Strategic Foreign Direct Investment
in Vertically Related Markets∗
Jota Ishikawa†

Eiji Horiuchi

Hitotsubashi University

Teikyo University& RIETI
This Version: November 22, 2011

Abstract
By using a simple North-South trade model with vertically related markets, this paperdraws our attention to previously unidentified eﬀects of foreign direct investment (FDI),
namely that a North downstream firm aﬀects the pricing behavior of an input supplierthrough technology spillovers and market integration led by FDI. Whether the North firm
strategically undertakes FDI in the presence of technology spillovers depends on South firm’s
capacity to absorb North’s technology. When the capacity is not very high, the North firm
could actually gain from technology spillovers to the South firm. FDI may benefit all producers and consumers.
Keywords: FDI, technology spillovers, North-South model, segmented and integrated
markets, vertically related markets
JEL Classification: F12, F21, F23∗ An earlier version of this paper circulated under the title “Strategic Technology Transfer through FDI in

Vertically Related Markets” was written while Jota Ishikawa was visiting School of Economics, University of New
South Wales. Their hospitality is gratefully acknowledged. We are grateful to Makoto Tawada, Don Wright,
two anonymous referees and participants of seminars and conferences, including Hitotsubashi University, Kyoto
University, La Trobe University, National Dong Hwa University, National Taiwan University, University of Hawaii
at Manoa, the Asia Pacific Trade Seminars, the European Trade Study Group, the Midwest International Economics Group, the Hitotsubashi COE/RES Conference on International Trade & FDI, the Japanese Association
for Applied Economics, and the Conference of the European Association for Research in Industrial Economics forvaluable comments on earlier versions. Any remaining errors are our own responsibility. We also acknowledge
financial support from the Japanese Ministry of Education, Culture, Sports, Science and Technology under theCenter of Excellence Projects and RIETI.
† Corresponding author : Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan;
Fax: +81-42-580-8882; E-mail: jota@econ.hit-u.ac.jp1

1

Introduction

Foreign direct investment (FDI) has been expanding dramatically.1 FDI is undertaken for various
reasons such as cost saving, tariﬀ-jumping and information acquiring.2 The purpose of this paper
is to draw our attention to previously unidentified motives for FDI. In particular, we are concernedwith “strategic” motives. In an oligopolistic market, strategic interactions usually arise. Strategic
motives in the present study mean that firms undertake FDI to take advantage of such strategicinteractions under international oligopoly. Specifically, constructing a simple North-South modelwith vertically related markets,3 we identify strategic incentives for a North firm to invest inSouth.
The outline of our model is as follows. There are two countries, North and South. In eachcountry, there is a downstream firm, but the South downstream firm may be a potential entrant.
The final good is sold in North. There is an upstream firm in South. The North downstream
firm may strategically choose South as its plant location. The North downstream firm imports
the intermediate good if it locates in North, but exports the final good if it locates in South. We
explore the North firm’s decision in two cases. In the first case, the South downstream firm is apotential entrant (hereafter, the potential-entrant case). In the second case, it is an incumbent(hereafter, the incumbent case).
When constructing our model, we specifically take the following two features into account.
First, the price discrimination is widely observed between countries. However, it is not the casewithin a country. This is due to the presence of a regulation, an arbitrage opportunity within acountry, and so on. For instance, it is illegal to price-discriminate in the US under a federal law,
the Robinson-Patman Act. We should mention that intermediate goods are no exception to theprice discrimination. Examples include dumping in the semiconductor industry.4 ’5 Therefore,
it is assumed in our model that the upstream firm price-discriminates between two downstream
firms as long as they are located in the diﬀerent countries. However, if the North downstream
firm undertakes FDI and is located in South, the upstream firm sets the uniform price between
the North and the South downstream firms. That is, the intermediate-good market is segmented
without FDI, but is integrated with FDI.
Market integration has been analyzed in the international trade literature, particularly in the
1 For example, see the online data base of the United Nations Conference on Trade and Development (UNCTAD)(http://stats.unctad.org/FDI/).
2 See Dunning (1977) and Caves (2007), for example. Chakrabarti (2001) summarizes the determinants of FDI
in diﬀerent studies.
3 The literature on FDI acknowledges the importance of vertically related markets. For example, Barrios etal. (2005) say “multinationals’ demand for intermediate inputs, ..., can induce changes in the domestic industrial
structure and can kick-start the development of local industry” and confirm this by using Irish data.
4 A well-known example is that the Semiconductor Industry Association accused the Japanese
semiconductor industry of conducting dumping in the US market in the mid 1980’s.
5 For arguments over the price discrimination in the input market, see Katz (1987), DeGraba (1990), Yoshida(2000) and Valletti (2003), among others.

2context of regional trade agreements such as customs unions and free trade agreements.6 As far
as we know, however, no study has connected FDI with market integration in the intermediategood market. An interesting point is that FDI could be motivated by price discrimination in theintermediate-good markets. This motive should be distinguished from another motive to reducetransport and other trade costs. In this paper, the eﬀect that FDI leads to market integration of
the intermediate good is referred to as “the market integration eﬀect”.
Typical examples fitting our argument are natural resources. The Chinese government has
been controlling the exports of rare earth to increase the prices in the foreign markets.7 By
doing so, the Chinese government intends to induce high-tech firms using rare earth as the key
inputs to produce in China. In fact, Hitachi Materials and Showa Denko have recently decided toshift the production of high-performance magnets and high-performance alloys, respectively, toChina.8 They have never produced those goods outside of Japan to prevent technology leakage.
Similarly, to attract FDI, petroleum exporting countries in the Middle East strategically oﬀermaterials such as natural gases to foreign petrochemical companies at low prices. The material
price paid by Petro Rabigh, which is a joint venture between Sumitomo Chemical and Saudi
Aramco and is one of the largest petrochemical plants in the world, is about one tenth of that
paid by foreign rivals in developed countries (Nikkei, November 11, 2009). Not only Sumitomo
Chemical but also Asahi Kasei, Dow Chemical, and Mitsubishi Chemical have invested or areplanning to invest in Saudi Arabia.9
Second, FDI generates technology or knowledge spillovers to local rivals. Keller (2004) says
“For instance, both micro-econometric studies and case studies point in the same direction. The
evidence suggests that there can be FDI spillovers, ...”10 The advanced technology of the Northdownstream firm spills over to South’s rival only if the North firm builds its plant in South.11 In
this paper, this eﬀect is referred to as “the technology spillover eﬀect”. In the potential-entrant
case, the technology spillover eﬀect may lead South’s potential entrant to enter the market. It has
been pointed out that technology spillovers crucially depend on South firm’s capacity to absorb
North firm’s technology.12 Following Cohen and Levinthal (1989, 1990), we call such a capacity
6 For example, see Smith and Venables (1988), Ishikawa (2004) and Ishikawa et al. (2007).
7 The Ministry of Economy,

