GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.159

Multi-market Competition, R&D, and Welfare in Oligopoly

Akio Kawasaki, Ming Hsin Lin, and Noriaki Matsushima

October 2010

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

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

Multi-market competition, R&D, and welfare in oligopoly∗
Akio Kawasaki
Faculty of Education, Kagoshima University
Ming Hsin Lin
Faculty of Economics, Osaka University of Economics
Noriaki Matsushima†
Institute of Social and Economic Research, Osaka University
October 4, 2010

Abstract
We investigate a multi-market Cournot model with strategic process R&D investments wherein a multi-market monopolist meets entrants that enter one of the markets.
We find that entry can enhance the total R&D expenditure of the incumbent firm. Thatis, entry can stimulate R&D effort. Moreover, the incumbent’s profit nonmonotonicallychanges as the number of entrants increases. Depending on the fixed entry costs andR&D technologies, both insufficient and excess entry can appear.

JEL classification: L13, O32, L11
Key words: multi-market, oligopoly, process R&D, entry, welfare∗

An earlier version of this paper was presented at Applied Economics Workshop held at Kyushu University.
The authors wish to thank Nobuaki Hori (Kyushu University), Konari Uchida (Kyushu University), and otherparticipants for their useful comments. We gratefully acknowledge financial support from Grant-in-Aid fromthe Japanese Ministry of Education, Science and Culture. Needless to say, we are responsible for any remaining
errors.
†Corresponding author: Noriaki Matsushima, Institute of Social and Economic Research, Osaka University,
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. E-mail: nmatsush@iser.osaka-u.ac.jp

1

Introduction

Asymmetric competition between multi-product firms and single-product firms is commonly
observed. In the retail industry, nationwide retailers (Walmart, Metro, etc.) compete withlocal retailers in each region. In the airline industry, network carriers operating multiple
routes compete with regional carriers or low-cost carriers on certain routes. In the vehicleindustry, automobile (cars, buses, and trucks) producers compete with some automakers
that specialize in the production of cars. In those industries, multi-product firms can havecompetitive advantages relative to their competitors because of their product multiplicities.
This is because those multi-product firms are able to apply their technologies to multiple
production lines. In addition, because those firms apply the outcomes of R&D to theirproducts, their returns from R&D are greater, and the multiplicities of products can generatecompetitive advantages.1 Given these observations, this paper investigates how market entry
affects the multi-product firms’ process R&D and profits, as well as how social welfare is
influenced.
The basic model structure is as follows. An incumbent provides a product (call it A).
Rival firms can also produce product A. The incumbent also provides another product (callit B). No potential entrants can supply product B. In other words, the incumbent is themonopolist in market B. There are several possible reasons why no entrant produces productB. For instance, product B includes advanced technologies that are available only to theincumbent. Potential entrants do not have sufficient skills to use those advanced technologies
and/or those technologies are patented by the monopolist. Another reason is that market
B is regulated by governmental authorities. For instance, this is because the incumbent
engages in lobbying activities to protect market B.
Unlike the result that is expected in a standard Cournot model (i.e., an entry will diminish
1

The standard model of strategic R&D is formulated by Brander and Spencer (1983), and the literature

dealing with strategic R&D competition is now fairly abundant (Spence, 1984; d’Aspremont and Jacquemin,
1988; Suzumura, 1992; Lahiri and Ono, 1999; and Kitahara and Matsumura, 2006).

