OSIPP Discussion Paper : DP-2008-E-005

Outward Foreign Direct Investment in Unionized Oligopoly:
Welfare and Policy Implications
March 27, 2008
Junichiro Ishida
Osaka School of International Public Policy (OSIPP), Osaka University

Noriaki Matsushima
Graduate School of Business Administration, Kobe University【キーワード】R&D investment, vertical relation, transport cost, welfare, wage
bargaining【要約】It is often argued, though mostly informally, that outward foreign direct
investment (FDI) is a synonym for the export of employment and thus detrimental to thehome economy. To see whether and under what conditions this intuition indeed holds
true, we construct a model of unionized duopoly and examine welfare implications ofoutward FDI on the home country. It is found that the welfare effect of FDI is mostly
non-monotonic: an asymmetric pattern of FDI, where only one firm undertakes FDI in
the duopolistic case, is socially desirable for a wide range of parameter values in thepresence of strong unions. This amounts to a critical policy implication that there areindeed such things as “excessive FDI” and any form of government intervention to
encourage outward FDI can be beneficial only up to some point. We also show that,when FDI reduces welfare, this negative effect arises more at the expense of consumers
rather than the unions: in fact, quite contrary to the popular belief, FDI may actually
benefit the unions because it serves to soften price competition between them. The
paper points out that welfare effects of outward FDI hinges crucially on the nature ofdomestic competition, and policymakers must carefully take this aspect into
consideration.

Outward Foreign Direct Investment in Unionized Oligopoly:
Welfare and Policy Implications∗
Junichiro Ishida
Osaka School of International Public Policy, Osaka University
andNoriaki Matsushima†
Graduate School of Business Administration, Kobe University
March 27, 2008

Abstract
It is often argued, though mostly informally, that outward foreign direct investment (FDI)
is a synonym for the export of employment and thus detrimental to the home economy. To see
whether and under what conditions this intuition indeed holds true, we construct a model ofunionized duopoly and examine welfare implications of outward FDI on the home country. It isfound that the welfare effect of FDI is mostly non-monotonic: an asymmetric pattern of FDI,
where only one firm undertakes FDI in the duopolistic case, is socially desirable for a wide rangeof parameter values in the presence of strong unions. This amounts to a critical policy implicationthat there are indeed such things as “excessive FDI” and any form of government intervention to
encourage outward FDI can be beneficial only up to some point. We also show that, when FDI
reduces welfare, this negative effect arises more at the expense of consumers rather than the unions:in fact, quite contrary to the popular belief, FDI may actually benefit the unions because it serves
to soften price competition between them. The paper points out that welfare effects of outward
FDI hinges crucially on the nature of domestic competition, and policymakers must carefully takethis aspect into consideration.

JEL classification numbers: F21, J31, L13.
Key words: R&D investment, vertical relation, transport cost, welfare, wage bargaining∗ We thank Laixun Zhao for helpful comments and suggestions. The authors gratefully acknowledge financial supports

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.
† Corresponding author: Noriaki Matsushima, Graduate School of Business Administration, Kobe University, Rokkodai 2-1, Nada-Ku, Kobe, Hyogo 657-8501, Japan. Phone: +81-78-803-6981. E-mail: nmatsush@kobe-u.ac.jp1

1

Introduction

Should a government encourage, or even subsidize, globalization of domestic firms? If so, then to what
extent? With the increasing degree of globalization,1 those questions become more and more criticalfor policymakers these days. Specifically at issue, regarding those questions, is the welfare effect ofoutward FDI on the home country: a policy intervention that encourages domestic firms to expand
abroad can be justified only if outward FDI indeed proves to be welfare-improving. While the answer
to this question is not necessarily straightforward, many government authorities in reality appear to
be in favor of outward FDI and are often eager to encourage globalization of domestic firms in various
ways. To name a few, the Canadian Trade Commissioner Service and the Japan External Trade
Organization (JETRO) provide information and various types of support, as one of their missions,to help Canadian and Japanese firms, respectively, to expand overseas. The Swiss Organization for
Investment Facilitation (SOFI) was set up in 1997 by the Swiss Secretariat for Economic Affairs to offer
a wide scope of services to promote outward FDI. The Spanish Institute for Foreign Trade organizes
fairs named Expotecnia in various countries in an attempt to boost outward FDI as well as exports.
Countries such as Singapore, South Korea and Mexico have gone even further by creating what is called“comfort zones” in host countries to facilitate outward FDI.2 In many cases, attempts are made not
only to reduce or remove potential barriers but also to actively promote outward FDI through several
policy instruments, ranging from disseminating information on investment opportunities to providing
investment insurance against political risk.
This tendency seems to suggest that there is an emerging global consensus, at least among policymakers, that outward FDI is generally beneficial for the home country and should therefore be
encouraged. To justify this policy stance, there is certainly a bright side of outward FDI because firmsthat undertake FDI can improve their productive efficiency through several channels. First, firms may
invest abroad to save transport costs, including tariffs and other non-tariff trade barriers, which allows
them to serve the foreign market more efficiently. Second, especially when firms invest in developing
economies, FDI allows them to gain access to cheap raw material and labor force. Finally, outward FDI
is also a means to acquire knowledge and to diversify country risk. Proponents of outward FDI would
thus argue that FDI plays quite a similar role to R&D investment, which is normally welfare-improving
1 The amount of outward FDI has steadily increased over time and now reached 778.7 billion dollars worldwide in2005, compared to the annual average of 553.1 billion over 1994-1999 (UNCTAD, World Investment Report 2006).
2 One notable example of comfort zones is the China-Singapore Suzhou Industrial Park. The basic idea behind thisproject is “to offer a one-stop point of access to various government ministries as well as Singapore-style education,
health and recreation facilities, and an international school (UNCTAD, World Investment Report 2006, p.211).”2

