This paper presents a two-country model of duopolistic market with vertical relations which leads to a paradoxical result: when upstream firms possess sufficient bargaining power, cost-reducing FDI may actually enhance the rival firm's profit.Cournot competition

Junichiro Ishida

Noriaki Matsushima

English

Research Papers in Economics

FDI may help rival firms 
Junichiro Ishida Noriaki Matsushima
Osaka University Kobe University
Abstract
This paper presents a two−country model of duopolistic market with vertical relations which
leads to a paradoxical result: when upstream firms possess sufficient bargaining power,
cost−reducing FDI may actually enhance the rival firm's profit.
We thank Hiroshi Mukunoki and an associate editor for helpful comments and suggestions. We also gratefully acknowledge
financial support from Grant−in−Aid for Encouragement of Young Scientists from the Japanese Ministry of Education, Science
and Culture. Needless to say, we are responsible for any remaining errors.
Citation: Ishida, Junichiro and Noriaki Matsushima, (2005) "FDI may help rival firms." Economics Bulletin, Vol. 6, No. 22 pp.
1−8
Submitted: July 2, 2005.  Accepted: November 15, 2005.
URL: http://www.economicsbulletin.com/2005/volume6/EB−05F20005A.pdf1 Introduction
In standard Cournot models of oligopoly with no external eﬀect, a ﬁrm engaging in cost-reducing
investment is always a threat to other rival ﬁrms. The same conclusion applies for multicountry models
of international oligopoly where ﬁrms potentially undertake foreign direct investment (hereafter, FDI).
In this context, FDI plays exactly the same role as cost-reducing investment in the foreign market as
it allows the ﬁrm to save transport costs including tariﬀs and various non-tariﬀ trade barriers. With
the ﬁrm gaining more eﬃciency in the foreign market through FDI, rival ﬁrms are inevitably made
worse oﬀ since they are now able to make less proﬁt in the foreign market.
In this paper we construct a two-country model of duopoly with vertical relations and show that
this seemingly robust conclusion can be overturned once strategic price-setting behavior of upstream
ﬁrms is explicitly taken into account. Suppose that a ﬁrm undertakes FDI and becomes more eﬃcient
in the foreign market. While this fact itself is certainly detrimental to the rival ﬁrm, the story does not
end here when proﬁt-maximizing upstream input suppliers have suﬃcient bargaining power. Facing
more intense competition, there arises an incentive for the upstream input supplier of the rival ﬁrm
to lower input prices in order to compete in the foreign market. As we will see shortly, this strategic
reduction in input prices is sometimes large enough to compensate for the loss arising from more
intense competition in the foreign market.
There are now several papers which examine the relationship between unionization and FDI.1 In
those previous studies, however, the eﬀect of FDI on its domestic rival ﬁrms has not been investigated.
In the sense that strategic price-setting behavior of upstream input suppliers leads to a paradoxical
result in an otherwise standard model of oligopolistic market, the result obtained here is also related
to Naylor (2002) who shows that industry proﬁts can increase with the number of ﬁrms in the market.
In this paper we take a diﬀerent route and present a situation where cost-reducing FDI can actually
increase its rival ﬁrm’ proﬁts without any external eﬀect assumed explicitly.
2 The model
The model is a slightly modiﬁed version of Lommerud et al. (2003). We consider two countries,
countries H (home) and F (foreign), and two downstream producers, ﬁrms A and B. Initially, each
ﬁrm has a plant located in country H.2 To export to country F, a ﬁrm must incur a per unit transport
1See, for instance, Bughin and Vannini (1995), Zhao (1995), Leahy and Montagna (2000), Skaksen and Sørensen
(2001), Naylor and Santoni (2003), and Lommerud et al. (2003).
2This is a diﬀerence from Lommerud et al. (2003) where one ﬁrm is initially located in country H while the other is
in country F.