1

the incumbent’s incentive to engage in R&D investment), we first show that entry canenhance the total R&D expenditure of the incumbent if the level of the incumbent’s costreducing technology is higher than a threshold level. Note that the threshold level can belower than the levels of the entrants’ cost-reducing technologies. That is, even though thecost-reducing technology of the incumbent is inferior to that of entrants, entry can stimulate
the incumbent’s R&D. We now discuss the intuition behind the result. On the one hand,entry in market A steals the incumbent’s quantity supplied and weakens its incentive toengage in R&D. The existence of market B, however, allows the incumbent to maintain its
total quantity supplied because entry only occurs in market A. This high level of supply
maintains the incumbent’s incentive for cost-reducing R&D efforts. On the other hand, there
exists a strategic effect of entry in which the R&D effort reduces the entrant’s quantity, which
benefits the incumbent by raising the price. The strategic effect can dominate the decreasein the quantity supplied in market A. As a result, the incumbent enhances its R&D efforts
following entry.
Moreover, we find that the incumbent’s profit nonmonotonically changes as the numberof entrants increases. Specifically, an additional entry increases the incumbent’s profit when
the number of existing entrants is large. As described in the first result, entry can accelerate
the R&D incentive of the incumbent. This implies that entry can be used as a credible
commitment of the incumbent to invest more. This commitment diminishes the incentivesof entrants to invest. Because the strategic effect is related to the entrants’ reactions, as thenumber of entrants increases, the strategic effect mentioned above is stronger. This is why
an additional entry can increase the incumbent’s profit when the number of existing entrants
is large.
Concerning a single product market, Ishida et al. (2010) show that entry of inefficientfirms can stimulate cost-reducing R&D by the efficient incumbent firm. Moreover, entry
of inefficient firms can enhance the profit of the incumbent firm if the incumbent’s ex ante2

marginal cost is small enough.2 That is, a significant cost advantage of the incumbent is thedriving force that enhances the profit of the incumbent by entry. It is noteworthy here thatour property is quite different from that in Ishida et al. (2010). Our model assumes thatthe cost-reducing technology of the incumbent in itself can be inferior to those of potential
entrants, whereas Ishida et al. (2010) assume that the incumbent has a superior ex ante
marginal cost.3 Adding our new results, we can say that the difference in ex ante marginal
costs plays an important role in inducing aggressive R&D investments by the incumbent in asingle market case; however, such a difference is not necessarily important in a multi-productmarket.
Our analysis on social welfare focuses on the effect of entry. In the previous papers dealing
with the entry problem, excess entry always happens in the standard Cournot models (e.g.,
Mankiw and Whinston, 1986; Suzumura and Kiyono, 1987). Moreover, Okuno-Fujiwara andSuzumura (1993) show that the excess entry theorem holds even when symmetric firms inthe single product market engage in cost-reducing R&D investments. The main reason is thebusiness-stealing effects of entry. Our paper also finds that the first entry tends to enhance
consumer welfare although it is excessive from the viewpoint of social welfare. However,excess entry does not always hold under free entry. We show that depending on fixed entry
costs and R&D technologies, both insufficient and excess entry can appear. When the fixedentry costs are small and the incumbent firm’s R&D technology is not so inefficient when2

Several recent studies have discussed instances where an increase in the number of firms may actually

increase firm profit. Coughlan and Soberman (2005), Chen and Riordan (2007), and Ishibashi and Matsushima(2009) belong to this line of research, but the underlying mechanism of our model differs substantially fromtheirs. In these previous studies, market entry works as a commitment device to soften market competition,
so that the market actually becomes less competitive as it is entered by more firms. Moreover, those papers
do not include R&D investments. Using vertical relationships between upstream and downstream firms,
Tyagi (1999), Pack and Saggi (2001) and Mukherjee et al. (2009) show that entry can enhance the profits ofincumbents. Using asymmetric Stackelberg oligopoly models, Pal and Sarkar (2001) and Mukherjee and Zhao
(2009) show the possibilities of increases in existing firms’ profits by entry. In the two papers, asymmetry
among the firms is a key factor in deriving their main result, whereas the main mechanism in deriving ours
is quite different.
3
In Ishida et al. (2010), similar results can be derived even when the incumbent has a superior costreducing technology given that the ex ante marginal costs of entrants and the incumbent are common.

