GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.92

Domestic Competition and Foreign Direct Investment
in Unionized Oligopoly

Junichiro Ishida and Noriaki Matsushima

October 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

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

Domestic Competition and Foreign Direct Investment inUnionized Oligopoly∗

Junichiro Ishida
Institute of Social and Economic Research, Osaka University
andNoriaki Matsushima†
Institute of Social and Economic Research, Osaka University
October 1, 2009

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, weconstruct a model of unionized duopoly and examine welfare implications of outward FDI
by paying special attention to the role of domestic competition. We ﬁnd that the welfare
eﬀect of FDI is largely non-monotonic, and there are indeed such things as “excessive
FDI.” 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 popularbelief, 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 cruciallyon the nature of domestic competition, and policymakers must carefully take this aspect
into consideration.

JEL classiﬁcation numbers: F21, J31, L13.
Key words: R&D investment, vertical relation, transport cost, welfare, wage bargaining∗

This is a substantially revised version of the manuscript “Outward FDI in Unionized Oligopoly: Theory
and Policy Implications.” 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, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. E-mail:E-mail: nmatsush@iser.osaka-u.ac.jp

1

Introduction

Should a government encourage, or even subsidize, globalization of domestic ﬁrms? If so, thento what extent? With the increasing degree of globalization,1 those questions become more
and more critical for policymakers these days. Speciﬁcally at issue, regarding those questions,is the welfare eﬀect of outward 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 bewelfare-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 CanadianTrade Commissioner Service and the Japan External Trade Organization (JETRO) provide
information and various types of support, as one of their missions, to help Canadian andJapanese 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 Tradeorganizes fairs named Expotecnia in various countries in an attempt to boost outward FDI aswell 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 toactively promote outward FDI through several policy instruments, ranging from disseminating
information on investment opportunities to providing investment insurance against politicalrisk.
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 ﬁrms that undertake FDI can improve their productive eﬃciency through several channels. First, ﬁrms may invest abroad to save transport costs, including tariﬀs andother non-tariﬀ trade barriers, which allows them to serve the foreign market more eﬃciently.
1

The amount of outward FDI has steadily increased over time and now reached 778.7 billion dollars worldwide in 2005, 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 this project is “to oﬀer a one-stop point of access to various government ministries as well as Singaporestyle education, health and recreation facilities, and an international school (UNCTAD, World Investment
Report 2006, p.211).”1

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 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 the home 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 theexpense of domestic workers.3
While the welfare analysis of outward FDI oﬀers critical policy implications, studies on
the eﬀect of outward FDI are relatively scarce, both theoretically and empirically.4 The paper
intends to ﬁll this gap. In particular, the main purpose of this paper is to examine whether andunder what circumstances the intuition mentioned above (that outward FDI may reduce social
welfare) actually holds true. Special attention is paid to the role of domestic competition,i.e., how welfare implications of FDI are related to and inﬂuenced by the nature of market
competition in the domestic market. 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 from its own union which possesses somebargaining 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 to follow its rival: for
expositional clarity, we say that the ﬁrst FDI (the second FDI) is undertaken when ﬁrm A(ﬁrm B) sets up a foreign plant.
Within this framework, we examine welfare and policy implications of outward FDI. We
ﬁrst show that when there is only one domestic ﬁrm in the market to begin with, outward
FDI is always welfare-improving when the home and foreign markets are comparable in size.
3

For instance, Skaksen and Sørensen (2001) show that unions are likely to lose on FDI if domestic andforeign activities are substitutable.
4
The literature on the welfare eﬀect of FDI has mainly focused on the eﬀect of inward FDI, i.e., the eﬀectof FDI on the host country. See Lipsey (2004) for an extensive survey on this issue.

2Given this result, one might be tempted to conjecture that outward FDI is in general welfareimproving even in the presence of strong labor unions. As it turns out, however, this conclusion
does not necessarily hold true with the addition of another rival ﬁrm. When there are morethan one domestic ﬁrm-union pair, one ﬁrm’s FDI decision aﬀects 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 home and 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., the eﬀect of outward FDI can be purely negative. In general,
an asymmetric pattern of FDI is socially desirable and hence the amount of FDI caneasily 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 toeﬀects that are 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 asfollows. When a ﬁrm sets up a foreign plant, its union is consequently forced to concentrateon the home market that it can serve 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 inthe cost of supplying to the foreign market. Because of this, the union of the less productive
ﬁrm, the one that does not undertake FDI, must lower its wage to stay competitive in theforeign market, and intense price rivalry between the unions arises as a result: the presenceof 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 (andthe last, in this case) FDI is undertaken. The wages suddenly go up and the increase in thewages results in 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
3

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 theexpense of the unions, as one might anticipate. The more dominant factor in this is rather areduction in consumer surplus, resulting from higher wages. The eﬀect of FDI, especially thesecond one, on the unions is less clear. The ﬁrst FDI puts downward pressure on the wages inorder to compete in the foreign market, and the price competition between the unions can beexcessively intense from the unions’ viewpoint. The second FDI may be beneﬁcial for them,quite contrary to the popular belief, because it releases them from this downward pressure.
In other words, as the option of exporting is no longer available, the second FDI serves as astrong commitment device to substantially soften price competition between the unions andconsequently beneﬁts them.
The present analysis is related to a line of research which deals with FDI in the presenceof labor 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 andMatsushima, 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 asymmetric pattern of FDI is normally desirablefrom 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 the amount of FDI can beexcessive, it is due to the presence of the ﬁxed cost: that is, they show that there arises a casein their model where the welfare gain from FDI is exceeded by the ﬁxed cost of investment.
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

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), Skaksen (2004), Lommerud
et al. (2006), and Lommerud et al. (2009).

