GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 276

Quality improvement to meet competitive fringe

Noriaki Matsushima and Ren-Jye Liu

August 2012GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

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

Quality improvement to meet competitive fringe∗
Noriaki Matsushima†
Institute of Social and Economic Research, Osaka University
Ren-Jye Liu
Industrial Engineering and Enterprise Information, Tunghai University
August 7, 2012

Abstract
We investigate what kind of competitive pressure induces existing ﬁrms to engage inmore intensive innovation activities. We examine two types of competitive pressure: aprice decrease in competitive fringe ﬁrms and a quality improvement therein. We use anoligopoly model with vertical diﬀerentiation to investigate this question. We show that adecrease in the exogenous price of competitive ﬁrms induces the two existent leading ﬁrms
(one high-quality ﬁrm and one mid-quality ﬁrm) to engage in quality investments more if
the ex ante quality level of the high quality product is large enough; otherwise, only the
mid-quality ﬁrm engages more in quality investment. We also show that an increase in theexogenous quality level of competitive ﬁrms diminishes the incentive of the mid-quality ﬁrm
to engage in quality investments.

JEL classiﬁcation: L13, O31, D43
Key words: fringe ﬁrms, competitive pressure, investments, vertical diﬀerentiation∗

The ﬁrst author gratefully acknowledges the ﬁnancial support in the form of a Grant-in-Aid for Basic
Research from the Japanese Ministry of Education, Science and Culture. Needless to say, we are responsible forany remaining errors.
†
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

Almost all ﬁrms suﬀer from competitive pressures applied by domestic and foreign competitors. As a reaction to competitive pressure, many ﬁrms try to restructure their production
environments. For instance, they try to improve their production eﬃciencies (engage in process innovation) and their product qualities (engage in product innovation). Because mostﬁrms in the real world face these problems, investigating this reaction is important.
In reality, companies in the People’s Republic of China (China) pose severe competitive
challenges to companies in many industries around the world. As a real world example in thebicycle industry, we refer to how non-Chinese incumbent ﬁrms react to competitive pressureby Chinese ﬁrms.1 To meet the threat of low-cost, low-price competition posed by small-sized
Chinese bicycle ﬁrms, the Republic of China (Taiwan)’s two leading bicycle assemblers, Giantand Merida (which are known around the world), have formed Taiwan’s A-Team, an associationof Taiwanese bicycle assemblers and suppliers, since 2002. These two companies are the prime
movers of Taiwan’s A-Team. The A-Team also includes 19 suppliers—11 original members andan additional 8 suppliers that joined a year after the organization was founded. Taiwan’s bicycle
industry A-Team has had a mandate for improving industry performance in three main areas:
production eﬃciency, product development, and market intelligence. Antony Lo, who serves
as the president of Giant and A-Team, told journalists that he hoped for the establishment ofA-team to break the myth that it is not possible for competitors to cooperate in Taiwan. He
also noted that A-Team’s mandate was to use existing, high quality labor and technology tofocus on product diﬀerentiation to increase value adds so that Taiwanese bicycle production
might be seen as distinct from that in China and elsewhere. In total, three goals for the venture
were put forward: (1) the implementation of lean production both within assembly plants andthroughout the supply chain, (2) eﬀective co-innovation with suppliers, and (3) co-marketing.
This case in the bicycle industry implies that the two leading assemblers, Giant and Merida,need to further improve their product quality. This also means that a higher intensive com1

The assertions in this paragraph are based on Brookﬁeld et al. (2008).

