2009-3
Profit enhancing competitive pressure
in vertically related industries
Noriaki Matsushima Tomomichi Mizuno

Profit enhancing competitive pressure in vertically related industries∗

Noriaki Matsushima†
Graduate School of Business Administration, Kobe University
Tomomichi Mizuno
Graduate School of Economics, Kobe University
February 5, 2009

Abstract
Under a simple Cournot model with vertical relations, when downstream firms engage in process
R&D, the profits of upstream firms in which upstream competition exists may be larger than thosein which each upstream firm has a bilateral monopoly relation with its buyer (downstream firm).

JEL classification numbers: L13, O31.
Key words: upstream firm, competition, bilateral oligopoly∗ 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. Needless to say, we are responsible for any remaining
errors.
† Corresponding author: Noriaki Matsushima, Graduate School of Business Administration, Kobe University, Rokkodai
2-1, Nada, Kobe, Hyogo 657-8501, Japan. Phone: +81-78-803-6981. E-mail: nmatsush@kobe-u.ac.jp

1

Introduction

A standard view concerning market competition posits that more intense market competition, measured in almost any way, reduces firm profit. Consequently, it should be in the best interest of profitmaximizing firms to reduce the degree of market competition. One way to do this is to gain market power
through product differentiation. Another way, although it is sometimes subject to legal restrictions, isto reduce the number of competitors in a given market by such means as collusion, entry deterrence,
predation and horizontal mergers. In any event, firms are expected to earn higher profits if they canplace themselves in less competitive environments.
We investigate how upstream competition affects the profitability of firms and incentives for downstream firms to invest in cost-reducing R&D. The model in this paper is set as follows. There are two
upstream and two downstream firms. Each downstream firm produces a final product, and must buy
input from upstream firms. Each downstream firm engages in process R&D. Each upstream firm faces
competitive pressure from potential suppliers.
The model setting is motivated by the following situation. Many manufacturers have relationships
with many input suppliers. For instance, in the aircraft industry, the jet (turboprop) engine and aircraft
industries are vertically related. To produce a product, aircraft firms must procure suitable equipment.
Engine companies also have relations with many buyers, and potentially with all of them (Bonaccorsi
and Giuri (2001)). In the automobile industry, Toyota procures electric parts from many input suppliers
including Denso, which is one of the largest auto part manufacturers. Denso supplies other automobile
manufacturers, for instance, Daimler Chrysler (Ahmadjian and Lincoln (2001)). Thus, electric parts
may be used in automobiles from different manufacturers. When manufacturers make products, they
may face constraints that stem from the technological capacities of suppliers. When the manufacturers
are able to negotiate with many suppliers of suitable inputs, they can procure such inputs at reasonable
prices. Conversely, when there are only few suitable suppliers, the manufacturers must pay them higher
prices. That is, competitiveness in input markets affects the procurement conditions of manufacturers.
We show that upstream competition always leads to higher investment levels by downstream firms.
We also show that the wholesale price for which each upstream firm faces competitive pressure may behigher than that in which each upstream firm has a bilateral monopoly relation with its buyer. Moreover,the profit of each upstream firm when it faces competitive pressure may be larger than when it has abilateral monopoly relation with its buyer. In other words, competition pressures on the upstream firms
do not always harm their profitability.
1This paper is related to the discussion on how vertical structure affects incentives of upstream and/or
downstream firms to undertake innovative activities. In the context of vertical market structures andcompetition environments, Ishii (2004) and Milliou (2004) discuss spillover effects of R&D investments.
Banerjee and Lin (2003), Brocas (2003), and Buehler and Schmutzler (2008) focus on the relation ofvertical market structure and cost-reducing investment in an oligopoly. Those papers do not consider
how competitiveness in upstream markets affects profitability of upstream firms when downstream firms
engage in process R&D.
Several recent studies have discussed instances where an increase in competitive pressure (the numberof firms) may actually increase firm profit. Coughlan and Soberman (2005), Chen and Riordan (2007),and Ishibashi and Matsushima (2009) belong to this strand, but the underlying mechanism of our model
differs substantially from theirs. In these previous studies, market entry works as a commitment device
to soften market competition, so that the market actually becomes less competitive as more firms enter
it. Ishida et al. (2008) also show a market condition in which an increase in the number of firms may
increase the profit of a firm. They consider a simple Cournot model with strategic R&D investments
wherein an efficient (dominant) firm competes against less efficient (fringe) firms. Asymmetry among
the firms is a key factor to derive their main result, whereas the main mechanism to derive ours is quite
different.
The paper proceeds as follows. The next section outlines the basic environment. Section 3 provides
an analysis of the model. Finally, Section 4 offers conclusion.

