Multinational Entry and Organizational Change*
Hiroshi Kitamura†Misato Sato‡

Shiro Takeda§

March 26, 2021
Abstract
This study explores domestic firms’ vertical organizational changes with increased openness to new foreign multinational firms’ entry into a host country. We focus on the two-sided
hold-up problem between input suppliers and heterogeneous firms. When the severity of holdup problems is endogenously determined by the total number of firms in the sector, the newforeign multinational firms’ entry induces some domestic firms to change the organizational
choice between vertical integration and outsourcing. We show that the cross-sectoral differences in the input intensity of production explain the different shifts in the prevalence of vertical integration and outsourcing across the countries and sectors.

JEL classifications code: F23, L12, L41, L42, C72.
Keywords: Multinational entry; Organizational form; Two-sided hold-up problems; Input intensity* We thank Takanori Adachi, Maggie Chen, Akifumi Ishihara, Atsushi Kajii, Noriaki Matsushima, Michael Moore,
Tadashi Sekiguchi, Steven Suranovic, and Kazuhiro Yamamoto, as well as the conference participants at Japan Association for Applied Economics and seminar participants at George Washington University and Kagoshima University
for their insightful comments. We gratefully acknowledge the financial support from JSPS KAKENHI Grant Number
JP17J03400 and JP20K13485. The usual disclaimer applies.
†
Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto, Kyoto 603-8555,
Japan. E-mail: hiroshikitamura@cc.kyoto-su.ac.jp‡
Corresponding Author: Graduate School of Humanities and Social Sciences, Okayama University, Tsushima-naka
3-1-1, Kita-Ku, Okayama 700-8530, Japan. E-mail: msato@okayama-u.ac.jp§
Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto, Kyoto 603-8555,
Japan. E-mail: shiro.takeda@cc.kyoto-su.ac.jp

1

Introduction

Multinational firms have increased their share of global production in recent decades. According
to UNCTAD (2015), multinational firms contributed 34.4 percent of the global GDP in 2013.
Sales by foreign affiliates to foreign customers are essential methods of serving foreign markets.
For example, the Direct Investment and MNE data from the Bureau of Economic Analysis of theUnited States for 2013 indicate the sales of the foreign affiliates of U.S. multinational firms to beslightly more than $7 trillion, whereas U.S. exports are about $2.3 trillion.1
As more foreign multinational firms enter and serve foreign markets in host countries, theimpact of multinational entry becomes one of the vital economic topics. Among the impacts ofmultinational entry, local firms’ organizational change is an important concern. In business literature, several studies report cases of vertical integration in the face of increased competition (Dyer,
1996; Bhattacharya and Michael, 2008).2 Moreover, the upward trend in the vertical integrationin the manufacturing and service sectors has sometimes been discussed (McGrath, 2009).3 Conversely, during the past couple of decades, the aggregate statistics demonstrate the general trend of
the increasing international disintegration of production under globalization (Feenstra and Hanson,
1996; Campa and Goldberg, 1997).4 In summary, we observe both the integration and disintegra1

The data is available at the website of the U.S. Bureau of Economic Analysis (https://apps.bea.gov/
iTable/iTable.cfm?isuri=1&reqid=2&step=1#isuri=1&reqid=2&step=1).
2

Bhattacharya and Michael (2008) refer to mergers and acquisitions of Focus Media, a Chinese outdoor advertising
firm, when facing competition with America’s Clear Channel Communications and France’s JCDecaux. By scaling
up rapidly through mergers and acquisitions, Focus Media obtains the leading market position in China. Dyer (1996)
documents the restructuring of Chrysler, a U.S. automaker, in the face of the increased competition with Japanese
automobiles. Chrysler creates “American Keiretsu,” which is based on the strong vertical ties of firms, by modifying
Japanese business practices.
3

See also the news article “Companies More Prone to Go ‘Vertical’” The Wall Street Journal, November 30, 2009(https://www.wsj.com/articles/SB125954262100968855), and “What’s Behind the Current Wave of Vertical Integration?” Kellogg Insight January 5, 2018 (https://insight.kellogg.northwestern.edu/article/
whats-behind-the-current-wave-of-vertical-integration) for example.
4

Feenstra and Hanson (1996) and Campa and Goldberg (1997) calculate the imported intermediate-input sharesand provide empirical evidence on the increase in the share for several countries. See also Feenstra (1998) for thesurvey on the global disintegration trend.

1

tion evidence.
This study aims to provide an economics analysis for local firms’ organizational changes whenfacing increased openness to multinational entry. Among organizational forms’ decisions, thisstudy focuses on the vertical relation of production to capture the domestic firm’s choice between
the insourcing and outsourcing of intermediate inputs. More importantly, we consider how thesector’s features affect the domestic firms’ organizational choices.
We construct a model of domestic firms’ organizational choices based on a framework established by Antràs and Helpman (2004). In each sector, there are suppliers and heterogenous firms(final-good producers). Every variety of final goods is produced by a pair of a supplier and a firm.
The production of the final goods requires two relationship-specific inputs, supplied by both the
supplier and the firm. Among the sector-specific features, we primarily focus on the input intensity, the degree of the contribution of each relationship-specific input to the production of the final
goods.
Before starting the production, the firms determine whether to outsource the intermediate inputs to suppliers or insource them. When the firms choose outsourcing, they are required to incur
low organizational costs, whereas there exists a two-sided hold-up problem because they sign an
incomplete contract, which is not ex-ante enforceable. We assume that the firm’s and the supplier’s
revenue under outsourcing is determined by the ex-post bargaining, which takes the form of generalized Nash bargaining. Alternatively, when firms choose vertical integration, they must incur
higher organizational costs, although they can achieve joint profit maximization because vertical
integration solves the two-sided hold-up problem. This study’s notable feature is that the ex-postbargaining outcome under outsourcing depends on the total number of firms in each sector. This is
one of the formulations to capture the market thickness.
In this setting, we theoretically explore how the fraction of domestic vertical integration oroutsourcing changes in a market through multinational entry. Subsequently, we investigate the impact of multinational entry on the number of each organizational form of domestic firms by using2