2

petitive pressure enhances the incentives of those ﬁrms to engage in quality investments. As
summarized in Vives (2008) and Schmutzler (2009), however, the well-known theories in industrial organization do not clearly explain situations in which more intensive competitive pressure
enhances the incentives of those ﬁrms to engage in quality investments. Although several papers consider the investment incentives of ﬁrms that produce vertically diﬀerentiated goods(Motta, 1992, 1993; Rosenkranz, 1995), these papers do not discuss the relation between competitive pressure and the incentives of such ﬁrms to engage in quality investments. Greenstein
and Ramey (1998) is an exception in that it considers such a relation. The main purpose of
their paper is to reassess Arrow’s (1962) results concerning the eﬀect of market structure on
the returns from process innovation in the two cases: a vertically diﬀerentiated duopoly and amonopoly with competitive fringe. Previous papers do not discuss the change in competitive
pressure caused by competitive fringe ﬁrms in the context of R&D investments. We need toknow what kind of competitive pressure induces existing ﬁrms to engage in more intensive
innovation activities. We therefore provide a simple model to explain it.
The model structure is as follows. There are two leading ﬁrms and a competitive fringe ofﬁrms. The leading ﬁrms produce vertically diﬀerentiated products. The quality level of the two
products is higher than that of competitive ﬁrms. Given the exogenous price of competitiveﬁrms, the two leading ﬁrms compete in the ﬁnal product market. In this market, therefore,
each consumer has the following four options: he/she purchases (1) the highest quality product,(2) the mid-quality product, (3) the lowest quality product, and (4) nothing. We investigate
how a decrease in the exogenous price of competitive ﬁrms changes the marginal gains of thetwo leading ﬁrms from quality improvements in the two products. We interpret the decrease in
the exogenous price of competitive ﬁrms as intensiﬁed competitive pressure. We believe that
this model setting captures the example of the Taiwanese bicycle industry mentioned earlier:the two leading ﬁrms are analogous to Giant and Merida, and the decrease in the exogenous
price of competitive ﬁrms is akin to the threat of low-cost, low-price competition by small
Chinese bicycle ﬁrms. Note that the situation discussed in our paper is related in the context
of minimum quality standard (Scarpa, 1998; Valletti, 2000). A minimum quality standard

3

compulsorily enhances the product quality of ﬁrms that would produce lower quality products
if the standard did not exist. This standard is related to the exogenous competitive pressure
discussed in our paper. The models in Scarpa (1998) and Valletti (2000) cannot distinguishbetween the eﬀect of the changes in the price and quality of low quality ﬁrms (which enforce aminimum quality standard) on the ﬁrms that produce high quality products.
We show that a decrease in the exogenous price of competitive ﬁrms induces the existingleading ﬁrms to engage more in quality investments if the ex ante quality level of the highest
quality product is large enough; otherwise, only the mid-quality ﬁrm engages more in quality
investment. We also show that an increase in the exogenous quality level of competitive ﬁrms
diminishes the incentive of the mid-quality ﬁrm to engage in quality investments. Because ourpaper distinguishes between the two eﬀects of competition enhancement, a price decrease incompetitive products and a quality improvement in competitive products, we can clarify thediﬀerence between the two eﬀects. Our results add a new insight to the existing knowledge on
R&D and on the quality standard. Moreover, in the bicycle industry, the result is consistent
with the ﬁeld experience of Brookﬁeld et al (2008) when they visited Giant in September 2011.
Brookﬁeld et al observed site innovation and an innovation-driven atmosphere in Giant. For
example, the logistics chain of the subcontractor parts right from subcontractors’ facilities tothe company’s plant is not only smooth but also considers the quality requirements. Many
operators have implemented measures to ensure quality in both the machining line and theassembly line to meet quality assurance standards. Furthermore, our result clearly indicatesthe condition that existing ﬁrms can collaborate with each other in their R&D activities, which
provides a useful managerial implication for existing companies facing competitive threats fromemerging ﬁrms.
Ishida et al. (2011) is closely related to our paper. They consider a Cournot competition
model with heterogeneous ﬁrms engaging in cost-reducing activities. They show that the entryof weak ﬁrms, which can also engage in cost-reducing R&D, enhances the incentive of existing
eﬃcient ﬁrms to engage in cost-reducing investments. This implies that the leading ﬁrms inthis market enhance their R&D incentives. In their model, because ﬁrms produce homogenous