if its investment cost is negligible, directed at the foreign market.
Despite those virtues, however, there may also be a cost associated with outward FDI when the
production process involves some immobile factors such as labor. In such a case, the effect of outward
FDI is no longer identical to that of R&D investment. It is often argued, though mostly informally,that FDI can be regarded as the export of employment and hence is detrimental to workers in thehome country. Based on this argument, the overall welfare effect of FDI on the home country is
ultimately determined by the tradeoff between firms’ gains and workers’ losses. FDI is not necessarily
welfare-improving if firms gain only at the expense of domestic workers.3
While the welfare analysis of outward FDI offers critical policy implications, studies on the effectof outward FDI are relatively scarce, both theoretically and empirically.4 The paper intends to fill thisgap. In particular, the main purpose of this paper is to examine whether and under what circumstances
the intuition mentioned above (that outward FDI may reduce social welfare) actually holds true. To
this end, we construct a model of unionized duopoly where there are two downstream firms, firms A
and B, and two unions (or, more generally, upstream suppliers). Each firm procures labor input fromits own union which possesses some bargaining power. We then look at a situation where firm A first
determines whether to set up a plant in the foreign market and then firm B determines whether tofollow its rival: for expositional clarity, we say that the first FDI (the second FDI) is undertaken whenfirm A (firm B) sets up a foreign plant.
Within this framework, we examine welfare and policy implications of outward FDI. We first showthat when there is only one domestic firm in the market to begin with, outward FDI is always welfareimproving when the home and foreign markets are comparable in size. Given this result, one might betempted to conjecture that outward FDI is in general welfare-improving even in the presence of strong
labor unions. As it turns out, however, this conclusion does not necessarily hold true with the additionof another rival firm. When there are more than one domestic firm-union pair, one firm’s FDI decisionaffects not only its own union but also the other union as well. The main findings of the paper are
summarized as follows:
1. FDI may reduce welfare in the presence of domestic competition. In particular, when the homeand foreign markets are comparable in size, the second FDI always reduces welfare. Moreover,this holds true even when we disregard any fixed cost necessary to set up foreign plants, i.e.,
3 For instance, Skaksen and Sørensen (2001) show that unions are likely to lose on FDI if domestic and foreign activities
are substitutable.
4 The literature on the welfare effect of FDI has mainly focused on the effect of inward FDI, i.e., the effect of FDI on
the host country. See Lipsey (2004) for an extensive survey on this issue.

3the effect of outward FDI can be purely negative. In general, an asymmetric pattern of FDI issocially desirable and hence the amount of FDI can easily be excessive in that sense.
2. The main reason why FDI reduces welfare is a reduction in consumer surplus. That is, FDI
reduces welfare at the expense of consumers, rather than the unions. In fact, under certain conditions, the second FDI actually benefits the unions because it serves to soften price competition
between them.
At the core of these results is the presence of domestic competition, which gives rise to effects thatare hardly straightforward and have critical bearings on social welfare. The reason why the second
FDI reduces social welfare and is especially detrimental to consumers is as follows. When a firm sets
up a foreign plant, its union is consequently forced to concentrate on the home market that it canserve more effectively, and thus responds to this by raising its wage. The magnitude of this effect,
however, depends heavily on the structure of FDI. When only one of the two firms undertakes FDI,
there arises a differential between them in the cost of supplying to the foreign market. Because ofthis, the union of the less productive firm, the one that does not undertake FDI, must lower its wage
to stay competitive in the foreign market, and intense price rivalry between the unions arises as aresult: the presence of the rival firm thus functions as an anchor to keep the wages low in the domestic
market. This is welfare-improving since lower wages lead to more output, which particularly benefits
consumers. The effect of this price rivalry is totally wiped out, however, when the second (and thelast, in this case) FDI is undertaken. The wages suddenly go up and the increase in the wages resultsin less output, which entails welfare losses. The result indicates that the welfare effect of outward FDI
hinges critically on the nature of domestic competition, especially in its relation to upstream suppliers:
when the price rivalry among upstream suppliers is intense, the amount of outward FDI can easily be
excessive, even if the effect of fixed costs is fairly negligible. In light of this finding, we argue that any
government intervention to encourage outward FDI could be beneficial only up to some point.
While the first result roughly confirms a popular view that outward FDI may reduce social welfare
under certain conditions, it is important to note that this is not necessarily at the expense of theunions, as one might anticipate. The more dominant factor in this is rather a reduction in consumer
surplus, resulting from higher wages. The effect of FDI, especially the second one, on the unions is lessclear. The first FDI puts downward pressure on the wages in order to compete in the foreign market,
and the price competition between the unions can be excessively intense from the unions’ viewpoint.
The second FDI may be beneficial for them, quite contrary to the popular belief, because it releases

4them from this downward pressure. In other words, as the option of exporting is no longer available,
the second FDI serves as a strong commitment device to substantially soften price competition between
the unions and consequently benefits them.
The present analysis is related to a line of research which deals with FDI in the presence oflabor unions (Bughin and Vannini, 1995; Zhao, 1995, 2001; Leahy and Montagna, 2000; Skaksen and
Sørensen, 2001; Naylor and Santoni, 2003; Lommerud et al., 2003; Ishida and Matsushima, 2005).5
Among them, the paper is most closely related to Lommerud et al. (2003), on which our model
framework is based. The difference lies in its goals and objectives: their model has only one domestic
firm and hence does not consider domestic competition, which proves to be crucial for our main results.
This difference amounts to different welfare and policy implications. We show that an asymmetricpattern of FDI is normally desirable from the social point of view whereas, in their mode with only
one domestic firm, this situation by design cannot arise. Moreover, while they also point out that theamount of FDI can be excessive, it is due to the presence of the fixed cost: that is, they show that
there arises a case in their model where the welfare gain from FDI is exceeded by the fixed cost ofinvestment. In contrast, we argue that the pure welfare effect of FDI is often negative, meaning that
FDI reduces welfare even when its fixed cost approaches zero, in the presence of domestic competition.
The paper proceeds as follows. The next section outlines the basic model. Section 3 analyzes asa benchmark a case with only one domestic firm and shows that outward FDI is normally welfareimproving. Section 4 extends the analysis to a case with two domestic firms and illustrate how market
outcomes driven by upstream competition are affected by the amount of FDI. Finally, section 5 offerssome concluding remarks.

2

The model

2.1

Basic environment

There are two markets, home and foreign, and two firms, denoted by A and B. Both of the firms are
initially located in the home market.6 Labor is unionized in the home market, whereas it is not in theforeign market. Each firm procures its labor input from its firm-specific union: we refer to the union
5 There is also a growing body of literature on international unionized oligopoly. Examples along this line include
Brander and Spencer (1988), Naylor (1998, 1999), Straume (2002, 2003), Lommerud et al. (2006), and Skaksen (2004),
just to name a few.
6 In Lommerud et al. (2003), there is only one firm that initially is located in the home market. The other firm islocated in the foreign market and is non-unionized. The presence of domestic competition proves to give rise to strategicinteractions and welfare implications absent in the case with only one domestic firm, as stated in the introduction. Itshould also be noted that our main results are qualitatively unchanged even when there exists a foreign firm (in theforeign market).

5

of firm i as union i in the subsequent analysis. The assumption that the unions are disintegrated turns
out to be insignificant and innocuous as we can obtain qualitatively similar results even when they areintegrated as an industry-wide union. Needless to say, the unions can interchangeably be regarded as
the upstream input suppliers.

2.2

Production and market competition

Each firm uses labor as the sole input and produces output in a constant-returns-to-scale technology.
Let xi denote i’s sale in the home market and y i denote i’s sale in the foreign market (i ∈ {A, B}). We
assume that the two countries are symmetric and the demand function for each country is given byp=

1 − (xA + xB ),

(1)

q

=

1 − (y A + y B ).

