Discussion Paper Series No.217
Competing to Invest in the Foreign Market

Laixun ZHAOOKAMURA Makoto

March

Kobe University
Hiroshima University

2008

The Discussion Papers are a series of research papers in their draft
form, circulated to encourage discussion and comment. Citation anduse of such a paper should take account of its provisional character.
In some cases, a written consent of the author may be required.

Competing to Invest in the Foreign Market

Laixun Zhao*

Makoto Okamura**

Kobe University

Hiroshima University

Abstract This paper analyzes foreign-direct-investment (FDI) competition in a three-country
framework: two Northern countries and one Southern country. We have in mind the competition of
Airbus and Boeing (or GM and Volkswagen) in a developing country. The host-country government
endogeneizes tariffs, while Airbus and Boeing choose domestic output and FDI. Wages andemployment in the home countries are bargained over between labor and management. We find thatin the unique equilibrium, both Airbus and Boeing compete to undertake FDI in the developing
country. This arises because the host country can play off the multinational corporations, which inturn stems from three factors: (a) Oligopolistic rivalry; (b) Quid prod quo FDI, which reduces tariffs;(c) Strategic outsourcing—FDI drives down the union wages at home if the host-country wage issufficiently low. However, if the host-country wage is sufficiently high, then the union wage
increases under FDI. In such cases, FDI competition benefits the multinationals, the labor unions aswell as the host country. If Boeing undertakes FDI while Airbus does not, then: (i) Boeing’s market
share and profits are higher than Airbus’s; (ii) the tariff facing Boeing is lower than that facing Airbus.

JEL Classification Number: F21, F23, F16
Keywords: FDI Competition, Quid Pro Quo FDI, Labor Union, Political Economy, Emerging
Markets____________
Author addresses:*: Corresponding author. Research Institute for Economics & Business, Kobe University, Kobe 657-

8501, Japan, zhao@rieb.kobe-u.ac.jp, Fax: 81-78-803-7059.
: Dept. of Economics, Hiroshima University, Hiroshima, Japan, okamuram@hiroshima-u.ac.jp.

**

1

1. Introduction
Developing countries are taking over as the most attractive destinations for foreign direct
investment (FDI) in recent years. In 2003, China, the U.S. and India ranked 1, 2, 3 as the largest FDI
host countries. A UNCTAD survey (UNCTAD/PRESS/PR/2005/03105/09/05) shows that bothexperts and transnational corporations answer that the five most attractive business locations for theyears 2005-2006 are in the following order: China, USA, India, Russia and Brazil. Such large
emerging markets in the developing countries offer new opportunities to firms from developed
countries, in terms of huge pools of both final consumers and cheap workers. China in particular,
with its accession to the WTO in 2001, trade and investment restrictions are expected to decrease
substantially. Given the potential market of more than 1.3 billion people and near unlimited labor
supply at low wages, multinationals vie each other to establish production and distribution facilities
there. Feenstra (1999) states that FDI in China is one of the most important multinational activities,
which will have fundamental effects on the patterns of world trade and investment.
While the potential in such emerging markets is large, a priori the net effects of the multinational
activities on both the host and home countries are unclear. The purpose of this paper is to investigate
such effects. Given that both the multinational firms and the emerging markets are big players, we
adopt a game-theoretic framework. Specifically, we have in mind the competition of large
multinationals, say Airbus and Boeing (or General Motors and Volkswagen, Kodak and Fuji Film,etc.) in a large developing country, say China (or India, or Russia). 1

1

Other examples are, “Airbus angles to compete with Boeing in China’s skies,” Wall Street Journal, Aug. 20, 2001, “Airbus
wants to … not only in selling aircraft but also working with China's aviation industry, citing the production of wings ofAirbus 320 in China,” China Daily, Mar. 2, 2002, and “Boeing, Airbus face off in China,” The Seattle Times, Nov. 2, 2002.
Regarding FDI in China, Branstetter and Feenstra (2002) show that FDI inflows reflect political openness and state
ownership there; Cheng and Kwan (2000) and Lardy (1995) find that large regional market, good infrastructure, andpreferential policy are important determinants of FDI in China; Feenstra and Hanson (2003) examine the organization ofexport processing operations of foreign MNEs in China and test the property rights model. Benkard (2000) conducts adynamic analysis of the market for wide-bodied aircraft. Baldwin and Krugman (1987), Klepper (1990), and Neven andSeabright (1995) adopted simulations to analyze the competitive interactions of Airbus and Boeing. Irwin and Pavcnik(2001) examined the interactions of Airbus and Boeing, and found that the future entry of Airbus’ A-380 could reduce themarket share of Boeing 747 by 14 percent, using commercial aircraft data from 1969 to 1998.