2

The model

We consider a market with two downstream and two upstream firms. There is only one factor of
production, which we refer to as the input. Each firm produces a differentiated final good in a constantreturns-to-scale process where one unit of the input is turned into one unit of the final good. Eachdownstream firm is able to do this conversion at no cost.
We assume that the two downstream firms compete in quantity. Now let xi denote i’s sales. The
inverse demand function is given by
p = 1 − x1 − x2 ,where p is the price of the final good.
Let zi denote the amount of the input supplied to firm i. Each input supplier sets a wholesale price2

wi to maximize its profit function:
πU i = wi zi , i = 1, 2.
The fact that the input suppliers unilaterally set the wholesale prices implies that they possess fullbargaining power.
In this paper, we consider two cases concerning the technologies of upstream firms:
1. Neither upstream firm faces a competitor.
2. Each upstream firm faces competitors that are potentially able to supply each downstream firm.
If a competitor incurs a marginal cost, k, it is able to supply its input to downstream firm i, where
k is a positive constant.
The first case means that each upstream firm has a monopoly position with its trading partner.
The second case means that each upstream firm faces potentially harmful competitive forces. Thosecompetitive forces include the upstream firms supplying to the downstream firm (that is, upstream firm
i is a potential competitor of upstream firm j (i = 1, 2, i 6= j)). For instance, in the aircraft industry,
while Rolls Royce and CFM International sometimes exclusively supply highly specific turbofan engines
to Airbus and Boeing respectively, these engine suppliers are potential suppliers of either company.
We consider the downstream firm’s investments in process R&D. We assume that the constantmarginal cost of firm i is determined by firm i’s investment in process R&D, denoted by ci (i = 1, 2).
The marginal cost of firm i is c − ci . The cost of process R&D is given by G(di ) = φc2i (φ is a positive
constant). The game structure in this section is as follows.
1. Each downstream firm engages in process R&D.
2. Each upstream input supplier sets its wholesale price(s).
3. Given those prices, each firm simultaneously chooses quantities.

3

Analysis

3.1

Case 1: no potential supplierIn this case, neither upstream firm faces a competitor. Upstream firm i unilaterally offers its wholesale
price wi (i = 1, 2) to downstream firm i.
The profits of firms 1 and 2 are
πDi = (1 − xi − xj − wi − (c − ci ))xi , i 6= j.
3The first-order conditions lead to
1 − c − 2(wi − ci ) + (wj − cj ), i 6= j.
3

xi =

(1)

The profit of the input supplier is
πU i =wi (1 − c − 2(wi − ci ) + γ(wj − cj )), i 6= j.
3

The first-order conditions lead to5(1 − c) + 7ci − 2cj, i 6= j.
15(2)

4(5(1 − c) + 7ci − 2cj )2− φc2i , i 6= j.
2025

(3)

w
ei =
The profits of downstream firms are:πDi =The first-order conditions lead toNcN
1 = c2 =28(1 − c).
405φ − 28(4)

The equilibrium profits of the upstream and downstream firms are
NNπU
1 = πU 2 =12150(1 − c)2 φ24(1 − c)2 φ(2025φ − 196)
N
N
,
π
=
π
=
.
D1
D2
(405φ − 28)2
(405φ − 28)2

(5)

135(1 − c)φ.
405φ − 28(6)