numerical analysis. In both analyses, when multinational entry occurs, both the fraction and thenumber of vertical integrations (outsourcings) change, depending on the sector’s input intensity.
More precisely, multinational entry is more likely to facilitate domestic vertical integrations (outsourcings) if the sector is relatively intensive in the firms’ (suppliers’) inputs, and the firms haveweak (strong) bargaining power.
To comprehend this result, consider the impact of multinational entry on a two-sided hold-up
problem between a supplier and a domestic firm under outsourcing. When the industry experiences
increased openness to new foreign multinational entry, an increase in the sector’s firms induces
richer outside options for the suppliers under the ex-post bargaining. Such a change of outside
options allows the suppliers to possess a higher revenue share, enhancing the suppliers’ ex-ante
incentive for the input supply. Conversely, the domestic firms have a lower revenue share, eliminating the domestic firms’ ex-ante incentive to supply their input. When the sector is relatively
intensive in the firms’ inputs, and the firms have weak bargaining power, the firms’ under-supply
becomes a more severe problem. Therefore, the contracting party’s joint profit under outsourcing
decreases. Thus, the domestic firms are more likely to choose vertical integration.
This study is related to the literature on the analysis of how multinational activities influence
different aspects of domestic economies, given the increasing presence of multinational firms ina host country. An growing number of empirical studies demonstrate that increased openness toforeign multinational entry leads to productivity gains (Keller and Yeaple, 2009; Alfaro and Chen,
2018), factor market reallocation, and an increase in wages (Aitken, Harrison, and Lipsey, 1996;
Feenstra and Hanson, 1997; Alfaro and Chen, 2018).
A few theoretical studies explore the local firms’ organizational changes facing trade liberalization and the firms’ relocations. Conconi, Legros, and Newman (2012) find that free trade andthe suppliers’ mobility between two countries change vertical organizational structures. Their core
determinants of a vertical organizational structures are the price of output and the terms of trade.
McLaren (2000) provides an analysis on the impact of the market thickness on an organizational
3choice through input trade liberalization. Our study’s significant distinction is that we provide
a model framework to explain that a cross-sectoral distinction in the input intensity explains thedifference in the prevalence of vertical integration and outsourcing across countries and sectors
through two-sided hold-up problems between the suppliers and firms.
There are studies on vertical organizational form choices of homogeneous firms in a market, inwhich firms endogenously determine whether to produce inputs independently or purchase fromthe suppliers (Grossman and Helpman, 2002, 2003). They do not consider multinational entry or
heterogeneous firms, whereas this study follows their essential concept of a trade-off between the
low fixed cost of outsourcing and the efficient production of vertical integration by assuming firms’
heterogenity.
The remainder of this study is organized as follows. Section 2 introduces the model. Section
3 characterizes the equilibrium, and Section 4 provides a comparative statics analysis to perceive
the change in the relative prevalence of domestic outsourcing and domestic vertical integration
after foreign multinational entry. In Section 5, we provide a numerical analysis. Some concluding
remarks are provided in Section 6. Finally, Appendix A introduces a numerical analysis underanother parameter set, and Appendix B provides the proofs of all the results.

2

Model

We construct a model of the organizational choices in the presence of multinational entry, basedon the concept of a firms’ organizational decisions in Antràs and Helpman (2004). The two majordifferences between this study and Antràs and Helpman (2004) are that (i) vertical integration
enables firms to write a complete contract with the suppliers, and (ii) the bargaining outcome
under outsourcing depends on the total number of firms (final-good producers) in the sector.
The rest of this section is organized as follows. While Subsection 2.1 characterizes consumers,
and Subsection 2.2 characterizes producers, Subsection 2.3 introduces the game timing. The variables and parameters used in this study are provided in Table 1.
4

[Table 1 about here]

2.1

Consumers

Consider a single-country’s economy with J ∈ N+ sectors and populated by a unit measure of
consumers.5 We assume that consumers have identical preferences represented byJ

U = x0 +1X µ
X , 0 < µ < 1,
µ j=1 jwhere x0 is the consumption of a homogeneous good, X j is an index of the aggregate consumption
in sector j ∈ {1, 2, .., J}, and µ is the share that a consumer spends on the products of sector j. The
aggregate consumption in sector j is a constant elasticity of substitution (CES) function,

Xj =

"Z

# α1

α

x j (i) di, 0 < α < 1,of the consumption of different varieties x j (i). A parameter α measures the degree of the productdifferentiation. In other words, as α becomes larger, the product is less differentiated. We assume
that α > µ, meaning that the varieties within a sector can be substituted more for one another thanfor x0 or for the varieties from a different sector. The elasticity of substitution between any twovarieties in sector j is given by 1/ (1 − α). We assume that the parameters µ and α are the same forevery sector. Given the above preferences, the inverse demand function of good i in sector j canbe provided as

p j (i) = X µ−αx j (i)α−1 .
j
5

(1)

To clearly understand the logic of a foreign multinational entry’s impact, we construct a simple single-country
model to focus on domestic firms’ decisions. The single-country model used here can be justified as follows. A
domestic firm’s decision to become a multinational and serve a foreign country does not affect other domestic firms’
decisions in the home country. This is because multinationals obtain the profits in each country independently, andthe consumers’ preferences introduced in this study are quasi-linear. Thus, we can disregard the economic activity byforeign subsidiaries of domestic multinational firms. This model setting focuses on understanding the domestic firms’
decisions in an organizational form when a domestic market experiences new foreign multinational entry.