3

compared with those of entrants, market entry is insufficient from the viewpoint of social
welfare. This is because entry of new firms can enhance the incumbent’s R&D investment in
our model, while entry always diminishes R&D investment in Okuno-Fujiwara and Suzumura(1993). When the incumbent’s R&D technology is efficient, this effect is strong and then its
market share becomes large. In this situation, the incumbent’s R&D should be stimulatedby entry from the viewpoint of social welfare. However, the incumbent’s stronger incentive
for R&D diminishes the profitability of each entrant and then it deters entry. Consequently,
entry is insufficient.
Several papers have already shown market structures in which insufficient entry appears
in equilibrium. Anderson and Engers (2001), Matsumura and Okamura (2006), and Gu andWenzel (2009) investigate equilibrium entry in spatial models a la Vickrey (1964, 1999) andSalop (1979). Mukherjee and Mukherjee (2008) investigate a Cournot model with licensing.
Schmidt (2009) investigates vertical differentiation models. Ghosh and Morita (2007a,b) and
Mukherjee et al. (2009) take into account vertical relationship. Those papers do not consider
R&D investments in oligopoly.
The remainder of this paper is organized as follows. Section 2 presents the model. Section
3 derives the outcomes of the monopoly and duopoly cases to nvestigate the effects of strategic
R&D investments by the first entry. Section 4 deals with the oligopoly case. Section 5
concludes the paper.

2

Multi-product Monopolist and Entrants

A multi-product monopolist exists. It produces two products, A and B. Product A is
produced with a standard technology that is also available to potential entrants (we explain
entry of those entrants later). Product B is produced with the standard technology and an
advanced technology that is not available to potential entrants. For instance, the advanced
technology is patented by the incumbent monopolist. As a result, potential entrants cannot

4

produce product B. In other words, the incumbent operates as a monopolist of product B.4
For the products, the inverse demand functions are assumed as follows:
pA = 1 − QA , pB = 1 − QB ,where pi is the price of product i and Qi is the total quantity of product i (i = A, B).
We now assume that there are n entrants in market A (we discuss the case in which n
is endogenously determined in Section 4). The incumbent and the n entrants are able toengage in cost-reducing investments related to the standard technology. Assume that c isan initial common constant marginal cost. When the incumbent (I)/an entrant (E) engages
in cost-reducing R&D, it reduces its marginal cost from c to c − ei (i = I, E) and incurs
the investment cost ki e2i , where ei is the R&D effort level of i and ki is a positive constant(i = I, E). To simplify the analysis, we assume that kI = k > kE = 1 and k > 3/2. The
assumption k > 3/2 ensures that each entrant supplies a positive quantity for any n (evenwhen k < 3/2, our main results hold). That is, each entrant has a more efficient cost-reducing
technology than the incumbent. For instance, entrants can concentrate their efforts toward
the cost reductions concerning the standard technology whereas the incumbent has to put
its effort toward both the standard and the advanced technologies.
The profit of the incumbent isÃ!
nX
qEi − (c − eI ) qAI + (1 − qBI − (c − eI ))qBI − ke2I ,πI = 1 − qAI −

(1)

i=1

where qjI is the quantity supplied by the incumbent in market j (j = A, B), and qEi is thequantity supplied by entrant i in market A (i = 1, 2, . . . , n).
The profit of entrant i is
πEi = 1 − qAI − qEi −X

qEj − (c − eEi ) qEi − e2Ei .

(2)

j6=i

4

For expositional simplicity, we assume that only one firm supplied its products to the two markets. This

assumption is not essential to derive our main results.

5

We consider two cases: (i) the incumbent is a monopolist; and (ii) entrants also produce
product A. We consider the following two-stage game. First, the firm(s) simultaneously
set(s) the effort level(s) eI and eEi (i = 1, 2, . . . , n). Second, the firm(s) simultaneously
set(s) the quantities supplied qjI (j = A, B) or qEi (i = 1, 2, . . . , n). The solution concept is
a subgame perfect Nash equilibrium.

3

Equilibrium: Monopoly and Duopoly

We first show the results under the cases of monopoly and duopoly. In Section 4, we show
the results under the cases of oligopoly and free entry.