The wholesale prices are
w1N = w2N =3.2

Case 2: potential suppliers

In this case, potential suppliers can sell their input to both downstream firms. If k is insufficiently large,
upstream firm i faces a constraint that its wholesale price for downstream firm i cannot be larger thank because potential suppliers can undercut this price and deprive it of the demand of downstream firm
i. Therefore, when we consider the determination of the wholesale prices, we must take this constraint
into account.
Upstream firm i unilaterally offers its wholesale prices wi (i = 1, 2) to downstream firm i. Given thewholesale prices, the quantities supplied by the downstream firms are equivalent to the previous case,xi in (1). We now concentrate our discussion on the case in which the constraint wi ≤ k is binding foreach firm. Therefore, the wholesale prices are
w1 = w2 = k.
4

The profits of the downstream firms are:((1 − c − k) + 2ci − cj )2− φc2i , i 6= j.
9

πDi =The first-order conditions lead to

S
S
cP
= cP
=
1
2

2(1 − c − k).
9φ − 2(7)

The equilibrium profits of the upstream and the downstream firms are
PSPSπU
1 = πU 2 =3φ(1 − c − k)k(1 − c − k)2 φ(9φ − 4)
PS
PS
, πD1
= πD2
=
.
9φ − 2(9φ − 2)2

(8)

We must ascertain whether the constraint wi ≤ k is binding when the upstream firms face the constraints.
S
Given the values of cPi , if the optimal wholesale price of each upstream firm is larger than k, theSinto wei in (2), we have the condition that the constraint isconstraint is binding. Substituting cPibinding (wei > k):k<9(1 − c)φ≡ k̄.
27φ − 4(9)

We now concentrate our discussion on the case in which k < k̄.

3.3Comparison

We now compare the equilibrium outcomes in the cases discussed above.
Investment

PS
We first compare cN(potential suppliers). After somei (no potential supplier) with ci

Scalculus, we find that for any k < k̄, cP> cN
ii . That is, upstream competition always enhances thedownstream firms’ incentives to invest. When there is no potential supplier, no upstream firm cancommit not to set a higher price given that each downstream firm has already invested. Anticipating
this exploitation, the downstream firms diminish their efforts to invest. Price competition acts as acommitment to set their wholesale prices at a lower level. Those low prices encourage the downstream
firms to invest.
Wholesale price

We compare wiN with wiP S . There exists k such that wiP S = k > wiN ≡ k w because

the following inequality satisfies (see Figure 1):k̄ − wiN =288(1 − c)φ> 0.
(405φ − 28)(27φ − 4)5

Although price competition restricts the ability of upstream firms to set their wholesale prices freely,
it may lead to higher wholesale prices than in the case without potential suppliers. When there is nopotential supplier, the investment levels of the downstream firms are low. This low investment prevents
the upstream firms from setting higher wholesale prices because the expansion in demand induced by
the investments is small. Therefore, when price competition between the upstream firms is not intense(k is large), the wholesale prices are higher than those in the firm-specific input case.
Upstream firm

N
PS
PS
N
We now compare πU
i with πU i . After some calculus, we find that πU i > πU i if andonly if k > k U wherekU≡(405φ − 28 −p

18225φ2 + 9720φ + 784)(1 − c).
2(405φ − 28)

After some calculus, we find that k U is smaller than k̄ (see Figure 1). That is, for k U < k < k̄, pricecompetition leads to higher upstream profits. In other words, competition between upstream firms andpotential suppliers may enhance the profitability of the upstream firms. The existence of potential
suppliers induces higher levels of investment by the downstream firms. The increases in investment
increase the quantities supplied to the downstream firms. Moreover, when k is large, the wholesale
prices caused by price competition are larger than in the case without potential suppliers. Because thedemand and the wholesale price are larger than in the case without potential suppliers, the profit ofeach upstream firm is larger.

4

Conclusion

We investigate how upstream competition affects incentives for downstream firms to make cost reducing
R&D investments and the profitability of the firms. We show that upstream competition always leads
to higher investment levels by downstream firms. We also show that the wholesale price at which each
upstream firm faces competitive pressures may be higher than when it has a bilateral monopoly relation
with its buyer. Moreover, the profit of each upstream firm when it faces competitive pressure may
be larger than when it has a bilateral monopoly relation with its buyer. In other words, competitionpressures on the upstream firms do not always harm their profitability.
[2009.2.4, 907]6

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7

k
0.22

k̄
2

4

6

8

10

0.18

kw
0.16
0.14

kU

Figure 1: The threshold values (c = 1/2).

8Ǿ