5

2.2

Producers

A continuum of suppliers (intermediate-input suppliers) and one unit of a continuum of firms (finalgood producers) are located in every sector j. Only the firms are aware of how to produce the finalgood varieties. Every sector has two types of firms: domestic (denoted by H) and multinational(denoted by M).6 For each type l ∈ {H, M}, firms are heterogeneous in terms of the productivity of
the final goods, θ > 0. For each type l, the productivity level of the firms in sector j is drawn froma common distribution, G (θ), whose probability density function is denoted by g(θ). In Section 5,
we introduce the case in which G(θ) is defined as a Pareto distribution.
The production of the final goods’ varieties requires a combination of two relationship-specificinputs, y j (i) and z j (i). While y j (i) is the firm’s investments (firm’s inputs), in which only thefirms invest,7 z j (i) represents the intermediate inputs (the supplier’s inputs) produced only by the
suppliers. The output of each final good is a sector-specific Cobb–Douglas function of inputs,
"
# "
#


y j (i) η j z j (i) 1−η j
x j y j (i) , z j (i) = θ,ηj
1 − ηj(2)where the productivity parameter θ is firm-specific, and the parameter η j is sector-specific. One
can easily see that as the productivity θ increases, the level of the final-good production increases
as well. More importantly, as the value of η j becomes larger (smaller), sector j becomes thefirm’s investment intensive (intermediate-input intensive). The revenue from the final-good sales
is R j (i) = p j (i) x j y j (i) , z j (i) . From equations (1) and (2), we have#αη j "#"
z j (i) α(1−η j )µ−α α y j (i).
R j y j (i) , z j (i) = X j θηj
1 − ηj(3)

Both firms and suppliers face a perfectly elastic labor supply, and the wage rate c is fixed for6

For simplicity, the domestic country does not have multinational firms that have subsidiaries in foreign countries.
Because the utility function in this study is quasi-linear, the higher gains from the multinational activities increase thefirms’ income levels in foreign countries. However, it does not affect the domestic firms’ decision to be a multinational,
even after new entry.
7

The firm’s investment can be interpreted as the investments in advertisement, managerial skills, and R&D.

6

simplicity.8 We assume that both the firms and the suppliers use one unit of labor to supply one unitof relationship-specific input. In other words, the cost to supply one unit of relationship-specificinput is c.

2.3

Timing of gameThe game’s timing is as follows (See also Figure 1). The game consists of four stages. In Stage 1,
all the firms observe their productivity level θ and decide whether to be active. If the firms decide
to be inactive, they earn zero profits.
[Figure 1 about here]
In Stage 2, the active firms decide on their organizational form. In other words, they choose
outsourcing (denoted by O) or vertical integration (denoted by V). Subsequently, the firms incur
fixed organizational costs. Following Antràs and Helpman (2004), we assume that the organizational costs in the host country are denominated in terms of labor. We denote the organizational
cost in sector j, when a type l ∈ {H, M} firm chooses an organizational form k ∈ {O, V} as c fl|k j .
For the sake of a simple discussion in Section 4, we assign fl|k j as the organizational costs. Furthermore, in every sector j, we assume higher organizational costs in vertical integration than inoutsourcing because firms must invest in subsidiaries. Thus, the organizational costs in sector j
can be ranked as follows. For each l ∈ {H, M},
jfl|O< fl|Vj .

(4)

In addition, in every sector j, we assume higher organizational costs in multinational firms thanin domestic firms; that is, for each k ∈ {O, V}, we obtainjj
fH|k< f M|k.
8(5)This may be justified in a general equilibrium by considering c the productivity of the labor required to produce
x0 and the labor supply which is adequately large for the country to produce x0 .

