2005•39

Outward Foreign Direct Investment in Unionized Oligopoly:
Some Welfare Implications
Junichiro Ishida
Noriaki Matsushima

Outward Foreign Direct Investment in Unionized Oligopoly:
Some Welfare Implications∗
Junichiro Ishida
Osaka School of International Public Policy, Osaka University
andNoriaki Matsushima†
Graduate School of Business Administration, Kobe University
October 7, 2005

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 presence of domestic competition gives rise to effects which have critical bearings
on social welfare. There are two main findings. First, due to strategic interactions between theunions, the welfare effect of FDI can be negative, even when we disregard the fixed cost of FDI.
Second, this negative effect arises more at the expense of consumers, rather than the unions: infact, quite contrary to the popular belief, FDI may actually benefit the unions because it serves
to soften price competition between them. The analysis reveals that the welfare effect of outward
FDI hinges critically on the nature of domestic competition, especially among input suppliers, andtheir bargaining power against their respective downstream producers.

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, those questions become more and more criticalfor policy makers 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 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. 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. Thistendency seems to suggest that there is an emerging global consensus, at least among policy makers,
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 the firm that
undertakes FDI can improve its efficiency through several channels. First, firms may invest abroad tosave 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 in the longrun, 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 necessarily2welfare-improving if firms gain only at the expense of domestic workers.1
While the welfare analysis of outward FDI offers critical policy implications, studies on the effectof outward FDI are relatively scarce, both theoretically and empirically.2 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 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 two markets, home and foreign, 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 twomarkets are comparable in size, the second FDI is always welfare-reducing. 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.
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 where the unions are competing
1 For instance, Skaksen and Sørensen (2001) show that unions are likely to lose on FDI if domestic and foreign activities
are substitutable.
2 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

against one another through downstream market competition. The strategic interaction between themgives rise to effects 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 concentrate on thehome 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 in the 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 the foreign market, and intense price rivalry between theunions arises as a result: 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 thesecond (and the last, in this case) FDI is undertaken. The wages suddenly go up and the increase in
the wages results in less output, which entails welfare losses. The result indicates that the welfare effectof outward FDI hinges critically on the nature of domestic competition, especially among upstream
suppliers: when the price rivalry among upstream suppliers is intense, the amount of outward FDI caneasily be excessive, even in the long-run where the effect of fixed costs can be fairly negligible.
While the first result confirms a popular view that outward FDI may reduce social welfare undercertain conditions, it is important to note that this is not necessarily at the expense of the unions,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 less clear.
The first FDI puts downward pressure on the wages in order to compete in the foreign market, andthe price competition between the unions can be excessively intense from their viewpoint. The second
FDI may be beneficial for them, quite contrary to the popular belief, because it releases them from thisdownward pressure. In other words, as the option of exporting is no longer available, the second FDI
serves 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, 2004).3
Among them, the paper is closest in spirit to Lommerud et al. (2003), on which our model framework
3 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. (2004), and Skaksen (2004),
just to name a few.

4

is based. The difference is that there is only one domestic firm in their model and hence do not consider
domestic competition, which is the driving force of our model. This difference amounts to different
welfare and policy implications. Although they also point out that the amount of FDI can be excessive,
it is mostly due to the presence of the fixed cost: that is, there arises a case in their model where thewelfare gain from FDI is exceeded by the fixed cost of investment. In contrast, we argue that the purewelfare effect of FDI is often negative, meaning that FDI reduces welfare even when the fixed cost ofinvestment 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

The basic structure of our model closely follows Lommerud et al. (2003), except for the number ofdomestic firms.4 Although it appears to be an innocuous extension, it proves to give rise to strategicinteractions absent in the case with only one domestic firm, as stated in the introduction. There are
two markets, home and foreign, and two firms, denoted by A and B. Initially, A and B are located in
the home market. Labor is unionized in the home market, whereas it is not in the foreign market. Eachfirm 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-scale technology.
Let xi denote i’s sale in the home market and yi 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 − (yA + yB ).

(2)=4 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.

5

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 the transport cost is sufficiently small:t ≤ t̄ ≡ 2 −

√

2.

(3)

Under this restriction, each firm chooses a nonnegative quantity 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 of their productive capacities abroad. More precisely, A
and B can establish a new production facility in the foreign market, which allows them to supply tothat market without incurring any transport cost. The plant set up in the foreign market is used solely
to supply to that market.5 There are generically three distinct cases, depending on how many firms
undertake FDI. Let j ∈ {0, 1, 2} denote the number of firms that undertake FDI, which we also referto as the degree of FDI for expositional simplicity.