1cost, denoted by t ≥ 0.3 To avoid the corner solution, we assume that the transport cost is suﬃciently
small:
t ≤ t ≡
160(31 − 15
√
2)(1 − ¯ w)
3577
' 0.4378(1 − ¯ w). (1)
This condition assures that the ﬁrms choose nonnegative quantities to export in equilibrium. Within
this setup, we look at a situation where FDI is potentially undertaken by ﬁrm A: more precisely, ﬁrm
A may set up another plant in country F, which allows it to avoid the transport cost. Since our interest
lies in the external eﬀect of FDI, we do not consider its ﬁxed cost, at least for a moment.
There is only one factor of production, which we refer to as the input. Each ﬁrm procures its
input from its own (plant-speciﬁc) upstream input supplier and produces a homogenous ﬁnal good
in a constant-returns-to-scale process where one unit of the input is turned into one unit of the ﬁnal
good. If ﬁrm A chooses to set up a plant in country F, it must procure its input from a foreign input
supplier: that is, the number of input suppliers varies depending on ﬁrm A’s FDI decision.4 Let z
j
i
denote the amount of the input supplied by the input supplier of ﬁrm i located in country j. Each
input supplier sets a wholesale price w
j
i to maximize its proﬁt function:
U
j
i = (w
j
i − ¯ w)z
j
i, i = A,B, j = H,F, (2)
where ¯ w < 1 is the marginal cost of producing a unit of the input, which is identical for all input
suppliers.5
We assume that competition between the two ﬁrms is Cournot and adopt the segmented market
hypothesis: both ﬁrms thus choose separate quantities for the two markets. Now let x
j
i denote i’s sales
in country j. The inverse demand function in the two countries is symmetric and given by
pj = 1 − (x
j
A + x
j
B), j = H,F, (3)
where pj is the price of the ﬁnal good in country j.
To summarize, we model the game structure as follows:
1. Firm A decides whether to set up a plant in country F;
2. Each upstream input supplier sets its wholesale price;
3. Given this, each ﬁrm simultaneously chooses quantities.
3Among other things, the transport cost is meant to capture tariﬀs and non-tariﬀ trade barriers.
4It should be noted, however, that it is not critical how ﬁrm A procures its input in country F. The same result can
be obtained if the ﬁrm procures its input at the competitive price, as assumed in Lommerud et al. (2003).
5If the input supplier is a labor union, ¯ w can be considered as the competitive (non-union) wage level.
23 Analysis
Notice that the model has fairly standard features: (i) the ﬁrms produce a homogenous ﬁnal good
(perfect substitute); (ii) the production technology is independent between the ﬁrms (no productive
externality). Under this setup, since FDI makes ﬁrm A more eﬃcient in country F, it appears that
FDI undertaken by ﬁrm A can only be detrimental to its rival, ﬁrm B. We now show that, quite
contrary to this intuition, this is not necessarily the case and the external eﬀect of FDI can actually
be positive under certain conditions.
3.1 No FDI
Suppose ﬁrst that ﬁrm A chooses to remain entirely in country H. In this case, there are two input
suppliers to be considered, both located in country H. Given the wholesale prices (wH
A and wH
B) set
by each of the two input suppliers, each ﬁrm maximizes
xH
i ,xF
i = arg max
xH
i ,xF
i
[(1 − (xH
i + xH
−i) − wH
i )xH
i + (1 − (xF
i + xF
−i) − wH
i − t)xF
i ], i 6= −i. (4)
Solving the ﬁrst-order conditions, we obtain
xH
i =
1 − 2wH
i + wH
−i
3
, xF
i =
1 − 2wH
i + wH
−i − t
3
. (5)
When t is in the appropriate range, the optimal input price is obtained as a solution to the following
problem:6
max
wH
i
UH
i = (wH
i − ¯ w)(xH
i + xF
i ) =
(wH
i − ¯ w)(2 − 4wH
i + 2wH
−i − t)
3
. (6)
The ﬁrst-order condition then implies
∂UH
i
∂wH
i
= 0 ⇔
2 + 4 ¯ w − t − 8wH
i + 2wH
−i
3
= 0, (7)
which leads to
wH
i =
2 + 4 ¯ w − t
6
. (8)
In equilibrium, therefore, each ﬁrm chooses
xH
i =
4(1 − ¯ w) + t
18
, xF
i =
4(1 − ¯ w) − 5t
18
. (9)
Finally, the equilibrium proﬁt with no FDI, πiN, is computed as
πiN =
16(1 − ¯ w)2 − 16(1 − ¯ w)t + 13t2
162
. (10)
6We can show that the solution to this problem indeed maximizes the union’s utility. The proof is available upon
request.