7This assumption can be justified because the fixed costs of searching, monitoring, and communication are significantly high in a foreign country.9
To commence the final-good production, every firm is required to contract with a supplier for
the intermediate inputs. The firm offers a contract stipulating some fixed fees for the supplier to
pay when the supplier participates in a relationship with the firm, T l|k (i) ≥ 0. We assume thatthe supplier’s size is adequately large to allow the firm to choose T l|k (i) so that the supplier’s net
profits are equal to its ex-ante outside of the option earnings. For simplicity, we further assume thatthe ex-ante outside option earning of the supplier is zero; therefore, each supplier earns nothing inequilibrium. The amount of type l ∈ {H, M} firms engaged in an organizational form k ∈ {O, V} insector j is denoted by Nl|kj ∈ [0, 1]. Thus, the total amount of firms engaged in an organizationaljjform k in sector j can be denoted by Nkj . By definition, we have Nkj = NH|k
+ N M|k. In addition, theamount of active firms in sector j can be denoted by N j , where N j ≡ NOj + NVj .
In Stage 3, firms and suppliers choose the supply level of relationship-specific inputs. The
supply level of the inputs highly depends on the organizational form determined in Stage 2. Whena firm chooses vertical integration in Stage 2, the firm and the supplier can sign a complete contract.
They can choose the supply levels to maximize their joint profit in Stage 3.10
Conversely, when the firm chooses outsourcing in Stage 2, the firm and the supplier sign an
incomplete contract as in Antràs and Helpman (2004). In other words, they cannot sign an ex-ante
enforceable contract specifying the purchase of relationship-specific intermediate inputs for a certain price, the amount of labor hired, and the sales revenue when the final goods are sold. Thus,
every firm–supplier pair bargains over their joint profit after their relationship-specific inputs havebeen supplied. We assume that the ex-post bargaining takes the form of a generalized Nash bargaining game, wherein the firm obtains a fraction β ∈ (0, 1) of the ex-post gain from the contracting
9This organizational cost for becoming a multinational firm is paid for by the headquarter in the home country.
Subsequently, it enters the host country.
10

This setting is different from Antràs and Helpman (2004), and the modeling strategy helps us focus on thedetermination of the outside options under outsourcing.

8
parties’ joint revenue R j y j (i) , z j (i) .
Unlike Antràs and Helpman (2004), our fundamental assumption is that the ex-post outside
option earnings of each contracting party are endogenously determined by the amount of active
firms N j . In the case of failure to reach an agreement on the distribution of surplus, the supplier
may sell the intermediate inputs to one of the firms in the downstream market (for example, at
an auction).11 Because the intermediate inputs are relationship specific, the matched firms pur chase them at a fraction σ j N j ∈ (0, 1) of the revenue from the final-good production. Thisoccurs although these processes are costly and generate a loss of a fraction 1 − γ j ∈ (0, 1) of
the final-good production. Therefore, the outside option earnings of outsourcing firms become    
γαj 1 − σ j N j R j y j (i) , z j (i) , and those of the suppliers become γαj σ j N j R j y j (i) , z j (i) . We 
assume that σ j N j has the following property.12 13
Assumption 1. The possibility that the intermediate inputs are highly evaluated by other firms
 
becomes higher as the amount of active firms increases. In other words, σ0j N j > 0.
Under Assumption 1, a firm’s (the supplier’s) share of the outside option earnings under outsourcing decreases (increases) as the amount of active firms increases.14
In Stage 4, the production of the final goods commences with two inputs, and the final goods
are sold to the final consumers. In the equilibrium, firms earn all the joint profit, whereas the11This can be justified if the suppliers have a low level of internal reserves and assets. In such a case, the supplierdeems it difficult to raise money for all the transfers T l|k (i) and wages cz j (i), when no agreement is reached on the
distribution of a surplus. Thus, the supplier has to naturally go bankrupt and sell all the intermediate inputs at an
auction.
12

We obtain a similar property under the successive Cournot model. The change in the revenue share is analogous
to that in the price of intermediate inputs in successive Cournot competition with a fixed number of suppliers, a lineardemand, and a quadratic-cost function. In this setup, the intermediate-input price in outsourcing can increase from thehigher demand due to additional entry, thus raising the upstream revenue share.
The results demonstrate no qualitative changes even when we assume that the functional form of σ (·) is σ (NO ).
This could capture the successive Cournot competition in the outsourcing market. More precisely, the results do not
qualitatively change if σ (·) is a function of a variable that increases by multinational entry.
13

14

When considering the suppliers selling their products at an auction, this assumption can be interpreted as anincrease in the bid price as the number of bidders rises.

9

suppliers earn nothing. A firm’s net profit, including its organizational cost, can be denoted byπkj (θ, fl|kj ), where l ∈ {H, M} and k ∈ {O, V}.15

3

Equilibrium

This section explores the decision on the organizational form. Because we focus on a particularsector, we omit index j from all variables. Let θl|k be the cutoff productivity of type l ∈ {H, M}
firms, the lowest value of θ that would induce a firm to choose the organizational form k ∈ {O, V}.
Although many equilibrium patterns exist, this study focuses on the following equilibrium, which
is most reasonable under condition (4): for each l ∈ {H, M},
θl|O < θl|V .

(6)

Assuming the order of cutoff productivities (6), we first characterize the profit of the firms under their organizational form k in Subsection 3.1. Subsequently, we examine the existence of an
equilibrium and derive each cutoff productivity in Subsection 3.2.

3.1

Two-organizational forms

In this subsection, we derive the equilibrium’s profit of the firms. We first characterize the case ofvertical integration and then the case of outsourcing.
Vertical integration
When a firm and supplier integrate in Stage 2, they sign a complete contract and choose the supply
levels for the relationship-specific inputs that maximize their joint profits in Stage 3. The equilibrium production levels of the relationship-specific inputs under vertical integration is denoted byyl|V (i) and zl|V (i) and can be obtained by solving the following joint profit maximization problem:
yl|V (i) , zl|V (i) ≡ argmax R (y (i) , z (i)) − c (y (i) + z (i)) ,y(i),z(i)15The profits of intermediate-input suppliers are not depicted because they earn zero profits in an equilibrium.

10subject to equation (3). By using a fixed transfer T l|V , the firm extracts all the joint profit, andhence, the supplier earns nothing. Because the firm incurs c fl|V after choosing the organizational
form, the net profit of the type l ∈ {H, M} firm under vertical integration becomesµ−ααπV θ, fl|V = X 1−α ψV θ 1−α − c fl|V ,

(7)

where
ψV = (1 − α)α α  1−αc.

