Firm-productivity and cross border merger
Arijit Mukherjee
Nottingham University Business School and CFGE, Loughborough University, UK, CESifo and
INFER, Germany, and GRU, City University of Hong Kong, Hong Kongand

Umut Senalp
Loughborough University, UK

Preliminary draft
December 2015

Abstract: We show that the market concentration effect plays an important role in determining
the relation between firm-productivity and cross border merger. In contrast to the existing
theoretical literature but in line with some empirical evidence, we show that a low-productive
firm may prefer cross border merger whereas a high-productive firm may either prefer greenfieldforeign direct investment or export.

Key words: Cross border merger; Export; Foreign direct investment; Productivity
JEL Classifications: F21; F23; G34; L23; D24

Correspondence to: Arijit Mukherjee, Nottingham University Business School, Jubilee
Campus, Wollaton Road, Nottingham, NG8 1BB, UK.
Email: arijit.mukherjee@nottingham.ac.uk; Fax: +44 (0)115 84 66667

Firm-productivity and cross border merger

1. Introduction
Following the trade and investment liberalization wave in the world economy, the number offirms involved in international trade and foreign investment activities has dramatically increased.
Cross-border mergers and greenfield foreign direct investments are two important ways throughwhich many multinational firms serve foreign markets. Additionally, over the last two decades
cross-border mergers, have become more popular compared to greenfield FDI. The share ofcross-border mergers in total foreign direct investment (FDI) flows has increased and almost
caught up with the share of greenfield FDIs (UNCTAD 2008).1
Following the recent trend in the international trade literature, the literature on trade andinvestment has started to uncover the effects of firm-productivity on cross-border mergers. In a
recent paper, Nocke and Yeaple (2007: here-after NY) examines the relationship between firmproductivity and foreign market entry decisions in a heterogeneous firm framework. In theirpaper, NY consider that the efficiency motive is the main driver of merger activities, and showthat the most productive firms engage in cross-border mergers, while relatively less efficientfirms choose greenfield FDI, and the least efficient firms export or only serve the domestic
market.2
The present paper follows NY’s line of research and contributes to the literature byincorporating the industry concentration effect of cross-border mergers. Focusing on amonopolistically competitive environment, NY ignore any strategic motives for a merger. In this1

As a result of the global economic crisis of 2008-09, both total FDI flow, and the level of cross-border mergers
decreased dramatically, but, recently they have tended to recover from the crisis episodes (UNCTAD 2013).
2
This result is valid for Sector M in NY, where the firms differ in terms of their mobile capabilities, which is themain interest of this paper.

1paper, we introduce the market-concentration effect of cross-border mergers by developing a
two-country oligopoly model of product differentiation, where the firms compete in the productmarket.
The main finding of our paper is that, in the presence of a higher market-concentration
under merger, a relatively low productive firm may prefer cross-border merger while a relatively
high productive firm may prefer either greenfield FDI or export. Our results are more likely tohold if the product differentiation is low, so that the associated competition effect is large and thegain from product-market concentration is high. Thus, in contrast to NY, our results suggest thata strict productivity ranking in terms of cross border merger may not occur. While NY is more
applicable for conglomerate mergers, our paper is more appropriate for mergers between thecompetitors in a particular industry. Our paper also complements NY by showing that their result
may hold even if the firms are engaged in strategic competition.
Empirical evidence on this issue is very limited. Some recent empirical studies provide
mixed results regarding the relationship between entry mode decision and firm productivity,
which is consistent with our predictions. Trax (2011), for instance, finds that the most efficientUK firms choose cross-border merger over greenfield FDI in high intangibles industries, while
she cannot find such evidence in the low intangibles sector. In contrary, Raff et al. (2012) showthat the most productive Japanese firms prefer greenfield FDI over cross-border merger. Looking
at the US firms, Nocke and Yeaple (2008) also find that the higher productive firms prefergreenfield FDI over cross border merger. show that Our results, showing that the relationshipbetween productivity and merger is non-monotonic, can offer an explanation for the mixed
empirical results.

2

The remainder of the paper is organized as follows. In section 2, we provide a review ofrecent theoretical and empirical literature. We describe the model and discuss the results in
sections 3 and 4. Section 5 considers some extensions of our analysis. We provide concluding
remarks and a future research agenda in Section 6. Many mathematical details are relegated toAppendices.