33.2 FDI
Now suppose that ﬁrm A chooses to set up a new plant in country F to avoid the transport cost.
In this case, there are three input suppliers to be considered, two in country H and one in country
F. Given the wholesale prices (wH
A, wH
B and wF
A) set by each of the three input suppliers, each ﬁrm
maximizes
xH
A,xF
A = arg max
xH
A,xF
A
[(1 − (xH
A + xH
B) − wH
A)xH
A + (1 − (xF
A + xF
B) − wF
A)xF
A], (11)
xH
B,xF
B = arg max
xH
B,xF
B
[(1 − (xH
A + xH
B) − wH
B)xH
B + (1 − (xF
A + xF
B) − wH
B − t)xF
B]. (12)
Solving the ﬁrst-order conditions, we obtain
xH
A =
1 − 2wH
A + wH
B
3
, xF
A =
1 − 2wF
A + wH
B + t
3
, (13)
xH
B =
1 + wH
A − 2wH
B
3
, xF
B =
1 − 2(wH
B + t) + wF
A
3
. (14)
Given this, each input supplier maximizes
UH
A = (wH
A − ¯ w)xH
A =
(wH
A − ¯ w)(1 − 2wH
A + wH
B)
3
, (15)
UH
B = (wH
B − ¯ w)(xH
B + xF
B) =
(wH
B − ¯ w)(2 + wH
A − 4wH
B − 2t + wF
A)
3
, (16)
UF
A = (wF
A − ¯ w)xF
A =
(wF
A − ¯ w)(1 − 2wF
A + wH
B + t)
3
. (17)
The ﬁrst-order conditions then imply
∂UH
A
∂wH
A
= 0 ⇔
1 + 2 ¯ w − 4wH
A + wH
B
3
= 0, (18)
∂UH
B
∂wH
B
= 0 ⇔
2 + 4 ¯ w − 2t + wH
A − 8wH
B + wF
A
3
= 0, (19)
∂UF
A
∂wF
A
= 0 ⇔
1 + 2 ¯ w + t + wH
B − 4wF
A
3
= 0, (20)
which lead to
wH
A =
40 + 80 ¯ w − 7t
120
, wH
B =
10 + 20 ¯ w − 7t
30
, wF
A =
40 + 80 ¯ w + 23t
120
. (21)
In equilibrium, therefore, each ﬁrm chooses
xH
A =
40(1 − ¯ w) − 7t
180
, xF
A =
40(1 − ¯ w) + 23t
180
, (22)
xH
B =
80(1 − ¯ w) + 49t
360
, xF
B =
80(1 − ¯ w) − 161t
360
. (23)
Finally, the equilibrium proﬁt with FDI, πiF, is computed as
πAF =
1600(1 − ¯ w)2 + 640(1 − ¯ w)t + 289t2
16200
, πBF =
6400(1 − ¯ w)2 − 8960(1 − ¯ w)t + 14161t2
64800
. (24)
43.3 External eﬀects of FDI
We are now ready to examine how ﬁrm B’s proﬁt is aﬀected by ﬁrm A’s FDI. To this end, deﬁne
∆π(t) ≡ πBF − πBN =
−t(2560(1 − ¯ w) − 8961t)
64800
. (25)
Then, FDI undertaken by ﬁrm A beneﬁts ﬁrm B if ∆π(t) > 0. We can now state the following result.
Proposition 1 There exists some nonempty interval T ≡ (t,t] such that ∆π(t) > 0 for all t ∈ T.
Proof: We can show this by simple algebra. It directly follows from (25) that ∆π(t) > 0 if and only
if
t >
2560(1 − ¯ w)
8961
≡ t. (26)
Given this it is immediate to verify t < t.
Q.E.D.