(2)

p is the price level that prevails in the home market, while q is the price level in the foreign market.
The firms engage in Cournot competition in each market. Following the convention, we adopt thesegmented market hypothesis where the firms choose separate quantities for the two markets. If a
firm in one market exports to the other, it must incur a transport cost per unit, denoted by t > 0.
The transport cost is meant to capture various trade barriers, most notably tariffs. Throughout theanalysis, we restrict our attention to a case where t ≤ 0.5 ≡ t̄. Under this restriction, the firms choose
nonnegative quantities to export.
Within this framework we consider a situation where firms A and B in the home market may
potentially undertake FDI by shifting part (or all) of their productive capacities abroad. More precisely,
each firm chooses one of the three alternatives, denoted by j ∈ {N, P, F }:1. No FDI (j = N ): A firm remains entirely in the domestic market and exports, if necessary, tothe foreign market.
2. Partial FDI (j = P ): A firm sets up a plant in the foreign market, which is used strictly tosupply to that market.
3. Full FDI (j = F ): A firm sets up a plant in the foreign market, which is used to supply to bothof the market.
In the case of partial FDI, the firm operates two plants, one in each market, and the option of importingfrom its foreign plant is ruled out.7 For most part, we examine the effect of partial FDI by restricting
7 This assumption can be considered as a type of capacity constraint.

6

attention to the case where full FDI is not an available option. The model is later extended toincorporate the possibility of full FDI in section 5, mainly to show that this addition would not affectthe substance of our model.

2.3

UnionsThe difference in unionization across the two markets implies different costs of production. In thispaper we focus on a situation where the two unions are disintegrated and each union independently
supplies labor to its firm. The competitive wage in the two countries is set equal to w̄ = 0.8 Taking
this as their reservation wage, the unions in the home market independently set wages to maximize
the following utility function:ui = wi z i , i = A, B.

(3)z i is firm i’s production in the home country where z i = xi (z i = xi + y i ) if its downstream firm
undertakes FDI (no FDI).

2.4

Timing

The timing of the model is summarized as follows:

1. the domestic firms sequentially choose whether to undertake FDI;
2. the unions simultaneously set wages to maximize their utilities;
3. the firms simultaneously choose quantities for each country to maximize their profits.

3

Benchmark: one domestic firm

3.1

Equilibrium wages and quantities

Before we proceed further, we first consider as a benchmark a case with only one domestic firm (forthe analysis, we abbreviate the superscript i). The analysis of this benchmark case is instrumental inillustrating the role of domestic competition in unionized international oligopoly.
(N-FDI):

In the absence of FDI, the monopolist maximizesmax (1 − x − w)x + (1 − y − t − w)y,x,y

8 This is strictly to simplify the analysis since the competitive wage plays no role in a qualitative sense.

7

subject to the constraint that all the quantities are nonnegative (this evidently applies for all subsequent
problems). The first-order condition then leads to
1−w 1−t−w,.
22x, y =(4)

Taking this into account, the union sets its wage to maximize the union utility. Depending on thetransport cost, there arise two distinct cases. The firm chooses a positive quantity to export if thewage set by the union is sufficiently low relative to the transport cost, i.e., 1 − t ≥ w. In this case, theunion maximizes
max w(x + y) =zw(2 − t − 2w), s.t. 1 − t ≥ w.
2

If the wage is sufficiently high, i.e., 1 − t < w, the union maximizes
max wx =w

w(1 − w)
, s.t. 1 − t < w.
2

It is then straightforward to obtain(2 − t),4(5)

2 + t 2 − 3t
,
.
8
8

(6)

w=
and
x, y =

Given the firm’s FDI choice j, the profit, the union utility, and the domestic consumer surplus are:πN =(P-FDI):4 − 4t + 5t2, uN =
32

µ

2−t
4

¶2

, CSN =

(2 + t)2
.
128

(7)

If the monopolist undertakes partial FDI, it maximizesmax (1 − x − w)x + (1 − y)y.
x,yThe first-order condition leads tox, y =

1−w 1
, .
2
2

(8)

The union loses the foreign market when its firm establishes a plant in the foreign market. The
union’s problem is thus defined aswx =w(1 − w).
2

The union never sets the wage above the transport cost because it loses all the employment by doing
so. Given this, we can show that
w=
8

1
.
2

(9)

and
x, y =

1 1
, .
4 2

(10)

The profit, the union utility, and the domestic consumer surplus are:
πP =

3.2

5
1
1
, uP = , CSP =
.
16
8
32

(11)

Welfare effects of FDI with one domestic firm

We measure the social efficiency of FDI by what we refer to as the domestic welfare Wj , defined as
Wj ≡ πj + uj + CSj . The primary purpose here is to show that FDI is in general welfare-improving
in the absence of domestic competition when the fixed cost of FDI is sufficiently small. This is despite
the fact that the size of the market that the union can serve is cut in half when its firm undertakes
FDI. This positive effect arises because FDI is a type of cost-reducing investment which allows thefirm to save transport costs, and always dominates the loss of employment.9
In order to investigate the relationship between the firm’s optimal choice and the overall social
efficiency, we need to explicitly incorporate the fixed cost into the model. Let CP denote the fixed cost
necessary for partial FDI. Given this, the monopolist undertakes FDI if and only if
πP − CP ≥ πN ⇔6 + 4t − 5t2≥ CP .
32(12)

It is, on the other hand, socially efficient to undertake FDI if and only if
WP − CP ≥ WN ⇔8 + 44t − 29t2
≥ CP .
128(13)

Examining these two conditions one can see that (12) is implied by (13) for t ≤ t̄, indicating thatthe incentive for FDI is in general excessive. This implies that simple transfer payments to subsidize
outward FDI would never improve welfare.
Although simple transfers would not work even in this monopolistic case, the government can ingeneral do more than just distributing subsidies. As stated in the introduction, the government may
provide public goods and services (hereafter, we simply call them public goods), through disseminating
information or providing various types of support, to reduce the fixed cost of FDI, thereby encouraging
domestic firms to expand abroad. To see whether this type of government intervention can be everwarranted, we suppose that the government is able to provide public goods which reduce the fixed costof FDI to λ0 Cj whereas the cost of providing those public goods is denoted by λ1 Cj . Let λ ≡ λ0 + λ1
9 This conclusion holds when the home and foreign markets are comparable in size. If the foreign market is sufficiently
larger than the home market, the loss of employment becomes more significant and a situation arises where FDI is
welfare-reducing.

9

denote the social cost of FDI (the total cost incurred by the home country) where λ captures the social
efficiency of the government intervention. We assume λ ∈ (0, 1) so that the government intervention
itself is efficient in that it decreases the social cost of FDI. Our question is then whether and when thegovernment intervention of this type is justified. Under this formulation, the condition for the social
efficiency is now given by
8 + 44t − 29t2
≥ λCP .
128

(14)

Note that the left-hand side is always positive for t ≤ t̄, meaning that this condition holds for any
given CP if λ is sufficiently small. This suggests that the government intervention is indeed justifiable
as long as it is sufficiently efficient.

