi ] + (1 − αi ) log πD ,wi(2)where αi ∈ [0, 1] measures the bargaining power of supplier i relative to that of the downstream ﬁrm. This is a departure from Laussel (2008) where each input supplier has the samebargaining power. Needless to say, the case of αA = αB is a special case of our speciﬁcation.
Moreover, we thoroughly investigate how procurement conditions of the downstream ﬁrm
aﬀect the decision about vertical separation (see Sections 3 and 4).
The game runs as follows. First, the suppliers and the downstream ﬁrm negotiate thewholesale prices wi (i = A, B).6 Second, given the wholesale prices, the downstream ﬁrm
sets its quantity supplied.

3

ResultWe ﬁrst consider two cases: (1) the downstream ﬁrm produces units of input B, and (2)the downstream ﬁrm separates from its input production unit. We then compare the twocases.

Japanese ones. However, as mentioned in Section 4, the existence of independent input suppliers including alabor union in itself triggers the emergence of other vertically separated input units. Therefore, the second
explanation is plausible in the case of US and Japanese auto assemblers.
6

We only consider the case in which each upstream ﬁrm uses a simple linear price contract. Even thoughthose upstream ﬁrms use two-part tariﬀ contracts, the essence of our main result does not change.

8

3.1

No vertical separation

In this subsection, the downstream ﬁrm has the input production unit that makes input B.
Given the wholesale price wA , the maximization problem of the downstream ﬁrm ismax (1 − Q − wA )Q.
Q

The ﬁrst-order condition leads to
Q = qA =1 − wA(1 − wA )2, πD =.
2
4

As mentioned earlier, the wholesale price wA is determined through Nash bargaining(see (2)). Applying the maximization problem in (2) to this situation, we haveNwA=

αA (2 − αA )(2 − αA )2
αA
N
N
, πA
=
, πD
=
,
2
8
16

(3)

where the superscript ‘N’ denotes the equilibrium outcome in which the downstream ﬁrm
does not separate. As the bargaining power of supplier A increases, the wholesale price wA
and the proﬁt of supplier A increase.

3.2

Vertical separation

In this subsection, the downstream ﬁrm separates from its input production unit, andthen receives inputs from suppliers A and B. Given the wholesale prices wA and wB , themaximization problem of the downstream ﬁrm ismax (1 − Q − wA − wB )Q.
Q

The ﬁrst-order condition leads to
Q = qA = qB =1 − wA − wB
(1 − wA − wB )2, πD =.
2
4

As mentioned earlier, the wholesale prices wA and wB are determined through Nashbargaining (see (2)). Applying the maximization problem in (2) to this situation, we have9the ﬁrst-order conditions of the Nash bargaining problems:
2wA − αA + αA wB = 0, 2wB − αB + αB wA = 0.

(4)

Solving the simultaneous equations, we have
(2 − αB )αA(2 − αA )αB
2(αA + αB − αA αB )
S
S
S
, wB
=
, wA
+ wB
=
,
(5)
4 − αA αB
4 − αA αB
4 − αA αBαA (2 − αA )(2 − αB )2
αB (2 − αB )(2 − αA )2(2 − αA )2 (2 − αB )2
S
S
S
πA
=
,
π
=
,
π
=
, (6)
B
D
2(4 − αA αB )22(4 − αA αB )24(4 − αA αB )2S=
wA

where the superscript ‘S’ denotes the equilibrium outcome in which the downstream ﬁrm
separates. As the bargaining power of supplier A increases, wA increases but wB decreases.
The converse also holds. As the bargaining power of supplier B increases, wB increases
but wA decreases. Because the competition structure between the suppliers is strategic
substitute (see (4)), an increase in the wholesale price of supplier i leads to a decrease inthat of supplier j (i = A, B, j ̸= i).