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 = 0.6 Taking
this as their reservation wage, the unions in the home market independently set wages to maximize
the following utility function:ui = wi zi , i = A, B.

(4)

zi is i’s production in country H where zi = xi (zi = xi + yi ) if its downstream firm undertakes FDI(no FDI).

2.4

National welfare

The main purpose of the paper is to examine welfare effects of outward FDI. To this end, we adopt
the national welfare as the measuring stick. Let N W j (t) denote the national welfare as a function of
5 Lommerud et al. (2003) refer to this strategy as ‘partial FDI’ to distinguish it from ‘full FDI’ where a firm shift allof their productive capacities. We also rule out the option of importing from its foreign plant. These assumptions canbe considered as a type of capacity constraint.
6 This is strictly to simplify the analysis since the competitive wage plays no role in a qualitative sense.

6

t when the degree of FDI is given by j. The national welfare is defined as the sum of the firms’ profit
πij (t), the unions’ utility uji (t) and the consumer surplus in the home market CS j (t):N W j (t) ≡ Πj (t) + U j (t) + CS j (t),jjwhere Πj (t) ≡ πA(t) + πB(t) and U j (t) ≡ ujA (t) + ujB (t).

2.5

Timing

The timing of the model is summarized as follows:

1. the domestic firms sequentially choose whether to undertake FDI;
2. the unions 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. The
analysis is instrumental in illustrating the role of domestic competition in unionized international
oligopoly. In this monopoly case, we abbreviate the subscript i for notational simplicity.
(no 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
,
.
2
2

(5)

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
7

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

(6)

2 + t 2 − 3t
,
.
8
8

(7)

w=
and
x, y =(FDI):

If the monopolist undertakes 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=

1
.
2

(9)

x, y =

1 1
, .
4 2

(10)

and

3.2

Welfare effects of FDI with one domestic firm

Figure 1 depicts the national welfare N W j as a function of t. In the present context, FDI gives riseto two welfare effects. First, there is a pure productive gain as FDI allows the firm to gain accessto cheaper labor as well as to save the transport cost. This productivity effect in general raises thefirm’s profit and thus improves welfare. Second, there is also an indirect distributional effect of FDI
since with the firm going abroad, its union now faces a smaller market to serve. This wage effect ispotentially welfare-reducing since it can raise the equilibrium wage set by the union. When the twomarkets, home and foreign, are comparable in size, however, the former effect always dominates the8latter so that FDI is always welfare-improving.7 To summarize, we state the following result, which
can immediately be seen from figure 1.
Proposition 1 When (i) there is only one domestic firm and (ii) the two markets are symmetric insize, outward FDI is always welfare-improving.
[figure 1 about here]

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.
When there are two domestic firms that may undertake FDI, there are generically three possible
pairs of FDI decisions: (i) none of the firms undertakes FDI (no FDI, no FDI); (ii) only one of thefirms undertakes (FDI, no FDI); (iii) both of the firms undertake FDI (FDI, FDI). We now examine
each case in turn.
(no FDI, no FDI):

With both of the firms remaining in country H, each firm maximizesmax (1 − (xi + x−i ) − wi )xi + (1 − (yi + y−i ) − wi − t)yi ,xi ,yiwhere i 6= −i throughout the analysis. Solving the first-order conditions, the optimal quantities are
obtained as
xi , yi =1 − 2wi + w−i 1 − t − 2wi + w−i
,
.
3
3

(11)

Each union thus maximizes
max wi (xi + yi ) =wi

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

It is conceptually straightforward to solve this problem (see Appendix A for detail). The equilibrium
wages and quantities are given by
wi =

2−t
,
6

(12)

7 The productivity gain is evidently not significant when the foreign market is relatively small. As a result, there mayarise an exceptional situation where the wage effect prevails. See Appendix B for this.

9xi , yi =(FDI, no FDI):

4 + t 4 − 5t
,
.
18
18

(13)

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 sets up a plant in theforeign market.
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 − (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 − 2wA 1 + t + wB,3
3
1 − 2wB + wA 1 − 2t − 2wB
,
.
3
3

(14)
(15)

Since firm A has two plants, the unions are now asymmetric. Each union maximizes
wA (1 + wB − 2wA ),3wB (2 − 2t + wA − 4wB )max wB (xB + yB ) =.
wB3max wA xA =
wA

(16)
(17)

It also follows from (15) 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 − 2wA 1,
3
2
1 − 2wB + wA
,0
3

(18)
(19)

and each union now maximizes
max wi xi =wiDefinewi (1 + w−i − 2wi ).
3√54 − 31 2≈ 0.212.
t ≡48∗

With some algebra (see Appendix A), the equilibrium wages are given by½(10 − 2t)/31 if t ∈ [0, t∗ )wA =1/3
if t ∈ [t∗ , t̄],
10

(20)

½
wB =

(9 − 8t)/31 if t ∈ [0, t∗ )1/3
if t ∈ [t∗ , t̄].