2. Related Literature
Two recent developments in the literature on FDI are worth mentioning.3 Until recently, theliterature has focused on the determinants of an internationalization decision of a firm by treating
firms within an industry as homogeneous. However, the emerging empirical literature shows thatfirms selling abroad are rare among all producers in both developing and developed countries,
and their decisions to participate in international markets are not random (Bernard and Jensen,
1999). Furthermore, Bernard and Jensen (1999) show that firms engaging in international trade
are different in terms of their size, productivity and capital intensity than those who operatedomestically only.
Following these new findings, the seminal paper by Melitz (2003) and Bernard et al.
(2003) provide theoretical analysis for the link between firm-level productivity and the export
decisions of firms. The main finding of Melitz (2003) is that more productive firms exports while
the less productive firms operate only domestically. Head and Ries (2003) and Helpman et al.
(2004) contribute to this literature by explicitly considering two ways to serve the foreign market– export and FDI – and show that only the most productive firms within an industry undertake
FDIs, while the less efficient firms serve the foreign markets via export. Head and Ries (2003)
also show that less productive firms may undertake FDI in the presences of wage difference3

See Markusen (2002) and Antràs and Yeaple (2014) for a survey.

3

between countries. Mukherjee and Marjit (2009) show that the theoretical results of Helpman etal. (2004) my not hold in the presence of wage bargaining between the labour union andmanagement. Mukherjee (2010) shows that the particular preference function considered in
Helpman et al. (2004) may be important for their result and their result may not hold under adifferent consumer preference function. Mrazova and Neary (2013) confirm the findings ofHelpman et al. (2004) only if a firm’s variable cost of production and the transportation cost it
faces are complementary. Moreover, they show that it may not be the case when they consider
different preference structures, where firms cannot be sorted on the basis of their productivity ina way that Helpman et al. (2004) proposed.
The second important development in the FDI literature concerns the composition of
FDI. Although cross-border merger is considered to be an important type of FDI (UNCTAD,
2008), the above-mentioned literature did not pay attention to this aspect. Some recent papers,such as Ferrett (2005), Bjorvatn (2004), Mattoo et al. (2004), and Neary (2009), explicitly model
the two different components of FDI to examine the internationalization decisions of the firm.
Although these papers provide several important insights, unlike our paper, they did not analyze
the effects of firm-productivity on cross border mergers.
As already mentioned, the paper by NY, considered the relation between firmproductivity and cross border merger. Since this paper is most closely related to our paper, it isworth discussing that paper in a greater detail. NY consider firm heterogeneity along with theheterogeneous nature of FDI, where firms which want to sell abroad have the following options:
export, greenfield FDI, and cross border merger. In their paper, firm heterogeneity arises fromthe fact that firms have different types of capability. They consider two sectors: sectors M and N.
Firms are heterogeneous in terms of their internationally mobile capabilities in sector M, while in4

sector N, the source of heterogeneity is the immobile capabilities that firms own.4 NY suggestthat the motivation of a firm engaging in a cross border merger is closely linked to a firm’sheterogeneous capabilities. A target or an acquiring firm’s main motivation for undertaking crossborder merger is to exploit complementarities when combining the firm-specific capabilities.
When considering sector M, where firms differ in terms of their internationally mobile
capabilities only, they show that the more productive firms prefer cross border merger overgreenfield FDI. However, they show that firms that engage in cross border merger are the least
efficient in industry N, where firms differ in terms of internationally non-mobile capabilities.
Unlike our paper, NY consider that the efficiency motive is the only motive for a merger, andignore any strategic motive, which is our focus.
There is another paper by Nocke and Yeaple (2008) where they show that the highproductive firms prefer greenfield FDI compared to cross border merger. However, their reason
is different from ours.
They consider a model of “vertical FDI” with complementary “headquarter input” and“production input”. Merger in their paper means acquisition of a higher productive production
unit by a firm with a lower productive production unit. Hence, merger in their paper allows theacquirer to enjoy a cost reduction by taking over a higher productive production unit and because
the target production union is efficient than the acquirer, the acquirer’s benefit from cost
reduction is independent of its productivity. Since the acquirer profit increases with its
productivity, it is then immediate that the acquirer’s gain from merger decreases with its
productivity, a higher productive acquirer prefers greenfield FDI than cross border merger. It is
worth noting that if the acquirer has more efficient production unit than the target production

4

While the production technology of a firm is considered as an example of mobile capabilities, local marketing
experience or supply networks are associated with immobile capabilities.