4

products, all ﬁrms directly compete with each other. In other words, only their cost conditions
diﬀer. On the other hand, in our paper, the products are vertically diﬀerentiated. This implies
that the entry of low-quality competitive ﬁrms does not equally inﬂuence the incumbents.
Moreover, our paper shows that an entry does not enhance the incentive of the leading ﬁrm,
which produces the highest quality product, but does enhance the incentive of the mid-levelﬁrm, which produces the second-best quality product. This property of the relation between
competitiveness and innovation incentives in Ishida et al. (2011) is quite diﬀerent from ours.

2

Model

The utility of a consumer depends simply on the price and the quality of the product. Eachconsumer is supposed to buy a unit of product from the ﬁrm that ensures to him/her thehighest utility, except if all the prices exceed his/her income. Consumers are supposed to havethe same income y but are diﬀerent in their intensity of preference for quality.
Before we discuss a duopoly model with competitive ﬁrms, we explain a simple monopoly
model with competitive ﬁrms, which clariﬁes the eﬀect of competitive ﬁrms on the incentivesof dominant ﬁrms to engage in quality investments.
Suppose that there are a dominant ﬁrm and competitive fringe ﬁrms. We call this situationa “monopoly with fringe ﬁrms.” The product quality of the dominant ﬁrm is qd and that ofcompetitive fringe ﬁrms is qc . The former is larger than the latter, that is, qd > qc . The
conditional indirect utility of a consumer of type θ buying one unit of product i (i = d, c) is
given byVi (θ) = y − pi + θqi ,(1)

where pi is the price of product i. Consumers are supposed to be distributed on [0, 1]. The
parameter θ ∈ [0, 1] is interpreted to be the intensity of preference for quality. The distribution
and the density functions are given by F (θ) and f (θ) = F ′ (θ). We assume that the functions
satisfy the standard second-order condition of the monopolist’s optimization problem.
We assume that the price of competitive fringe ﬁrms, pc , is exogenously given. This meansthat competitive fringe ﬁrms do not have any market power. Their available production tech5

nology determines the price of their products. For instance, when the factors for production(e.g., labor, material, facility) are cheap, the price pc is low. The marginal cost of the dominantﬁrm is constant and assumed to be zero for simplicity.
We consider a simple one-shot game. The dominant ﬁrm sets its price pd . Under the model,
we investigate the eﬀects of the changes in pc and qc on the incentive of the dominant ﬁrm toengage in quality investments.

3

Result3.1

Price reduction

First, we investigate the eﬀects of a decrease in pc on the incentive of the dominant ﬁrm toengage in quality investments.
Let p∗d be the equilibrium price. The proﬁt of the dominant ﬁrm is
πd (p∗d ) = p∗d

(

( ∗
))
pd − pc
1−F.
qd − qc

The marginal gain from the quality improvement is given by∂πd (p∗d )p∗ (p∗ − pc )
= d d
f
∂qd
(qd − qc )2)( ∗pd − pc.
qd − qc

If a decrease in pc increases the derivative, it enhances the incentive of the dominant ﬁrm to
improve its product quality; that is, the latter statement holds if∂ 2 πd (p∗d )< 0.
∂qd ∂pc
We now show that this inequality holds. A simple calculation yields
[ ( ∗
)
(
)]
∂ 2 πd (p∗d )p∗dpd − pcp∗d − pc ′ p∗d − pc
=−
f
+
f
(2)
∂qd ∂pc(qd − qc )2
qd − qc
qd − qc
qd − qc
[
( ∗
)
(
)] ∗
pd − pcp∗d (p∗d − pc ) ′ p∗d − pc
dpd
1
∗
+
(2p
−
p
)f
+
f
.
c
d
2
(qd − qc )qd − qc
qd − qc
qd − qc
dpc
Using the ﬁrst-order condition, we derive dp∗d /dpc :
dp∗d
=
dpc