3.3

Comparison

We now compare the results in the previous two subsections. First, we compare the total
wholesale prices in the two cases. When the input unit is not separated (resp. separated),
N (resp. w S + w S ). The diﬀerence between them isthe wholesale price is wA
A
B
S
S
N
wA
+ wB
− wA
=

αB (2 − αA )2≥ 0.
2(4 − αA αB )(7)

Except for the case in which αB = 0, vertical separation increases per unit production
cost of the downstream ﬁrm. This is related to the discussion in Cournot (1838). When
independent upstream ﬁrms sell perfect complements, the total price of the complements
is ineﬃciently higher because those upstream ﬁrms do not internalize the double marginalization problem. In fact, we can easily ﬁnd that vertical separation decreases the proﬁt ofthe downstream ﬁrm:
S
N
πD
− πD
=−

αB (2 − αA )3 (8 − αB (2 + αA ))≤ 0.
16(4 − αA αB )210(8)

We now show the incentive to separate from an input production unit. To investigate
D + π D in (6) with π N in (3). The diﬀerence between them isthis incentive, we compare πD
B
D
S
S
N
πD
+ πB
− πD
=

2 )α )αB (2 − αA )2 (8αA − (4 + αA
B.
2
16(4 − αA αB )(9)From this equation, we have the following proposition.
Proposition 1 The integrated downstream ﬁrm has an incentive to separate its input production unit if and only if
αB <

8αA
2 .
4 + αA(10)

We easily derive the corollaries of Proposition 1.
Corollary 1 When supplier A has full bargaining power with respect to the downstreamﬁrm (αA = 1), vertical separation is always proﬁtable for the integrated downstream ﬁrm.
Corollary 2 For any αA (> 0), there exists ᾱB (> 0) such that for any αB < ᾱB , verticalseparation is proﬁtable for the integrated downstream ﬁrm.
Roughly speaking, the equilibrium incentive of vertical separation might be reminiscent of
the term “divide and rule” (“divide et impera”) which is an economic strategy of gaining
and maintaining power by breaking up larger concentrations of power into chunks that
individually have less power than the one implementing the strategy.
N in (3) with w S in (5).
To explain the intuition behind Proposition 1, we compare wAA

The diﬀerence between them is
S
N
wA
− wA
=−

αA αB (2 − αA )≤ 0.
2(4 − αA αB )(11)

Vertical separation induces supplier A to lower its wholesale price wA when αA > 0 and
αB > 0. This is because upstream ﬁrms do not fully exert monopoly power because of
the double marginalization problem mentioned above (Cournot (1838) and Sonnenschein11

(1968)). This diminishes the proﬁt of supplier A, and a portion of the monopoly proﬁtof supplier A is transferred to supplier B through competition between the suppliers (seeFigure 2). In particular, if the bargaining power of supplier A is strong (αA is large), thedecrease in the wholesale price wA is large (see (11)).7 Note that because vertical separation
causes the standard double marginalization problem, it diminishes the quantity suppliedby the downstream monopolist from QN to QS (see Figure 2).
[Figure 2 here]

Robustness

Using a setting similar to that in this section, we now discuss the robustnessof Proposition 1. This proposition states that when the bargaining power of supplier B is
weak, vertical separation tends to be proﬁtable. We now slightly alter the basic setting
to show a similar result to Proposition 1. We suppose that potential suppliers are able tosupply input B at a constant marginal cost c. Supplier B has full bargaining power with respect to the downstream ﬁrm. When c is suﬃciently low, supplier B sets its wholesale priceat c because of the Bertrand competition among them. The joint proﬁt of the downstream
and the separated upstream ﬁrm (supplier B) isΠ ≡ [P (Q(wA (c) + c)) − (wA (c) + c)]Q(wA (c) + c) + cQ(wA (c) + c),
where P (·) is the price of the ﬁnal product, Q(·) is the quantity supplied by the downstream
ﬁrm, and wA (c) is the wholesale price set by supplier A. Note that when c = 0, this isequal to the proﬁt when they are integrated. Diﬀerentiating the joint proﬁt with respect