5

unit, merger does not occur in their paper. Further, if the wage rates are the same in bothcountries, thus eliminating the benefit from greenfield FDI in their paper, cross border merger isalways the preferable strategy.
In contrast to Nocke and Yeaple (2008), we consider “horizontal FDI” with nofragmentation of production. Second, unlike them, merger in our paper does not create any costsynergy. Thirdly, unlike them, the acquirer (whose productivity is the point of focus) is always
more productive compared to the target firm and merger can be profitable in our paper even if
the wages are the same in both countries. While the reason for our paper is due to the market
concentration effect following a merger, the benefit from cost synergy is the driving force for
their result.

3. The Model
Consider an economy with two countries: home (H) and foreign (F), and two rival firms, eachalready settled in one of these countries. Assume that Firm F is located in the foreign country,
while Firm H is located in the home country.5 We assume that these firms produce differentiatedproducts and compete in the home-country market. Firm F can serve country H in the following
ways:
Export (X): Firm F serves country H through export by incurring a positive per-unit
transportation cost t.
Greenfield FDI (G): Under greenfield FDI, Firm F sets up a plant in country H by incurring a
setup cost, G, and serves country H from that plant.

5

We show in Section 4.5 that our qualitative results also hold when we consider that there are N number of firms
located in the home country, where N>2.

6

Cross border Mergers (M): Under cross border merger, Firms F and H merge, the merged firm
produces with the best available technology and the merger activity involves a fixed cost, K.
This cost may occur due to organizational, managerial or technological factors (see, e.g., Hart
and Tirole, 1990).
Although Firm F has another option, i.e. not serving the home-country market, we willassume the parameters values in a way so that this option will not occur in equilibrium. We will
do this because considering the option of not serving the home-country by Firm F will not add
much new insights to our analysis.
As in NY, we consider that labour is the only factor of production, and the wage rates inboth countries are the same and equal to w. The same wage rate in our paper eliminates thereason for FDI found in Nocke and Yeaple (2008). Firms differ in terms of their labour

productivities, and the technology of Firms F and H are  =  , and  = , respectively,


where

is the inverse of labour productivity. Lower

implies higher labour productivity, andthis implies that Firm F is more productive than Firm H.6 We finally assume that Firm F cantransfer its technological advantage to the merged entity so that it can produce at the same
marginal cost it faces in its home country. This assumption makes our results comparable to theresults of NY for Sector M in their paper, where firms are heterogeneous in terms of theirinternationally mobile capabilities.
Following Bowley (1924), we assume that the representative consumer in country H has
the following utility function:7=  +  − 
67

 
+  −   + 
2
2Hence we obtain labour demand for Firm F and H:  =  and  = The Bowley type of market demand function is commonly used in the industrial organization literature.

7

where m stands for the numeraire commodity, and the parameter  ∈ [0,1] is the degree of

product differentiation. The resulting inverse demand functions for goods  and  are: = 1 −  −  = 1 −  − 

where  and  are prices,  and  are outputs. The products are perfect substitutes if  = 1,

while the goods are isolated for  = 0.

We consider the following two-stage game. At stage 1, Firm F determines whether to export
or to undertake greenfield FDI or to merge with Firm H. At stage 2, the firms compete in country
H if Firm F either exports or undertakes greenfield FDI. There is no competition if Firms F andH merge, and the merged firm becomes a monopolist with two differentiated products. The
profits are realized according to Firm F’s production decision. We solve the game throughbackward induction.
We will consider Cournot competition in the next section and will consider Bertrand
competition in Section 4.5.1, if Firm F either exports or undertakes greenfield FDI. Although the
duopoly market structure helps us to show our results in the easiest way, we show later on that
our qualitative results hold even if there are n number of host-country firms.

4. Equilibrium Analysis
4.1. Export vs. greenfield FDI
If Firm F chooses to export, it determines output by maximizing the following expression:!" 1 −  −  −# − $  .

(1)

Expression (1) shows that Firm F can sell  units of product with a transportation cost of $

while the production cost is equal to # .

8

Firm H determines its output to maximize the following expression:!" 1 −  −  − #  .

(2)

Maximizing (1) and (2), we get the equilibrium outputs of Firms F and H respectively:
% =&'&( &' &)*&'+

&'&( &' ,'), % =*&'+.