Trade and Industry of Japan points out that the price gaps between Chinese

markets and foreign markets are extraordinarily large.
8 Toyota has recently announced to produce key parts such as engines for hybrid vehicles in China, because rareearth is indispensable to those high-tech parts (Nikkei, September 4, 2011).
9 With respect to manufacturing, Nikkei Business (October 4, 1993) reports that the prices of intermediate
inputs (such as ABS polymer, polystyrene and galvanized sheet steel) for a Japanese consumer electronics company
are more than 30% lower in Thailand than in Japan. Recently, the largest Japanese consumer electronics company,
Panasonic, has decided to shift the procurement department from Japan to Singapore to procure cheap parts andproduce outside Japan (Nikkei, August 11, 2011).
1 0 For emprical evidences, see Kokko (1994), Dimelis and Louri (2002), Griﬃth et al. (2002), Görg and Strobl(2002,2003), Smarzynska Javorcik (2004), and Branstetter (2006), for example. For theoretical studies, see Findlay(1978), Ethier and Markusen (1986), and Glass and Saggi (1999,2002), for example.
1 1 Empirical studies such as Eaton and Kortum (1999), Branstetter (2001) and Keller (2002) suggest thatknowledge spillovers are geographically localized.
1 2 See, for example, Findly (1978), Kokko (1994) and Glass and Saggi (1998).

3

“absorptive capacity”. We show that South firm’s absorptive capacity also plays a crucial role in
our analysis.
In the presence of FDI spillovers, FDI seems detrimental to the interests of the investing
firm, because it makes competition tougher either by making the local incumbent firm more
eﬃcient or by creating a new rival. In the potential-entrant case, however, the “investing” firm
may gain from FDI spillovers. In other words, the investing firm may take advantage of FDI
spillovers. When FDI induces the entry of a potential entrant, this aﬀects the pricing behavior of
the upstream firm and hence the profits of the investing firm. In fact, under certain situations,
all producers as well as consumers gain from FDI, that is, market integration of the intermediate
good and technology spillovers through FDI result in Pareto gains. In the incumbent case, FDI
spillovers are mostly harmful for the investing firm,13 but it could still gain from FDI because of
the market integration eﬀect. Pareto gains are also possible in the incumbent case.
Another contrast between the potential-entrant case and the incumbent case is that FDI
induces the South firm to enter the market in the former, while it may force the South firm
to exit the market in the latter. In general, the entry is induced by the technology spillover
eﬀect, while the exit is due to intensified competition.14 In our incumbent case, FDI increases
the intermediate-input price due to the market integration eﬀect, which could dominate thetechnology spillover eﬀect and induce exit.
There are not many studies that deal with strategic motives of FDI. Horstmann and Markusen(1987) and Vannini (1998) consider the preemptive motive for FDI. Under this motive, a multinational enterprise (MNE) undertakes FDI to delay the entry of local firms. Similarly, Lin and
Saggi (1999) argue that a MNE may undertake FDI to delay other MNEs’ switch from exports to
FDI. The delay is caused because FDI makes the local firm’s imitation of an advanced technology
easier and intensifies competition in the South market. Our incumbent case is somewhat related
to the preemptive motive. FDI raises the cost of the intermediate input and makes the local firm
less competitive and hence it is forced to exit the market under certain circumstances. Bjorvatn
and Eckel (2006) show another reason why a North firm (the leading firm) may invest in Southregardless of technology spillovers to a local firm (the lagging firm). They point out that FDI by
the leading firm deters the lagging firm from technology sourcing FDI.
Our potential-entrant case is related to Pack and Saggi (2001), Ishikawa (2007) and Horiuchi
and Ishikawa (2009) that consider strategic uses of other types of international technology transfer
in vertically related markets. Pack and Saggi (2001) also show a possibility of Pareto-improving
technology transfer. However, their focus is diﬀerent from ours. They are primarily concernedwith vertical technology transfer (through outsourcing) rather than horizontal one. In Ishikawa(2007) and Horiuchi and Ishikawa (2009), a vertically integrated North firm strategically transfers
technology to a South potential entrant through trade in an intermediate product in order to
1 3 Even in the incumbent case, the investing firm could gain from technology spillovers (see Proposition 3).
1 4 It is widely observed that FDI leads to both entry and exit of local firms depending on countries and industries.

See Görg and Strobl (2002,2003), De Backer and Sleuwaegen (2003), Smarzynska Javorcik (2004), and Barrios etal. (2005), for example.