3.1

Monopoly

We first solve the monopoly case to provide a comparison between the monopoly and the
duopoly cases.
Given eI , the quantities supplied by the incumbent are
qAI = qBI =1 − c + eI.
2

In the first stage, the incumbent determines eI . The first-order condition is∂πI
2(1 − c) − 2(2k − 1)eI
=
= 0.
∂eI
2
This leads to
eM
I =

1−c
.
2k − 1

The quantities supplied and the profit are
M
M
qAI
= qBI
=

(1 − c)k(1 − c)2 k, πIM =.
2k − 12k − 1

The consumer surplus and the social surplus are
CS M =(1 − c)2 k 2(1 − c)2 k(3k − 1)
M
,
SW
=
.
(2k − 1)2
(2k − 1)2

6

3.2

Duopoly

We solve the duopoly case. We compare this case with the monopoly case discussed above.
Given eI and eE (we omit “1” from “E1”), the quantities supplied by the incumbent andthe entrant areqAI =1 − c + eI
1 − c + 2eE − eI
1 − c + 2eI − eE
, qBI =
, qE =.
3
2
3

In the first stage, the incumbent determines eI and the entrant determines eE . The
first-order conditions are∂πI
17(1 − c) − (36k − 25)eI − 8eE
=
= 0,
∂eI
18
∂πE
2(2(1 − c) − 5eE − 2eI )
= 0.
=
∂eE
9
The first-order conditions lead toeDI =4(6k − 7)(1 − c)23(1 − c)
, eD
.
E =
60k − 4760k − 47

The quantities supplied by the incumbent and the entrant areDqAI=

3(1 − c)(4k + 3)
6(1 − c)(5k − 2)
6(1 − c)(6k − 7)
D
D
, qBI
, qE
.
=
=
60k − 4760k − 4760k − 47

The profits of the incumbent and the entrant areπID =(1 − c)2 (1044k 2 − 1033k + 225)
20(1 − c)2 (6k − 7)2
D
,
.
π
=
E
(60k − 47)2
(60k − 47)2

The consumer surplus and the social surplus are
SW D =
Quantity(1 − c)2 (6732k 2 − 9314k + 3643)
9(1 − c)2 (356k 2 − 432k + 137)
D
,
.
CS
=
2(60k − 47)22(60k − 47)2
We now briefly discuss the quantities supplied by the firms. By entry, theM > q D , (ii) q M ≤quantities supplied by the incumbent are changed as follows: (i) qAIAIBI
D iff k ≤ 12/7. The inequality (i) reflects the fact that competition reduces the quantity.
qBI

The reason why the inequality (ii) holds is that the incumbent’s R&D effort can be stimulated7

by entry. In market A, the difference between the quantities supplied by the incumbent andD − q D ≤ 0 iff k ≥ 17/8. If the entrant’s cost-reducing technology
the entrant is as follows: qAIE

is highly efficient, it produces more than the incumbent. These discussions can be appliedalso to the oligopoly case in the next section.
An entry and R&D effort

We now compare the R&D efforts of the incumbent in thetwo cases. The difference between the R&D efforts isMeD
I − eI =2(1 − c)(12 − 7k).
(2k − 1)(60k − 47)(3)

From the equation, we have the following proposition.
Proposition 1 The incumbent’s investment level under duopoly is larger than that undermonopoly if and only if k < 12/7.
That is, if the cost-reducing technology of the incumbent is not so inefficient, an entry
enhances the R&D incentive of the incumbent.
We now explain the mechanism behind Proposition 1. The effect of the investment on
the incumbent’s profit is written as
∂πID
=
∂eI

D
D ∂qE
D
D
p0A qAI+ (qAI+ qBI) − I 0 (eI ),
{z
}
|
∂eI
| {z }
cost-reducing effectstrategic-effectwhere I(·) is the investment cost of the incumbent. The cost-reducing effect is based on
the total quantity supplied by the incumbent. The total quantity decreases because of theentry. This decrease diminishes the incentive to engage in R&D. The strategic effect consistsof two elements: one is that a reduction in the rivals’ quantities leads to an increase in theprice; the other is that the benefit from an increase in the price is proportional to its own
quantity in market A. The first element is not correlated to the value of k, but the second is
D is related to the value of k. That is, whenindirectly correlated to the value of k because qAI