Let -% -% represent Firm F's (Firm H's) equilibrium profit if Firm F chooses to export. The
equilibrium profits of Firms F and H are:-% =&'&( &' &) +-% =&'&( &' ,') +(3)*&'+ +*&'+ +

We assume that % and % are positive, i.e. $ <&'&(,('


.

(4)

≡ $ ̅.

If Firm F undertakes greenfield FDI, it maximizes the following profit function:!" 1 −  −  −#  − 1(5)while the profit function for Firm H is:!" 1 −  −  − #  .

(6)

Maximizing (5) and (6), we obtain the equilibrium outputs of Firms F and H respectively:
2 =&'&( &'*&'+, 2 =

&'&( &'*&'+.

Let -2 -2 represent Firm F's (Firm H's) equilibrium profit if Firm F undertakes greenfield FDI.
The equilibrium profits of Firms F and H are:-2 =&'&( &' +-2 =&'&( &' +We assume that 2 , 2 are positive, i.e. # <*&'+ +*&'+ +

&'

&'

9

≡#
3.

−1

(7)

.

(8)

Firm F prefers greenfield FDI compared to export if -2 > -% or:1<−*) &,),(,'&('&*,'+ +

≡ 15

(9)where 15 > 0. Firm F prefers export over greenfield FDI for 1 > 15 . Differentiating 15 withrespect to

we find that

627
6

=−

8()

&*,'+ +

< 0.

The following result is immediate from the above discussion.

Proposition 1: If greenfield FDI is the alternative to export, Firm F's incentive for greenfield
FDI increases with its productivity, i.e.,

627
6

< 0.

The reason for the above result is that if the productivity of Firm F increases, it produces
more, and faces a higher trade cost in total. Since this cost can be avoided by greenfield FDI,
Firm F's incentive for greenfield FDI increases. This result is in line with Helpman, Melitz andYeaple (2004).

4.2. Export vs. cross border merger
From equation (9) we know that Firm F prefers export over greenfield FDI if 1 > 15 . Now wewill see Firm F’s preference for cross-border merger when export is the alternative to merger.
We know from (3) and (4) that if Firm F exports, the profits of Firms F and H are-% =&'&( &' &) +*&'+ +, and -% =&'&( &' ,') +*&'+ +. On the other hand, if Firms F and H

merge, the merged entity maximizes the following profit function:!" , 1 −  −  −#  + 1 −  −  − #  − 9.
10

(10)

The merged firm produces differentiated products in county H. Merger allows Firm F to avoid
the trade cost but the merged firm incurs a cost of merger, K. Since Firm F is more efficient thanFirm H, the merged firm uses the technology of Firm F andstands for the productivity of themerged firm.
If Firms F and H merge, the equilibrium outputs and the profit of merged firm arerespectively:
: = : =

1− #
2 1+

5&( +:-,=  5,' − 9.

(11):
, exceeds the total
Merger between firms F and H occurs if the profit of merged firm, Firm -,profits of Firms F and H under export by Firm F, i.e. if::-,> -% + -% .

Since how the profit of the merged firm getting divided is not important for our purpose, we
focus on the total profits after and before merger.
It follows from (3), (4) and (11), that Firm F prefers cross-border merger compared toexport if:
9<5&( +

 5,'−;

&'&( &' &) +*&'+ ++

&'&( &' ,') +*&'+ +< ≡ 95 .

(12)

The above condition shows the maximum gain from merger compared to export, thus a higher
value of 95 suggests that the firms have a higher incentive to pursue a cross-border merger.
Now we show how the incentive for merger changes with respect to productivity.
Equation (12) shows that 95 consists of the profit of the merged entity and the profits of Firm F
and H when Firm F chooses to export. All these profits in equation (12) depend on productivity
term . Therefore, the relationship between 95 and11depends on how these three profit terms

react to the productivity change. If the difference between the profit of the merged firm and the
combined profit of Firms F and H under export by Firm F increases (decreases) in , we canconclude that a lower

increases (decreases) Firm F's merger incentive.

Before examining this, we define:$∗ =8# 1 +  − −2 +   ?2 +   + 2 @ + # 8 +  −8 + ?−10 +  −2 +  @2 1 +  4 + 

where $ ∗ > 0 if # >'& + ,' ,'

8' 5,' , 8,' &8,' &5B, '& '≡ # ∗ and # ∗ > 0.