4competition.
The paper proceeds as follows. The next section outlines the basic model. Section 3
analyzes as a benchmark a case with only one domestic ﬁrm and shows that outward FDI
is normally welfare-improving. Section 4 extends the analysis to a case with two domesticﬁrms and illustrate how market outcomes driven by upstream competition are aﬀected by
the amount of FDI. Section 5 extends the baseline model to include the option of full FDI.
Finally, section 6 oﬀers some 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 the foreign market. Each ﬁrm procures its labor input from its ﬁrm-speciﬁc
union: we refer to the union of ﬁrm i as union i in the subsequent analysis. 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-scaletechnology. 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 by
p = 1 − (xA + xB ),q = 1 − (y A + y B ).
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 the segmented market hypothesis where the ﬁrms choose separate quantities for thetwo markets. If a ﬁrm in one market exports to the other, it must incur a transport cost per
6
In Lommerud et al. (2003), there is only one ﬁrm that initially is located in the home market. The otherﬁrm is located in the foreign market and is non-unionized. The presence of domestic competition proves to giverise to strategic interactions and welfare implications absent in the case with only one domestic ﬁrm, as statedin the introduction. It should also be noted that our main results are qualitatively unchanged even when there
exists a ﬁrm in the foreign market. See Appendix B for the case with a foreign ﬁrm.

5

unit, denoted by t > 0. The transport cost is meant to capture various trade barriers, mostnotably tariﬀs. Throughout the analysis, 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, to the foreign market.
2. Partial FDI (j = P ): A ﬁrm sets up a plant in the foreign market, which is used strictly
to supply to that market.
3. Full FDI (j = F ): A ﬁrm sets up a plant in the foreign market, which is used to supply
to both of the market.
In the case of partial FDI, the ﬁrm operates two plants, one in each market, and the option ofimporting from its foreign plant is ruled out.7 For most part, we examine the eﬀect of partial
FDI by restricting attention to the case where full FDI is not an available option. The modelis later extended to incorporate the possibility of full FDI in section 5, mainly to show that
this addition would not aﬀect the substance of our model.

2.3

UnionsThe diﬀerence in unionization across the two markets implies diﬀerent costs of production.
In this paper we focus on a situation where the two unions are disintegrated and each union
independently supplies labor to its ﬁrm.8 The competitive wage in the two countries is set
equal to w̄ = 0.9 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.
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).
7This assumption can be considered as a type of capacity constraint.
The assumption that the unions are disintegrated turns out to be insigniﬁcant and innocuous as we canobtain qualitatively similar results even when they are integrated as an industry-wide union. See Appendix B
for this extension.
9This is strictly to simplify the analysis since the competitive wage plays no role in a qualitative sense.
8

6

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 domesticﬁrm (for the analysis, we abbreviate the superscript i). The analysis of this benchmark caseis instrumental in illustrating 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,ysubject to the constraint that all the quantities are nonnegative (this evidently applies for all
subsequent problems). The ﬁrst-order condition then leads tox, y =

1−w 1−t−w,.
22

Taking this into account, the union sets its wage to maximize the union utility. Dependingon the transport cost, there arise two distinct cases. The ﬁrm chooses a positive quantity toexport if the wage set by the union is suﬃciently low relative to the transport cost, i.e.,
1 − t ≥ w. In this case, the union 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

7

It is then straightforward to obtainw=(2 − t)
2 + t 2 − 3t
, x, y =,.
488Given 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

(

2−t
4

)2

, CSN =

(2 + t)2
.
128

(1)

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

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 that1
1 1
w = , x, y = , .
2
4 2
The proﬁt, the union utility, and the domestic consumer surplus are:
πP =

3.2

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

(2)

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 welfareimproving 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 of8cost-reducing investment which allows the ﬁrm to save transport costs, and always dominates
the loss of employment.10
In order to investigate the relationship between the ﬁrm’s optimal choice and the overallsocial eﬃciency, we need to explicitly incorporate the ﬁxed cost into the model. Let CP denotethe ﬁxed cost necessary for partial FDI. Given this, the monopolist undertakes FDI if andonly if
πP − CP ≥ πN ⇔6 + 4t − 5t2≥ CP .
32(3)

It is, on the other hand, socially eﬃcient to undertake FDI if and only if
W P − CP ≥ W N ⇔8 + 44t − 29t2
≥ CP .
128(4)

Examining these two conditions one can see that (3) is implied by (4) for t ≤ t̄, indicatingthat the 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 in general do more than just distributing subsidies. As stated in the introduction, thegovernment 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 ever warranted, we suppose that the governmentis able to provide public goods which reduce the ﬁxed cost of FDI to λ0 Cj whereas the costof providing those public goods is denoted by λ1 Cj . Let λ ≡ λ0 + λ1 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
the government intervention of this type is justiﬁed. Under this formulation, the condition
for the social eﬃciency is now given by
8 + 44t − 29t2
≥ λCP .
128
10

(5)

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 situationarises where FDI is welfare-reducing.