4

Main Results

4.1

Equilibrium wages and quantities

We now extend the analysis by introducing another domestic firm (firm B) and examine the effect ofdomestic competition on the home market. Suppose that a new firm (firm B) along with its union(union B) enters into the market for some exogenous reasons. Firm B is assumed to be identical tofirm A in every aspect. The addition of a competing domestic rival results in strategic interactions
absent in the benchmark case.
With this addition, the model becomes increasingly complicated because there are generically threepossible pairs of FDI decisions: (i) none of the firms undertakes FDI (N-FDI, N-FDI); (ii) only one of
the firms undertakes partial FDI (P-FDI, N-FDI); (iii) both of the firms undertake partial FDI (P-FDI,
P-FDI). We now examine each case in turn.
(N-FDI, N-FDI):

With both of the firms remaining in the home country, each firm maximizes
¡
¢
¡
¢
max
1 − (xi + x−i ) − wi xi + 1 − (y i + y −i ) − wi − t y i ,
i i
x ,y

where i 6= −i throughout the analysis. Solving the first-order conditions, the optimal quantities are
obtained as
xi , y i =1 − 2wi + w−i 1 − t − 2wi + w−i,.
33

Each union thus maximizes
max wi (xi + y i ) =wi

wi (2 − t − 4wi + 2w−i ), s.t. 1 − t − 2wi + w−i ≥ 0.
3
10

(15)

It is conceptually straightforward, though computationally tedious, to solve this problem (see Appendix
A for more detail). The equilibrium wages and quantities are given by(2 − t),
6(16)

4 + t 4 − 5t
,
.
18
18

(17)

wi =
xi , y i =iLet πjk, uijk , CSjk denote the (equilibrium) profit, the union utility and the consumer surplus when

the pair of FDI choices is given by (j, k), j, k ∈ {N, P }. With some algebra, we obtain
i
πN
N =

(P-FDI, N-FDI):

16 − 16t + 13t2
(2 − t)2(4 + t)2, uiN N =, CSN N =
.
162
27
162

(18)

This is an intriguing case which apparently never occurs with one domestic firm.

In this situation each union faces different demand schedules for labor: as a consequence, two different
wages prevail in equilibrium. Without loss of generality, suppose that firm A undertakes partial FDI.
Suppose that firm B chooses a nonnegative quantity to export (because the wage set by its union
is sufficiently low relative to the transport cost). Each firm’s problem is then defined as¢¡¢¡
max 1 − (xA + xB ) − wA xA + 1 − (y A + y B ) y A
A
A
x ,y
¢
¡
¢
¡
max 1 − (xA + xB ) − wB xB + 1 − (y A + y B ) − wB − t y B .
xB ,y B

Solving the first-order conditions, the optimal quantities are obtained as
xA , y A=

xB , y B=

1 + wB − 2wA 1 + t + wB,3
3
1 − 2wB + wA 1 − 2t − 2wB
,
.
3
3

(19)
(20)

Since firm A has two plants, the unions are now asymmetric. Each union maximizes
wA (1 + wB − 2wA ),3wAwB (2 − 2t + wA − 4wB ).
max wB (xB + y B ) =3wB

max wA xA =

(21)
(22)

It also follows from (20) that if (1 − 2t − 2wB )/3 ≤ 0, firm B chooses not to export. The optimalquantities in this case are given by
xA , y A=

xB , y B=

1 + wB − 2wA 1
,
3
2
B
A
1 − 2w + w
,0
3

11

(23)
(24)

and each union now maximizes
max
wi xi =
iw

Definewi (1 + w−i − 2wi ).
3√54 − 31 2∼ 0.212.
t ≡48∗

With some algebra (see Appendix A), the equilibrium wages are given by2(5 − t)if t ∈ [0, t∗ )

31
A
w =

1


if t ∈ [t∗ , t̄],3
 9 − 8t

if t ∈ [0, t∗ )

31
B
w =

 1
if t ∈ [t∗ , t̄].
3
It follows from these that the equilibrium quantities are4(5 − t) 40 + 23t
,
if t ∈ [0, t∗ )

93
93
A A
x ,y =
2 1
 ,if t ∈ [t∗ , t̄],9 2 23 + 14t , 13 − 46t if t ∈ [0, t∗ )
B
B
93
93
x ,y =
 2, 0
if t ∈ [t∗ , t̄].
9
The profit, the union utility, and the consumer surplus are
πPAN =

(25)

(26)

(27)

(28)

16(5 − t)2(23 + 14t)2(40 + 23t)2(13 − 46t)2+, πPBN =
+
,
8649
8649
8649
8649

(29)

8(5 − t)24(9 − 8t)2
(43 + 10t)2, uB, CSN P =
,
PN =
2883
2883
17298

(30)

uA
PN =
for t ∈ [0, t∗ ) and497, πPBN =
,
324
81
2
16
B
, CSP N =,uA
P N = uP N =27
162
πPAN =(31)(32)

for t ∈ [t∗ , t̄).
(P-FDI, P-FDI):

Suppose that firm B follows firm A and sets up a plant in the foreign market.

When each of the firms has two plants, each firm maximizes
¡
¢
¡
¢
max
1 − (xi + x−i ) − wi xi + 1 − (y i + y −i ) y i .
i i
x ,y

12

Solving the first-order conditions, we obtain
xi , y i =1 − 2wi + w−i 1
, .
3
3

(33)

In this case, the wage set by a union has no effect on the foreign market. With no strategic consideration, each union simply maximizes
max wi xi =wiwi (1 − 2wi + w−i ).
3

It is straightforward to obtain
1
,
3
2 1
xi , y i = , .
9 3
wi =

(34)
(35)

The profit, the union utility, and the consumer surplus are
πPi P =

4.2

2
13 i
8
=
, u
, CSP P =.
81 P P
27
81(36)

Equilibrium FDI patterns(N-FDI, N-FDI):

The pair appears as an equilibrium outcome if and only ifAiπN
N ≥ πP N − CP⇔iCP ≥ πPAN − πN
N ≡ H1 .

(37)

It is intuitively clear that no firm undertakes FDI when its fixed cost is large, relative to the transport
cost t.
(P-FDI, N-FDI):

The pair appears as an equilibrium outcome if and only ifiBiπPAN − CP ≥ πN
N , πP N ≥ πP P − CP

⇔ H1 ≥ CP , CP ≥ πPi P − πPBN ≡ H2 .