Proposition 2: If Firm F prefers export over greenfield FDI, i.e. 1 > 15 , a higher productivityof Firm F increases (decreases) the incentive for cross-border merger if t ∈ ($ ∗ ,$̅) or if (t ∈(0, $ ∗ .

Proof: By using condition (12) we can show that

6C7
6

< > 0 for $ > < $ ∗ , where , $ ∗ < $̅. ■The above result is in contrast to Nocke and Yeaple (2007) for $ < $ ∗ , showing that the
incentive for a cross border merger is higher for a higher productive firm. If the trade cost is
high, i.e. $ > $ ∗ , Firm H is a near monopoly and in this situation, a lower productivity of firm F
reduces the industry profit under export. Hence, to keep the benefit of a near monopoly, the firms
incentive for merger increases with a lower productivity of Firm F. On the other hand, if the
trade cost is low, i.e. $ < $ ∗ , competition is fierce under export and a lower productivity of Firm
F increases the industry profit under export by increasing production efficiency. A lower
productivity of Firm F increases profit of the merged firm also. Since the total output is higher
under export compared to merger, the effect of a lower productivity of Firm F is stronger under12

export compared to merger, thus reducing the incentive for cross border merger following ahigher productivity of Firm F.
In order to see the effect of the level of product differentiation on our findings, let us now
consider how $ ∗ changes with respect to the level of .
Proposition 3: A lower level of product differentiation, i.e. higher , increases the range for t6) ∗over which a lower productivity of Firm F reduces the incentive for merger, i.e. 6' > 0.

Proof: Differentiating $ ∗ with respect to , we find that:
6) ∗
6'

=

?&*,'+ @ &8&';8,'?5D,' ,' @<,( &8 5,' + ,E5D,';*,'?*,' ,' @<F 5,' + *,'+ +> 0. ■As product differentiation reduces, it increases competition and the output effect underexport becomes more important compared to merger, thus increasing the possibility of a lower
incentive for merger following a higher productivity of Firm F.

4.3 Greenfield FDI vs. cross border merger
Now we consider the case where G < 15 , i.e. Firm F prefers greenfield FDI compared to export.
We know from equations (7), and (8) that if Firm F undertakes greenfield FDI, the profits offirms Firms F and H are -2 =&'&( &' +*&'+ +− 1, and -2 =&'&( &' +*&'+ +:
merge, we know from (11) that the profit of the merged entity is -,=. If Firms F and H

5&( +

 5,'

− 9.

If greenfield FDI is the alternative to merger, a merger between firms F and H isprofitable if::-,
> -2 + -2 .

13

Hence, the cross-border merger occurs if:
9<5&( +

 5,'−;

&'&( &' +*&'+ ++

&'&( &' +*&'+ +− 1< ≡ 9 .

(13)

The value of 9 shows the maximum gain of Firm F from merger compared to greenfield FDI. A
higher value for 9 suggests that Firm F has a higher incentive for cross-border merger.
Before further analysis we define:#′ ='& + ,' ,'

8' 5,' , 8,' &8,'?&5B,' &,' @> 0.

Proposition 4: If greenfield FDI is the alternative to merger, i.e. 1 < 15 , Firm F's incentive forundertaking cross-border merger increases (reduces) with a higher productivity of Firm F, i.e.
with a lower , if w ∈ (0, w') or if (w ∈ (w',#3)).

Proof: The proof follows from rearranging the derivative of 9 with respect to.

6C

Straightforward calculation shows that 6+ < > 0 for # < > # ′ . The rest of the proof follows
immediately.8 ■If the wage is high, i.e. # > # G Firm F is a near monopoly and a lower productivity ofFirm F strengthen Firm F’s near monopoly position and reduces its incentive for cross bordermerger. However, if the wage is low, i.e. # < # G , competition is fierce and the firm’s incentive
for monopolizing the market increases the incentive for cross border merger following a lower
productivity of Firm F.
Now we show how the range of w over which a higher productivity of Firm F reduces the
incentive for a cross border merger varies with product differentiation.
8

Please see Appendix 3 Section C.1 for the proof of #3 > #′.

14

Proposition 5: A lower level of product differentiation, i.e. higher , increases ( w − w′) ', i.e.
increases the range of w over which a higher productivity of Firm F reduces the incentive for across border merger.