Outsourcing
When a firm chooses outsourcing in Stage 2, the firm and the supplier bargain over their joint profit
after the relationship-specific inputs have been supplied in Stage 3. Under the generalized Nashbargaining game, the firm obtains its ex-post outside option earnings γα (1 − σ (N)) R (y (i) , z (i)),
and a fraction β of the ex-post net gains from the contracting party (1 − γα ) R (y (i) , z (i)). For thebargaining outcome in this stage, see also Figure 2. Thus, the firm’s revenue becomes βO R (y (i) , z (i)),
whereβO = β (1 − γα ) + γα (1 − σ (N)) .

(8)

Similarly, the supplier earns revenue (1 − βO ) R (y (i) , z (i)). Contrary to vertical integration, eachfirm under outsourcing chooses an input supply level that maximizes its operating profits, given
the trading partner’s input supply level. The firm’s maximization problem in Stage 3 is given bymax βO R (y (i) , z (i)) − cy (i) ,
y(i)

(9)

subject to (3). Conversely, the supplier’s maximization problem under outsourcing in Stage 3 isgiven bymax (1 − βO ) R (y (i) , z (i)) − cz (i) ,
z(i)

(10)

subject to (3). By solving first-order conditions (9) and (10) with respect to y (i) and z (i), we obtain
the equilibrium supply levels of relationship-specific inputs under outsourcing, denoted by yl|O (i)11and zl|O (i). At the beginning of Stage 2, the firm anticipates this equilibrium outcome and chooses
a fixed transfer T l|O , which is equal to the supplier’s operating profit. The firm, therefore, extracts
the entire joint profit, while the supplier earns nothing. The type l ∈ {H, M} firm’s net profit,
including the organizational cost under outsourcing becomesµ−ααπO θ, fl|O = X 1−α ψO θ 1−α − c fl|O ,

(11)

where
ψO =

1 − α (βO η + (1 − βO ) (1 − η)).
α  η 
1−η  1−α
c
α

1
βO

1
1−βO

[Figure 2 about here]
Note that ψO is interpreted as the severity of a two-sided hold-up problem, which plays a crucialrole in this analysis. In the following sections, we explore the properties of ψO and how they affectfirms’ organizational decisions.

3.2

Decision of organizational forms

In this subsection, we compare the profits’ sizes obtained in the previous subsection and derive theorder of the cutoff productivities that satisfy condition (6). A simple comparison of equations (7)αand (11) indicates that the firms’ profits πk (θ, fl|k ) linearly increase in θ 1−α but depend on the degreesof ψk and fl|k for all organizational forms. From condition (4), we have fl|O < fl|V . Conversely, thefollowing lemma characterizes the relationship between ψV and ψO .
Lemma 1. ψV > ψO always holds.
The result in Lemma 1 implies that if organizational costs coincide ( fl|O = fl|V = f ), then all
the active firms choose vertical integration; that is, πV (θ, f ) > πO (θ, f ) for all θ. This is because
under outsourcing, the two-sided hold-up problem occurs, where firms under outsourcing have a12

smaller incentive to supply the relationship-specific inputs. To clarify this, we rewrite the first
order condition with respect to y (i) under vertical integration Ry yl|V (i) , z = c, as follows:
βO Ry yl|V (i) , z + (1 − βO ) Ry yl|V (i) , z = c.
Conversely, the first-order condition under outsourcing is βO Ry yl|O (i) , z = c. Because Ry (y, z) >0 for all y > 0 and z > 0, yl|O (i) < yl|V (i) holds if zl|O (i) ≤ zl|V (i). Similarly, zl|O (i) < zl|V (i) if
yl|O (i) ≤ yl|V (i). Thus, outsourcing induces the suppliers and the firms to choose a smaller input
supply level, and this prevents them from maximizing their joint profit. This is because each firmand supplier cannot internalize a positive input-production externality. Therefore, an increase in
the input production of a supplier (a firm) increases the profit of the firm (the supplier).
The result in Lemma 1 also implies that a firm with a sufficiently high productivity levelchooses vertical integration regardless of the organizational cost. However, for a small or intermediate productivity level, the organizational decision depends on the organizational cost level.
Assuming the order of the cutoff productivities (6), we can derive the following cutoff productivities by using equations (7) and (11), should they exist.
Definition 1. For each l ∈ {H, M}, the two types of cutoff productivity are defined as follows:
1. Cutoff productivity for lO; πO θl|O , fl|O = 0.
θl|O = Xα−µα"c fl|O
ψO

# 1−α
α

.