(38)

The pair is supported as an equilibrium if CP is neither too large nor too small, as expected. The
lowerbound of CP is determined by firm B which has not undertaken FDI. As can be seen from Figure
1, the lowerbound of CP is not monotonic with respect to t: that is, an increase in the transport
cost may actually reduce the incentive to undertake FDI. This somewhat counterintuitive result stems
from the fact that wB , the wage paid by firm B, actually decreases with t because firm B now faces
intense competition with firm A in the foreign market and its union is hence forced to lower the wage
demands.10 Since this effect is wiped out and wB suddenly goes up once firm B undertakes FDI, theincentive to undertake FDI could decrease with an increase in t.
10 See Ishida and Matsushima (2005) for more detail on this.

13

(P-FDI, P-FDI):

The pair appears as an equilibrium outcome if and only if
πPi P − CP ≥ πPBN⇔

H2 ≥ CP .

(39)

Both of the firms apparently undertake FDI when CP is sufficiently small.

The equilibrium pattern depends on the fixed cost CP as well as the transport cost, which is
depicted in Figure 1.
[Figure 1 about here]

4.3

Welfare effects of FDI with two domestic firms

When there is only one domestic firm, FDI is welfare-improving when its fixed cost is sufficiently small.
This leads us to the following question: is more FDI in general beneficial for the home economy? As
it turns out, the answer to this question is mostly negative; this is so even when we disregard the fixed
cost of FDI. We in particular show that the second FDI is normally welfare-reducing in this two-firm
setting.
Outward FDI gives rise to two distinct effects of particular interest. First, FDI improves the firm’s
efficiency as it allows the firm to gain access to cheaper labor as well as to save the transport cost. Bothof them apparently contribute to a reduction in the cost of production and thus play a similar role
to cost-reducing R&D investment directed at the foreign market. We refer to this as the productivity
effect of FDI, which is generally welfare-improving.
When the production process involves immobile factors such as labor, FDI also has an impact
on the factor prices because the union’s wage-setting behavior hinges critically on the productivityof its downstream firm. When FDI is undertaken, the union is consequently forced to concentrateon the home market. Since the firm can serve the home market more effectively by the margin of
the transport cost, there arises an incentive for the union to raise its wage to take advantage of thissituation. The consequences of this incentive are not simply a matter of distributional concern since
the wage levels subsequently determine the output levels. We refer to this as the factor-price effect of
FDI. The factor-price effect may or may not be welfare-improving, depending crucially on the structureof FDI. When only firm A undertakes FDI, there arises a productivity gap between the two firms interms of supplying to the foreign market. In order to fill this gap and to compete in the foreign market,
union B has a strong incentive to lower its wage, which also places downward pressure on the wage set
by union A. The presence of the rival firm, which remains entirely in the home market, thus acts as an
14

anchor to keep the wages low and improves welfare under certain conditions. Note that this incentive
is totally wiped out when firm B follows its rival and undertakes FDI. The wages tend to go up rather
sharply as a consequence. To see this, Figure 2 illustrates the relationship between the equilibrium
wages and the pattern of FDI. The figure shows that the wages are likely to be lower when only one
firm undertakes FDI.
[Figure 2 about here]
We are now ready to examine the social efficiency of FDI in this duopolistic setting. To this end,
as above, define the domestic welfare given the pair of FDI choices (j, k) as
B
B
A
+ uA
+ πjk
Wjk ≡ πjk
jk + ujk + CSjk .

(40)

The domestic economy consists of three components: the firms, the unions and domestic consumers.
In order to identify who gains and who loses, we examine each component in turn.
Total profit:

It can be shown that the firm that undertakes FDI can always increase its profit. This

does not necessarily mean, however, that FDI always increases the firms’ total profit because a firm
may gain at the expense of its rival firm.
To see this, Figure 3 depicts the total profit as a function of t. First, it can be seen from thefigure that the first FDI unambiguously increases the total profit. The productivity effect is evidently
a crucial contributing factor in this. Moreover, when the transport cost is sufficiently small, the wage
effect also works positively for the firms as it invites intense competition between the unions. While
the factor-price effect leads to higher wages as the transport cost increases, the productivity effectgenerally prevails and the overall effect of the first FDI on the total profit is in general positive.
[Figure 3 about here]
While the first FDI in general increases the total profit, the effect of the second FDI is more
ambiguous. In particular, when t ∈ [t∗ , t̄], the second FDI actually decreases the total profit. This isbecause, in this range, the transport cost is so large that firm B (or more precisely union B) chooses
not to export to the foreign market: as a result, firm A can monopolize the foreign market. The total
profit naturally declines as the foreign market becomes duopolistic. In any event, though, the figure
indicates that the effect of the second FDI on the total profit seems to be fairly negligible, compared tothat of the first FDI. This implies that the firms’ gains associated with FDI are almost fully exploitedby the first FDI.
15

Total union utility:

With the relocation of productive capacities, the unions inevitably lose em-

ployment to foreign workers. Intuition thus suggests that the unambiguous loser of FDI is the unions.
This intuition is in general true for the first FDI, but there are situations where the unions are actually
made better off by the second FDI. The driving force behind this result is the presence of domestic
competition. When only firm A undertakes FDI and t ∈ [0, t∗ ], union B is placed in a difficult situation
since it needs to lower its wage to compete in the foreign market. Note that this downward pressure
works adversely for union A as well since it must also lower its wage in response to union B’s wagesetting behavior. The second FDI may be beneficial for the unions as a whole because they no longer
have this competitive pressure on their wages. This implies that the fact that the firm can export andpotentially capture the foreign market may sometimes work adversely for the unions because it leads
to excessive price competition between them.11 As a result, there may arise a situation where FDI
benefits the unions because it serves to soften price competition between them by depriving them of
the option of exporting altogether. See Figure 4. The next proposition summarizes this result.
Proposition 1 When (i) there are two domestic firms and (ii) the two markets are symmetric in size,
there exists some t̃ ∈ (0, t∗ ) such that the unions benefit from the second FDI for t ∈ [t̃, t∗ ].
[Figure 4 about here]
While the incentive to lower the wage to compete in the foreign market becomes stronger as tincreases, it eventually reaches a point where it no longer pays off for union B to continue to do so.
The union then gives up the foreign market and instead raises its wage to compensate for the loss ofthe market: that is, the union behaves as if its firm undertakes FDI. This also releases union A fromthe downward pressure on its wage. When t ∈ [t∗ , t̄], therefore, the second FDI has no effect on how
union B behaves because its firm does not export in the first place. As a result, nothing changes as
far as the unions are concerned when the second FDI is undertaken.
Domestic consumers:

The consumer surplus is ultimately determined by the wages set by theunions. Higher wages are detrimental to consumers since they result in higher prices and less output.
By comparing Figures 4 and 5, one can see that the unions’ gains are roughly consumers’ losses andvice versa. In this sense, the consumer surplus can be seen as a flip side of the union utility.
[Figure 5 about here]
11 Apparently, the unions can avoid this problem if the union, whose firm does not undertake FDI, can somehow
credibly commit itself to setting higher wages and thus staying out of the foreign market.