2

Since the purpose of such FDI is to take advantage of cheap labor (i.e., outsourcing) and to
capture the potential large consumer markets in the emerging economies, we assume that upstream
production can be conducted in the home countries or outsourced to the host country, while final
assembly is made in the host countries only (Our analysis can be straightforwardly extended to areverse setup of the upstream and downstream productions above). The host government
endogeneizes tariffs, while Airbus and Boeing determine domestic output and FDI. Wages andemployment in the home countries (called Europe and the U.S. respectively) are bargained overbetween labor and management. Thus, the model incorporates not only the interactions ofmultinationals, labor unions and the government, but also intermediate and final productions, as wellas the choice between exporting and FDI.
We find that the unique Nash equilibrium is the case when both Airbus and Boeing compete toundertake FDI in China. This arises because the host country can ‘play off’ the multinational
corporations, which in turn is due to three factors: (a) Oligopolistic rivalry between Airbus andBoeing; (b) Quid pro quo FDI--by undertaking FDI, the import tariffs in China can be reduced; (c)Strategic outsourcing to erode the labor union’s power—FDI drives down the union wages in thesource countries if the Chinese wage is sufficiently low (as in rural areas).
However, if the Chinese wage is sufficiently high (as in Shanghai, Shenzhen and other coastal
cities), then the union wage can increase under FDI. In such cases, FDI competition benefits themultinationals, the labor unions as well as the host country. In addition, if Boeing invests in China
while Airbus does not, then: (i) Boeing’s market share and profits are higher than Airbus’s; (ii) the
tariff facing Boeing is lower than that facing Airbus. These findings seem to fit well with the current
FDI situation in China and some other developing countries.
In the literature of tax competition (e.g., Janeba, 1995, Haufler and Wooton, 1999), several host(usually less developed ) countries compete to lower taxes to attract FDI from multinationals. In asense, the multinationals can play off the host countries. In the present paper, the opposite is true.

3

Our model can explain for the phenomenon of ‘quid pro quo’ FDI, see for instance, Bhagwati etal (1987, 92), Wong (1989), Dinopoulos and Wong (1991), and Dinopoulos (1992). This literaturesuggests that FDI may be used as an instrument to defuse a protectionist threat, which Blonigen andFeenstra (1997) subsequently find strong statistical support. However, the literature assumes a
reduced-form protection function, so that the level of protection falls as FDI rises. This approach has
been criticized as being ‘a black box’, since the details in the protection function are not clearly
explained.
In the present paper we do not use a protection function. Instead, we assume that the Chinese
government maximizes an objective function, which includes a wage premium, consumer surplus andtariff revenue (zero profits because no Chinese firms are involved). Thus, the essential results of quid
pro quo FDI are generated under oligopolistic rivalry: FDI provides employment incentives for thehost country to reduce import barriers, creating scope for mutual gains for both the host country andthe multinationals.
Our results indicate that outward FDI can raise domestic wages, when the wage level in the hostcountry is sufficiently high. This is in contrast to Glass and Saggi (1999), who show that outward FDI
lowers wages in the home country by shifting out the demand for labor. Recently, Leahy andMontagna (2000) analyzes the welfare effects on the host country, and Lommerud, Meland andSorgard (2003) show that trade liberalization can induce FDI because the firm uses FDI to battle withthe union. Haaland and Wooton (2002, 2003) examine how country risks related to labor markets andindustry affect the decisions of multinationals in location selection.
Perhaps the part on FDI and unions is more closely related to Skaksen and Sorensen (2001), who
use a CES production function with several inputs, and allow the firm to produce one of the inputs
overseas. They find that under Leontief technology, the union always gains from the firm becoming a
multinational; On the other hand, with perfect substitutes, the union always loses. Skaksen (2004)
extends the analysis in a general equilibrium model with sector-specific capital, under potential andrealized outsourcing. However, their results essentially hinge on production technology. All4interactions occur within one multinational firm, i.e., between management and labor. Possible
interactions across firms (as found in Irwin and Pavcnik, 2001), and those between the multinationals
and the host government are not modeled.
In contrast, the present paper focuses on oligopolistic interactions in three countries, with the hostgovernment playing an active role. We show that if the wage in the host country is sufficiently high,outward FDI can benefit not only the firm but also the labor union, as well as the host country. This
arises because FDI increases domestic final output and labor demand by reducing the cost of
production and intensifying oligopolistic competition. However, if the host-country wage issufficiently low, then strategic outsourcing arises—FDI not only avoids high union wages at home,
but also drives them down. Thus, the paper complements the recent literature on outsourcing, forinstance, Feenstra and Hanson (1996), McLaren (2000), Baldwin and Ottaviano (2001), and Yeaple(2003). In addition, the paper is in spirit related to Markusen and Venables (1999), who establish
circumstances in which FDI is complementary to local industries by raising their productivity indeveloping countries, and show how FDI may lead to the establishment of local industrial sectors.
The rest of the paper is organized as follows. Section 2 sets up the basic model, section 3 presents
a benchmark case of no FDI by either Airbus or Boeing, section 4 investigates FDI competition,section 5 compares the cases of no FDI and FDI competition, section 6 looks into the case of
unilateral FDI by one firm only, and finally, section 7 provides concluding remarks.

2. The Basic Setup of the Model
Consider a world consisting of three countries: China, Europe and the U.S. Europe is home to
Airbus and the U.S. is home to Boeing. For simplicity, we assume that Airbus and Boeing sell
aircrafts only in China, aiming to capture the empirical evidence that multinationals go there for the5potential market. 2 The variables denoted with x or A are related to the productions of Airbus, thosedenoted with y or B are related to the productions of Boeing, and those denoted with C are related tothe productions in China.
Production consists of two processes. One is the production of an intermediate input, the otheris combining the intermediate input and labor to produce the final output. Examples of theintermediate input are: aircraft doors, chairs, luggage cabinets, lavatories, landing gear, and wings, etc.
An example of the final output is the whole aircraft including the engine. Airbus and Boeing do notsell intermediate inputs to each other and there is no other source to purchase the intermediate input
except producing it inside the firm.
For simplicity, we assume that labor is the only factor needed to produce the intermediate
input, according to the following input requirement function:φ ( m) = m 2 / 2 .