9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 isindeed 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 of domestic 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 to ﬁrm 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 three 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 theﬁrms 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 max-

imizesmax (1 − (xi + x−i ) − wi )xi + (1 − (y i + y −i ) − wi − t)y i ,xi ,y iwhere i ̸= −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

It is conceptually straightforward, though computationally tedious, to solve this problem (seeAppendix A for more detail). The equilibrium wages and quantities are given bywi =(2 − t)
4 + t 4 − 5t
, xi , y i =
,
.
6
18
18

10

i , ui , CS
Let πjk
jk denote the (equilibrium) proﬁt, the union utility and the consumer surplus
jkwhen 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
This is an intriguing case which apparently never occurs with one do-

mestic ﬁrm. In this situation each union faces diﬀerent demand schedules for labor: as aconsequence, two diﬀerent wages prevail in equilibrium. Without loss of generality, supposethat 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
asmax (1 − (xA + xB ) − wA )xA + (1 − (y A + y B ))y A

xA ,y Amax (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

(6)

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 =It also follows from (6) that if (1 − 2t − 2wB )/3 ≤ 0, ﬁrm B chooses not to export. The
optimal quantities in this case are given by
xA , y A =1 + wB − 2wA 1
1 − 2wB + wA
, ; xB , y B =
,0
3
2
3

and each union now maximizes
max wi xi =
wi

Deﬁne

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

11

With some algebra (see Appendix A), the equilibrium wages are given bywA =
2(5 − t)
if t ∈ [0, t∗ )



 1

if t ∈ [t∗ , t̄],

31

3

wB =


9 − 8t

if t ∈ [0, t∗ )


1



if t ∈ [t∗ , t̄].

31

3

It follows from these that the equilibrium quantities are4(5 − t) 40 + 23t


,


93
x ,y =
 2, 19 2
AA

xB , y B =93

if t ∈ [0, t∗ )if t ∈ [t∗ , t̄],
23 + 14t 13 − 46t


,

93

 2, 0
9

93

if t ∈ [0, t∗ )if t ∈ [t∗ , t̄].

The proﬁt, the union utility, and the consumer surplus are16(5 − t)2 (40 + 23t)2(23 + 14t)2 (13 − 46t)2+, πPBN =
+
,
8649
8649
8649
8649
8(5 − t)24(9 − 8t)2
(43 + 10t)2
uA, uB, CSN P =
,
PN =
PN =
2883
2883
17298

πPAN =

for t ∈ [0, t∗ ) andπPAN =

9742
16B, πPBN = , uA
, CSP N =,P N = uP N =
324
81
27
162

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 maximizesmax (1 − (xi + x−i ) − wi )xi + (1 − (y i + y −i ))y i .
xi ,y i

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

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 ).
312

It is straightforward to obtain1
2 1
w i = ; xi , y i = , .
3
9 3
The proﬁt, the union utility, and the consumer surplus are
πPi P =

4.2

13 i
2
8
, uP P = , CSP P = .
81
27
81

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

The pair appears as an equilibrium outcome if and only ifiAπN
N ≥ π P N − CPi
⇔ CP ≥ πPAN − πN
N ≡ H1 .

It is intuitively clear that no ﬁrm undertakes FDI when its ﬁxed cost is large, relative to thetransport 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 .

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 canbe 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 theforeign market and its union is hence forced to lower the wage demands.11 Since this eﬀect iswiped out and wB suddenly goes up once ﬁrm B undertakes FDI, the incentive to undertake
FDI could decrease with an increase in t.
(P-FDI, P-FDI):

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

⇔ H 2 ≥ CP .

Both of the ﬁrms apparently undertake FDI when CP is suﬃciently small.
11

See Ishida and Matsushima (2005) for more detail on this.

13

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 forthe home economy? As it turns out, the answer to this question is mostly negative; this is soeven when we disregard the ﬁxed cost of FDI. We in particular show that the second FDI isnormally 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 thetransport cost. Both of 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
productivity of its downstream ﬁrm. When FDI is undertaken, the union is consequently
forced to concentrate on 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 this situation. 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 structure of FDI. When only ﬁrm A
undertakes FDI, there arises a productivity gap between the two ﬁrms in terms 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 anchor to keep the wages low and improves welfare under certain conditions. Notethat 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 the14relationship between the equilibrium wages and the pattern of FDI. The ﬁgure shows that thewages 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
AB
B
Wjk ≡ πjk
+ πjk
+ uA
jk + ujk + CSjk .