(21)

It follows from these that the equilibrium quantities are½

if t ∈ [0, t∗ )if t ∈ [t∗ , t̄],(22)

(23 + 14t)/93, (13 − 46t)/93 if t ∈ [0, t∗ )2/9, 0
if t ∈ [t∗ , t̄].

(23)

(20 − 4t)/93, (40 + 23t)/93
2/9, 1/2

xA , yA =½
xB , yB =(FDI, FDI):

Finally, 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 − (yi + y−i ))yi .
xi ,yi

The first-order condition implies that the optimal wages must satisfy
1 + w−i.
4(24)

1 − 2wi + w−i 1
, .
3
3

(25)

wi =
Solving the first-order conditions, we obtain
xi , yi =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 , yi = , .
9 3
wi =

4.2

(26)
(27)

Welfare effects of FDI with two domestic firms

When there is only one domestic firm, FDI is always welfare-improving, provided that the two markets
are comparable in size. 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 even when we
disregard the fixed cost of FDI. We in particular show that, in a two-firm setting, the second FDI isin general welfare-reducing even in the long run: that is, the amount of FDI can be excessive.
11

As in the case with only one domestic firm, outward FDI gives rise to two distinct effects of particularinterest. First, FDI improves the firm’s efficiency as it allows the firm to gain access to cheaper laboras well as to save the transport cost. Both of them apparently contribute to a reduction in the costof 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. This effect is generally welfare-improving
when its fixed cost is negligible.
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 ofits 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 thetransport cost, there arises an incentive for the union to raise its wage to take advantage of this. The
consequences of this incentive are not simply a matter of distributional concern since the wage levels
subsequently determine the output level. We refer to this as the wage effect of FDI. The wage effectmay 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 theforeign 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. Note that this incentive is totally wipedout when firm B follows its rival and undertakes FDI. The wages tend to go up rather excessively as aconsequence. See figure 2 for the relationship between the equilibrium wages and the amount of FDI.
[figures 2 about here]
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 the figurethat 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
12

effect also works positively for the firms as it invites intense competition between the unions. While
the wage effect leads to higher wages as the transport cost increases, the productivity effect generally
prevails and the overall effect of the first FDI on the total profit is in general positive.
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.
[figure 3 about here]
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 the magnitude of the loss is again fairly negligible
for the second FDI. In fact, the unions are actually made better off by the second FDI when t is in
an intermediate range. 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 wage-setting behavior(see figure 2). 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.8 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. The next proposition summarizes this result.
Proposition 2 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∗ ].
8 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.

13

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.
[figure 4 about here]
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.
As can be seen from figure 5, the unions’ gains are roughly consumers’ losses and vice versa. In thissense, the consumer surplus can be seen as a flip side of the unions’ utility.
In general, the consumer surplus is minimized when both of the firms undertake FDI because thewage effect pushes the wages upward. The first FDI is beneficial for consumers when t ∈ [0, t∗ ] because
the 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. The loss incurred by consumers dues to the second FDI constitutes a substantial partof the overall welfare loss, as we will see next.
Proposition 3 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.
[figure 5 about here]
National welfare: There are several forces at work as illustrated, depending on t. Figure 6 consistently reveals, however, that there exists a non-monotonic relationship between national welfare andthe amount of FDI: the first FDI is always welfare-improving while the second FDI is always welfarereducing. The driving force behind this is again the presence of upstream competition. In particular,
the 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, when14

t is sufficiently small, the national welfare is minimized when both of the firms undertake FDI, i.e.,(FDI, FDI) is worse, in terms of the national welfare, than not only (FDI, no FDI) but also (no FDI,
no FDI). This draws clear contrast to the case with one domestic firm where outward FDI is always
welfare-improving, provided that the markets are symmetric in size. When there are two domestic
firms, the increase in the firms’ total profit, the most important part of welfare gains, are not sufficient
to totally compensate for the losses because the foreign market is now duopolistic and hence morecompetitive. The following statement summarizes the main result of the paper.
Proposition 4 When (i) there are two domestic firms and (ii) the two markets are symmetric insize, the national welfare is maximized for any t ∈ [0, t̄] when only one of the firms undertakes FDI.
Alternatively, the second FDI is always welfare-reducing.
[figure 6 about here]