4

deter a North rival from entering the market.
Our analysis is also related to Markusen and Venables (1999) which develops a theoreticalmodel with monopolistically competitive industries where FDI generates both backward andforward linkages in the host country. In their model, there is initially no local production atall. Then FDI makes it possible for local suppliers to enter the local market by creating demand
for non-tradable intermediate goods (backward linkage) and this in turn induces local final-good
producers to enter the local market (forward linkage). In their model, however, technology
spillovers are absent. Moreover, they highlight a possibility that local production eventually
overtakes and forces out FDI plants. It should be noted that in contrast with Markusen and
Venables (1999), our backward linkage is not directly created by FDI. That is, the investing
downstream firm gains from FDI which aﬀects the intermediate-good supplier indirectly throughhorizontal technology spillovers to the local downstream firm. Thus, this is not a simple backward
linkage often indicated in the literature of technology transfer.
The rest of the paper is organized as follows. Section 2 presents the basic model. Section 3
shows that the North firm may have incentives to undertake FDI because of market integrationand technology spillovers. Section 4 concludes the paper.

2

The Basic Model

There are two countries, North and South, each with one downstream firm denoted by firm Nand firm S, respectively. There is a single upstream firm, firm M , which is located in South.
Using the intermediate good, firm N and firm S produce a homogeneous final good. The final
good is consumed in North.15 Firm N chooses its plant location, either North or South. That is,
firm N either imports the intermediate good to produce the final good in North or undertakes
FDI to purchase the intermediate good and produce the final good in South. Technology does
not spill over to firm S if firm N locates in North, while it does if firm N locates in South. To
neutralize the motive for FDI associated with trade costs, we assume that there is no trade cost
between two countries.
The model involves four stages of decision. In stage 1, firm N chooses its plant location. In
stage 2, firm M sets the price(s) of the intermediate good. In stage 3, firm S decides whether
to serve the final-good market. If it does, firms N and S engage in Cournot competition in the
final-good market in stage 4. If firm S does not serve the market, firm N monopolizes the market.
The inverse demand for the final good is given byp(X) = b − aX,
1 5 The assumption that firm M is in South and consumers of the final product are in North is innocuous.

(1)
The

main results still hold without this assumption. This assumption follows from the case of natural resources in
Section 1.

5

where p and X are, respectively, the price and the demand of the final good.16 One unit of theintermediate good is required for each unit of the final good. The MC to produce the intermediate
good is normalized to be zero. If firms N and S are, respectively, located in North and South,
firm M can set the diﬀerent prices across firms, rN and rS , because of market segmentation.17 If
both firms are located in South, however, firm M is forced to set the uniform price, r, because ofa single market. The MC to produce the final good from the intermediate good is cN for firm Nand cS for firm S. When firm N does not invest in South, cS is equal to cS which is exogenously
given. When firm N undertakes FDI, on the other hand, cS depends on the firm S’s capacity toabsorb firm N ’s technology (i.e., “absorptive capacity”). For simplicity, the absorptive capacity,α, is exogenously given. Specifically, in the presence of FDI, the relationship between the MC
and the absorptive capacity is given by
cS = cS − α(cS − cN ) = (1 − α)cS + αcN , α ∈ [0, 1].

(2)

α = 0 implies the nil capacity and cS = cS holds. On the other hand, α = 1 implies the perfectcapacity and cS = cN .
The profits of firms M , N , and S are, respectively, given byπM= rN xN + rS xS,

πN= [p − (cN + rN )]xN −fN ,πS= [p − (cS + rS )]xS − fS ,where xi (i = N, S) is the output of firm i; and fi (i = N, S) is the setup fixed cost (FC). To
focus on the strategic motive for FDI, we assume that for firm N, both MC and FC are identicalbetween North and South. That is, there is no cost-saving motive for firm N to undertake FDI.
Since the setup FCs are not crucial to derive our main results, we set fi = 0 (i = N, S) for
simplicity.

3

Strategic Motives for FDI

In this section, we show that firm N may have incentives to undertake FDI because of the market
integration eﬀect and the technology spillover eﬀect. We consider two cases. In the first case, cS
is too high for firm S to enter the market. That is, firm S is a potential entrant and its entry is
possible only if firm N undertakes FDI (i.e., the potential-entrant case). In the second case, cS
is low enough for firm S to serve the final-good market, that is, firm S can serve the final-goodmarket without firm N ’s FDI (i.e., the incumbent case).18
1 6 Even if the demand function is non-linear, the essence of our results would not change.
1 7 Market segmentation stems from regulations, laws, transport costs, etc.

For example, if parallel imports areprohibited by law, then arbitrage across countries would not occur. If market segmentation is due to the presenceof trade costs, we need to introduce trade costs into the model. However, this modification would not aﬀect theessence of our results.
1 8 The conditions under which each case arises are given in footnote 22.

6

3.1

The Potential-Entrant Case

We solve the game by backward induction. There are two cases in the last stage. Firm S does
not enter the market in the first case and does in the second case. Without firm S’s entry, firm N
monopolizes the market. In either case, a single intermediate-good price prevails. In the absenceof firm S, firm N is a monopolist in the final-good market.
In the first case, given the intermediate-good price, rN , the equilibrium is given by
N
=
xN
N =X

b − cN − rN
b + cN + rN N
(b − cN − rN )2> 0, pN =, πN =
,
2a
2
4a

(3)

where a superscript “N ” stands for the case without firm S’s entry.
With firm S’s entry, the duopoly between firms N and S arises. Given rSS , we obtain
xSS
N

=

X SS

=

π SS
N

=

b + (cS + rSS ) − 2(cN + rSS ) SSb + (cN + rSS ) − 2(cS + rSS ), xS =
,
3a
3a
SS
SS
2b − (cS + r ) − (cN + r ) SS
1
, p = (b + 2r + cN + cS ) ,3a3[b + (cS + rSS ) − 2(cN + rSS )]2 SS[b + (cN + rSS ) − 2(cS + rSS )]2, πS =
,
9a
9a

(4)
(5)
(6)

where a superscript “SS” stands for the case with firm S’s entry. In stage 3, firm S enters themarket if and only if π SS
S > 0.
We now consider stage 2 in which given the FDI decision of firm N , firm M sets the price in
the intermediate-good market to maximize its profits under the derived demand. Without FDI,
noting xM = xN (where xM is the output of firm M ), we have
∗
xN
M
∗
xN
N