k is small (the cost-reducing technology of the incumbent is not so inefficient), the strategic8effect becomes significant. To sum up, the entry enhances the strategic effect whereas it
diminishes the cost-reducing effect.
Figure 1 summarizes the explanation. On the one hand, the decrease in the cost-reducing
effect lowers the incumbent’s marginal benefit of investment. On the other hand, the strategic
effect enhances the incumbent’s marginal benefit of investment. Therefore, the marginal
benefit function under the duopoly case (M B D in the figure) is steeper than that under themonopoly case (M B M ) because there is no strategic effect in the monopoly case. Dependingon the value of k, the entry effect on R&D is determined.
[Figure 1 here]
This property is quite different from Ishida et al. (2010) who also show the investmentenhancing effect of entry. Our model assumes that the cost-reducing technology of theincumbent in itself is inferior to those of potential entrants, whereas Ishida et al. (2010)
assume that the incumbent has a superior production technology.
An entry and welfare

The entry tends to enhance consumer welfare although it isexcessive from the viewpoint of social welfare (see Figure 2). The increment in consumer(social) welfare is larger (smaller) than the profit of the entrant. This is because the entry canincrease the incentives of R&D investments and decreases the market price of product A. The
duplication of the R&D investments is wasteful from the viewpoint of social welfare. This issignificant when k is small (the incumbent’s marginal investment cost is small). This logic,
however, does not always hold when the number of entrants is endogenously determined.
[Figure 2 here]

4

Equilibrium: Oligopoly and Free Entry

We first consider an entry in the case where n entrants exist in market A. Next, we investigate
welfare under free entry in market A.

9Given eI and eEi (i = 1, 2, . . . , n), the quantities supplied by the incumbent and theentrants areP
1 − c + (n + 1)eI − ni=1 eEi
1 − c + eIqAI =, qBI =,
n+22P
1 − c + (n + 1)eEi − eI − j6=i eEj
qEi =
.
n+2
In the first stage, the incumbent determines eI and each entrant determines eEi (i =1, 2, . . . , n). The first-order conditions areP(1 − c)(n2 + 8n + 8) − (4(n + 2)2 k − (5n2 + 12n + 8))eI − 4(n + 1) ni=1 eEi
∂πI
=
= 0,
∂eI
2(n + 2)2P
2((1 − c)(n + 1) − (2n + 3)eEi − (n + 1)eI − (n + 1) j6=i eEj )
∂πEi
=
= 0.
∂eEi
(n + 2)2
The first-order conditions lead to(1 − c)(n3 + 4n2 + 10n + 8),
4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8)
2(1 − c)(n + 1)(2(n + 2)k − (3n + 4))
eO
.
Ei =
4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8)eO
I =The quantities supplied by the incumbent and the entrants are(1 − c)(n + 2)(4k + n(n + 2)),
4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8)
2(1 − c)(n + 2)((n2 + 2n + 2)k − n(n + 1))
O
qBI
=
,
4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8)
2(1 − c)(n + 2)(2(n + 2)k − (3n + 4))
O
qEi
=
.
4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8)O
qAI=

The profits of the incumbent and the entrants are(1 − c)2 (n + 2)2 (4k + n(n + 2))2(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))24(1 − c)2 (n + 2)2 ((n2 + 2n + 2)k − n(n + 1))2+(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))2
(1 − c)k(n3 + 4n2 + 10n + 8)2−,(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))24(1 − c)2 (2n + 3)(2(n + 2)k − (3n + 4))2
O
.
πEi
=
(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))2
πIO =

10

The social surplus and consumer surplus are
CS O =(1 − c)2 (n + 2)2 (4(n + 1)2 k − (5n + 6)n)22(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))22(1 − c)2 (n + 2)2 ((n2 + 2n + 2)k − (n + 1)n)2+,(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))2O
SW O = CS O + πIO + nπEi.