2. Cutoff productivity for lV; πO θl|V , fl|O = πV θl|V , fl|V .
" # 1−αα−µc fl|V − fl|O α,
θl|V = X α
ψV − ψO

(12)

(13)

where
N=

Z ∞
θH|O

g(θ)dθ +Z ∞g(θ)dθ,1−α1 
 α  1−µ
 α(1−µ)X Z θl|VX Z ∞αη
α(1−η)1−α1−αX=βO (1 − βO )g(θ)dθ +g(θ)dθ
.
cl∈{H,M} θl|Vl∈{H,M} θl|O

13

(14)

θF|O

(15)

The following proposition identifies the existence of an equilibrium:
Proposition 1. For each l ∈ {H, M}, there exists the order of the cutoff productivities (6) characterized by conditions (12) and (13) if flV is sufficiently high.
The results in Proposition 5.1 are summarized in Figure 3. A few comments are necessaryregarding the results. First, Proposition 5.1 does not provide the exact condition of fl|O , fl|V ∈ R2++that satisfies the order of cutoff productivities (6). Thus, an equilibrium can be determined moreeasily to exogenously set a pair θl|O , θl|V such that θl|V > θl|O > 0 in numerical analysis. Second,
multinational firms’ cutoff productivity is always higher than that of firms in the host country
because the fixed organizational costs of multinational firms are higher than that of domestic firms.
[Figure 3 about here]

4

Comparative statics: fraction of domestic firms

This section investigates how the multinational entry in outsourcing impacts domestic firms’ organizational form in terms of the fraction. More precisely, this study examines how a decrease in themultinational firms’ organizational costs for outsourcing f M|O affects the domestic firms’ incentive
to vertically integrate or outsource in terms of the fraction of the firms. For the analysis of thissection, we choose G (θ) as a Pareto distribution with shape δ and scale b. In other words, theprobability density function is g (θ) = δbδ θ−δ−1 and" #δ
bfor θ ≥ b > 0,
G (θ) = 1 −θ(16)where δ > α/ (1 − α). 16 Under the Pareto distribution, N and X can be rewritten as follows:
"
N=

b
θH|O

#δ

"
+

16

b
θ M|O

#δ
,

(17)

In this case, the sales distribution also becomes Pareto. It is consistent with the several empirical evidences suchas Helpman, Melitz, and Yeaple (2004).

14

! 1−α ααηαα(1−η)δbδ α(1−µ)  1−α1−α −δ
1−α −δ
1−α
(1
)
X=
β
−
β
θ
+
θ
O
α
O
HO
MO
c
δ − 1−α1−α α  α(1−µ)αηαα(1−η)
−δ
−δ
1−α
1−α
1−α
+ 1 − βO (1 − βO ) 1−α θHV + θ MV.
1
 α  1−µ(18)Note that θl|k , N, and X are solutions of equations (12), (13), (17), and (18), where l ∈ {H, M} andk ∈ {O, V}. We also derive the amount of domestic vertical integration and outsourcing under the
Pareto distribution.
"
NH|V =

b

#δ

,
θH|V
"
#δ "
#δ
b
b
NH|O =
−
.
θH|O
θH|V

(19)
(20)

Equations (19) and (20) imply that the amount of domestic vertical integration and that of outsourcing are determined by the cutoff productivities. More concretely, NH|V is negatively related toθH|V . Conversely, NH|O is positively related to θH|V and negatively related to θH|O .
Moreover, in this section, we assume the following relationship between f M|O and N.
Assumption 2. A decrease in multinational firms’ organizational cost of outsourcing f M|O increases the amount of active firms. Therefore, ∂N/ ∂ f M|O < 0.
Equations (12) and (17) imply that a decrease in the multinational firms’ organizational cost ofoutsourcing, f M|O , directly reduces the cutoff productivity for the multinational firms engaged inoutsourcing, θ M|O . This leads to an increase in the amount of active firms, N. Although an indirect
effect could arise whereby some domestic firms engaged in outsourcing decide to be inactive (thatis, θH|O increases), we assume that multinational entry provides a dominant effect in this section.17
In the next section, by using numerical analysis, we determine large ranges in which the total
17

Forte (2016) provides a useful survey of the empirical analysis on the effects of multinational entry on thehost country’s market concentration, entry, exit, and survival of the host country’s firms. The summary on the hostcountry’s market concentration provides both positive and negative relationships between a multinational presence
and the concentration ratio. However, the productive multinational entry may expand the host country’s market size,
and the increase in the share of the productive multinational presence may increase the evaluation of each supplier’s
intermediate input in the host country.

15

amount of active firms, including multinational firms, increases.18
The fraction of the domestic firms engaged in vertical integration (outsourcing) is denoted by
φH|V , and that of the domestic firms engaged in outsourcing is denoted by φH|O . Under the Pareto
distribution, using equations (19) and (20), we have
NH|V
NH|O + NH|V"# δ(1−α)(ψV − ψO ) fH|O α=
,ψO fH|V − fH|O

φH|V =and φH|O = 1 − φH|V because φH|V + φH|O = 1 holds by definition. Indisputably, φH|V and φH|O do
not depend on X, which results in a simpler analysis. In addition, the change of f M|O affects onlyψO , which is the degree of the two-sided hold-up problem and is determined by bargaining underoutsourcing. To consider the relationship between φH|V and f M|O , we provide the partial derivativeof φH|V , with respect to f M|O , as
∂φH|V ∂φH|V ∂ψO ∂βO ∂N=.
∂ f M|O∂ψO ∂βO ∂N ∂ f M|O(21)

Thus, to find the relationship between φH|V and f M|O , it is necessary to examine the relationships
between βO and N, between ψO and βO , and between φH|V and ψO .
We first consider how the degree of the two-sided hold-up problem ψO affects the fraction ofdomestic vertical integration φH|V . The following lemma characterizes this relationship:
Lemma 2. As the two-sided hold-up problem becomes increasingly serious, the fraction of domestic vertical integration increases; that is, ∂φH|V /∂ψO < 0.
From equation (11), the profit under outsourcing πO is positively related to the value of ψO .
Therefore, ∂πO /∂ψO > 0. Thus, when the two-sided hold-up problem becomes more serious,
18

Using numerical analysis in the next section, we can determine the sets of parameter values under which thisrelation holds for all (β, η) ∈ (0, 1)2 . For example, the set of parameters in Table 2 satisfies this property. Conversely,
we have difficulty finding ∂N/ ∂ f M|O > 0, although we have conducted huge ranges of simulation trials with various
sets of parameter values. Such a relation is observed in only the very limited ranges of (β, η) ∈ (0, 1)2 , even if it exists.