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 seenfrom the ﬁgure that the ﬁrst FDI unambiguously increases the total proﬁt. The productivity
eﬀect is evidently a crucial contributing factor in this. Moreover, when the transport costis suﬃciently small, the wage eﬀect also works positively for the ﬁrms as it invites intensecompetition between the unions. While the factor-price eﬀect leads to higher wages as thetransport cost increases, the productivity eﬀect generally prevails and the overall eﬀect of theﬁrst 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 is because, 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 theforeign 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 proﬁtseems to be fairly negligible, compared to that of the ﬁrst FDI. This implies that the ﬁrms’
gains associated with FDI are almost fully exploited by the ﬁrst FDI.
15

Total union utility:

With the relocation of productive capacities, the unions inevitably

lose employment 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 andt ∈ [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 wage-setting behavior. The
second FDI may be beneﬁcial for the unions as a whole because they no longer have thiscompetitive 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.12 As a result, there may arise a situation
where FDI beneﬁts the unions because it serves to soften price competition between them bydepriving them of the option of exporting altogether. See Figure 4. The next propositionsummarizes this result.
Proposition 1 When (i) there are two domestic ﬁrms and (ii) the two markets are symmetricin size, there exists some t̃ ∈ (0, t∗ ) such that the unions beneﬁt from the second FDI fort ∈ [t̃, t∗ ].
[Figure 4 about here]
While the incentive to lower the wage to compete in the foreign market becomes stronger
as t increases, 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 of the market: that is, the union behaves as if its ﬁrm undertakes FDI. This also
releases union A from the downward pressure on its wage. When t ∈ [t∗ , t̄], therefore, thesecond 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.

12

Apparently, the unions can avoid this problem if the union, whose ﬁrm does not undertake FDI, cansomehow credibly commit itself to setting higher wages and thus staying out of the foreign market.

16

Domestic consumers:

The consumer surplus is ultimately determined by the wages set by

the unions. Higher wages are detrimental to consumers since they result in higher prices andless output. By comparing Figures 4 and 5, one can see that the unions’ gains are roughly
consumers’ losses and vice versa. In this sense, the consumer surplus can be seen as a ﬂip sideof the union utility.
[Figure 5 about here]
In general, the consumer surplus is minimized when both of the ﬁrms undertake FDI
because the factor-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 unions from this downward pressure on the wages. This
indicates that while FDI as a device to soften price competition beneﬁts the unions, it works
adversely for consumers because of less output resulting from higher wages. This result issummarized in the next proposition.
Proposition 2 When (i) there are two domestic ﬁrms and (ii) the two markets are symmetricin 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 ofthe overall welfare loss, as we will see next.
Domestic welfare:

There are several forces at work as illustrated, depending on t. Figure

6 compares equilibrium and social eﬃciency. The ﬁgure again indicates that the incentive toundertake 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 to facilitate outward FDI. To see this, Figure 7 illustrates the welfare eﬀect of
FDI when the ﬁxed cost of FDI vanishes to zero. The ﬁgure consistently reveals that there
exists a non-monotonic relationship between the domestic welfare and the amount of FDI: theﬁrst 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, the17ﬁrst FDI leads to intense rivalry between the unions and consequently results in welfare gains,
although the competition may be excessively intense from the unions’ viewpoint. Note also
that, when t is suﬃciently small, the domestic welfare is minimized when both 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 symmetricin size and (iii) the ﬁxed cost of FDI is negligibly small, the domestic welfare is maximized
for any t ∈ [0, t̄] when only one of the ﬁrms undertakes FDI. Alternatively, the second FDI isalways 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 formof government intervention, no matter how eﬃcient it is, can be beneﬁcial only up to somepoint.
[Figure 7 about here]

5

The case with full FDI

In the baseline case, we do not allow ﬁrms to relocate entirely to the foreign market. Undercertain conditions, however, it may be the best interest of a ﬁrm to shift all of its productive
capacity to the foreign market. We now introduce this additional option of full FDI andinvestigate how this modiﬁcation alters our analysis.

5.1

Benchmark with one domestic ﬁrm

We follow the same steps as in the main text and start with the benchmark case where there
is only one domestic ﬁrm. Here, the monopolist faces three alternatives, j ∈ {N, P, F }, to18choose from. Since the ﬁrst two alternatives, j = N, P , are already discussed, however, weonly 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

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

Let CF denote the ﬁxed cost of full FDI. It is perhaps more natural to assume thatCF > CP , but we do not impose any restriction on the relationship between CP and CF .
Figure 8 illustrates the social eﬃciency and the equilibrium pattern for diﬀerent values of t.
[Figure 8 about here]
There are two observations we can make here. First, the ﬁgure indicates that the incentive
to undertake 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

We now introduce another domestic ﬁrm to see the impact of domestic competition. 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 oneof the ﬁrms undertakes full FDI (F-FDI, N-FDI); (v) one of the ﬁrms undertakes full FDI andthe other does partial FDI (F-FDI, P-FDI); (vi) both of the ﬁrms undertake full FDI (F-FDI,
F-FDI). Since computation is tedious and mostly a repetition of what has been presented thus
far, the derivation of equilibrium is placed in Appendix A.
19

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 parameter values, the asymmetric pattern of FDI, where only one ﬁrm undertakes
either partial or full FDI, is socially 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 even when the ﬁxed costs tend to zero.13 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 the intervention is, even with theoption of full FDI.
[Figure 9 about here]

6

Conclusion

The paper constructs a model of unionized duopoly and explores welfare and policy implications of outward FDI. It is found that the presence of domestic competition gives rise
to welfare eﬀects that lead to a non-monotonic relationship between social welfare and theamount of FDI. With the strategic interaction between the unions, the amount of FDI can beexcessive even when FDI is totally costless. 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, especially in 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 pointof 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 some point. Although ultimate long-run consequences of outward FDI are not necessarilytransparent in our partial-equilibrium framework, the paper illuminates an important aspectthat should be carefully taken into account by policymakers. Since our analysis is conﬁned ina relatively simple framework to make our points succinctly, it is of some interest to extend
13

When the transport cost t becomes even smaller and tends to zero, there arises a small range of CF forwhich (F-FDI, F-FDI) is socially eﬃcient.