(1)

That is, m units of the intermediate input require m 2 / 2 units of labor. 3 To produce the final output,
both the intermediate input and labor are needed. We assume a one-to-one-to-one relationship among
the intermediate input, assembly labor input and the final output, by a proper choice of units. Thus, thetotal amount of labor required to produce m units of the final output is m + m 2 / 2 .
Labor is unionized in both Airbus and Boeing. Both wages and employment are determinedthrough negotiations. In other words, bargaining is efficient. 4 The unions in Airbus and Boeing have
Stone-Geary type utility functions:2

Allowing sales of the final product in other countries affects only the level of welfare. As will become clear later, thetrade-off mechanism between employment shift and employment expansion of FDI competition remains and so do the main
qualitative results in the paper. But the model can be straightforwardly extended to cover sales elsewhere.
3
We could also assume a decreasing marginal cost function, which would make our story stronger. However, corner
solutions would arise.
4
The amount of FDI the multinationals undertake may change if a different form of bargaining is adopted, such as in thecase when only wages are bargained while employment decision is left to the firm, or in the monopoly union model in which
the union can determine the wage unilaterally. Nevertheless, positive FDI still emerges in equilibrium.

6

u A ( x, wA ) = ( x + x A2 / 2)( wA − w0 ) ,(2a)

uB ( y, wB ) = ( y + yB2 / 2)( wB − w0 ) ,(2b)where terms x A2 / 2 and yB2 / 2 indicate respectively the amount of labor needed to produce theintermediate input in each firm’s home country, x and y are labor used for final assembly, wA and wB
are respectively the negotiated union wages in Europe and the U.S., and w0 is the (outside)reservation wage or unemployment compensation, which is assumed to be identical in Europe and the
U.S. for simplicity.
Airbus and Boeing can produce the intermediate input either in their home countries, or in
China. Final assembly is done only in the home countries. Their profit functions can be written
respectively as

π A = xp( x + y ) − ( x + x A2 / 2) wA − ( x − x A )2 wC / 2 − t A x ,(3a)π B = yp( x + y ) − ( y + yB2 / 2) wB − ( y − yB )2 wC / 2 − t B y ,(3b)where wC is the Chinese wage, taken as exogenously given, and p ( x + y ) is the inverse demand
function. In (3a), since the final output is x, the amount of intermediate input produced in China isx − x A . Variable tA is an import tariff imposed by the Chinese government on Airbus. Corresponding
variables and technology enter (3b), which is Boeing’s profit function.
The Chinese government maximizes the following objective function:

W = {( x − x A ) 2 + ( y − yB ) 2 }wC / 2 + U ( x + y ) − ( x + y ) p(⋅) + t A x + tB y ,

(4)

7

where {( x − x A ) 2 + ( y − yB ) 2 }wC / 2 can be considered as a wage premium from the intermediate
production of Airbus and Boeing in China, because the Chinese workers’ alternative is to work inlocal firms with lower wages, which are assumed to be zero without loss of generality,

U ( x + y ) − ( x + y ) p(⋅) is the consumer surplus, and t A x and t B y are tariff revenues. Tariffs are
imposed for shifting rents from foreign oligopolists and generating revenue. 5
We consider a three-stage game. In stage 1, Airbus and Boeing decide simultaneously
whether to undertake FDI or not; in stage 2, the Chinese government chooses t A and t B to maximize
its objective; 6 and in stage 3, each firm bargains simultaneously with its labor union for wages andemployment, i.e., wA , x, x A ; wB , y and yB , taking the actions of the other firm and union as given.
Thus, the amount of FDI is also determined in the third stage. It follows that the order of stages 1 and2 can be reversed and the qualitative results of the model remain intact (see discussions in the
concluding section). To ensure consistency, the game will be solved backwards.
We investigate sequentially three different cases: no FDI, FDI competition, and unilateral FDI.
The wages, employment, tariffs, firm profits, union utility and welfare in the three cases will becompared. To save on notation, subscripts NI , II , and I will be used to denote respectively “no FDI”,“FDI competition”, and “unilateral FDI”.

3. A Benchmark Case: No FDI
We look at the third stage first, in which the firms and the unions negotiate for wages andemployment through efficient Nash Bargaining. The Nash products can be written respectively as

5

In practice, the commercial aircraft industry in many countries is state-owned or partially so. The government would"reward" one of the foreign rivals for good behavior by directing the state-owned airlines to purchase its products. In such acase, an import quota is substituted for the tariff. And our results on quid pro quo FDI would carry through morestraightforwardly.
6
After its accession to the WTO, China must impose an identical tariff rate on different countries. However, China did
impose different tariff rates on different countries before the accession. In any case, in the present paper, we find that inequilibrium, China imposes an identical tariff rate on both Airbus and Boeing.

8

G ( x, wA ) = π Au A ,(5a)

H ( y, wB ) = π B uB .

(5b)

Airbus and its union negotiate over x and wA , to maximize (5a), and simultaneously, Boeing
and its union bargain over y and wB , to maximize (5b), taking the tariff rates as given, which are
determined in a prior stage by the Chinese government. We assume all workers are unionized inEurope and the U.S. Since final output is only produced at home, if bargaining breaks down, union
workers become unemployed and the firms produce zero outputs. This outcome is the threat-point of
the bargaining game, when the unions and the firms obtain zero utility and zero profits respectively.
Also, in this section, Airbus and Boeing are treated identically. It thus suffices to focus on Airbus only.
In the absence of FDI by either firm, x = x A and y = yB . Substituting into (5a) and (5b), we
find that the equilibrium satisfies the following first order conditions∂G / ∂x = ( wA − w0 )(1 + x )π A + [ p + xp '− (1 + x ) wA − t A ]u A = 0 ,(6a)∂G / ∂wA = ( x + x 2 / 2)π A − ( x + x 2 / 2)u A = 0 .