16the profit under outsourcing decreases, making the domestic firms more likely to choose vertical
integration.
We hereafter consider the relationship between βO and N. We summarize the relationship asfollows:
Lemma 3. As the amount of the active firms increases, the firms’ revenue share under outsourcing
decreases. In other words, ∂βO /∂N < 0.
Lemma 3 implies that as the amount of active firms increases, the outsourcing firms’ revenue
share decreases as the outside option earnings under outsourcing decrease. Under Assumption 2,
a decrease in the multinational firms’ organizational cost of outsourcing reduces the revenue shareof the firms under outsourcing: ∂βO / ∂ f M|O > 0.
Finally, we explore how the revenue share of firms under outsourcing βO affects the degree of a
two-sided hold-up problem ψO . The following lemma demonstrates that this relationship depends
on the values of βO and η.
Lemma 4. When the firms’ revenue share under outsourcing increases, the two-sided hold-up
problem becomes more serious (less serious) for a sufficiently high (low) fraction of the firms’
revenue share under outsourcing. In other words, ∂ψO /∂βO R 0 if and only if βO Q β∗O (η), wherepη (1 + αη − α) − η (1 − η) (1 − αη) (1 + αη − α)∗,(22)βO (η) =2η − 1and where ∂β∗O (η) /∂η > 0 with β∗O (0) = 0, β∗O (1) = 1 and limη→1/2 β∗ (η) = 1/2.
The properties of β∗O (η) are summarized in Figure 4.19 On the line of β∗O (η), we have ∂ψO /∂βO =0; that is, the firms’ profit under outsourcing is maximized. By interpreting the results in lemma
4 differently, the degree of the two-sided hold-up problem ψO becomes considerably more serious
for a small or large value of βO . Under the Cobb-Douglas production technology of the final goods,
The shape of β∗O (η) depends on the degree of the product differentiation α. It approaches being linear as the valueof α becomes higher.
1917

a small supply level by one party has an indirect effect of reducing the supply level by the otherparty. This becomes a dominant effect when βO is close to 0 or 1, because the supply level by one
party is close to 0 in such cases. Therefore, the extremely unbalanced revenue share between theoutsourcing firms and the suppliers leads to the serious two-sided hold-up problem.
[Figure 4 about here]
By expending the results in lemma 4, we have the relationship between βO and φH|V . For
βO > β∗O (η) (βO < β∗O (η)), we have ∂ψO /∂βO < 0 (∂ψO /∂βO > 0). This implies that if βO decreases
when βO > β∗O (η), ψO would increase. Because πO is positively related to ψO , a decrease in
the revenue share of the firms engaged in outsourcing would induce them to earn larger profits,
which, in turn, will induce domestic firms to prefer outsourcing to vertical integration. Thus, φH|V
decreases, whereas φH|O increases. Conversely, if βO decreases when βO < β∗O (η), ψO decreases.
In this case, as the revenue share of the firms engaged in outsourcing decreases, these firms earnsmaller profits, thus facilitating the vertical integration of the domestic firms. Thus, φH|V increases.
The intuitive logic underlying this result is as follows. Owing to the two-sided hold-up problem, a decrease in the revenue share of the outsourcing firms βO has two effects. First, a decreasein βO directly reduces the revenue of the outsourcing firms βO R (y, z), and hence, outsourcing firms
supply a smaller amount of relationship-specific inputs. Thus, the joint profits of the contracting parties decrease. Second, a decrease in βO increases the revenue share of the suppliers under outsourcing (1 − βO ) R (y, z), and this induces the suppliers to produce a larger amount of therelationship-specific inputs, increasing the joint profits of the contracting parties. Because the revenue share of outsourcing firms βO is positively related to β, and the revenue from the sales of the
final goods depends on η, the impact from the decrease in βO depends on the bargaining power andrelative intensity of the firm’s investment.
When firms have stronger bargaining power (higher β), and the sector is intensive in intermediate inputs (smaller η), the under-investment of the intermediate inputs may present a severe
18

problem. Because a decrease in the outsourcing firms’ revenue share can mitigate this problem,
the joint profit of the contracting parties πO increases. Conversely, when the firms have weakbargaining power (lower β), and the sector is intensive in the firm’s investment (higher η), theunder-investment by the firms can become a more severe problem. In this case, as the revenue
share of the outsourcing firms decreases, the under-investment of the firms becomes more severe
and thereby reduces the joint profit of the contracting parties.
From Assumption 2 and Lemmas 2, 3, and 4, the relationship between multinational entry andthe fraction of domestic vertical integration can be summarized as follows.
Proposition 2. Suppose that Assumption 2 holds. When the organizational cost of multinational
firm’s outsourcing f M|O decreases, the fraction of domestic vertical integration φH|V changes, depending on the firms’ revenue share under outsourcing βO and the relative intensity of inputs η;that is,∂φH|V
Q 0 ⇔ βO Q β∗O (η) .
∂ f M|O(23)

More concretely,
1. if firms have a sufficiently low revenue share, and the sector is relatively intensive in thefirms’ investments, the fraction of domestic vertical integration increases; and2. if firms have a sufficiently high revenue share, and the sector is relatively intensive in the
suppliers’ inputs, the fraction of domestic outsourcing increases.