20

the present analysis to various settings to gain further insight on the home-country welfare
eﬀect of outward FDI.

Appendix A
A1. Without full FDI
When each ﬁrm can choose either no FDI or partial FDI, there are generically three pairs of
FDI decisions. Since (P-FDI, P-FDI) is computationally straightforward, we cover the othertwo cases in more detail.
(N-FDI, N-FDI):In this situation, each ﬁrm may choose not to export, depending on thewage set by its union. If both of the ﬁrms choose to export, we obtainwi =2 + 2w−i − t,8which leads to
wi =

2−t
4 + t 4 − 5t
; xi , y i =
,
.
6
18
18

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

(A.1)

We now show that this pair of wages indeed constitutes an equilibrium. To see this,it suﬃces to show 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 fromexporting, the objective function becomesmax 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 =8 − 7tt
1 − t + w−i=, xi , y i = , 0.
2
123

The union’s utility when it deviates is thenui =(8 − 7t)t
.
36

21

(A.2)

There is no incentive to unilaterally deviate from the equilibrium if (A.1) is larger than (A.2),i.e.,(2 − t)2(8 − 7t)t≥.
27
36
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 thewage set by union B. Suppose ﬁrst that the wage set by union B is low enough for ﬁrm B toexport. The ﬁrst-order conditions then imply that1 − 2wA + wB 1 + wB,,
3
3
1 + wA − 2wB 1 − 2wB − 2t,.
xB , y B =33xA , y A =The maximization problem for each union becomeswA (1 − 2wA + wB ),3
wA
wB (2 + wA − 4wB − 2t)
1 − 2wB − 2t
max wB (xB + y B ) =, s.t.
≥ 0.
3
3wB
max wA xA =If t < 13/46, the constraint is not binding, the optimal wages must satisfy
wA =1 + wB
2 + wA − 2t
, wB =.
4
8

We can then show thatwA =10 − 2t
9 − 8t A A 20 − 4t 40 − 23t B B
23 + 14t 13 − 46t, wB =, x ,y =,, x ,y =
,
.
31
31
31
31
93
93

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

(A.3)

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 , y A =1 − 2wA + wB 1
1 + wA − 2wB, ; xB , y B =
, 0.
3
2
3

22

The maximization problem for each union now becomeswA (1 − 2wA + wB ),3
wA
wB (1 + wA − 2wB )1 − 2wB − 2t
max wB xB =, s.t.
< 0.
3
3wB
max wA xA =If t > 1/6, the constraint is not binding and the optimal wages and quantities are given by1
2 1
2
wA = wB = , xA , y A = , , xB , y B = , 0.
3
9 2
9It follows from these that union B’s utility is
uB =

2
.
27

(A.4)

Union B then chooses the latter strategy, which prevents ﬁrm B from exporting, if (A.4)
exceeds (A.3), i.e.,√24(9 − 8t)2
54 − 31 2−> 0, ⇒ t >∼ 0.212.
27
2883
48

A2. With full FDI
With the option of full FDI, there arise three additional pairs of FDI decision. We examine
each case in turn.
(F-FDI, N-FDI):In this situation each union faces diﬀerent demand schedules for labor: asa consequence, two diﬀerent wages prevail in equilibrium. Without loss of generality, supposethat 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 , y A =xB , yB =1 + wB − 2t 1 + t + wB,3
3
1 − 2wB + t 1 − 2t − 2wB
,
.
3
3
23

(A.5)

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 ).
3It also follows from (A.5) that if (1 − 2t − 2wB )/3 ≤ 0, ﬁrm B chooses not to export. The
optimal quantities in this case are given by
xA , yA =1 − 2wB + t
1 + wB − 2t 1
, ; xB , yB =
, 0.
3
2
3

and the union now maximizes
max wB xB =
wB

Deﬁne

wB (1 + t − 2wB ).
3√t∗∗ ≡ 3 2 − 4.