Proof: See Appendix 3 Section C.2 for the proof.■

If wage is higher, a higher competition due to a lower product differentiation increases
the possibility of a near monopoly by Firm F. Hence, a lower product differentiation reduces thepossibility of a cross border merger following a lower productivity of Firm F.

5. Robustness and extensions
5.1. Bertrand Competition
It is well know that the results under horizontal merger may depend on the type of productmarket competition, viz., Cournot or Bertrand competition, (Salant et al., 1983 and Deneckere
and Davidson, 1995). The purpose of this subsection is to see whether our results under Cournot
competition shown above hold under Bertrand competition .
In order to solve the Bertrand game, first we obtain the direct demand functions byutilizing the inverse demand functions. They take the following form: =5&' &H ,'H
5&'+and  =5&' &H ,'H5&'+For our analysis under Bertrand competition, we illustrate the calculations for equilibrium
outputs and profits in Appendix 3 Section A.

15

5.1.1. Equilibrium Analysis
Export vs. greenfield FDIConsider that Firm F chooses between export and greenfield FDI in order to serve country H. If
Firm F chooses to export, the equilibrium outputs % and % are positive if $ < 1 − # −(&5 '≡ $̅. However, if Firm F undertaked greenfield FDI, the equilibrium outputs 2 and 2'+ &

are positive if <'&5 ,'', '+ &≡#
3 . We assume that these conditions hold.

Firm F chooses to undertake greenfield FDI if and only if -2 > -% or:
1′ < ;)?&,'+ @ & &,),( , &5,( ','+ &,),(&*,'+ + &5,'+< ≡ 1 .

(14)

Export vs. cross border merger
From equation (14), we know that Firm F prefers export over greenfield FDI if 1 ′ > 1 . we findthat cross border merger is profitable compared to export if:
5&( +

9 ′ <  5,' — ; − &5,),( ,'&('& &5,),( '+ +&*,'+ + &5,'++ −,' &5,)&' ,( &,' ,'&*,'+ + &5,'++< ≡ 9J .
(15)

Let's define:$ ∗∗ =
where $ ∗∗ > 0 if # >&8,8 5,( ','+ &* 5,( K ,L ,M &( &8,' 5D,' ,' &8,','+
 *&J'+ ,'L'&5 ', + ,' &,'*' &,' + , &8,' 5D,' ,γ &8,','+

16≡ # ∗∗ .

Proposition 6: If export is the alternative to merger, (G' > 1 ), a higher productivity of Firm F
increases (reduces) the incentive for cross-border merger, if t ∈ $ ∗∗ , $̅ or if (t ∈ ( 0, $ ∗∗ ).

Proof: By using condition (15) we can show that

6CK
6

< > 0 for $ > < $ ∗∗ where $ ∗∗ > $̅. ■Like the case under Cournot competition, this result is in contrast to NY for $ < $ ∗∗ . The
intuition is similar to that of Proposition 2.

Greenfield FDI vs. cross border merger
Now consider that G' < 1 , i.e. greenfield FDI is preferable over export. We find that crossborder merger is profitable compared to greenfield FDI by Firm F if:
9 ′′ <

5&( +

 5,'

— E−

+

&,','+ &(?&,' ,' @&*,'+ + &5,'+

F + E−+

,' &5,(&' ,'?&,'+ @&*,'+ + &5,'+

F − 1 ′  ≡ 9* .
(16)

Condition (16) tells us that Firm F prefers to do cross-border merger over greenfield FDI if andonly if 9 ′′ < 9* .
Let's define:# ′′ =&8,8','+ &*'K ,'L ,'M&8&8',5D','+ ,*'K &8'K ,'L ,'M

17

> 0.

Proposition 7: If greenfield FDI is the alternative to merger, i.e. G' < 1 , the incentive for crossborder merger increases (reduces) with higher productivity of Firm F if w ∈ (0, w'') or if (w ∈(w'', #
3 )).

Proof: By using condition (16) we can show that

6CL
6< > 0 for # < > # ′′ . ■The intuition is similar to that of for Proposition 4.

5.2. N Firms in the country H
To convey our point in the simplest way, we assumed in section 2 that there is only one firm incountry H. We show in this section that our findings of section 2 hold true when there are nsymmetric firms in country H, where n>2 .
If the products are homogeneous,9 the inverse demand functions for Firm F and for the ith
home-country firm are respectively:P = 1 −  − N OP

OQ5

O = 1 − N O − 
where  and O are prices,  , O are outputs.