1
b − cN N∗
1(b − cN ) , rN ∗ =, πM =(b − cN )2 ,
4a
2
8a
1
1
1
2
∗
= XN∗ =(b − cN ) , pN ∗ = (3b + cN ) , πN(b − cN ) .
N =
4a
4
16a
=

(7)
(8)

Asterisk “∗”denotes equilibrium value.
With FDI, on the other hand, firm M has two options: charging the high price so that only
firm N is served or charging the low price to accommodate firm S’s entry. Firm M compares its
profits between these two cases. In the former case, the equilibrium is given by (7) and (8). In
the latter, facing the derived demand (5), firm M charges the uniform pricerSS∗ =

2b − cN −cS
4

for the intermediate good. Therefore,
2b − 7cN + 5cS SS∗ 2b − 7cS + 5cN, xS =,
12a12a2b − cN − cS SS∗ 1= (4b + cN + cS ) ,X SS∗ =
,p
6a
6
1
1
2
2
π SS∗
=
=
(2b − 7cN + 5cS ) , πSS∗(2b − 7cS + 5cN ) ,
N
S
144a
144a
2
(2b − cN − cS )
=
π SS∗
.
M
24a
xSS∗
=
N

7

(9)

For xSS∗> 0, we need 2b − 7cS + 5cN > 0, i.e., cS < (2b + 5cN )/7 ≡ e
c.19
S
0

The above two cases are depicted in Figure 1. In panel (a), dN dN is the derived demand forthe intermediate good without FDI. The marginal revenue (MR) curve associated with dN dN

0

is dN mN . Since M C = 0, the equilibrium in the intermediate-good market is given by point
0

E N . Once FDI is undertaken, the derived demand and its MR curve become dN dSS dSS and00

dN mN plus mSS mSS , respectively. Since the demand curve kinks at dSS , the MR curve becomes
discontinuous and consists of two segments. Then the equilibrium becomes E SS . In the presenceof FDI, firm M obtains the higher profits at E SS than at E N and hence induces firm S to enter.
In panel (b), dSS is located to the southeast of E N . Then, both E N and E SS are a candidate for
equilibrium. If point E N gives the higher profits for firm M , it charges rN ∗ for the intermediate
good. Hence, firm S cannot enter even with FDI.
The diﬀerence in the profits of firm M between the two cases is
¢
1 ¡ 2
(10)
b + 2bcN − 4bcS − 2c2N + 2cN cS + c2S ,24a√ ¢ ¡√√ ¢√¡¢¡where ∆πE
3 + 1 cN and 2 − 3 b+( 3−1)cN (≡ cSS=N).20
M = 0 holds at cS = 2 + 3 b−
M
SS∗
N∗
∆πE
M ≡ πM − πM =A superscript “E” stands for the potential-entrant case. We can verify cN < cSS=N
< e
c <
M
√ ¢
¡√
¢
¡
3 + 1 cN .
2+ 3 b−Thus, the following lemma is immediate.

Lemma 1 When firm N undertakes FDI, firm M induces firm S’s entry if and only if cN ≤cS < cSS=N.
M

Intuitively, firm M is likely to benefit from the presence of firm S as a result of FDI, because
the demand for the intermediate good rises. However, if firm S is not very eﬃcient (i.e., if
cS ≥ cSS=N), firm M has to lower the intermediate-good price suﬃciently to serve both firms N
M

and S. In this case, since the firm M ’s profits fall, firm M serves only firm N by charging highprice. This case is equivalent to the case without FDI. Thus,
Lemma 2 Firm M never loses from FDI.
We now consider stage 1. Comparing the profits of firm N with and without firm S’s entry,
we have
SS∗
∗
− πN
∆π E
N ≡ πNN =¢5 ¡ 2−b − 2bcN + 4bcS + 8c2N − 14cN cS + 5c2S .
144a

N=SS
=SS
). Noting 2cN − b < cN < cN<
∆π E
N = 0 holds at cS = 2cN − b and (b + 4cN )/5(≡ cNN<ec and Lemma 1, we establish the following lemma.
cSS=N
M

=SS
< cS < cSS=N.
Lemma 3 Firm N benefits from FDI if and only if cNN
M

1 9 Since c
SS∗ > 0 holds if xSS∗ > 0.
N ≤ cS , xNS
2 0 cA=B is a threshold for firm i meaning the following. Firm i’s profits are greater under market structure “A”
ithan under market structure “B” with cS < cA=B
and vice versa with cS > cA=B
.
i
i

8

The reason why firm N benefits from FDI is as follows. Suppose that firm S enters the market
as a result of FDI. Although the presence of a rival makes the final-good market more competitive,
it reduces the intermediate-good price by shifting the derived demand for the intermediate good.21=SS
If the latter eﬀects dominate the former (i.e., if cN< cS ), firm N gains. As the absorptiveN

capacity of firm S becomes lower (i.e., as cS increases), the intermediate-good price becomes
lower and hence firm N is more likely to gain. Put diﬀerently, by creating a technologicallyinferior rival, FDI can weaken firm M ’s market power. In the presence of FDI, therefore, firm
N faces a trade-oﬀ between the presence of a rival and the lower intermediate-good price. If=SS
cN ≤ cS < cN
, firm N has no incentive to undertake FDI.
N