With some algebra, the equilibrium wage is given by{wB =(2 − t)/8 if t ∈ [0, t∗∗ )(1 + t)/4 if t ∈ [t∗∗ , t̄],It follows from these that the equilibrium quantities are10 − 17t 10 + 7t
,


if t ∈ [0, t∗∗ )24
24
xA , yA =
5 − 7t 1
,
if t ∈ [t∗∗ , t̄],122
 2 + 5t , 2 − 7t if t ∈ [0, t∗∗ )


12
12
xB , 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
B
uA
+
u
=
,
CS
=
.
F
N
FN
FN
48
1152
πFAN =

for t ∈ [0, t∗∗ ), and61 − 70t + 49t2
(1 + t)2, πFBN =,144
36(7 − 5t)2(1 + t)2
B, CSF N =.
uA
F N + uF N =24
288
πFAN =

for t ∈ [t∗∗ , t̄).
24

(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 , y A =1 − 2wB + t 1
1 + wB − 2t 1
, ; xB , y B =
, .
3
3
3
3

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

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

1+t
.
4

The equilibrium quantities are
xA , yA =1+t 1
5 − 7t 1, ; xB , yB =
, .
12
3
6
3

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

This case is quite simple as it is reduced to a standard Cournot modelwith no union. 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 =

1−t 1
1−t 1
, ; xB , y B =
, .
3 3
3 3

The proﬁt and the consumer surplus are
πFi F =

2 − 2t + t2
2(1 − t)2
, CSF F =
.
9
9

25

Appendix B: Extensions
In the analysis thus far, we have only considered a particular environment to make our points.
In this appendix, we extend the basic setup in two diﬀerent ways to show the basic insight isrobust to these alternations.

B.1

The case with a foreign ﬁrm

We introduce a foreign ﬁrm into the baseline case, along with one or two ﬁrms in the domestic
market. The foreign ﬁrm, denoted by F , produces its product with a constant marginal costwhich is normalized to zero and supplies its products to both markets if it chooses to doso. Every other aspect of the model follows the baseline case in the main text. To makecomparison easier, all the results are summarized in ﬁgures 1F-7F, each of which corresponds
to ﬁgures 1-7 for the baseline case.
(N-FDI, N-FDI):

With both of the ﬁrms remaining in the home country, each ﬁrm max-

imizesmax (1 − (xi + x−i + xF ) − wi )xi + (1 − (y i + y −i + y F ) − wi − t)y i ,xi ,y imax (1 − (xA + xB + xF ) − t)xF + (1 − (y A + y B + y F ))y F .

xF ,y F

Solving the ﬁrst-order conditions, the optimal quantities are obtained as
1 + t − 3wi + wj 1 − 2t − 3wi + wj,,;
4
4
1 − 3t + wA + wB 1 + 2t + wA + wB
xF , y F =,.
44xi , y i =Each union thus maximizes
max wi (xi + y i ) =wi

wi (2 − t − 6wi + 2wj ).
4The equilibrium wages and quantities are given bywi =(2 − t)3(1 + 2t) 3(1 − 3t); xi , y i =
,
.
10
20
20

i , ui , CS
Let πjk
jk denote the (equilibrium) proﬁt, the union utility and the consumer surplus
jkwhen the pair of FDI choices is given by (j, k), j, k ∈ {N, P }. With some algebra, we obtain
i
πN
N =

2 − 2t + 13t2
3(2 − t)2
(13 − 4t)2
, uiN N =, CSN N =
.
72
200
800
26

(P-FDI, N-FDI):In this situation, ﬁrm B may choose not to export, depending on thewage set by union B. Suppose ﬁrst that the wage set by union B is low enough for ﬁrm B toexport. The ﬁrst-order conditions then imply that
xA , y A =1 + t − 3wA + wB 1 + t + wB
1 + t − 3wB + wA 1 − 3t − 3wB,; xB , y B =
,
.
4
4
4
4

The maximization problem for each union becomeswA (1 + t − 3wA + wB ),4wA
wB (2 − 2t − 6wB + wA )1 − 3wB − 3t
max wB (xB + y B ) =, s.t.
≥ 0.
4
4wB
max wA xA =If t < 8/45, the constraint is not binding, the optimal wage is
wA , wB =14 + 10t 13 − 11t
,
.
71
71

We can then show that
xA , yA =3(7 + 5t) 8 − 45t
23 + 57t 3(7 − 5t),; xB , yB =
,
.
142
71
142
71

It follows from these that the union’s utility isuI =3(13 − 11t)2
.
10082

(B.6)

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 , y A =1 + t − 3wB + wB
1 + t − 3wA + wB 1
, ; xB , y B =
, 0.
4
3
4

The maximization problem for each union now becomeswA (1 + t − 3wA + wB ),4wA
wB (1 + t − 3wB + wA )1 − 3t − 3wB
max wB xB =, s.t.
< 0.
4
4wB
max wA xA =If t > 1/9, the constraint is not binding and the optimal wages and quantities are given by
wi =

1+t
3(1 + t), xA = xB =.
5
20

It follows from these that the union’s utility isui =3(1 + t)2
.
100
27

(B.7)

The union then chooses the latter strategy, which prevents ﬁrm B from exporting, if (B.7)
exceeds (B.6), i.e.,√3(1 + t)2 3(13 − 11t)2
12191 − 8520 2−> 0, ⇒ t >∼ 0.0981 ≡ tF .
100
10082
1009
The proﬁt, the union utility, and the consumer surplus are
90(49 + 70t + 25t2 ) B
1570 − 516t + 22698t2, πP N =
,
40328
40328
3(13 − 11t)2(93 − 35t)2
3(7 + 5t)2
, uB
, CSN P =
,
uA
PN =
PN =
5041
10082
40328