16

In general, the consumer surplus is minimized when both of the firms undertake FDI because thefactor-price effect pushes the wages upward. The first FDI is beneficial for consumers when t ∈ [0, t∗ ]because upstream competition between the unions over the foreign market drives down the wages.
The second FDI is, on the other hand, always detrimental to consumers because it releases the unionsfrom this downward pressure on the wages. This indicates that while FDI as a device to soften pricecompetition benefits the unions, it works adversely for consumers because of less output resulting fromhigher wages. This result is summarized in the next proposition.
Proposition 2 When (i) there are two domestic firms and (ii) the two markets are symmetric in size,
the consumer surplus is minimized when both of the firms undertake FDI.
The loss incurred by consumers dues to the second FDI constitutes a substantial part of the overall
welfare loss, as we will see next.
Domestic welfare:

There are several forces at work as illustrated, depending on t. Figure 6 com-pares equilibrium and social efficiency. The figure again indicates that the incentive to undertake FDI
is generally excessive, as in the case with one domestic firm. This shows that simple transfer payments
to encourage FDI would never be welfare-improving.
As far as policy issues are concerned, we are more interested in the case where the government
can to some extent reduce the fixed cost of FDI by removing barriers or providing public goods tofacilitate outward FDI. To see this, Figure 7 illustrates the welfare effect of FDI when the fixed costof FDI vanishes to zero. The figure consistently reveals that there exists a non-monotonic relationshipbetween the domestic welfare and the amount of FDI: the first FDI is always welfare-improving while
the second FDI is always welfare-reducing. The driving force behind this is again the presence of
upstream competition. In particular, the first FDI leads to intense rivalry between the unions andconsequently results in welfare gains, although the competition may be excessively intense from theunions’ viewpoint. Note also that, when t is sufficiently small, the domestic welfare is minimized whenboth of the firms undertake FDI, i.e., (P-FDI, P-FDI) is worse, in terms of the domestic welfare,than not only (P-FDI, N-FDI) but also (N-FDI, N-FDI). This draws clear contrast to the case with
one domestic firm where outward FDI is always welfare-improving, provided that the markets arecomparable in size. The following statement summarizes the main result of the paper.
Proposition 3 When (i) there are two domestic firms, (ii) the two markets are symmetric in size and(iii) the fixed cost of FDI is negligibly small, the domestic welfare is maximized for any t ∈ [0, t̄] when
17

only one of the firms undertakes FDI. Alternatively, the second FDI is always welfare-reducing.
[Figure 6 about here]
Note that this result overturns the insight obtained in the case with only one domestic firm, where
any government intervention to encourage outward FDI is warranted as long as the government can
reduce the fixed cost down to some negligible level. This finding amounts to a critical policy implication:
there are indeed such things as “excessive FDI” and any form of government intervention, no matter
how efficient it is, can be beneficial only up to some point.
[Figure 7 about here]

5

Extension: the case with full FDI

In the analysis thus far, we have only considered the case where the firms can shift only a part oftheir productive capacities. We now add to the analysis the possibility that they may shift all of
their capacities abroad, i.e., they may undertake full FDI. By doing so, we show that the basic insightobtained in the previous section still holds in a qualitative sense, even with this additional option.

5.1

Benchmark with one domestic firm

In order to investigate how this modification alters our analysis, we follow the same steps as above andstart with the benchmark case where there is only one domestic firm. Here, the monopolist faces threealternatives, j ∈ {N, P, F }, to choose from. Since the first two alternatives, j = N, P , are alreadydiscussed, however, we only need to look at the case where the monopolist undertakes full FDI.
(F-FDI):

If the monopolist undertakes full FDI, it maximizesmax (1 − x − t)x + (1 − y)y.
x,yThe first-order condition leads tox, y =

1−t 1
, .
2 2

(41)

In this case, the union ends up with zero rent. The profit and the domestic consumer surplus are:πF =(1 − t)2
2 − 2t + t2
, CSF =
.
4
8

(42)

Let CF denote the fixed cost of full FDI. It is perhaps more natural to assume that CF > CP ,but we do not impose any restriction on the relationship between CP and CF . Figure 8 illustrates thesocial efficiency and the equilibrium pattern for different values of t.
18

[Figure 8 about here]
There are two observations we can make here. First, the figure indicates that the incentive toundertake FDI, either partial or full, is in general excessive. Second, FDI is socially desirable when its
fixed cost is negligible. These observations are basically in line with those when only partial FDI is an
option, and hence all the welfare and policy implications are preserved.

5.2

Domestic competition and full FDI

With the addition of full FDI, there are generically six possible pairs of FDI decisions: (i) none of
the firms undertakes FDI (N-FDI, N-FDI); (ii) only one of the firms undertakes partial FDI (P-FDI,
N-FDI); (iii) both of the firms undertake partial FDI (P-FDI, P-FDI); (iv) only one of the firms
undertakes full FDI (F-FDI, N-FDI); (v) one of the firms undertakes full FDI and the other does
partial FDI (F-FDI, P-FDI); (vi) both of the firms undertake full FDI (F-FDI, F-FDI). Since thecomputation is tedious and mostly a repetition of what has been presented thus far, the derivation ofequilibrium is placed in Appendix B.
The results are summarized in Figure 9, which illustrates the socially efficient pattern of FDI for
different values of t. The socially efficient pattern is slightly more complicated than in the case where
only partial FDI is available, but the main message remains intact: for a wide range of parametervalues, the asymmetric pattern of FDI, where only one firm undertakes either partial or full FDI, issocially desirable. This is so even when the fixed costs of FDI, both CP and CF , are negligibly small.
For instance, when t = 1/10, both firms undertaking any form of FDI is never socially efficient evenwhen the fixed costs tend to zero.12 This result again roughly confirms our main contention that any
form of government intervention can be beneficial only up to some point, no matter how efficient theintervention is, even with the option of full FDI.
[Figure 9 about here]

6

Conclusion

The paper constructs a model of unionized duopoly and explores welfare and policy implications ofoutward FDI. It is found that the presence of domestic competition gives rise to welfare effects thatlead to a non-monotonic relationship between social welfare and the amount of FDI. With the strategicinteraction between the unions, the amount of FDI can be excessive even when FDI is totally costless.
12 When the transport cost t becomes even smaller and tends to zero, there arises a small range of C for which (F-FDI,F
F-FDI) is socially efficient.