(6b)p + xp '− (1 + x) w0 − t A = 0 ,(6a’)

π A − uA = 0 .

(6b’)

Rearranging to yield:

Analogously, the bargaining game in Boeing satisfies similar first order conditions.
Condition (6a’) implies that the firm and the labor union first choose employment tomaximize their joint rents—the sum of profits and union utility. And then condition (6b’) states that9

the two players choose the negotiated wage at a level so that their net gains are equalized. Totallydifferentiating (6a’) and (6b’), we obtain the familiar comparative statics results on outputs, which arereported in Appendix 1 (A1).
Next we turn to the second stage of the game, in which we substitute the equilibrium values ofall variables (obtained in the 3rd stage) into the Chinese government’s objective function andmaximize it to find the equilibrium tariff rates. Lobbying activities within China are not considered
because the Chinese political system is different from democracies in the West. One could argue that
FDI competition is a kind of lobbying by Airbus and Boeing to reduce tariffs, the essence of quid pro
quo FDI in the literature.
From (4), in the absence of FDI, the Chinese government maximizes the following function,choosing tariff rates t A and t B .

W = U ( x + y ) − ( x + y ) p( x + y ) + t A x + tB y .

(7)

Substituting the equilibrium values of x and y obtained in the third stage into (7) and differentiating,
we have∂W∂( x + y)∂x∂y= −( x + y ) p '+ x + tA
+ tB
= 0,
∂t A
∂t A
∂t A
∂t A

(8a)

∂W
∂( x + y)∂x∂y= −( x + y ) p '+ y + tA
+ tB
= 0.
∂t B
∂t B
∂t B
∂t B

(8b)

Rearranging to give respectively

xΔ NI − ( x + y )dp '+ (b + d )t A − bt B = 0 ,(8a’)

yΔ NI − ( x + y )dp '+ (a + d )t B − at A = 0 ,

(8b’)

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where a = p '+ xp " < 0 , b = p '+ yp " < 0 , d = p '− w0 < 0 , and Δ NI = (a + b + d )d > 0 . From(6b’) and the corresponding equation for Boeing, we have ( x − y )( p '− w0 ) − (t A − t B ) = 0 . And
using (8a’) and (8b’), we obtain the following symmetry of outputs and tariffs,

x = y,t A = tB = t .

(9)

It is straightforward to show that in the absence of FDI, the optimum equilibrium tariff rates are
positive if − xp "/ p ' ≤ (1 − w0 ) / p ' , i.e., a condition for goods x and y to be strategic substitutes.
Substituting (9) into (6a’) and (8a’) to give respectively

p + xp '− (1 + x) w0 − t = 0 ,(10a)−2 xp '+ (a + b + d ) x + t = 0 ,(10b)f ( x) ≡ p + 2( p '+ xp "− w0 ) x − w0 = 0 .

(11)which can be combined to define:Equation (11) determines the equilibrium level of x when neither firm undertakes FDI. Sincex = y in equilibrium, then p = p(2 x) . Differentiating (11) yields
f '( x) = 4 p '− 2 w0 + 4(2 p "+ xp "') x .

(12)

A sufficient condition for (12) to be negative is p '+ 2 xp "+ x 2 p "' ≤ 0 , and we assume this to be thecase so that function f(x) is negatively sloped. For example, if p "' ≅ 0 and the demand curve is not
too convex, expression (12) is always negative.

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4. Competing to Undertake FDI
In this section, we investigate the case in which both Airbus and Boeing undertake FDI in China.
We show that the final production of both firms increases compared to the case of no FDI, due tothree reasons that will become clear soon, under general demand conditions. For simplicity, we
assume away the fixed costs of FDI. Analyses emphasizing fixed costs and transportation costs
include for instance, Dei (1990) and Markusen and Venables (1998).
If both firms produce a portion of the intermediate input in China, then final assembly
employment x , the union wage wA and the home intermediate employment x A are negotiated in the
Airbus bargaining game, and similarly y , wB and yB are negotiated in the Boeing bargaining game.
Substituting xC = x − x A and yC = y − yB into (5a) and (5b) and maximizing them, we can derive thefirst order conditions to determine x , wA , x A ; and y , wB and yB . Since both firms undertake FDI,
again it suffices to focus on the bargaining game in Airbus. We havep + xp '− ( x − x A ) wC − w0 − t A = 0 ,(13a)

π A − uA = 0 ,(13b)( x − x A ) wC − w0 x A = 0 .

(13c)

The first order conditions for the Boeing game can be obtained in a similar fashion, just replacing x
with y and A with B.
Condition (13c) says that the marginal cost of the intermediate input produced by Airbus in
China should equalize that produced in Europe, to minimize the total cost of intermediate production.
It follows that if wC rises, then more intermediate input is produced in the source country, and if w0
rises, more intermediate input is produced in the host country. Substituting (13c) into (13a) yields

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p + xp '− (1 − β ) w0 x − w0 − t A = 0 , β = w0 /( wC + w0 ) .