πPAN =

for t ∈ [0, tF ) andπPAN =

481 + 162t + 81t2
9(1 + t)2
3(1 + t)2
(13 − 7t)2
, πPBN =, uiP N =, CSP N =
,
3600
400
100
800

for t ∈ [tF , 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 maximizesmax (1 − (xi + x−i + xF ) − wi )xi + (1 − (y i + y −i + y F ))y i .
xi ,y i

Solving the ﬁrst-order conditions, we obtain
xi , y i =1 + t − 3wi + wj 1
, .
4
4

In this case, the wage set by each union has no eﬀect on the foreign market. Each union
simply maximizes
max wi xi =wiwi (1 + t − 3wi + wj ).
4

It is straightforward to obtain
wi =

1+t
3(1 + t) 1
; xi , y i =
, .
5
20
4

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

34 + 18t + 9t2
3(1 + t)2
(13 − 7t)2
, uiP P =, CSP P =
.
400
100
800

28

B.2

The case with an integrated union

We now consider the case where all domestic workers are represented by an integrated union.
The integrated union provides labor force and unilaterally oﬀers a common wage wI to thedownstream ﬁrms. The fact that the unions are integrated is the only departure from thebaseline case. Again, to make comparison easier, all the results are summarized in ﬁgures
1I-7I, each of which corresponds to ﬁgures 1-7.
(N-FDI, N-FDI):

With both of the ﬁrms remaining in the home country, each ﬁrm max-

imizesmax (1 − (xi + x−i ) − wI )xi + (1 − (y i + y −i ) − wI − t)y i .
xi ,y i

Solving the ﬁrst-order conditions, the optimal quantities are obtained as
xi , y i =1 − wI 1 − t − wI,.
3
3

Each union thus maximizes
max 2wI (xi + y i ) =wI

2wi (2 − t − 2wi ).
3The equilibrium wages and quantities are given bywi =2 + t 2 − 3t
(2 − t); xi , y i =
,
.
4
12
12

i , ui , CS
Let πjk
jk denote the (equilibrium) proﬁt, the union utility and the consumer surplus
jkwhen 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):

4 − 4t + 5t2(2 − t)2(2 + t)2, uIN N =, CSN N =
.
72
12
72

In this situation, ﬁrm B may choose not to export, depending on thewage set by the integrated union. Suppose ﬁrst that the wage set by the union is low enoughfor ﬁrm B to export. The ﬁrst-order conditions then imply that
xA , y A =1 − wI 1 + wI
1 − wI 1 − 2wI − 2t,
; xB , y B =
,
.
3
3
3
3

The maximization problem for each union becomesmax wI (xA + xB + y B ) =wIwI (3 − 4wI − 2t)
1 − 2wI − 2t
, s.t.
≥ 0.
3
3
29

If t < 1/6, the constraint is not binding, the optimal wage iswI =3 − 2t.
8

We can then show that
xA , y A =5 + 2t 11 + 6t
5 + 2t 1 − 6t,
; xB , yB =
,
.
24
24
24
12

It follows from these that the union’s utility isuI =(3 − 2t)2
.
48

(B.8)

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 , y A =1 − wI 1
1 − wI, ; xB , y B =
, 0.
3
2
3

The maximization problem for each union now becomesmax wB (xA + xB ) =wI

1 − 2wI − 2twI (2 − wI ), s.t.
< 0.
3
3

For any t, the constraint is not binding and the optimal wages and quantities are given by1
1
w I = , x A = xB = .
2
6
It follows from these that the union’s utility is
1
uI = .
6(B.9)

The union then chooses the latter strategy, which prevents ﬁrm B from exporting, if (B.9)
exceeds (B.8), i.e.,√
1 (3 − 2t)2
3−2 2−
> 0, ⇒ t >∼ 0.0858 ≡ tI .
6
48
2
The proﬁt, the union utility, and the consumer surplus are
πPAN =

29 − 28t + 148t2(3 − 2t)2(5 + 2t)2
73 + 76t + 20t2
, πPBN =, uIP N =, CSN P =
,
288
576
48
288

for t ∈ [0, tI ) andπPAN =

5
1
1
1, π B = , uIP N = , CSP N = ,18 P N36
618

for t ∈ [tI , t̄).
30

(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 maximizesmax (1 − (xi + x−i ) − wI )xi + (1 − (y i + y −i ))y i .
xi ,y i

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

In this case, the wage set by the integrated union has no eﬀect on the foreign market. The
union simply maximizes
max wI (xA + xB ) =wIwI (2 − 2wI ).
3

It is straightforward to obtain
1 1
1
wI = , xi , y i = , .
2
6 3
The proﬁt, the union utility, and the consumer surplus are
πPi P =

5
1
1
, uIP P = , CSP P = .
36
6
18

31

References
Brander, J.A., Spencer, B.J., 1988, Unionized oligopoly and international trade policy, Journalof International 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., 2005, 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 andlocation choice, Economic Journal 113, 782-800.
Lommerud, K.E., Straume, O.R., Sørgard, L., 2006, National versus international mergers inunionized oligopoly, Rand Journal of Economics 37, 212-33.
Lommerud, K.E., Meland, F., Straume, O.R., 2009. Can deunionization lead to international
outsourcing? Journal of International Economics 77, 109-19.
Naylor, R.A., 1998, International trade and economic integration when labour markets are
generally unionized, 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 ofInternational 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,
Journal of International Economics 55, 379-90.
Straume, O.R., 2002, Union collusion and intra-industry trade, International Journal of Industrial Organization 20, 631-52.
32

Straume, O.R., 2003, International merger and trade liberalization: implications for unionizedlabour, 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, Journalof International Economics 55, 187-202.