19

The present analysis identifies a possible mechanism through which outward FDI actually reduces
welfare in the home economy, as often argued informally, and thus raises a critical policy implication:
whether outward FDI should be encouraged depends on the nature of domestic competition, especiallyin its relation to upstream input suppliers. When the unions possess strong bargaining power, asymmetric patterns of FDI, where only a subset of firms undertakes FDI, are desirable from the social
point of view for a wide range of parameter values. This implies that there are indeed such things as“excessive FDI” and encouraging (or even subsidizing) more FDI could be beneficial only up to somepoint. Although ultimate long-run consequences of outward FDI are not necessarily transparent inour partial-equilibrium framework, the paper illuminates an important aspect that should be carefully
taken into account by policymakers. Since our analysis is confined in a relatively simple framework to
make our points succinctly, it is of some interest to extend the present analysis to various settings togain further insight on the home-country welfare effect of outward FDI.

Appendix A(N-FDI, N-FDI):In this situation, each firm may choose not to export, depending on the wage set

by its union. If both of the firms choose to export, we obtainwi =2 + 2w−i − t
,
8

(A.1)

which leads to2−t,
6
4 + t 4 − 5txi , yi =
,
.
18
18
wi =

(A.2)
(A.3)

It follows from this that each union’s utility isui =(2 − t)2
.
27

(A.4)

We now show that this pair of wages indeed constitutes an equilibrium. To see this, it suffices toshow that each union has no incentive to deviate from this wage level taking the other union’s wage
as given. If a union unilaterally deviates and prevents its firm from exporting, the objective function
becomes
max wi xi =wiwi (1 − 2wi + w−i ), s.t. 1 − t − 2wi + w−i < 0.
3

If t < 8/13, the constraint is binding and we havewi =1 − t + w−i
8 − 7t
=
.
2
12
20

(A.5)

t
, 0.
3

(A.6)

(8 − 7t)t
.
36

(A.7)

xi , yi =The union’s utility when it deviates is thenui =There is no incentive to unilaterally deviate from the equilibrium if (A.4) is larger than (A.7), i.e.,(2 − t)2(8 − 7t)t
≥
.
27
36

(A.8)

It is straightforward to verify that this holds for any t.

(P-FDI, N-FDI):In this situation, firm B may choose not to export, depending on the wage set

by union B. Suppose first that the wage set by union B is low enough for firm B to export. The
first-order conditions then imply that1 − 2wA + wB 1 + wB
,
,
3
3

(A.9)

1 + wA − 2wB 1 − 2wB − 2t,.
3
3

(A.10)

xA , yA =xB , yB =The maximization problem for each union becomeswA (1 − 2wA + wB ),3
1 − 2wB − 2twB (2 + wA − 4wB − 2t)
max wB (xB + yB ) =, s.t.
≥ 0.
wB
3
3

max wA xA =wA

(A.11)(A.12)

If t < 13/46, the constraint is not binding, the optimal wages must satisfy
wA

=

wB

=

1 + wB,
4
2 + wA − 2t.
8

(A.13)(A.14)

We can then show that10 − 2t,31
9 − 8twB =,31
20 − 4t 40 − 23t,,
xA , yA =31
31
23 + 14t 13 − 46t
xB , yB =
,
.
93
93
wA =

21

(A.15)(A.16)(A.17)(A.18)

It follows from these that union B’s utility isuB =4(9 − 8t)2.
2883

(A.19)

Now suppose that union B raises the wage to the level that makes firm B unable to export. Solving
the first-order conditions, we have
xA , yA =1 − 2wA + wB 1
, ,3
2

(A.20)

xB , yB =1 + wA − 2wB, 0.
3(A.21)The maximization problem for each union now becomeswA (1 − 2wA + wB ),3
1 − 2wB − 2twB (1 + wA − 2wB ), s.t.
< 0.
max wB xB =wB3
3

max wA xA =wA

(A.22)(A.23)

If t > 1/6, the constraint is not binding and the optimal wages and quantities are given by
wA = wB =

1
,
3

2 1
, ,
9 2
2
xB , yB = , 0.
9xA , yA =(A.24)(A.25)(A.26)

It follows from these that union B’s utility is
uB =

2
.
27

(A.27)

Union B then chooses the latter strategy, which prevents firm B from exporting, if (A.27) exceeds(A.19), i.e.,√4(9 − 8t)2
54 − 31 22−> 0, ⇒ t >∼ 0.212.
27
2883
48

(A.28)

Appendix B: the case with full FDI
With the option of full FDI, there are three additional strategy pairs. In this appendix, we examine
each case in turn.

22

(F-FDI, N-FDI):In this situation each union faces different demand schedules for labor: as aconsequence, two different wages prevail in equilibrium. Without loss of generality, suppose that firm
A is the one to undertake full FDI
Suppose that firm B chooses a nonnegative quantity to export (because the wage set by its union
is sufficiently low relative to the transport cost). Each firm’s problem is then defined asmax (1 − (xA + xB ) − t)xA + (1 − (yA + yB ))yA

xA ,yAmax (1 − (xA + xB ) − wB )xB + (1 − (yA + yB ) − wB − t)yB .

xB ,yB

Solving the first-order conditions, the optimal quantities are obtained as
xA , yA=xB , yB=

1 + wB − 2t 1 + t + wB,3
3
1 − 2wB + t 1 − 2t − 2wB,.
3
3(A.29)(A.30)

Since firm A does not have plants at the domestic market, only the union of firm B exists. The union
maximizes
max wB (xB + yB ) =wBwB (2 − t − 4wB ).
3(A.31)It also follows from (A.30) that if (1 − 2t − 2wB )/3 ≤ 0, firm B chooses not to export. The optimalquantities in this case are given by
xA , yA=xB , yB=

1 + wB − 2t 1
, ,3
2
1 − 2wB + t, 0.
3(A.32)(A.33)and the union now maximizes
max wB xB =wB

wB (1 + t − 2wB ).
3Define√t∗∗ ≡ 3 2 − 4.
With some algebra, the equilibrium wage is given by½(2 − t)/8 if t ∈ [0, t∗∗ )wB =(1 + t)/4 if t ∈ [t∗∗ , t̄],It follows from these that the equilibrium quantities are 10 − 17t 10 + 7t

,

24
24
xA , yA =

5
−
7t
1

,
12
2
23

if t ∈ [0, t∗∗ )if t ∈ [t∗∗ , t̄],(A.34)(A.35)

 2 + 5t 2 − 7t
,
if t ∈ [0, t∗∗ )1212xB , yB = 1 + t, 0
if t ∈ [t∗∗ , t̄].
6
The profit, the total union utility, and the consumer surplus are
4 − 4t + 37t2
100(1 − t) + 169t2, πFBN =,288
72(2 − t)249(2 − t)2
BuA, CSF N =.
F N + uF N =48
1152

πFAN =(A.36)(A.37)(A.38)

for t ∈ [0, t∗∗ ), and(1 + t)2
61 − 70t + 49t2
, πFBN =,144
36(1 + t)2(7 − 5t)2
B
uA, CSF N =.
F N + uF N =24
288

πFAN =(A.39)(A.40)

for t ∈ [t∗∗ , t̄).
(F-FDI, P-FDI):

Without loss of generality, suppose that firm A is the one to undertake full FDI.