(14)

A similar condition can be derived for Boeing.
The comparative static analysis is contained in Appendix 1 (A2), which we now use to solve
the game in the second stage; that is, the Chinese government determines the tariffs. Using first orderconditions (13a-c) for both firms, and xC = x − x A and yC = y − yB , the Chinese government’s
objective function becomes

W = ( x 2 + y 2 ) β 2 wC / 2 + U ( x + y ) − p( x + y ) + t A x + t B y .

(15)

The first order conditions for t A and t B are respectively{Δ II + β 2 wC (b + d + β w0 )}x − (d + β w0 )( x + y ) p '− bβ 2 wC y + (b + d + β w0 )t A − bt B = 0 ,(16a){Δ II + β 2 wC (a + d + β w0 )} y − (d + β w0 )( x + y ) p '− a β 2 wC x + (a + d + β w0 )t B − at A = 0 ,(16b)where Δ II = {a + b + p '− (1 − β ) w0 }{ p '− (1 − β ) w0 } > 0 . Combining to yield{Δ II + β 2 wC (a + b + d + β w0 )}( x − y ) + (a + b + d + β w0 )(t A − t B ) = 0 .

(17a)

And from (14) and a similar condition for Boeing, we also obtain(d + β w0 )( x − y ) − (t A − t B ) = 0 .

(17b)Using (17a) and (17b) to give{2(d + β w0 ) + β 2 wC }(a + b + d + β w0 )( x − y ) = 0 ,which can be substituted back into (17a) and (17b) to show that under FDI competition, we must have13

x = y,t A = tB = t .

(18)

Substituting (18) into (16a) to give ( β 2 wC + a + b + d + β w0 ) x − 2 xp '+ t = 0 , which can be
combined with (14) to define the following equationg ( x) ≡ p + {2 p '+ 2 xp "− (1 − β )(2 − β ) w0 }x − w0 = 0 .

(19)Expression (19) determines the level of x in the case when both firms undertake FDI. Noting thatp = p(2 x) under symmetry, and differentiating (19) yields
g '( x) = 4 p '− (1 − β )(2 − β ) w0 + 4(2 p "+ xp "') x .

(20)

It is negatively signed if p '+ 2 xp "+ x 2 p "' ≤ 0 . We are now in a position to state:

Lemma 1 (output expansion): The equilibrium final outputs are larger in the case when both firms
undertake FDI than in the case of no FDI.

Proof: Subtracting (11) from (19) gives rise tog ( x) − f ( x) = β (3 − β ) w0 > 0 .
Thus, in figure 1, curve g(x) always lies above f(x).

(21)

QED

The output expansion effect of FDI arises due to three reasons. Firstly, the wage in the hostcounty is lower than in the source countries; secondly, intermediate production exhibits increasing
marginal costs. These two factors enable FDI in China to reduce the cost of intermediate production;and finally, the output expansion is larger under oligopolistic rivalry than if there were only amonopoly multinational firm.

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5. Comparisons under Linear Demand
We now compare the values of the final output, tariffs, union wages, employment, utility andfirm profits, respectively under no FDI and under FDI competition. In order to obtain explicit
expressions, we shall make use of the following linear demand function wherever necessary

p = n − ( x + y) , n > 0 ,(22)where as usual, n represents the market size, which is taken as given here.
Using f ( x) = 0 in (11), and (22), we obtain the levels of the output of each firm, the tariffs,
the negotiated employment and wages in the case of no FDI.

xNI = ( n − w0 ) /(4 + 2 w0 ) ,(23a)t NI = (1 + w0 )(n − w0 ) /(4 + 2 w0 ) ,

(23b)

2
E NI = xNI + x NI
/2,

(23c)

wNI = {(1 + w0 ) xNI + w0 }/(2 + xNI ) + w0 / 2 .

(23d)Using (19) and (22) we also obtain the counterparts under FDI competition:

xII = ( n − w0 ) /{4 + (2 − β ) β wC } ,(24a)t II = {1 + (1 − β ) β wC }x II ,(24b)

E II = x II + ( xII − x A ) 2 / 2 ,

(24c)

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wII = {[1 + (1 − β − β 2 / 2) w0 ] x II + w0 }/[2 + (1 − β ) 2 x II ] + w0 / 2 .

(24d)

Differentiating (24a) yields∂x II / ∂wC = −(2 − β ) β xII2 /( n − w0 ) < 0 .

(25)That is, an increase in the Chinese wage raises the cost of intermediate production and in turn reduces
the final output.
Now, we compare the values of the tariffs, firm profits, union utility, wages and employment
under no FDI and FDI competition. Conditions (23b) and (24b) give rise tot NI − t II = β {(3 + w0 ) β wC + 2 w0 }xII /(4 + 2 w0 ) > 0 ,(26)which can be stated as,

Lemma 2: The tariffs are lower under FDI competition than under no FDI.

Lemma 2 represents the effect of quid pro quo FDI. In the present model, through FDI, Airbus
and Boeing bring wage income to China. The Chinese government takes this into consideration whenchoosing tariffs to maximize its objective. As a result, FDI defuses the protectionist threat and reduces
the tariffs the Chinese government imposes.
We now turn to the changes in union employment in the home countries, which include thosefor both intermediate and final production. By Lemma 1, final production is always higher under FDI
competition than under no FDI (the output expansion effect of FDI competition). However, FDI also
has an employment shift effect, because some intermediate production is shifted to the host country. If
the expansion effect dominates the shift effect, then total employment goes up. From (23c) and (24c)
we obtain the difference in employment as

16

E II − E NI = x II − x NI + [(1 − β ) x II + xNI ]{(1 − β ) xII − xNI }/ 2 .