An entry and R&D effort

As explained in the previous section, an increase in n canstimulate the R&D efforts of the incumbent. The partial derivative of eO
I with respect to nis∂eO
4(1 − c)[(n4 + 16n3 + 46n2 + 48n + 16) − 4(2n3 + 7n2 + 8n + 2)k]I=.
∂n(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))2

(4)

From the equation, we have the following proposition.
Proposition 2 The incumbent’s investment level is increasing in n if and only ifk<n4 + 16n3 + 46n2 + 48n + 16.
4(2n3 + 7n2 + 8n + 2)

This is summarized in Figure 3. For any n ≥ 1, the right-hand side is increasing in n. Whenn = 1, this is 127/76 ' 1.671.5 The reason why the inequality holds is similar to that in theprevious section.
[Figure 3 here]
Entry and the profit of the incumbent

The partial derivative of the incumbent’s

profit is∂πIO
16(1 − c)2 (n + 1)(4k + n(n + 2))=−∂n(4(n + 2)(n2 + 2n + 2)k − (5n3 + 16n2 + 18n + 8))3(5)× [(n + 1)(7n2 + 20n + 16) − (48 + 90n + 54n2 + 11n3 )k + 4(n + 2)3 k 2 ].
From the equation, we have the following proposition.
5Note that the upper bound of k is different from that in the duopoly case. In this subsection, we use

differentiation to derive the upper bound whereas in the previous subsection we use the difference between
the duopoly and the monopoly cases. The methodological difference leads to slightly different results.

11

Proposition 3 The incumbent’s profit is increasing in n if and only ifk<11n3 + 54n2 + 90n + 48
8(n + 2)3√
9n6 + 84n5 + 384n4 + 984n3 + 1380n2 + 960n + 256+.
8(n + 2)3

(6)

This is summarized in Figure 4. When n is large and k is small, an additional entry canincrease the profit of the incumbent. As explained before, when k is small, an increase in
the number of entrants accelerates the R&D incentive of the incumbent. An entry can bea credible commitment of the incumbent to invest more. This commitment diminishes the
incentives of entrants to invest. As a result, an additional entry can increase the incumbent’s
profit.
[Figure 4 here]
Entry and welfare

In this model, we can make examples of both excess and insufficient

entry. When k is small, whether or not entry is excessive depends on the fixed entry costs.
We can also show that when k is large, excess entry appears.
In Figure 5, we depict three curves. The curve πE = F indicates the equilibrium numberof entrants given k. This curve shows that the equilibrium number of entrants increases
with the increase in k. The curve ∂SW O /∂n = F indicates a necessary condition that social
welfare is maximized. The curve SW M = SW O − nF indicates that social welfare under themonopoly case is equal to that under the n-firm oligopoly case. The upper (lower) regionof SW M = SW O − nF indicates that SW M > SW O − nF (SW M < SW O − nF ). If∂SW O /∂n = F is on the lower region of SW M = SW O − nF , the social optimal number ofentrants is indicated by the thick curve on ∂SW O /∂n = F ; otherwise, the optimal number
is zero (monopoly is the best). For instance, we now suppose that k is smaller than 1.57.
The social optimum number of entrants is more than 30 although the equilibrium numberof entrants is less than 10. This is an example of insufficient entry. We now suppose that k
is larger than 1.6. The social optimum number of entrants is zero although the equilibrium
12

number is larger than five. This is an example of excess entry. This property is summarized
in the following proposition.
Proposition 4 When k is small enough, the equilibrium number of firms is excessive fromthe viewpoint of social welfare.
[Figure 5 here]
We now discuss the intuition behind the tendency. As in the standard Cournot models,
the business-stealing effect leads to excess entry (Mankiw and Whinston, 1986; Suzumura
and Kiyono, 1987; and Okuno-Fujiwara and Suzumura, 1993). In our model, additional
effects exist. When k is small (the cost-reducing technology of the incumbent is not so
inefficient), entry enhances the investment of the incumbent (Proposition 2). This has two
effects: one is positive, the other is negative. The positive effect is that the improvementof production efficiency enhances competition. The negative effect is the duplication of the
R&D investments undertaken by the firms. When k is large, the negative effect is significant
because the incumbent’s R&D technology is inefficient. On the other hand, the incumbent’s
stronger R&D incentive caused by entry diminishes the incentives of potential entrants toenter the market. That is, this strong incentive of the incumbent can deter beneficial entry.
When k is small enough, this entry deterrence effect dominates the standard business-stealing
effect.
In Figure 6, we change the level of the entry cost F . The left-hand (right-hand) figure
shows a case in which F is large (small). As the value of F decreases, the range of k, whichleads to insufficient entry, increases.
[Figure 6 here]
When F is small, the socially optimal number of entrants is large. As mentioned earlier, alarge number of entrants tends to deter beneficial entry because the large number enhances
the incumbent’s R&D investment. Therefore, when F is small enough, the equilibrium
number of entrants tends to be insufficient.
13