The diﬀerence in the total output is∆X E ≡ X SS∗ − X N ∗ =

³ √
´
1
1
(b + cN − 2cS ) >(b − cN ) 2 3 − 3 > 0,12a12a

. As is expected, the total output is larger in thewhere the inequality comes from cS < cSS=N
M
presence of firm S. Therefore,
Lemma 4 Consumers never lose from FDI. If FDI leads firm S to enter the market, consumers
as well as firm S necessarily gain.
The above analysis establishes the following proposition.
Proposition 1 Suppose that firm S cannot enter the market without firm N ’s FDI. Firm N
has an incentive to undertake FDI if and only if the absorptive capacity of firm S is medium so=SS=SS< cS < cSS=N
holds. With cN< cS < cSS=N, FDI induces firm S to enter thethat cN
N
M
N
M

market. FDI results in Pareto gains, that is, FDI benefits all producers (i.e. firms M , N and S)
and consumers.
∗
N∗
This proposition is depicted in Figure 2. In the figure, πN
N and π M are horizontal because

they are independent of the the absorptive capacity, or, cS . As the absorptive capacity rises (i.e.,
N =SS
decreases but π SS∗
increases. As long as cS > cN
, firm N is willing to
as cS falls), π SS∗N
M

invest. However, firm M does not allow firm S’s entry if cS > cSS=N. On the other hand, as longM, firm M is willing to accommodate firm S’s entry but firm N does not undertake
as cS < cSS=N
M.
FDI if cS < cN=SS
N

3.2

The Incumbent Case

We next consider the incumbent case. There are two cases in the last stage. In the first case, firm
N undertakes FDI and both firms N and S are located in South. This case has been examinedin the last subsection. As we see below, however, firm S may be forced to exit the market in thiscase. This depends on the pricing behavior of firm M .
In the second case, firms N and S, respectively, produce in North and in South. In thiscase, there exist no technology spillovers and hence cS = cS . Also firm M can price-discriminate
2 1 Since firm S cannot be more eﬃcient than firm N, firm S’s enty never increases the intermediate-good price.

9

between firms N and S, because of market segmentation. Given the intermediate-good prices,NS
rN
and rSN S , the equilibrium is given by
S
xN
N

=

XNS

=

S
πN
N

=

NS
NS
b + (cS + rSNS ) − 2(cN + rN
b + (cN + rN
) NS
) − 2(cS + rSN S ), xS =
,
(11)
3a
3a
NS
¢
2b − (cS + rSNS ) − (cN + rN
1¡
) NS
NS
=
+ cN + cS ,(12),p
b + rSN S + rN
3a
3
NS
NS 2
NS
NS 2
[b + (cS + rS ) − 2(cN + rN )][b + (cN + rN ) − 2(cS + rS )]S, πN, (13)=
S
9a
9a

where “N S” stands for the case in which firms N and S, respectively, produce in North and inSouth.
With price discrimination, firm M sets the prices of the intermediate good, rN and rS as
follows:N S∗
rN=b − cN N S∗ b − cS
,rS =
.
2
2

(14)

Then,22b − 2cN + cS NS∗ b + cN − 2cS, xS =,
6a6a2b − cN − cS N S∗ 1
= (4b + cN + cS ) ,X N S∗ =
,p
6a
6
1
1
2
S∗
S∗
πN
=
=
(b − 2cN + cS ) , πN
(b + cN − 2cS )2 ,
N
S
36a
36a
¢
1 ¡ 2
S∗
πN
=
b − bcN − bcS + c2N − cN cS + c2S .
M
6a
S∗
xN
=
N

(15)

There are two opposing eﬀects of firm N ’s FDI on firm M ’s profits. Under FDI, firm M isforced to set the uniform price, which reduces firm M ’s profits relative to the case without FDI.
On the other hand, FDI generates technology spillovers from firm N to firm S, which allows firm
M to increase the intermediate-good price relative to the case without any technology spillovers.
Thus, firm M may or may not gain from FDI. We haveNS∗=
∆π IM ≡ π SS∗
M − πM¢1 ¡ 2
c + 2cS cN − 4bcS − 3c2N + 4cN cS − 4c2S + 4bcS ,24a S√
where a superscript “I” stands for the incumbent case. ∆π IM = 0 holds at cS = 2b − cN − 2 Z(≡
√
S
cSS=N
) and 2b − cN + 2 Z, where Z ≡ b2 − bcN − bcS + c2N − cN cS + c2S = (b − cS )2 + (b −M√<ec < 2b − cN + 2 Z, ∆π IM > 0 (∆πIM < 0) if and only if
cN )(cS − cN ) > 0. Since cSS=NS
M
S
S(cSS=N< cS ≤ cS ).23 cS < cSS=N
implies that the technology spilloverscN ≤ cS < cSS=NS
M
M
M

from firm N to firm S are large enough to benefit firm M .

When ∆πIM < 0, firm M has two options in the presence of FDI. One is to keep serving both
firms N and S. The other is to stop serving firm S by charging a high price for the intermediate
good. It should be noted that in either case, firm N ’s FDI is harmful to firm M , which neveris decreasing with respect
happens in the potential-entrant case (recall Lemma 2). Since πSS∗
M
2 2 We can conclude from (15) that the incumbent case arises if c < (b + c )/2 and the potential-entrant caseS
Narises if cS ≥ (b + cN )/2.
2 3 The appendix shows that there exist some parameter values under which c
SS=N S holds.
N < cM

10

¡ ¡√
¢
¡√
¢¢
S∗
∗
SS=NS
to cS and πN> πN< cSS=N(≡ cS
3 + 1 − b 3 − 1 /2). Also by
M
M , we have cMMnoting Lemma 1, the following lemma is immediate.