(27)

A sufficient condition for it to be positive is (1 − β ) xII − xNI ≥ 0 . Substituting in relevant
variables, it can be reduced down to

wC ≥ 4 w0 /( w0 − 4) .

(28)

That is, the Chinese wage should not be too low. Otherwise most of the intermediate production will
be shifted to China, and as a consequence union employment falls. If we restrict the Chinese wage not
to be higher than the reservation wages in the home countries, i.e., wC ≤ w0 , combined with (28), we
have w0 ≥ 8 , i.e., the home-country reservation wage should not be too low either.
What happens if the host-country wage is very low? Let us consider a special case, wC = 0 .
Substituting into (27) to give

E II − E NI = −( n − w0 ){n − (5w0 + 2 w02 )}/[2(2 + w0 ) 2 ] < 0 .

(29)

Since the parameter n measures the size of the Chinese market, we assume it is large enough such thatn − (5w0 + 2w02 ) > 0 . Then expression (29) is negatively signed; that is, union employment is lower
under FDI competition than under no FDI if the host country wage is sufficiently low. This arises
because most of the intermediate production is shifted to the host country under FDI competition, but
not under no FDI.
From (28), (29) and the explanations following them, we can state

Proposition 1: The union employment in the source countries is higher (lower) under FDI
competition than under no FDI if the reservation wage in the source countries and the wage in thehost country are sufficiently high (low).

17

Proposition 1 basically arises from the shift effect and the expansion effect of FDI. If theformer dominates, then employment in the source countries decreases. Note that in Skaksen andSorensen (2001), FDI could also raise employment, but due to the complementarity of inputs, insteadof due to FDI competition as in the present model.
Next, we look into the union wages. Comparing (23d) and (24d) yields

wII − wNI =(2 + xNI ){xII + w0 + (1 − β − β 2 / 2) w0 } − {(1 + w0 ) xNI + w0 }{2 + (1 − β ) 2 xII }. (30)(2 + xNI ){2 + (1 − β ) 2 xII }Expression (30) has the same sign as its numerator, which can be rewritten asNum =3β w0 ( n − w0 ) (wC − 2 w0 / 3)
(2 + w0 ) β x NI x II
( w − 2) w0+{wC − 0} , (30’)
wC + w02( wC + w0 )[4 + (2 − β )(1 − β ) w0 ]2( w0 + 1)

whose sign depends on the two expressions in curled braces. Because the following inequality holds

0 < ( w0 − 2) w0 /[2( w0 + 1)] < 2 w0 / 3 < w0 ,(31)

we can establish

Proposition 2: (i). If w0 > wC ≥ 2 w0 / 3 , then (30’) is positively signed and the union wage is higher
under FDI competition than under no FDI; (ii). If ( w0 − 2) /[2( w0 + 1)] ≥ wC , then (30’) is
negatively signed and the union wage is lower under FDI competition than under no FDI; (iii). If

2 w0 / 3 > wC > ( w0 − 2) /[2( w0 + 1)] > 0 , then the sign of (30’) is ambiguous.

Proposition 2 has some interesting implications, which follow naturally from Proposition 1.
Firstly, if the Chinese wage is close to the level of the reservation wages in the home countries, then
the negotiated wage increases as a result of FDI competition. This is in stark contrast to the results in18

the literature, for instance, Glass and Saggi (1999), who show that wages fall under outward FDI. In
the present model, by using cheaper labor for intermediate production in China, FDI has two effects
on employment, as analyzed in Proposition 1—the expansion effect and the shift effect. It turns outthat when the Chinese wage is close to the reservation wages in the home countries, the expansion
effect dominates the shift effect, which pushes up the demand for labor, and as a result, the negotiatedwages rise in Airbus and Boeing.
Secondly, if the Chinese wage is much lower than the reservation wages in the home countries,
most intermediate production will be shifted to China, which results in a large reduction of union
employment in the host countries that cannot be compensated by the increase in final production (seeProposition 1). Thus FDI has an effect of strategic outsourcing; that is, by undertaking FDI
competition, Airbus and Boeing can drive down the negotiated union wages at home.
Next, we are interested in the conditions for union utility and firm profits to increase under
FDI. Combining condition (28’) and Proposition 2 gives rise to

Proposition 3: If w0 > wC ≥ 2 w0 / 3 , wC ≥ 4 w0 /( w0 − 4) , and w0 ≥ 8 , then both the negotiatedwages and employment are higher under FDI competition than under no FDI, and union utility andfirm profits are also higher.

Proposition 3 describes the case of `high’ wages in the host country, which arises if Airbus
and Boeing employ workers from big cities near the coastal areas in China. In figure 2, area I satisfies
Proposition 3, in which both firm profits and union utility are higher under FDI competition thanunder no FDI. This is a case deserving more emphasis, because the labor union also benefits fromoutward FDI. As a consequence, FDI competition becomes the equilibrium.
Finally, we look into the objective function of the host country. We can establish

19

Proposition 4: The host country is better off under FDI competition than under no FDI.

Proof: Substituting relevant variables into (4), the objective function under no FDI and FDI
competition can be rewritten respectively as

W ( xNI ) = U (2 xNI ) − 2 xNI P(2 xNI ) + 2t NI xNI ,(32a)

W ( xII ) = wC β 2 xII2 + U (2 xII ) − 2 xII P(2 xII ) + 2tII xII .