33

CP
0.35
0.3
HN-NL

0.25
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
W
i

0.34
wi NN

0.32

Π
0.4

i

w PP
wA PN

w PN

ΠA PN +ΠB PN

ΠA PN +ΠB PN
2Πi PP

0.3

0.3
0.28

wB PN

0.2

0.26

2Πi NN

0.24

0.1

0.22
0.1

0.2

0.3

t
0.4

0.1

Figure 2: Equilibrium wages

t
0.4

0.3

Figure 3: Total proﬁt
CS
0.13

U
0.275
0.25
0.225
0.2
0.175
0.15
0.125

0.2

2ui NN

CSPN

0.12
0.11

A

B

u PN +u PN
2ui PP
0.1

CSNN

0.1
uA PN +uB PN
2ui PP
0.2

0.3

CSPN

CSPP
0.09

t
0.4

Figure 4: Total union utility

0.1

0.2

0.3

t
0.4

Figure 5: Domestic consumers surplus

34

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) : (i′ − j ′ ) indicates that the equilibrium is (i − j) while the socially eﬃcient
outcome is (i′ − j ′ ).
W
0.65
WPN
0.6
WPP
0.55
WNN

0.5
0.45
0.1

0.2

0.3

Figure 7: Domestic welfare

35

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 casewith full FDI
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

36

Figures related to Appendix B.1: The case with a foreign ﬁrm

CP
0.12
HN-NL
0.1
HP-NL

0.08
0.06
0.04

HP-PL

HN-NL
HP-PL

0.02
t
0.05 0.1 0.15 0.2 0.25 0.3 0.35

Figure 1F: Equilibrium with a foreign ﬁrm
w

Π

0.28

0.25

0.26
0.24
wi PP

0.22

2Πi PP

0.2

wi PP =wA PN =wB PN

ΠA PN +ΠB PN

0.15

A

w PN

0.2

wB PN

0.18

0.1

wi NN

2Πi NNΠA PN +ΠB PN

0.16
t
0.050.10.150.20.250.30.35

t
0.050.10.150.20.250.30.35

Figure 2F: Equilibrium wages

Figure 3F: Total proﬁt

U

CS

0.14
0.22
0.12

i

2u NN

2ui PP

0.1
0.08

0.18
uA PN +uB PN

CSPN

0.2

0.16

uA PN +uB PN

CSPP

CSNN
CSPN

0.14

0.06
t
0.050.10.150.20.250.30.35

Figure 4F: Total union utilityt0.050.10.150.20.250.30.35

Figure 5F: Domestic consumers surplus

37

CP
0.12

CP
0.12

0.1

0.1

HN-NL:HN-NL
HN-NL
HP-NL:HN-NL

0.08

0.08

0.06

HN-NL
:HN-NLHP-PL:HN-NL
0.06 HP-PL

0.04

HP-PL:HP-NL

0.04
HP-NL

0.02

0.02

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

HP-PLt
0.05 0.1 0.15 0.2 0.25 0.3 0.35

social eﬃciency

social eﬃciency and equilibrium

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

W
0.46
WPP

WPN
0.44

WPN
0.42
0.4
0.38

WNN
t
0.050.10.150.20.250.30.35

Figure 7F: Domestic welfare38

Figures related to Appendix B.2: The case with an integrated union

CP

0.25
HN-NL

0.2
0.15
0.1
0.05

HP-NL
t
0.05 0.1 0.15 0.2 0.25 0.3 0.35

Figure 1I: Equilibrium with an integrated union
w

Π
0.4

0.55
wPP

0.5

ΠA PN +ΠB PN

wPN =wPP

0.3

wNN

0.45

ΠA PN +ΠB PN
2Πi PP

0.2
0.4
wPN
0.3

2Πi NN0.1

0.35
t0.050.10.150.20.250.30.35

t
0.050.10.150.20.250.30.35

Figure 2I: Equilibrium wages

Figure 3I: Total proﬁt

U

CS

0.4

0.14

0.35

0.12

0.3

0.1

uNN

CSPN

0.08

0.25

CSNN

0.06
0.2
0.15

uPN
uPP

0.04
uPN =uPP

CSPP

CSPN =CSPP

0.02

t0.050.10.150.20.250.30.35

Figure 4I: Total union utilityt0.050.10.150.20.250.30.35

Figure 5I: Domestic consumers surplus

39

CP

CP

0.25

0.25

HN-NL:HN-NL

HN-NL

0.2

HP-NL:HN-NL

0.15

0.15

HP-NL:HP-NL

0.1

0.1

0.2

0.05

0.05
HP-NL

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

t0.05 0.1 0.15 0.2 0.25 0.3 0.35

social eﬃciency

social eﬃciency and equilibrium

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

W
0.6
0.55

WPN
WPN

0.5

WPP

0.45
WNN

0.4
0.35

t
0.050.10.150.20.250.30.35

Figure 7I: Domestic welfare

40