( ( ∗
)
( ∗
)) /( ( ∗)( ∗))pd − pcp∗dpd − pcp∗d′ pd − pc′ pd − pc
f
+
f
2f
+
f
qd − qc
qd − qc
qd − qc
qd − qc
qd − qc
qd − qc6Note that the denominator of this fraction is equal to the product of the second-order condition and −1. This implies that this denominator is positive. Substituting dp∗d /dpc into
∂ 2 πd (p∗d )/∂qd ∂pc , we have
∂ 2 πd (p∗d )pc=−f∂qd ∂pc(qd − qc )2( ∗) /( ( ∗)( ∗))pd − pc
pd − pcp∗d′ pd − pc
2f
+
f
< 0.
qd − qc
qd − qc
qd − qc
qd − qc

We have the following proposition.
Proposition 1 A decrease in pc enhances the incentive of the dominant ﬁrm to engage inquality improvement. That is,∂ 2 πd (p∗d )< 0.
∂qd ∂pc
A decrease in pc has two eﬀects. First, a decrease in pc makes the indiﬀerent consumer’s θlarger. In other words, consumers around this indiﬀerent consumer are highly sensitive toquality improvement (an eﬀect that we call the “direct eﬀect”). A slight improvement in the
product quality signiﬁcantly decreases the indiﬀerent consumer’s θ when pc is small. The direct
eﬀect enhances the incentive to improve product quality. This is related to the ﬁrst term of∂ 2 πd (p∗d )/∂qd ∂pc in (2). Second, a decrease in pc diminishes the demand for the dominant ﬁrm.
The decrease induces the dominant ﬁrm to lower its price pd (an eﬀect that we call the “pricing
eﬀect”). The pricing eﬀect diminishes the gain in quality improvement. This is related tothe second term of ∂ 2 πd (p∗d )/∂qd ∂pc in (2). In this model setting, the direct eﬀect dominates
the pricing eﬀect. Therefore, a decrease in pc enhances the incentive of the dominant ﬁrm toengage in quality improvement.

3.2

Quality improvement

We consider another scenario wherein the competitive condition of the dominant ﬁrm worsens.
An increase in qc also enhances the competitiveness of the market. If the marginal gain of
the dominant ﬁrm from the quality improvement is monotonically increasing in qc , an increasein qc enhances the incentive of the dominant ﬁrm to improve its product quality; that is, thelatter statement holds if∂ 2 πd (p∗d )> 0.
∂qd ∂qc
7

We now show that the inequality does not hold ; that is, an increase in qc diminishes the
incentive of the dominant ﬁrm to improve its product quality. A simple calculation yields
[ ( ∗
)
(
)]
∂ 2 πd (p∗d ) p∗d (p∗d − pc )pd − pcp∗d − pc ′ p∗d − pc
=
2f
+
f
(3)
∂qd ∂qc(qd − qc )3
qd − qc
qd − qc
qd − qc
[
( ∗
)
(
)] ∗
pd − pcp∗d (p∗d − pc ) ′ p∗d − pc
dpd
1∗(2pd − pc )f
+
f
.
+
2
(qd − qc )qd − qc
qd − qc
qd − qc
dqc
Using the ﬁrst-order condition, we have
(
( ∗
)
( ∗
))
pd − pcp∗d1∗′ pd − pc
(2p
−
p
)f
+
f
c
d
dp∗d
q − qcq − qcqd − qc
qd − qc
( ( ∗
)d
( ∗
))
=− d
.
∗
pd
pd − pc
dqc′ pd − pc
2f+fqd − qc
qd − qc
qd − qc
Substituting it into ∂ 2 πd (p∗d )/∂qd ∂pc , we have
∂ 2 πd (p∗d )
p2c
=−
f2
∂qd ∂qc(qd − qc )3) /( ( ∗
)
( ∗
))
( ∗
pd − pcp∗dpd − pc′ pd − pc
2f
+
f
< 0.
qd − qc
qd − qc
qd − qc
qd − qc