(32b)

Since xII > xNI , then U (2 xII ) − 2 xII P(2 xII ) > U (2 xNI ) − 2 xNI P(2 xNI ) . The differenceW ( xII ) − W ( xNI ) is positive if the following expression is non-negative.
W ≡ wC β 2 xII2 + 2t II xII − 2t NI xNI = ( xII − xNI ){n − w0 − 2( xII + xNI )} .

(33)

It can be shown that the last expression in (33) isn − w0 − 2( xII + x NI ) = {2 w0 (2 − 3β + β 2 )(1 + w0 ) + 4 w0 }x NI /(4 + 2 wC β − wC β 2 ) > 0 .
Therefore, equation (33) is positively signed. And it follows that the host country is better off under
FDI competition than under no FDI.

QED

Since xII > xNI , but t II < t NI , the tariff revenue may be lower under FDI competition thanunder no FDI. However, (33) demonstrates that the host country is better off because the wage
income from FDI dominates any possible reduction in tariff revenue. In addition, consumer surplus
increases from FDI. Thus FDI competition Pareto-dominates no FDI if the conditions given in
Proposition 3 are satisfied. And we are left to show that FDI competition is superior to unilateral FDI.

20

6. Unilateral FDI
When only one firm (say Boeing) undertakes FDI in China, while Airbus does not( xC = x − x A = 0 ), then Boeing produces yC = y − yB of the intermediate input in China, which isendogenously determined. We shall show that Airbus becomes worse off than Boeing.
Since Airbus does not undertake FDI, it follows that in the 3rd stage, the bargaining game in
Airbus can still be modeled by maximizing (5a), and the first order conditions are identical to (6a’)
and (6b’). In Boeing, the union utility and firm profit functions can still be expressed as in (2b) and(3b) respectively. If bargaining breaks down in Boeing, the union utility goes down to zero. Boeing’s
profit also goes down to zero, because final assembly is done in the U.S. only. Boeing and the labor
union bargain to determine y , yB and wB . Substituting xC = x − x A = 0 and yC = y − yB into(5b) and maximizing, we obtainp + yp '− ( y − yB ) wC − w0 − t B = 0 ,(34a)

π B − uB = 0 ,(34b)( y − yB ) wC − w0 yB = 0 .

(34c)

Next we turn to the second stage of the game, in which the Chinese government chooses
tariffs to maximize its objective. Again using xC = x − x A = 0 and yC = y − yB , the objectivefunction under unilateral FDI by Boeing can be rewritten as (see also footnote 5):

W = ( y − yB ) 2 wC / 2 + U ( x + y ) − p( x + y ) + t A x + tB y .

(35)

The Chinese government chooses t A and t B simultaneously to maximize (35), yielding the following
first order conditions.

21

xΔ I − ( x + y )( p '− w0 / 2) p '− byw0 / 4 + (b + p '− w0 / 2)t A − btB = 0 ,(36a)y Δ I − ( x + y )dp '+ ( a + d ) yw0 / 4 + ( a + d )tB − at A = 0 .

(36b)Where Δ I = bd + (a + d )( p '− w0 / 2) > 0 . In deriving the above, we have used condition (34a-c) andthe comparative statics results (a7-a12) in the appendix. Combining them to obtain(t A − tB )[4( a + b + d )d + 4Δ I ]/ w0 = ( a + b + d )dy + 2( x + y ) p '− 2 yΔ I .

(37)The long expression before (t A − t B ) on the LHS of (37) is positive.
Substituting the linear demand function in (22) into the first order conditions in the third stageof the game under unilateral FDI, i.e., (6a’), (6b’), and (34a-c), we havet A = n − w0 − (2 + w0 ) x − y ,(38a)t B = n − w0 − (2 + w0 / 2) y − x .

(38b)

Substituting these into (36a-b), straightforward calculations give

(Δ I + α ) x − (Δ I + γ ) y = −(n − w0 ) w0 / 2 < 0 ,(39)where α = ( w02 + 3w0 + 6) / 2 , and γ = ( w02 + 3w0 + 5) / 2 . Since Δ I > 0 and α > γ > 0 , condition(39) implies that under unilateral FDI, x < y , i.e., the final output (market share) of Airbus is lessthan that of Boeing.
Due to the asymmetry in FDI activities of Airbus and Boeing, further calculations become
very messy. What we do now is to simulate the model using numerical values for the exogenous

22

competitive wages in the home and host countries. We use three sets of values for ( wC , w0 ) : (4,5),(6,8), and (8,10). All three sets of values yield identical results (see Table 1), which can be stated as:

Proposition 5: If Boeing undertakes FDI while Airbus does not, then (i) Boeing’s market share andprofits are higher than Airbus’s; (ii) the tariff rate facing Boeing is lower than that facing Airbus.
Thus, the unique Nash equilibrium is FDI competition by both firms.

Proposition 5 arises because Boeing can take advantage of the lower wages in China byproducing a portion of the intermediate input there, and thus is able to expand output and market share.
It also receives a lower tariff rate for exporting due to quid pro quo FDI. As a result, profits increase.
Therefore, we can further conclude that in the first stage of the game, FDI competition is the unique
Nash equilibrium, because both firms would unilaterally want to undertake FDI.