S
Lemma 5 Firm M gains from FDI if and only if cN ≤ cS < cSS=N
but loses if and onlyM

S
< cS ≤ cS . When it loses, firm M forces firm S to exit the market if and only if
if cSS=N
M

cSS=N< cS ≤ cS .
M

Lemma 5 is illustrated in Figure 3 (a). If cS is in Region 1 or Region 2 as a result of FDI,
then the duopoly between firm N located in South and firm S located in South arises. Firm M
gains in Region 1 but loses in Region 2. If cS is in Region 3, then firm S is led to exit the market
and hence the monopoly by firm N arises. Firm M loses in Region 3.
The economic intuition behind Lemma 5 is similar to that in the potential-entrant case. The
greater the technology spillovers from firm N to firm S are, the larger the firm M ’s gains from
FDI. Since the case without FDI is the duopoly between firm N located in North and firm S
located in South, however, FDI (i.e., the duopoly between firm N located in South and firm S
located in South) hurts firm M if technology spillovers are not large enough. When technology
spillovers are too small (i.e., cSS=N< cS ≤ cS ), firm M can avoid a large loss by forcing firm S
M

to exit the market.

Before considering stage 1, we examine the eﬀect of FDI on consumers and firm S’s profitson the basis of Lemma 5. First of all, it is obvious that if only firm N is served under FDI, both
firm S and consumers lose from FDI. When firm M serves both firms N and S under FDI, FDI
benefits consumers, because pN S∗ > pSS∗ . The final-good price is lower with FDI than without
FDI, because technology spillovers make firm S more eﬃcient.24 The diﬀerence in the profits offirm S isS∗∆πIS ≡ πSS∗
− πN
=
S
S

1
(3cN − 7cS + 4cS ) (4b − 7cS + 7cN − 4cS ) .
144a

S∆π IS = 0 holds at cS = (4b + 7cN − 4cS ) /7 and (3cN + 4cS )/7(≡ cSS=N). In view of (9) andSS< cS < (4b + 7cN − 4cS ) /7. Thus, ∆πIS > 0 holds if and only if(15), we can verify cN < cSS=N
SS. The intuition is as follows. FDI makes the intermediate-good price higher forcN ≤ cS < cSS=N
S

firm S. However, technology spillovers through FDI make firm S more eﬃcient. If the spillovers), then firm S could gain from FDI. However, we should
are large enough (i.e., if cS < cSS=NSS
S< cSS=N
could hold (see the appendix). When cSS=N< cS < cSS=NS,
mention that cSS=N
M
S
M
S

firm M forces firm S to exit the market with FDI (recall Lemma 5).
S< cSS=NThe above result is illustrated in Figure 3 (b) and (c). In Figure 3 (b), cSS=N
S
M
S
holds, while, in Figure 3 (c), cSS=N< cSS=Nholds. In both figures, the monopoly by firm N
M
Sarises if cS is in Region 3, while the duopoly arises if cS is in Region 4 or Region 5 (i.e., in Region6). In Region 3, firm S loses. In Figure 3 (b), firm S gains if cS is in Region 4 but loses if cS isin Region 5. In Figure 3 (c), firm S gains in Region 6.
Thus, we obtain
2 4 Since the demand for the final good is linear, the final-good price is not aﬀected by market integration. Thus,

technology spillovers are crucial for the decrease in the final-good price.

11

S
Lemma 6 Firm S benefits from FDI if and only if cN ≤ cS < min{cSS=N, cSS=N}, but loses
MSS
if and only if min{cSS=N, cSS=N} < cS ≤ cS .
MSFor consumers, unless FDI leads firm S to exit the final-good market, FDI is beneficial. In
Figure 3, FDI benefits consumers unless cS is in Region 3. Thus, we obtain, but loses if and only
Lemma 7 Consumers benefits from FDI if and only if cN ≤ cS < cSS=N
M< cS ≤ cS .
if cSS=N
M

We next consider stage 1. In stage 1, firm N decides its plant location. For this, firm N
S∗
compares the profits of each location. If only firm N is served under FDI, firm N compares π NNwith π N∗
N . Since the intermediate-good prices for firm N are the same between these two market
N S∗
N∗
∗
SS=N
= rN
), π NS∗< πN< cS ≤ cS holds, then firm N
structures (i.e., rN
N
N holds. Thus, if cM

undertakes FDI and becomes the monopolist.

S∗
If firm M serves both firms N and S under FDI, on the other hand, firm N compares π NNwith π SS∗
N :S∗∆πIN ≡ πSS∗
− πN
=−
N
N

1
(3cN − 5cS + 2cS ) (4b + 5cS − 11cN + 2cS ) .
144a

S=SS
). Noting (11cN − 2cS − 4b) /5 <∆π IN = 0 holds at cS = (11cN − 2cS − 4b) /5 and (3cN +2cS )/5(≡ cN
N
S=SS
S=SS
, we have ∆πIN > 0 if and only if cN< cS ≤ cS . This result stems from thecN < cNN
N

following trade-oﬀ. Without FDI, firm M price-discriminates between firms N and S. Since firm
N is more eﬃcient than firm S, the price firm N faces is higher than that firm S does. On the one
hand, firm N ’s FDI makes firm S more eﬃcient because of technology spillovers: on the other
hand, it leads firm M to set the uniform price and firm N faces the lower intermediate-goodprice. If the latter eﬀect exceeds the former, firm N gains from FDI. This is likely to be the casewhen the technology spillovers are not very strong.
S=SS
Therefore, noting cN< cSS=N, we establish the following lemma.25
N
M
S=SS
Lemma 8 Firm N benefits from FDI if and only if cN< cS ≤ cS .
N
S=SS), firm N can avoid a loss
When technology spillovers are too large (i.e., cN ≤ cS < cN
N

< cS ≤ cS ),from FDI by locating in North. When technology spillovers are not large (i.e., cNS<SSN

FDI could result in two market structures: the monopoly by firm N and the duopoly between< cS ≤ cS
firm N located in South and firm S located in South. The former arises if cSS=N
M

holds, while the latter arises if cNS=SS< cS < cSS=N. In either market structure, firm N gains
NM
from FDI.
Whether firms M and S and consumers actually gain or lose from FDI crucially depends
S=SS< cN=SS< cSS=N< cS (seeon the size of thresholds. As was shown, we have cN < cN
N
N
M