We have the following proposition.
Proposition 2 An increase in qc diminishes the incentive of the dominant ﬁrm to engage inquality improvement. That is,∂ 2 πd (p∗d )< 0.
∂qd ∂qc
An increase in qc also has two eﬀects. First, an increase in qc makes the indiﬀerent consumer’sθ larger. This is similar to the direct eﬀect in the previous subsection. This is related to theﬁrst term of ∂ 2 πd (p∗d )/∂qd ∂qc in (3). Second, an increase in qc diminishes the demand for thedominant ﬁrm. This has two negative eﬀects: the “pricing eﬀect” and the “elasticity eﬀect.”
The former is similar to that in the previous section. The latter is that an increase in qc enhances
the price elasticity of demand. This is an additional negative eﬀect on the incentive to engage
in quality improvement although a decrease in pc merely diminishes demand for the dominantﬁrm. The two negative eﬀects are related to the second term of ∂ 2 πd (p∗d )/∂qd ∂qc in (3). In thismodel setting, the direct eﬀect is dominated by the two negative eﬀects. Therefore, an increasein qc diminishes the incentive of the dominant ﬁrm to engage in quality improvement.

8

4Duopoly with competitive fringe ﬁrms

We extend the basic model by incorporating another dominant ﬁrm. We call this situation a“duopoly with fringe ﬁrms.” Firms 1 and 2 produce products with quality q1 and q2 , respectively (q1 > q2 ). Competitive fringe ﬁrms produce products with quality qc . Firms 1 and 2
compete in quantity (Bonnano (1986) and Motta (1993)). To simplify the analysis, we assume
that F (θ) = θ.
Consumer θ1 is indiﬀerent between ﬁrms 1 and 2, and is represented as−p1 + θ1 q1 = −p2 + θ1 q2 → θ1 =p1 − p2.
q1 − q2

Consumer θ2 is indiﬀerent between ﬁrm 2 and competitive fringe ﬁrms, and is represented as−p2 + θ2 q2 = −pc + θ2 qc → θ2 =p2 − pc.
q2 − qc

The demands for ﬁrms 1 and 2, d1 and d2 , are given by
d 1 = 1 − θ1 = 1 −p1 − p2
p1 − p2 p2 − pc
, d 2 = θ1 − θ2 =−.
q1 − q2
q1 − q2
q2 − qc

We have to invert the system of demand functions. This gives the following inverse demand
functions:p1 (d1 , d2 ) = q1 + pc − qc − (q1 − qc )d1 − (q2 − qc )d2 ,(4)p2 (d1 , d2 ) = q2 + pc − qc − (q2 − qc )d2 − (q2 − qc )d1 .

(5)

The proﬁts of ﬁrms 1 and 2 are
π1 = p1 (d1 , d2 )d1 , π2 = p2 (d1 , d2 )d2 .
The ﬁrst-order conditions lead to
pc + 2q1 − q2 − qc,
4q1 − q2 − 3qc(2q1 − q2 − qc )pc + (q1 − qc )(q2 − qc )d∗2 =,(q2 − qc )(4q1 − q2 − 3qc )qc (q1 − qc )(q2 − qc ) − ((q1 − qc )2 + 2(q1 (q2 − qc ) + q2 (q1 − q2 )))pcd∗c =.
qc (q2 − qc )(4q1 − q2 − 3qc )

d∗1 =

9

Note that d∗c is the demand for fringe ﬁrms and is derived by dc = (p2 − pc )/(q2 − qc ) − pc /qc .
For any i ∈ {1, 2, c}, d∗i must be larger than 0. We therefore impose the following assumption:pc <qc (q1 − qc )(q2 − qc ).
2
(q1 − qc ) + 2(q1 (q2 − qc ) + q2 (q1 − q2 ))The proﬁts of the ﬁrms are
π1∗ = (q1 − qc )(d∗1 )2 ,π2∗ = (q2 − qc )(d∗2 )2 .