7

S
N
S
N
We can easily show this using a partial derivative of wA− wA. Diﬀerentiating wA− wA
with respect

to αA , we have2SN
αB (8(1 − αA ) + αA
αB )
∂(wA
− wA
)
=−
≤ 0.
2
∂αA
2(4 − αA αB )12to c, we have∂Π′′= − (wA(c) + 1)Q(wA (c) + c) + Q(wA (c) + c) + cQ′ (wA (c) + c)(wA(c) + 1)∂c′′
= − wA(c)Q(wA (c) + c) + cQ′ (wA (c) + c)(wA(c) + 1).
′ (0)Q(w (0)). This is positive if and only
When c converges to zero, this converges to −wAA′ (c) < 0 for any c. The condition seems to be natural. Firm A decreases its wholesale
if wA

price as the other (competitive) supplier sets a higher price equal to c.8
Proposition 2 Under a general (inverse) demand function P (·), when c is suﬃciently′ (c) < 0 for any c, vertical separation is proﬁtable for the downstream and thesmall and wA

separated upstream ﬁrm.

Potential suppliers

It may be claimed that the result depends on the assumption thatno potential competitors of the suppliers exist. Even if there are potential substitutes forthe incumbent suppliers, our result holds true under some conditions. For instance, supposethat potential suppliers are able to supply inputs A and B at constant marginal costs w̄A
and w̄B respectively. Those marginal costs are the upper bounds of the wholesale prices
set by the incumbent suppliers. In this setting, αA is large and w̄B is suﬃciently small, so
vertical separation of supplier B from the downstream ﬁrm tends to be proﬁtable.9 The
reason why this holds is simple. Because w̄B is the upper bound of the wholesale price wB
set by supplier B, a lower w̄B is somewhat similar to the case in which supplier B has lower
bargaining power, which compels it to set a higher wB .
Production technology

In this section, we assume that the production technologyof the downstream ﬁrm is Leontief. Some may claim that Leontief technology is crucial
8′wA(c) < 0 if wQ′′ (w + c) + Q′ (w + c) < 0 (this is a suﬃcient condition). This condition, of course,

includes the case in which the inverse demand function is linear.
9

The calculus is highly complex, and is available from the authors on request.

13

to derive our result. We can show that a similar result can be derived if the production
technology of the downstream ﬁrm is Cobb–Douglas (see Technical Appendix).10

4

Multiple suppliers

We extend the basic setting in the previous section. Consider a downstream monopolistthat requires N inputs. m inputs are produced by independent upstream suppliers Ii(i = 1, 2, . . . , m) respectively (m < N ). The remaining inputs are produced by production
units inside the downstream ﬁrm (Ii (i = m + 1, . . . , N )). To simplify the analysis, we
assume that the wholesale prices of input Ii are unilaterally determined by the suppliers.11
The demand for the product is the same as in the previous section. The production
function is expressed by
Q = min{qi , q2 , . . . , qN },where qi is the amount of input i (i = 1, 2, . . . , N ). That is, the production technology ofthe downstream ﬁrm is Leontief. The ﬁrms incur no marginal cost for units of product.
In this extended model, we consider the decision regarding the number of input production units that are separated from the downstream ﬁrm. We denote the number asn.
Given the wholesale prices wi (i = 1, 2, . . . , m + n), the optimal quantity supplied by

10

Thesmar and Thoenig (2007) also consider the situation in which vertical separation appears. Theyshow that an increase in the degree of vertical separation ampliﬁes elasticity to demand shocks of ﬁrms’
sales and employment. Moreover, by using French ﬁrm-level data sets from 1984 to 1999, they show that thetheoretical results are consistent with their empirical results. In their model, the monopoly downstream ﬁrm
uses two inputs and has Cobb–Douglas production technology. When one input division is separated, theseparated supplier and the downstream ﬁrms enter into a nonlinear price contract. Moreover, the propertyof the input is diﬀerent from that in our model. These diﬀerences lead to the diﬀerent results in their paper.
11

After we show the result in this section, we brieﬂy mention the case in which each independent supplier

has a diﬀerent bargaining power.

14the downstream ﬁrm is
Q=

1−

∑m+n
i=1

wi

2

.

The maximization problem of supplier i ismax πU i = wi

1−

∑m+n
i=1

2

wi

wi

.