By setting up a new plant in country F, ﬁrm A can save the transport cost and becomes more
eﬃcient by this margin. The proposition suggests that this cost-reducing FDI can actually be beneﬁcial
for the rival ﬁrm when the transport cost is suﬃciently large. This result is counterintuitive in two
respects: ﬁrst, cost-reducing investment may actually help its rival ﬁrm; second, this positive external
eﬀect is more likely to occur when FDI is more eﬀective.7
The logic behind this result is as follows. In standard Cournot models of oligopolistic market, the
presence of a more eﬃcient ﬁrm is always detrimental to other rival ﬁrms. Besides this conventional
eﬀect, however, FDI undertaken by ﬁrm A also gives rise to eﬀects that work in favor of ﬁrm B. To
see this, ﬁgure 1 depicts how ﬁrm A’s FDI aﬀects the wholesale prices that prevail in country H as
the transport cost increases. When ﬁrm A undertakes FDI, the input supplier of ﬁrm B is put under
pressure to lower the wholesale price in order to export. This downward pressure on the wholesale price
is naturally stronger when the transport cost is larger. An increase in the transport cost thus leads to a
downward shift in the reaction function of wH
B (the arrow in the ﬁgure indicates an increase in t). There
are two points to be noted as to what this shift brings about. First, the wholesale price in country
H, wH
B, is monotonically decreasing in the transport cost, which certainly beneﬁts ﬁrm B. Second,
it should also be noted that the reaction function of wH
A is totally independent of the transport cost,
because ﬁrm A does not export. This asymmetry virtually puts ﬁrm B in an advantageous position in
country H as it faces a lower wholesale price than its rival, i.e., wH
B < wH
A when t > 0. The proposition
7Note that in the current setup, the marginal value of FDI is equivalent to the transport cost.
5states that the gain from this downward pressure on the wholesale prices eventually dominates the
loss arising from facing more intense competition in the foreign market as the transport cost becomes
larger.
wH
B
wH
A
wH
B(wH
A)
wH
A(wH
B)
0
Figure 1: Reaction functions under FDI (upstream ﬁrms)
This rather paradoxical result also leads to a paradoxical implication. Suppose that FDI now
involves some ﬁxed cost: let Ci denote the ﬁxed cost of FDI by ﬁrm i. Suppose further that πAF−πAN ≥
CA while CB is prohibitively large so that ﬁrm B never undertakes FDI. In this case, the unique
equilibrium outcome is that only ﬁrm A undertakes FDI. Given this, if ∆π(t) > 0, there may arise a
case where
πBF > πAF − CA ≥ πAN = πBN. (27)
When this condition holds, the more eﬃcient ﬁrm actually ends up with less proﬁt in this unique
equilibrium outcome.
4 Conclusion
This paper presents a two-country model of duopoly with vertical relations and examines how FDI
undertaken by a ﬁrm aﬀects for its rival ﬁrm. We have shown that, contrary to the conventional
wisdom, cost-reducing FDI can actually beneﬁt the rival ﬁrm through its eﬀect on input prices when
upstream ﬁrms possess suﬃcient bargaining power.
References
Bughin, J., Vannini, S., 1995, Strategic direct investment under unionized oligopoly, International
Journal of Industrial Organization 13, 127-45.
6Leahy, D., Montagna, C., 2000, Unionisation and foreign direct investment: challenging conventional
wisdom? Economic Journal 110, C80-C92.
Lommerud, K.E., Meland, F., Sørgard, L., 2003. Unionized oligopoly, trade liberalization and location
choice, Economic Journal 113, 782-800.
Naylor, R.A., 2002. Industry proﬁts and competition under bilateral oligopoly, Economics Letters 77,
169-75.
Naylor, R.A., Santoni, M., 2003, Foreign direct investment and wage bargaining, Journal of Interna-
tional Trade and Economic Development 12, 1-18.
Skaksen, M.Y., Sørensen, J.R., 2001, Should trade unions appreciate foreign direct investment, Journal
of International Economics 55, 379-90.
Zhao, L., 1995. Cross-hauling direct foreign investment and unionized oligopoly, European Economic
Review 39, 1237-53.
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FDI may help rival firms

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