Each firm’s problem is defined asmax (1 − (xA + xB ) − t)xA + (1 − (yA + yB ))yA

xA ,yAmax (1 − (xA + xB ) − wB )xB + (1 − (yA + yB ))yB .

xB ,yB

Solving the first-order conditions, the optimal quantities are obtained as
xA , yA=xB , yB=

1 + wB − 2t 1,
3
3
1 − 2wB + t 1, .
3
3(A.41)(A.42)

Since firm A does not have plants at the domestic market, only the union of firm B exists. The union
maximizes
max wB xB =wB

wB (1 − 2wB + t).
3

(A.43)

With some algebra, the equilibrium wage is given by
wB =

1+t
.
4

(A.44)The equilibrium quantities are
xA , yA=xB , yB=5 − 7t 1
, ,
12
3
1+t 1
, .
6
3
24

(A.45)(A.46)

The profit, the total union utility, and the consumer surplus are
5 + 2t + t2
41 − 70t + 49t2
, πFBP =
,
144
36
2
2
(1 + t)(7 − 5t)
B
uA, CSF P =.
F P + uF P =24
288
πFAP =(F-FDI, F-FDI):(A.47)(A.48)

This case is quite simple as it is reduced to a standard Cournot model with nounion. Each firm’s problem is defined asmax (1 − (xA + xB ) − t)xA + (1 − (yA + yB ))yA

xA ,yAmax (1 − (xA + xB ) − t)xB + (1 − (yA + yB ))yB .

xB ,yB

Solving the first-order conditions, the optimal quantities are obtained as
xA , yA=xB , yB

=

1−t 1
,
3 3
1−t 1
, .
3 3

(A.49)(A.50)The profit and the consumer surplus are
πFi F =

2(1 − t)2
2 − 2t + t2
, CSF F =.
99(A.51)

References
Brander, J.A., Spencer, B.J., 1988, Unionized oligopoly and international trade policy, Journal ofInternational Economics 24, 217-34.
Bughin, J., Vannini, S., 1995, Strategic direct investment under unionized oligopoly, International
Journal of Industrial Organization 13, 127-45.
Ishida, J., Matsushima, N., 2004, FDI may help rival firms, Economics Bulletin 5, 1-8.
Leahy, D., Montagna, C., 2000, Unionisation and foreign direct investment: challenging conventional
wisdom? Economic Journal 110, C80-C92.
Lipsey, R.E., 2004, Home and host country effects of FDI, In: Baldwin, R.E. and Winters, L.A. (Eds.),
Challenges to Globalization, University of Chicago Press, Chicago.
Lommerud, K.E., Meland, F., Sørgard, L., 2003. Unionized oligopoly, trade liberalization and location
choice, Economic Journal 113, 782-800.
Lommerud, K.E., Straume, O.R., Sørgard, L., 2006, National versus international mergers in unionizedoligopoly, Rand Journal of Economics 37, 212-33.
25

Naylor, R.A., 1998, International trade and economic integration when labour markets are generallyunionized, European Economic Review 42, 1251-67.
Naylor, R.A., 1999, Union wage strategies and international trade, Economic Journal 109, 102-25.
Naylor, R.A., Santoni, M., 2003, Foreign direct investment and wage bargaining, Journal of International Trade and Economic Development 12, 1-18.
Skaksen, J.R., International outsourcing when labour markets are unionized, Canadian Journal of
Economics 37, 78-94.
Skaksen, M.Y., Sørensen, J.R., 2001, Should trade unions appreciate foreign direct investment, Journalof International Economics 55, 379-90.
Straume, O.R., 2002, Union collusion and intra-industry trade, International Journal of Industrial
Organization 20, 631-52.
Straume, O.R., 2003, International merger and trade liberalization: implications for unionized labour,
International Journal of Industrial Organization 21, 717-35.
Zhao, L., 1995. Cross-hauling direct foreign investment and unionized oligopoly, European Economic
Review 39, 1237-53.
Zhao, L., 2001. Unionization, vertical markets, and the outsourcing of multinationals, Journal ofInternational Economics 55, 187-202.

26

CP
0.35
0.3
0.25

HN-NL

0.2
0.15
HP-NL
0.1
0.05

HP-PL
t
0.05 0.1 0.15 0.2 0.25 0.3 0.35

Figure 1: Equilibrium with one domestic firm

27

W
0.34
i

0.32

w NN

wi PP
wA PN

wi PN

0.3
0.28

wB PN

0.26
0.24
0.22
0.1

0.2

0.3

Figure 2: Equilibrium wages

28

t
0.4

Π
0.4

ΠA PN +ΠB PN

ΠA PN +ΠB PN
2Πi PP

0.3
0.2

2Πi NN
0.1

0.1

0.2

0.3

Figure 3: Total profit

29

t
0.4

U
0.275
0.25
0.225
0.2
0.175
0.15
0.125

2ui NNuA PN +uB PN
uA PN +uB PN
2ui PP

i

2u PP
0.1

0.2

0.3

Figure 4: Total union utility

30

t
0.4

CS
0.13
CSPN

0.12
0.11

CSNN

0.1

CSPN

CSPP
0.09
0.1

0.2

0.3

t
0.4

Figure 5: Domestic consumers surplus

31

CP

Cp

0.35

0.35

0.3

0.3

0.25

0.25

0.2

HN-NL

HN-NL:HN-NL

0.2

0.15

0.15

0.1

0.1

HP-NL:HN-NL

0.05

HP-PL:HN-NL

HP-NL

0.05

t
0.05 0.1 0.15 0.2 0.25 0.3 0.35

HP-NL:HP-NL
HP-PL:HP-NLt0.05 0.1 0.15 0.2 0.25 0.3 0.35

social efficiency

social efficiency and equilibrium

Figure 6: Social efficiency and equilibrium with two domestic firms
Note: (i − j) : (i0 − j 0 ) indicates that the equilibrium is (i − j) while the socially efficient outcome is(i0 − j 0 ).

32

W
0.65
WPN
0.6
WPP
0.55
WNN

0.5
0.45
0.1

0.2

0.3

Figure 7: Domestic welfare

33

t
0.4

CF
0.5

CF
0.5
Partial FDI

Partial FDI

0.4

Non FDI

0.4

Non FDI

0.3

0.3

0.2

0.2

0.1

0.1

Full FDI

Full FDI
0.1

0.2

0.3

0.4

C
0.5 P

0.1

social efficiency

0.2

0.3

0.4

C
0.5 P

equilibrium

Figure 8: Social efficiency and equilibrium with one domestic firm: the case with full
FDI

34

CF
0.1

0.08

HN,PL

HN,NL

0.06

0.04
HN,FL
0.02

0.02

0.04

0.06

0.08

0.1

Cp

Figure 9: Social efficiency with two domestic firms: the case with full FDI

35