The ﬁrst-order conditions of the suppliers lead to
wi =

1
1
1
, πD =, πU i =.
1+m+n4(1 + n + m)22(1 + n + m)2(12)

The joint proﬁt of the downstream and n suppliers (πJ ) and the partial derivative of πJwith respect to n are
πJ ≡ πD + nπU i =2n + 1
m−n
∂πJ
=
,
.
4(1 + n + m)2∂n2(1 + n + m)3

πJ is maximized n = m if 2m ≤ N , otherwise n = N −m. We have the following proposition.
Proposition 3 The optimal number of production units to be separated from the monopoly
downstream ﬁrm is m if 2m ≤ N , otherwise N − m.
This proposition means that as the number of independent complementary input suppliers
increases, the downstream ﬁrm tends to separate from its input production units. We
now discuss the intuition behind this conclusion. As mentioned earlier, an increase in thenumber of input suppliers leads to an increase in the sum of the wholesale prices (the eﬀectof double marginalization). An additional increase in the sum of wholesale prices, however,decreases as the number of input suppliers increases.12 Therefore, in our model, given thatmany independent input suppliers exist, a separation of an input unit does not diminish
the quantity supplied by the downstream ﬁrm. In other words, the double marginalization
12

This is somewhat similar to the standard Cournot quantity setting model. In this model, while anentry of a ﬁnal product ﬁrm decreases the price, the additional contribution of the entry to the decrease in
price becomes smaller as the number of existing ﬁrms increases.

15

problem stemming from a separation is not severe. On the other hand, separation of an
input unit decreases the sum of the wholesale prices set by the other input suppliers. Thisis somewhat similar to the “business stealing eﬀect” in the standard Cournot model (Tirole(1988)). The reduction of the sum and the additional proﬁt of the separated input unit
beneﬁt the group of the downstream ﬁrm and the separated unit. When the number of
independent suppliers is large, the latter beneﬁt dominates the former cost. When thenumber of separated units is greater than one, an additional separation of an input unit
has a negative eﬀect on the group of the downstream ﬁrm and the separated units. The
additional separation reduces the proﬁt(s) of the other separated unit(s) because of thebusiness stealing by the additional unit. In other words, proﬁt cannibalization among theseparated units appears. This cannibalization diminishes the incentive to separate input
units from the downstream ﬁrm. In this model, when the number of separated input units isequal to that of independent complementary input suppliers, the positive and the negativeeﬀects of vertical separation are balanced out.13

Remark 1

Note that, we have assumed that each upstream supplier has full bargaining

power. When each upstream supplier has diﬀerent bargaining power, the downstream ﬁrm
separates at least one input unit if and only if
) m
(
m
∑ αi
∑
αi
> αj ,2 1+
2 − αi2 − αii=1

i=1where αi is the bargaining power of independent supplier i (i = 1, 2, . . . , m) and αj isthe bargaining power of the separated input unit. The left-hand side of the inequality is
increasing in each αi (i = 1, 2, . . . , m). As the number of independent suppliers and/or
the bargaining power of each independent supplier increase, the downstream ﬁrm tends toseparate from its input production unit.
13

Novak and Stern (2009) empirically show a similar tendency that the probability of vertical integrationfor each automobile system increases in share of other systems that are vertically integrated.

16

Remark 2

We have considered one-shot games concerning the decision of vertical sep-aration. If we consider the following story, Proposition 3 slightly changes. Initially, thedownstream ﬁrm, m independent suppliers, and many potential buyers of the downstream
ﬁrm’s input production units exist. The downstream ﬁrm has an opportunity to sell its
production units to buyers in each period. There is no time discount. In this case, theagents anticipate subsequent opportunities of vertical separation. As mentioned earlier,given the existence of independent input suppliers, the downstream ﬁrm has an incentive
to sell its input units. As the number of outside suppliers increases, the incentive becomesstronger. Therefore, each agent can anticipate that the downstream ﬁrm has an incentive
to sell its production units completely. This case is the worst for each upstream supplierbecause the proﬁt of each supplier is decreasing in n (see (12)). Potential buyers anticipate
the proﬁt of each suppliers as follows:
πU =

1
1
=
.
2
2(1 + (N − m) + m)
2(1 + N )2

This is also the willingness to pay of each buyer. The downstream ﬁrm’s maximization
problem is
max
n