OQ5

We assume in this section that the firms compete like Cournot oligopolists. We illustrate
the calculations for equilibrium outputs and profits in Appendix 3 Section B.

9

The revised version of the paper will include the differentiated goods case.

18Equilibrium Analysis
Export vs. greenfield FDIFirst, consider Firm F’s choice between export and greenfield FDI.
If Firm F chooses to export, the equilibrium outputs % and % are positive if $ <5&(,P(&P(
5,P≡ $.̅ On the other hand, if Firm F undertakes greenfield FDI, the equilibrium

outputs 2 and 2 are positive if # <

5

,

≡#
3. We assume that these conditions hold.

Firm F prefers greenfield FDI over export if:
1 ′′ < ;−5,P ) &,),P),( ,( &5,P, +< ≡ 1J .

(17)

If condition (17) is not satisfied, Firm F prefers export to greenfield FDI.

Export vs. cross border merger
We find that cross border merger is profitable compared to export by Firm F if:
9 ′′ <

5&P(,( P&5 +
P,5 +

—;

5&( P,5 &) P,5 ,(P +
P, +

+

5&(,(,) +P, +< ≡ 9R .

(18)

A cross-border merger between Firm F and the ith firm in country H is not preferable over export
if the cost of merger, 9 ′′ , is greater than 9R , showing the maximum gain from merger compared
to export.
Let's define:$ ∗∗∗ =
Moreover $ ∗∗∗ > 0 if # >&P J,P ,;,P S,RP &?,JP ,P @<(P,5 + ,P ,P

P J,P&,&SP,DP&RP+ ,JP+

19≡ # ∗∗∗ .

.

Proposition 8: If export is Firm F’s preferred choice as an alternative to merger, i.e. G'' > 1J ,Firm F’s higher productivity increases (reduces) the incentive for cross-border merger, ift ∈ (t *** , t ) ( t ∈ (0, t *** ) ).

Proof: By using condition (18) we can show that

6CM
6

< > 0 for $ > < $ ∗∗∗ , where $ ∗∗∗ < $.̅ ■This result is in contrast to Nocke and Yeaple (2007) for $ ∗∗∗ < $.̅

Greenfield FDI vs. cross border merger
We consider in this subsection that G'' < 1J , i.e. greenfield FDI is Firm F’s alternative to merger.
Firm F undertakes cross-border merger compared to greenfield FDI if :9 ′′ <

5&P(,( P&5 +
P,5 +

— ;

5&( P,5 ,(P +
P, +

<+;

5&(,( +P, +< − 1 ′′  ≡ 9D .

(19)

The value of 9D shows the maximum gain from merger compared to greenfield FDI. A higher

value for 9D suggests that Firm F has a higher incentive for cross-border merger.
Let's define:# ′′′ =

&JP&P+&,&SP,DP,RP+ ,JP+

20.

Proposition 9: If greenfield FDI is Firm F’s alternative to merger, i.e. G'' < 1J , the incentive
for undertaking cross-border merger increases (reduces) with its higher productivity ifw ∈ (0, w′′′) ( w ∈ ( w′′′, w) .
Proof: A straightforward calculation shows that

6CT
6

< > 0 for w<(>) w''' . The rest of the proof

follows immediately. ■Again, this result is in contrast to Nocke and Yeaple (2007) for w > w'''.

6. Conclusion and Future Research Agenda
In this paper, we showed how the productivity of a foreign firm affects the incentive for a crossborder merger. In a two-country oligopolistic model with differentiated goods, we showed thatthe predictions of Nocke and Yeaple (2007), suggesting that the most productive firms prefercross-border merger, may not hold true if the competition reducing effect of a merger isconsidered. We observed a non-monotonic relationship between productivity and a cross-bordermerger, and showed that our results hold under both Cournot and Bertrand competition.
In order to focus on the strategic motive for merger, we kept our model simple byassuming that there is only one foreign firm. However, it would be interesting to investigate amodel where there are two or more asymmetric (in terms of productivity) foreign firms, toexamine the strategy of different foreign firms, where competition among the foreign firms forgreenfield FDI and cross-border merger creates further strategic effects. We leave this issue for
future research.