4.1

Price reduction

As in the previous section, we derive the cross partial derivatives of the proﬁts to evaluate theeﬀect of a decrease in pc on the incentives of ﬁrm 1 and 2 to engage in quality investments.
The partial derivatives and the cross partial derivatives of the proﬁts are given as∂π1∗(pc + 2q1 − q2 − qc )(7(q1 − qc )2 + (q1 − q2 )2 − (4p1 + p2 − 5pc )pc )=,∂q1(4q1 − q2 − 3qc )3∂π2∗= ((q1 − qc )(q2 − qc ) + (2q1 − q2 − qc )pc )∂q2(q1 − qc )(q2 − qc )(4q1 + q2 − 5qc ) − (7(q1 − qc )2 + (q1 − q2 )2 )pc
×,(q2 − qc )2 (4q1 − q2 − 3qc )32((4q1 + q2 − 5qc )pc − (q2 − qc )2 )∂ 2 π1∗=−,∂q1 ∂pc(4q1 − q2 − 3qc )3∂ 2 π2∗2{(q1 − qc )(q2 − qc )3 + (2q1 − q2 − qc )(7(q1 − qc )2 + (q1 − q2 )2 )pc }=−.
∂q2 ∂pc(q2 − qc )2 (4q1 − q2 − 3qc )3
From the equations, we have the following proposition.
Proposition 3 A decrease in pc enhances the marginal gain from the marginal increase in qi(i = 1, 2) given the other values; that is, ∂ 2 πi∗ /∂qi ∂pc < 0 if and only if
qc (q1 − qc )(q2 − qc )(q2 − qc )2< pc <
2
4q1 + q2 − 5qc(q1 − qc ) + 2(q1 (q2 − qc ) + q2 (q1 − q2 )). Otherwise, a decrease in pc enhances the marginal gain from the marginal increase in q2 , butdiminishes that from the marginal increase in q1 .

10

As in the standard vertical diﬀerentiation model, the product of ﬁrm 2 is more similar to thatof fringe ﬁrms than that of ﬁrm 1. Because of this similarity, a change in pc aﬀects ﬁrm 2 more.
The inequality, ∂d∗2 /∂pc > ∂d∗1 /∂pc , reﬂects this property.
As in the previous section, a decrease in pc enhances the incentive of ﬁrm 2 to engage inquality investment. The decrease in pc , however, diminishes the amount of quantity supplied
by ﬁrm 2, d∗2 , due to the shrinking of the inverse demand for ﬁrm 2, p2 (d1 , d2 ). Because of thestrategic substitution between the productions of ﬁrms 1 and 2, the decrease in d2 enhances
the amount of quantity supplied by ﬁrm 1, d1 (an eﬀect we call the “strategic eﬀect”). The
decrease in pc , however, shrinks the inverse demand for ﬁrm 1, p1 (d1 , d2 ) (an eﬀect we callthe “direct eﬀect”). The latter two eﬀects are trade-oﬀs in the incentive of ﬁrm 1 to engage
in quality investment. On the one hand, the direct eﬀect does not depend on the exogenous
parameters (see (4) and (5)), which means that ∂pi (d1 , d2 )/∂pc = 1 is constant. On the other
hand, the strategic eﬀect depends on the exogenous parameters. We can easily ﬁnd this by
deriving the reaction functions of the ﬁrms:
q1 + pc − qc − (q2 − qc )d2,2(q1 − qc )q2 + pc − qc − (q2 − qc )d1
d2 (d1 ) =.
2(q2 − qc )d1 (d2 ) =

(6)
(7)

Because q1 − qc > q2 − qc , a decrease in pc diminishes d2 (d1 ) more than it reduces d1 (d2 ). Thistendency becomes stronger as the value of q1 increases. Because of this tendency, the strategic
eﬀect is stronger than the direct eﬀect if the value of q1 is large enough.
Numerical example