5

Conclusion

The paper constructs a model of unionized duopoly and examines the long-run welfare effect of outward
FDI on the home country. It is found that the presence of upstream competition gives rise to welfare
effects that lead to a non-monotonic relationship between national welfare and the amount of FDI.
With the strategic interaction between the unions, the amount of FDI can be excessive even when FDI
is totally free of cost. 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
policy implication: whether outward FDI should be encouraged depends on the nature of domestic
competition, especially among upstream input suppliers.
Since our analysis is confined in a relatively simple framework, there are several potential avenues
to extend the present analysis. For instance, the analysis in our model is confined to a case withdisintegrated unions. A natural extension is thus to consider a case where the upstream unions areintegrated and act as one utility-maximizing unit. Such an extension is potentially crucial since it
provides a framework to examine the impact of upstream merger when FDI is a concern. In future,
it is of some interest to extend the present analysis to various settings to gain further insight on thehome-country welfare effect of outward FDI.
[2005.10.7 729]

15

Appendix A(no FDI, no 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)

2−t
,
6

(A.2)

4 + t 4 − 5t
,
.
18
18

(A.3)

(2 − t)2
.
27

(A.4)

which leads towi =xi , yi =It follows from this that each union’s utility isui =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

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

16

(A.8)

(FDI, no 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 ),wA
3
wB (2 + wA − 4wB − 2t)
1 − 2wB − 2t
max wB (xB + yB ) =, s.t.
≥ 0.
wB
3
3

max wA xA =(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 =

(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 ),wA
3
wB (1 + wA − 2wB )1 − 2wB − 2t
max wB xB =, s.t.
< 0.
wB
3
3

max wA xA =17

(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
2
.
27

uB =

(A.27)

Union B then chooses the latter strategy, which prevents firm B from exporting, if (A.27) exceeds(A.19), i.e.,√24(9 − 8t)2
54 − 31 2−> 0, ⇒ t >∼ 0.212.
27
2883
48

(A.28)

Appendix B
In this appendix, we consider a case where the two markets are asymmetric in size and derive conditions
under which FDI reduces welfare. To this end, we redefine the demand function of the foreign market
as follows:q = a − y.

(A.29)The intercept a measures the (relative) size of the foreign market.
Even with this modification, the nature of the problem is virtually unchanged. In the case of no
FDI, we obtain½(1 + a − t)/4 if t̃(a) ≥ t
1/2
if t > t̃(a),(A.30)(3 − a + t)/8, (3a − 3t − 1)/8 if t̃(a) ≥ t
1/4, 0
if t > t̃(a).

(A.31)w=and½
x, y =

where t̃(a) ≡ 1 −√2 + a. Similarly, in the case of FDI, we obtain
w=

1
,
2

(A.32)

x, y =

1 a
, .
4 2

(A.33)

and18

To show that FDI is always welfare-improving, we need to consider two cases: (i) t̃(a) ≥ t and (ii)t > t̃(a) . For each case, the welfare effect of FDI is computed as½(−9 + 14a + 3a2 − 2(7 − 29a)t − 29t2 )/128 if t̃(a) ≥ t
10
NW − NW =a2 /4
if t > t̃(a).

(A.34)

It is immediate to see that the welfare effect is positive when t > t̃(a). This implies that FDI is
welfare-reducing if and only if (a, t) satisfies the following conditions:−9 + 14a + 3a2 − 2(7 − 29a)t − 29t2
< 0,
128
√
1 − 2 + a ≥ t.

(A.35)(A.36)The shaded region in figure 7 depicts the range for which FDI reduces welfare.

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20

N W j (t)
NW1

NW0

t
t

t̄

∗

Figure 1: National welfare with one domestic firmwij (t)
wi1

wi2
1
wA

wi0
1
wB

t
t

t̄

∗

Figure 2: Equilibrium wages
Πj (t)

Π1

Π2
Π1

Π0
t
t

t̄

∗

j
j
Figure 3: Total profit Πj ≡ πA
+ πB

20

U j (t)

U0

U1
U1

U2

t
t

t̄

∗

Figure 4: Total union utility U j ≡ ujA + ujB
CS j (t)

CS 0

CS 1

CS 1
CS 2

t
t

t̄

∗

Figure 5: Consumer surplus
N W j (t)
NW1
NW2

NW0

t
t∗

t̄

Figure 6: National welfare with two domestic firms

21

a
1

t

0
0

1
Figure 722