1
1
+n×
.
2
4(1 + n + m)
2(1 + N )2

The solution depends on the exogenous values m and N .14 Fortunately, we can say that
there are at most two candidates to be the optimal solution: n = 0 and n = N − m. We
can easily show that the downstream completely sells its input production units if and only
if N < m(3 + 2m). The main massage of Proposition 3 does not so change. That is, as
the number of independent complementary input suppliers increases, the downstream ﬁrm
tends to separate from its input production units.
14

The ﬁrst-order condition is(m + 1)3 − (N + 1)2 + n(3(m + 1)2 + 3(m + 1)n + n2 ).
2(N + 1)2 (1 + m + n)3

This is monotonically increasing in n. The second-order condition is positive. That is, the objective function
is a convex function of n.

17

5Discussion

We have shown that when independent suppliers have greater bargaining power and/or
when the number of independent suppliers is large, a downstream ﬁrm tends to separate
from its input production units.
We believe that the diﬀerence between Japanese and US auto manufacturers is a suitable
example of our results. Moreover, we suggest that our paper provides a new theoreticalinsight into those diﬀerences. From our results, we make the following prediction. When thenumber of high-quality input suppliers that tend to have stronger bargaining power is small,assemblers tend to produce other complementary components in-house, as US assemblers
did. The converse also holds true. When the number of high-quality input suppliers islarge, assemblers tend to separate from design and/or manufacture of other complementarycomponents, as Japanese assemblers did.
Relying on the survey provided by Cusumano and Takeishi (1991) and the discussion in
Richardson (1993) and Novak and Eppinger (2001), we now propose that Japanese suppliers
truly have strong bargaining power and/or provide high-quality product to auto assemblers.
More than two decades ago, Japanese auto manufacturers beneﬁted from signiﬁcant costadvantages over their US competitors. A visible diﬀerence between Japanese and US auto
assemblers is their vertical structures concerning supplier relations. Japanese auto assemblers are known to be substantially less vertically integrated than their US counterparts.
Large Japanese auto assemblers such as Toyota and Nissan rely on suppliers for both design and manufacture of components traditionally produced in-house by GM and Ford.
Cusumano and Takeishi (1991) discuss several diﬀerences among the US and the Japanese
automakers, including (1) number and type of suppliers; and (2) pricing practices.15 We
15

For the other diﬀerences of supplier–manufacturer relationships among US and Japanese automakers,

they list the following: role in product development, quality management, length and stability of relationships, and information exchanges and suggestions.

18

ﬁrst consider the number of suppliers and the types of suppliers. The Japanese automobile
industry tends to be organized in a pyramid structure. Suppliers that directly negotiatewith automobile assemblers also have their own suppliers. These sub-suppliers also havetheir own suppliers. As a result, hierarchies of suppliers (a pyramid of suppliers) are organized. In contrast, US automakers seem to buy more lower-level components and haveseveral independent suppliers for each component. Hence, Japanese automakers negotiatewith fewer suppliers than their US counterparts. In other words, Japanese automakers facea small number of (collected) bigger suppliers. Hence, Japanese automakers have weakerbargaining power than the US ﬁrms. We now consider pricing practices. US automakers choose their suppliers by utilizing competitive bidding, while the Japanese automakers
utilize target pricing in which they help their suppliers to reach their targets. Hence, it isdiﬃcult for US suppliers to raise their prices. That is, US automakers have stronger bargaining power; conversely, Japanese automakers have weaker bargaining power. Summarizing
the arguments, we conclude that there is a relationship between vertical integration andautomakers’ bargaining power. When suppliers have stronger bargaining power, assemblers
and input production units tend to be vertically separated.
Moreover, Cusumano and Takeishi (1991) compare supplier type by ﬁnancial aﬃliationand country of origin (see also Dyer (1996)). In their paper, the data indicate that 50%of the major suppliers for the US automakers were internal parts divisions while 45% wereindependent US suppliers; 5% (1 supplier) was from West Germany.16 For the Japanese
automakers responding to the survey, a mere 7% of their suppliers were in-house divisions;
33% were aﬃliated ﬁrms (deﬁned as minimum 20% equity ownership) and nearly 60% wereindependent.17 As mentioned in the introduction, Clark and Fujimoto (1991) and Clark
16

The sample size is relatively small. They do not provide statistical tests.