7. Concluding Remarks
In this paper, we have built a three-country model in which the government, multinational firms
and labor unions are all involved. Production consists of two processes in intermediate and final
outputs. And the firms can choose to export only or to export and undertake FDI simultaneously.
Many factors can explain to some extent for the recent FDI boom in China. We identified three,which are oligopolistic rivalry, strategic outsourcing and quid pro quo FDI. Each of these can cause
firms to engage in FDI competition in the host country, in addition to the explanations of low wages,
huge population and potential market size. In particular, we also found cases in which the firms, thelabor unions and the host country are all better off under FDI competition.
It is worth noting that our qualitative results remain valid even if the structure of the model isaltered somewhat. Consider the case of a two-stage game in which the Chinese government chooses
tariffs in the first stage, and all other endogenous variables (including wages, employment, and FDI

23

decisions etc.) are determined simultaneously in the second stage. To show robustness, we need toprove that in equilibrium both Airbus and Boeing undertake FDI. Because the bargaining structure
here is identical to those in section 4, first order conditions (13a)-(13c) still apply. Rewriting (13c) toobtain xC = w0 x /( w0 + wC ) and x A = wC x /( w0 + wC ) . As long the firm produces positive output(i.e., x > 0 ), then xC > 0 and x A > 0 . That is, each firm undertakes positive FDI in equilibrium.
In addition to intermediate goods, one could also incorporate final production in the host country.
In this case the firm’s payoff at the threat point becomes positive if bargaining with the union breaks
down, while that of the union stays at zero. This again would reduce the negotiated union wage.
Finally, introducing a local firm and endogenizing the wage rate in the host country would be anotherinteresting extension. Then the impacts of FDI competition on the host country can be examined in
more detail. All these constitute avenues for further research.
Finally, in the case of a quota instead of a tariff, our qualitative results on quid pro quo FDI would
carry through more straightforwardly. Basically, the government tended to reward firms by allocatinga larger market share to those following its plans and punishing those who obstruct such plans.

Acknowledgement: We are extremely grateful to Ryoichi Nomura for conducting the simulations, and to L.
Cheng and S. Yabuuchi for detailed comments. Helpful suggestions from F. Dei, T. Furusawa, K. Igawa, J.
Ishikawa, T. Kamihigashi, T. Kikuchi, K. Kiyono, J. Markusen, N. Nakanishi, R. Riezman, A. Woodland andother seminar participants at Kobe University, the University of Hong Kong, the University of Sidney and theJapanese Economic Association Meetings are also acknowledged. The usual disclaimer applies.

a

Appendix 1
This appendix contains the comparative statics results in the third stage under cases of no FDI,
unilateral FDI and FDI competition respectively.
A1. No FDI
Totally differentiating conditions (6a’) and (6b’) to obtain (under symmetry)∂x / ∂t A = ∂y / ∂tB = (2 p '+ yp "− w0 ) / Δ NI < 0 ,(a1)∂x / ∂tB = ∂y / ∂t A = −( p '+ yp ") / Δ NI > 0 ,(a2)∂ ( x + y ) / ∂t A = ∂ ( x + y ) / ∂tB = ( p '− w0 ) / Δ NI < 0 ,(a3)

where Δ NI = [3 p '+ ( x + y ) p "− w0 ]( p '− w0 ) > 0 .
A2. FDI Competition
Replacing x with y and A with B in (14) and totally differentiating it and also (14) itself yields∂y / ∂tB = ∂x / ∂t A = [2 p '+ yp "− (1 − β ) w0 ] / Δ II < 0 ,(a4)∂x / ∂tB = ∂y / ∂t A = −( p '+ yp ") / Δ II > 0 ,(a5)∂ ( x + y ) / ∂t A = ∂ ( x + y ) / ∂tB = [ p '− (1 − β ) w0 ]/ Δ II < 0 ,(a6)

where Δ II = { p '− (1 − β ) w0 }{3 p '+ ( x + y ) p "− (1 − β ) w0 } > 0 .
A3. Unilateral FDI
Substituting (34c) into (34a) and totally differentiating it and (6a’), we obtain∂x / ∂t A = (2 p '+ yp "− w0 / 2) / Δ I < 0 ,(a7)∂y / ∂t A = −( p '+ yp ") / Δ I > 0 ,(a8)∂x / ∂tB = −( p '+ xp ") / Δ I > 0 ,(a9)∂y / ∂tB = (2 p '+ xp "− w0 ) / Δ I < 0 ,(a10)∂ ( x + y ) / ∂t A = ( p '− w0 / 2) / Δ I < 0 ,(a11)∂ ( x + y ) / ∂tB = ( p '− w0 ) / Δ I < 0 ,(a12)where Δ I = ( p '+ xp ")( p '− w0 / 2) + (2 p '+ yp "− w0 / 2)( p '− w0 ) > 0 .

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i

Figure 1

w0

f(x)

g(x)
x

0

Figure 2

wC

wC = w0
wC =4w0
w0 − 4

Area I
8

wC =

2w0
3

20 / 3

0

8

10

w0

ii

Table 1: FDI by Boeing but not Airbus( wC , w0 )(4, 5)(6, 8)(8, 10)xx

59627
82445369085
1356148

7699
181226y1249028244531644931356148

18549
1812262821628244535008051356148

70289
1812262374628244533941011356148

53989
181226tA

tB

πA

24887653903(n − 5) 2 23863686125(n − 8) 2 355647606(n − 10) 2
4 × 679722749209
3678274795808
65685726152

πB

16467204582(n − 5) 2 73442999133(n − 8) 2 1108655181(n − 10) 2
679722749209
3678274795808
65685726152

Note: the values of the variables x, y, tA and tB have been divided by aconstant, (n-w0).