5Concluding Remarks

This paper has considered a multi-market model wherein an incumbent meets entrants in
one market while it is a monopolist in the other market, and investigates how the market
entry affects the incumbent’s R&D, its profits, and social welfare. We show that entry canenhance the total R&D expenditure of the incumbent. We also show that an additional entry
can increase the incumbent’s profit when the number of existing entrants is large. Furthermore, our analysis of social welfare shows that depending on the fixed entry costs and R&D
technologies, both insufficient and excess entry can appear in equilibrium. These findings
not only provide useful implications for firms’ strategic behaviors on R&D investments, butalso offer meaningful implications for entry regulators with welfare concerns.
Our model is a standard Cournot type with multiple markets, and has been constructedbased on some observations in which some leading firms with advanced technologies attempt
to provide other new products (i.e., those firms can enter into new markets) by fully exploiting
their standard and advanced technologies. Those leading firms also tend to encourage minor
firms to enter the market of products with standard technologies. Therefore, the market
structure of our model is applicable to various practical situations.
There remain some limitations of the model, which should be addressed in the future.
First, the two products discussed here are independent of each other on the demand side. It
is natural to consider the consumption relationship between the two products. For example,
Dawid et al. (2010) consider that a firm can provide a new product that is horizontallyand vertically differentiated from the current product by product innovation projects. The
consumption relationships might influence the effects of process R&D competition. This topic
can be considered in future research. Second, we can incorporate licensing into our model.
For instance, the incumbent firm can allow other firms to enter the monopolized market
subject to the acceptance of licensing contracts. In this setting, it is not obvious whether or
not the incumbent licenses its technology because new entry caused by the license alter the
incentives of the entrants to engage in R&D. This can also be addressed in future research.
14

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17

MB
MC

MC

MB
MC

M BD

MC

M BD

M BM

0

M
eD
I eI
(k is large)

M BM

0

eI

eM
eD
I
I
(k is small)eI

Figure 1: Marginal benefit and marginal cost of investment

18ΠE ,DSW,DCS
0.2

0.15

DCS

0.1

ΠE
0.05

DSW

1.6

1.8

2

2.2

2.4

k

Figure 2: πE , ∆SW , and ∆CS (the duopoly case)Note: πE , ∆SW , and ∆CS are divided by (1 − c)2 without loss of generality.

19

k
4
3
2
1
0

∂eO
I /∂n < 0∂eO
I /∂n > 05n10

Figure 3: Entries and the incumbent’s investment

20

k
7/4
∂πIO /∂n < 0∂πIO /∂n > 0
3/2
0

n
10

20

30

Figure 4: Entries and the incumbent’s profit

21

k
2

1.9

ΠE =F

1.8

1.7

¶SWO ¶n=F
SWM =SWO -nF

1.6¶SWO ¶n-F>0and
SWM <SWO -nF
10
20
30

40

50

n

πE = F and ∂(SW O − F n)/∂n = 0
Figure 5: Examples of insufficient/excess entries (F/(1 − c)2 = 1/1250)

22

k
2

1.9

k
2

1.9

ΠE =F

1.8

1.8

1.7

1.7

ΠE =F

¶SWO ¶n=F¶SWO ¶n=F
1.6

1.6

SWM =SWO -nF

SWM =SWO -nF
10

20

30

40

50

n

10

πE = F and ∂(SW O − F n)/∂n = 0

20

30

40

50

60

n

πE = F and ∂(SW O − F n)/∂n = 0

Figure 6: Examples of insufficient/excess entries(Left: F/(1 − c)2 = 1/500, Right: F/(1 − c)2 = 1/2500)

23