17

They conclude that these numbers appear consistent with previous reports of higher levels of vertical

integration for US automakers in contrast to more outside suppliers for the Japanese. The responses fromthe transplants resembled the Japanese in the low level of vertical integration, but with far more relianceon US suppliers.

19

(1989) found that Japanese suppliers have superior technologies that enable Japanese automakers to produce high-quality products (see also Hemmert (1999)). To avail themselvesof the large number of independent suppliers that have superior technology, Japanese automakers may separate from their input production units, and these units may then be
operated as aﬃliated suppliers. This organizational structure is quite diﬀerent from thatof US automakers.

6

Concluding Remarks

We provide a simple model to investigate decisions of vertical separation and show several
new results that have not been explained in previous research. The key feature in thismodel is that there is more than one input required to produce the ﬁnal product of thedownstream monopolist. This feature is consistent with the organizational structures in theaircraft, automobile, and computer industries. We show that as the bargaining power of the
independent supplier increases, the downstream monopolist tends to separate from its input
unit. A corollary of this result is that when the bargaining power of the independent supplieris suﬃciently large, vertical separation is always proﬁtable for the downstream monopolist.
We also show that as the number of independent complementary input suppliers increases,
the downstream monopolist tends to separate from its input production units. The results
are related to a visible diﬀerence between the vertical structures of Japanese and US auto
assemblers.
From our results, we have a testable hypothesis for vertical structures: the larger thenumber of independent suppliers that have superior skills, the larger the number of separated input units from assemblers. A rigorous empirical test is needed to show whether theprediction is plausible or not. This is a consideration for future research.

20

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25

A

UA

A

wA
B

UA

B

wA

wB

D

D

p

p

Consumers

Consumers

Integration

Separation

Figure 1: The market structure

26

UB

P

The gainsPS
The lossPN

S + wS
wA
B

N
wA

S
wA

Q
0
QS QN
Figure 2: The change caused by vertical separation

27

Technical Appendix
We now consider the case in which the technology function of the downstream ﬁrm has
1/2 1/2
a Cobb–Douglas form, Y = qA qB . Given the wholesale prices wA and wB , when thedownstream ﬁrm produces the amount of Q, it solves the following minimization problem:
min wA qA + wB qB

qA ,qB

1/2 1/2

s.t. Q = qA qB .

(13)

From the problem, we have the following equation:
(
qA =

wB
wA

)1/2

(
Q, qB =

wA
wB

)1/2
Q.

When the downstream monopolist produces the amount of Q, the production cost is
1/2

1/2

C(Q) ≡ 2wA wB Q.

(14)

From the maximization problem of the monopolist, the optimal quantity supplied is
Q∗ =

1/2

1/2

1 − 2wA wB
.
2

(15)

The objective functions of the upstream units are described as follows:
1/2

πA =

1/2

1/2

1/2

(wB − c)(1 − 2wA wB )(wA − c)(1 − 2wA wB ), πB =.
2
2(16)

The optimization problems lead towA = wB =

1+c
,
3

S
S
πD
+ πB
=

(1 − 2c)2
.
12

(17)

When the downstream ﬁrm integrates upstream unit B, wB = c. From ﬁrst-ordercondition yields√()2√
1 + 6c2 + 1 + 12c2
1
N
1/2
2
2
wA =
, πD =−3 + 2[1 + 6c + (1 + 12c ) ] .
(18)
18c
36
S + π S − π N , we have the following ﬁgure. Numerically solving π S + π S −By plotting πDBDD
B
N = 0 for c, we obtain c = 0.5. Because π S + π S ≥ π N , vertical separation is proﬁtable
πD
D
B
D
for the integrated downstream ﬁrm (see Figure A1).

28

0.02

ǸDS + ǸBS −ǸDN

0.01

c
0.1

0.3

0.2

0.4

S + πS ≥ πN
Figure A1: πD
B
D

29

0.5