We consider a two-stage game. First, ﬁrms 1 and 2 engage in quality

investments given their ex ante quality levels. Second, given the investment levels, the two ﬁrms
simultaneously determine their quantities supplied. We set the following numerical example:
qc = 1/10, q1 = 1/2 + e1 , q2 = 1/5 + e2 , and I(ei ) = e2i /2, where ei is the quality improvementlevel of ﬁrm i and I(ei ) is the investment cost of ﬁrm i. This kind of ex ante ﬁrm heterogeneity
is often used in the context of R&D. See, for instance, Barros and Nilssen (1999) and Ishida etal. (2011).

11

We choose two values of pc to check how a decrease in pc changes the incentives of the two
ﬁrms to engage in quality investments: (i) pc = 1/80 and (ii) pc = 1/100. Under the two cases,
the equilibrium investment levels of the ﬁrms are given as follows:(i) e1 = 0.251222, e2 = 0.081652; (ii) e1 = 0.251228, e2 = 0.082198.
We ﬁnd that the decrease in pc from 1/80 to 1/100 enhances the R&D incentives of the ﬁrms.

4.2

Quality improvement

We brieﬂy discuss the eﬀect of an increase in qc on the cross partial derivatives of the proﬁts.
Although the result of the calculus is highly complex, we ﬁnd the following properties of thecross partial derivatives. First, the sign of ∂ 2 π1∗ /∂q1 ∂qc is indeterminate. Second, the sign of∂ 2 π2∗ /∂q2 ∂qc is minus. The negative eﬀect of an increase in qc on the incentive of ﬁrm 2 issimilar to that in the previous section. Because of the negative eﬀect, the quantity supplied byﬁrm 1 can increase. This enhances the incentive of ﬁrm 1 to engage in quality investment.

5

Conclusion

We investigate what kind of competitive pressure induces existing ﬁrms to engage in more
intensive innovation activities. We examine two types of competitive pressure: a price decreasein competitive fringe ﬁrms and a quality improvement therein. We use an oligopoly modelwith vertical diﬀerentiation to investigate this question. This model setting enables us toinvestigate the eﬀect of competitive pressure on ﬁrms producing diﬀerent kinds of productqualities. We believe that this model setting captures the example of the Taiwanese bicycle
industry mentioned earlier in the Introduction: the two leading ﬁrms are analogous to Giantand Merida, and the decrease in the exogenous price of competitive ﬁrms is akin to the threatof low-cost, low-price competition by small Chinese bicycle ﬁrms.
We show that a decrease in the exogenous price of competitive ﬁrms induces the existingleading ﬁrms to engage more in quality investments if the ex ante quality level of the highest
quality product is large enough; otherwise, only the mid-quality ﬁrm engages more in quality

12

investment. We also show that an increase in the exogenous quality level of competitive ﬁrms
diminishes the incentive of the mid-quality ﬁrm to engage in quality investments. Because ourpaper distinguishes between the two eﬀects of competition enhancement, a price decrease incompetitive products and a quality improvement in competitive products, we can clarify thediﬀerence between the two eﬀects. Our results add a new insight to the existing knowledge on
R&D and on the quality standard. Moreover, our result clearly indicates the condition thatexisting ﬁrms can collaborate with each other in their R&D activities, which provides a usefulmanagerial implication for existing companies facing competitive threats from emerging ﬁrms.
We do not consider cooperative actions concerning R&D between existing ﬁrms. In particular, in the example discussed in our paper, the manner in which the ﬁrms collaborate is an
important topic. In our paper, we believe that we partially answer why ﬁrms form an R&D
collaboration network. One of the possible reasons is that both ﬁrms need product quality
improvements. If this does not hold, it is diﬃcult to form such an R&D collaboration network.
We need to further investigate why ﬁrms form an R&D collaboration network and how they
coordinate within the network. This is left for future research.

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