< cSS=N. Moreover, we can easily verify cNS=SS< cSS=NS(< cS ).
footnote 25) and cSS=NS
M
M
NS
2 5 Since π SS∗ is increasing with respect to c and π N S∗ < π N ∗ , we have cN S=SS < cN =SS .
S
N
N
N
N
N
=SS < cSS=N holds. Thus, we obtain c
N S=SS < cN =SS < cSS=N < c .
Subsection 3.1, cN
<
c
N
S
N
M
N
N
M

12

As shown in

S=SSS
The appendix shows that cN< cSS=N
could hold. In view of Lemmas 5-8, therefore,NM

FDI is actually undertaken and hurts firms M and S and consumers if cSS=N< cS ≤ cS holds.
M

In other words, FDI is actually undertaken and benefits firms M and S and consumers only if< cS < cSS=N.
cNS=SSNM
The above analysis is summarized in the following proposition.
Proposition 2 Suppose that firm S can serve the market without firm N ’s FDI. Firm N has an
S=SS
S=SS
< cS ≤ cS . Now suppose cN< cS ≤ cS
incentive to invest in South if and only if cNNNholds and hence FDI is undertaken. Then FDI forces firm S to exit the market and harms< cS ≤ cS ; FDI benefits firm M if cNS=SS< cS <
consumers and firms M and S if cSS=N
M
N
S
S=SS
S
cSS=N
, firm S if cN< cS < min{cSS=N, cSS=N}, and consumers if cNS=SS< cS <
M
N
M
S
N
S=SS
S
; and FDI results in Pareto gains if cN< cS < min{cSS=NS, cSS=N
}.
cSS=N
M
N
M
S

S=SS
Figure 4 shows a case in which Pareto gains could occur. FDI is undertaken if cS > cN.
N

< cS < cSS=NS,26 all producers and consumers gain from FDI. In the presence
As long as cNS=SS
N
S
of FDI, the following trade-oﬀ arises for each firm. For firm N , its technology spills over to firm
S, but the intermediate-good price falls because of market integration. For firm M , the pricediscrimination becomes impossible, but technology spillovers increase the derived demand for theintermediate good. For firm S, the intermediate-good price rises, but its technology improves
S=SS
S
because of technology spillovers. When cN< cS < cSS=N, the positive eﬀect dominatesNS

the negative eﬀect for each firm and all firms gain.
In view of Figure 4, it should be pointed out that we can obtain the following proposition.
Proposition 3 Firm N could benefit from technology spillovers to firm S not only in the potential
entrant case but also in the incumbent case.
To see this, first suppose that technology spillovers are absent in Figure 4. Then firm S’s MC∗remains cS with FDI. Firm S exits as a result of FDI and firm N ’s profits become πN
N . Now< cS < cSS=N
because of technology spillovers. Then firm
suppose that FDI results in cN=SS
N
M
N∗
N ’s profits, π SS∗
N , are larger than π N . That is, firm N ’s gain from FDI becomes larger in thepresence of technology spillovers. The economic intuition behind this proposition is the same asthat in the potential entrant case.

4

Concluding Remarks

We have identified strategic incentives for a North downstream firm to invest in South in verticallyrelated markets. Both the technology spillover eﬀect and the market integration eﬀect play crucial
roles. We explore two cases. In the potential-entrant case, the South downstream firm can enter
the market only if FDI is undertaken. In the incumbent case, the South downstream firm can serve
the market without FDI. In both cases, FDI makes the South downstream firm more eﬃcient and2 6 We can easily verify cSS=N S < cSS=N S holds if c
N = 0.
S
M

13

changes the derived demand for the intermediate good, which in turn aﬀects the intermediategood supplier. Although FDI could benefit the North downstream firm in both cases, the causes
are somewhat diﬀerent.
In the potential-entrant case, if FDI induces the potential entrant to enter the market, theintermediate-good price falls because the South entrant is less eﬃcient than the North firm. If
this positive eﬀect dominates the negative eﬀect caused by the creation of a new rival, then the
North downstream firm is willing to invest in South. Interestingly, all producers and consumers
benefit from such FDI. This is basically because the distortion due to double marginalization is
weakened. The upstream firm gains, because it has to decrease the intermediate-good price toserve both downstream firms but the derived demand for the intermediate good increases by theentry.
In the incumbent case, FDI makes the South downstream firm more competitive, but leads
the upstream firm to set the uniform price. Since the North firm is more eﬃcient than the South
firm, the uniform pricing either lowers the intermediate-good price faced by the North firm orforces the South firm to exit the market. If the South firm exits, the North firm gains from FDI
but the other firms and consumers lose. Even if the South firm remains to stay, the reduction of
the intermediate-good price may benefit the North firm. In this case, FDI could result in Pareto
gains. FDI generates technology spillovers to the South firm and hence the South firm can gaineven if FDI increases the intermediate-good price faced by it. FDI does not allow the upstream
firm to price-discriminate between two downstream firms anymore but technology spillovers to
the South firm expand the derived demand for the intermediate good. If the latter eﬀect (i.e., thetechnology spillover eﬀect) exceeds the former (i.e., the market integration eﬀect), the upstream
firm gains.
In concluding this paper, six final remarks are in order. First, both the technology spillover
eﬀect and the market integration eﬀect are necessary for the North downstream firm to benefit
from FDI in the potential-entrant case, while the market integration eﬀect alone makes theNorth downstream firm better oﬀ in the incumbent case. For the upstream firm and the South
downstream firm, the technology spillover eﬀect is beneficial, while the market integration eﬀect
is harmful. Thus, the technology spillover eﬀect is necessary for the upstream firm and the South
downstream firm to gain. For the North downstream firm, however, the technology spillover
eﬀect may or may not be harmful. As pointed out, the technology spillover eﬀect may further
increase the benefit for the North downstream firm.
Second, we have assumed that the upstream firm sets the monopoly price for the intermediate
good. If the North downstream has the monopsony power instead, the intermediate-good pricebecomes equal to the constant MC of the upstream firm. Obviously, our result would not holdwith the constant intermediate-good price. In fact, with the monopsony power of the Northdownstream firm,27 FDI may break its monopsony power because of the presence of the South
2 7 The monopsony power of the North downstream firm could be ruled out if the upstream firm exports theintermediate good to other foreign firms.