21

Appendix I Section A
Bertrand Competition and the International Organization of Production
Equilibrium Analysis

Export vs Greenfield Investment
First, consider firm F’s choice between export and greenfield FDI. If Firm F chooses to export,%
the objective functions for Firms F and H are π% = (U − # − $  and π
= (U − #  ,respectively. The resulting equilibrium prices, and profits are:If Firm F undertakes greenfield FDI, the objective functions for firms F and H are π2 = (U −#  − 1 ′ and π2 = (U − #  , respectively. The resulting equilibrium prices and profits

are:

22

Firm F undertakes greenfield FDI if and only if π2 > π% or:which can be shown as follows:

Export vs. cross border merger
From equation (A5) we know that Firm F prefers greenfield FDI if and only if G' < G2, otherwise
it prefers to export.
Let's assume that G' > G2, in other words, export is Firm F’s preferred choice as analternative to merger. We know from (A2) and (A3) that if Firm F exports, the equilibrium
profits of Firms F and H are:On the other hand, if firm F and H merge, the merged firm maximize the following expression:

The merged firm produces both the products, and the equilibrium prices and the profit of merged
firm are:Cross-border merger is profitable compared to export by Firm F if:
23%%
where, π:, denotes the profit of the merged firm, while π and π denote the profit of Firms F

and H under export by Firm F. Following (A1), (A2) and (A6), we get that cross-border merger
if preferable to export by Firm F if and only if:orGreenfield FDI vs. cross border merger
Now consider the case of G' < G2 i.e. greenfield FDI is Firm F’s preferred choice as analternative to merger. We know from (A3) and (A4) that when Firm F undertakes greenfield
FDI, the profits of firm F and H are:However, if Firms F and H merge, we know from (A6) that:

A cross-border merger between Firms F and H is profitable compared to greenfield FDI by Firm
F if:
24

2
2
where, π:, denotes the profit of the merged firm, while π and π denote the profits of Firms F

and H under greenfield FDI by Firm F. Following (A3), (A4) and (A6), we get that cross-bordermerger is profitable than greenfield FDI by Firm F if and only if:orSection B
N firms in country H
To show our results in the simplest way, we assumed in section 2 that there is only one firm in
the home country. We show in this section that our results in section 2 hold true even if there aren symmetric firms in the home country, where n>2 . If there are n home-country firms, theresulting inverse demand functions are:25

Equilibrium Analysis
Export vs. greenfield FDIFirst, consider the foreign firm’s choice between export and greenfield FDI. If Firm F exports, it
determines output by maximizing the following expression:

while profit maximization problem of ith firm in home country is:

The resulting equilibrium outputs, and profits are;and output and profit of ith home-country firm are:If firm F undertakes greenfield FDI, it maximizes the following profit function:

while profit maximization problem of the ith home-country firmis:

26

The resulting equilibrium outputs and profits are;and output and profit of i'th firm in home country are;So, Firm F prefers greenfield FDI compared to export if -2 > -%

which can be shown as follows;

Export vs. cross border merger
From (A.11) we know that Firm F prefers greenfield FDI if and only if G’’< G3, otherwise
prefers to export.
Let’s assume that G’’ > G3, export is Firm F?s available strategy as an alternative tomerger. We know from (A7) and (A8) that when Firm F chooses to export, the profits of Firm F
and the ith home-country firm are:27

However, if Firm F and the ith home-country firm merge, the merged firm determines output tomaximize the following profit function:and each of the remaining home-country firm, say, firm j, determines output to maximize thefollowing expression:

If Firms F and the ith home-country firm merge, the equilibrium output and the profit of merged
firm are:A merger between Firms F and the ith home-country firm is preferable compared to export by
Firm F if:

Following (A.7), (A.8) and (A.12) we get that merger occurs if and only if:28

Greenfield FDI vs. cross border merger
In this sub-section, we consider that G '' < 1J , i.e. greenfield FDI is Firm F’s available strategy as
an alternative to merger.
We know from equations (A9) and (A10) that if Firm F undertakes greenfield FDI, theprofits of firms Firm F and the ith home-country firm are:If Firm F and the ith firm merge, we know from (A3.12) that the profit of the merged firm is:

A merger between Firm F and the ith home-country firm is profitable compared to greenfield
FDI by Firm F if:or29Section C.1

Section C.2:

30

31

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