14

downstream firm. In this case, FDI is likely to increase the intermediate-good price and our
result would not follow. A crucial feature for our result is that FDI induces the upstream firm
to lower the price. However, the monopoly in the intermediate-good market is not essential. For
example, if a few firms compete in Cournot fashion in the intermediate-good markets, then our
main results are still valid.
Third, we have assumed that there is a single downstream firms in South. If non-zero setup
FCs are introduced, one could easily construct situations under which only one South downstream
firm can enter the market. However, as long as the number of South downstream firms is small,the North downstream firm can still gain from FDI even with more than one South firm.
Fourth, we have focused on FDI spillovers as a channel of technology transfer. We caneasily incorporate direct technology transfer or assistance under FDI into the model. The Northdownstream firm may have an incentive to undertake FDI and voluntarily transfer technology
to the South downstream firm if FDI spillovers are absent or too weak.28 However, transferredtechnology may be too sophisticated for the South downstream firm to handle. The absorptive
capacity in our model should be interpreted to include such a bottleneck.
Fifth, we can reinterpret the upstream as labor unions as in Mukherjee et al. (2008). Without
FDI, each firm hires workers from a separate labor union (i.e., a labor union in each country).
With FDI, however, both (downstream) firms hire workers from a common labor union in South,
which sets a uniform wage. We can also reinterpret the upstream as governments that intend
to maximize tax revenue.29 Whereas each firm faces a tax rate set by each government without
FDI, both (downstream) firms face a common tax rate imposed by the South government with
FDI.
Lastly, FDI creates various linkages between MNEs and local firms. Both horizontal andvertical linkages are important. However, the number of empirical studies that investigate theeﬀects of MNEs on local rivals through suppliers is rather limited.30 More empirical investigationof this kind of linkage including one suggested in our analysis is left for future research.

Appendix
S
First, we show that there exist parameter values under which cS < cSS=N
holds. In theM. We check if there
incumbent case, firm M gains from firm N ’s FDI if cN ≤ cS < cSS=NS
M

S
holds. Suppose cN = 0. Then,actually exist some parameter values under which cN < cSS=N
M
p
2
I
SS=NS
2
= 2(b − b − bcS + cS ). By recalling footnote 22, 0 < cS < b/2∆π M > 0 if 0 ≤ cS < cM√
SS=NS
takes the maximum value (2 − 3)b at cS = b/2 without any
for the incumbent case. cM√S< (2 − 3)b holds with 0 < cS < b/2. This implies that given
constraint. Thus, 0 < cSS=N
M
S
cS ∈ (0, b/2) and cN = 0, we can always find some range of cS which satisfies 0 ≤ cS < cSS=N.
M

2 8 In Figures 2 and 4, for example, firm N tries to make c = cSS=N by transferring technology if c > cSS=N .
SSM
M
2 9 Clausing (2007) finds that a revenue-maximizing corporate income tax rate for OECD countries is about 33%.
3 0 Görg and Strobl (2002) and Barrios et al.

(2005) examine the manufacturing sector in Ireland. Altomonteand Resmini (2002) and Kippenberg (2005) deal with Poland and the Czech Republic, respectively.

15

Second, we show that cSS=N
could be less than or greater than cSS=NS. We have
M
S
S
cSS=N
− cSS=N
=
M
S

³ √
´
´´
³ √
1³
−4cS − b 7 3 − 14 + cN 7 3 − 10 ,7√S
> cSS=Nholds if cS is
where 7 3 − 14 ≈ −1. 875 6 < 0 holds. By setting cN = 0, cSS=N
M
S

S
suﬃciently small but cSS=N< cSS=Nholds if cS is suﬃciently close to b/2.
M
S

By recalling that FDI results in Pareto gains if cNS=SS< cS < min{cSS=N, cSS=NS}, i.e.,
N
M
S
√ ¢
√
¡
S=SS
<
(3cN +2cS )/5 < cS < min{ 2 − 3 b+( 3−1)cN , (3cN +4cS )/7} (see Proposition 2), cN
N

S
cSS=N
is necessary for Pareto gains. We next show that there exist parameter values under
M

S=SS
S
< cSS=Nholds. Again, supposing cN = 0, we check the condition under which
which cN
N
M
S=SS
cNS=SS< cSS=NS
holds. We can easily verify cN< cSS=NS
if 0 < cS < 5b/8. By noting
N
M
N
M
S=SS
S
< cSS=N
always holds.
0 < cS < b/2 for the incumbent case, cN
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19

r dN
(a)

EN

dSS
rN*

ESS

mSS

rSS*

mN’
XN*
r dN

dN’
XSS*

mN

dSS’
X

mSS’

(b)

EN
rN*

dSS

rSS*

ESS

mSS
dSS’
XN*

X

XSS*
mSS’

mN
Figure 1: Intermediate-good market

M
 MSS *

 MN *

cN

c~

cS

cS

c~

cS

cS

N

 NN *
 NSS *

cN

Figure 2: Relationship between profits and marginal cost:
The potential-entrant caseduopoly
between firms N & S
Region 1

Region 2

monopolyby firm N
Region 3(a)Region 4

Region 5

Region 3(b)Region 6

Region 3(c)Figure 3: Relationship between profits and marginal cost:
The incumbent caseM

 MSS * MNS *
 MN *

cN

cS

cS

cS

cS

cS

cS

N

 NN *
 NNS *
 NSS *

cN

c4

S SSS *

 SNS *

cN

Figure 4: The incumbent case with Pareto gains