From the above results, we can conclude that multinational entry is more likely to increase thefraction of domestic vertical integration (outsourcing) (i) when the sector is sufficiently intensivein the firms’ investments (supplier’s inputs), and (ii) the firms have sufficiently weak (strong) bargaining power. Because the relative input intensity varies across the markets and countries, theresults here may explicate the cross-sectoral differences in the pattern of the changes in domestic
firms’ vertical structures through foreign multinational entry.
19

5

Numerical Analysis

This section examines how multinational entry affects domestic firms’ organizational forms withregard to the amount by using a numerical analysis. As in Section 4, an increase in multinational
entry is captured by the decrease in the organizational cost of multinational firms’ outsourcing
f M|O . Equation (19) implies that an increase in the amount of the domestic integration NH|V isequivalent to a decrease in the cutoff productivity of domestic vertical integration θH|V . Similarly,
equation (20) implies that the amount of domestic outsourcing NH|O is negatively related to θH|O
but positively related to θH|V . Thus, in this section, we first focus on the relationship between f M|Oand θH|V . Subsequently, we conduct the numerical analysis on the relationship between f M|O and
NH|O by focusing on the relationship between θH|O and f M|O .
For numerical analysis, we theoretically explore the relationships between θH|V and f M|O andbetween θH|O and f M|O . First, by partially differentiating θH|V with respect to f M|O , we have# # 1−α "µ "∂θH|VX − α c fH|V − fH|O α (1 − α) X ∂ψO∂X=+ (α − µ).
∂ f M|OαψV − ψO
ψV − ψO ∂ f M|O∂ f M|O(24)

Equation (24) demonstrates that a change in θH|V depends on the changes in ψO and X, both ofwhich are endogenously determined. As discussed in the previous section, multinational entry
affects the two-sided hold-up problem between a firm and supplier under outsourcing, as well as
the outsourcing firm’s profits πO , which is positively related to ψO . From Lemma 4, an increaseor decrease in ψO , which is equivalent to an increase or decrease in πO , depends on the bargaining
power of the firms, β, and the relative intensity of inputs η.
In contrast to the previous section, to analyze the relationship between θH|V and f M|O , we needto consider another effect on the aggregate production (consumption) X. Ordinarily, multinational
entry increases the aggregate production (that is, ∂X/∂ f M|O < 0), with the following effect on the
profit of the firms:
Lemma 5. ∂πV /∂X < ∂πO /∂X < 0.
20

Lemma 5 implies that an increase in X induces all firms to earn smaller profits. Moreover, theprofit reduction of vertical integration, given a fixed ψO , is more serious as compared to that ofoutsourcing. Thus, domestic firms are less likely to choose vertical integration, which increases
θHV (decreases NH|V ). Therefore, considering the change in the aggregate production X, we predictthat the amount of domestic vertical integration NH|V is less likely to increase as compared to thefraction of domestic vertical integration φH|V .
Thereafter, by partially differentiating θH|O with respect to f M|O , we have
# 1−α "#µ "∂θH|O X − α c fH|O α(1 − α) X ∂ψO∂X(α − µ)=−.
∂ f M|Oα
ψO∂ f M|OψO∂ f M|O(25)

As in the case of θH|V , a change in θH|O is determined by changes in ψO and X. A comparison
between equations (24) and (25) demonstrates that like θH|V , the increase in the aggregate production X reduces θH|O as the firms’ profits under outsourcing decrease. Unlike θH|V , θH|O increases
when the two-sided hold-up problem becomes increasingly serious because the firms prefer vertical integration to outsourcing under such environments. From equation (25), the possibility of∂θH|O /∂ f M|O > 0 exists when ∂ψO /∂βO < 0. Therefore, by considering the properties of ∂ψO /∂βO ,we predict that the amount of domestic outsourcing increases only when the firms have stronger
bargaining power, and the sector is relatively intensive in the intermediate inputs.
The remainder of this section is organized as follows. First, we introduce the parameters under
the numerical analysis in Subsection 5.1. Subsequently, we introduce the results of the numericalanalysis in Subsection 5.2.

5.1

Parameters

This subsection introduces the parameters to a numerical analysis. For the numerical analysis, wechoose G(θ) to be a Pareto distribution, which is defined in equation (16). In addition, we assume
that σ (N) has the following functional form:σ (N) = 1 − e−τN ,21

We now introduce the exogenous parameters (see also Table 2).20 Following Melitz and Redding (2013), we set α = 0.75 so that the elasticity of substitution between any two varieties satisfies
1/ (1 − α) = 4 and the Pareto shape parameter for the firm productivity δ = 4.25, under which wehave δ > α/ (1 − α).21 22 Following Melitz and Redding (2013), the Pareto scale parameter for thefirms’ productivity and wage rate are normalized to b = 1 and c = 1, respectively. As assumed
in Section 2, the parameter µ in preference has to satisfy µ < α = 0.75. Thus, we examine thecase of µ = 0.5. For the shape of the parameter σ (N) and the depletion rate, we choose τ = 50
and γ = 0.5. As Proposition 2 implies that the result highly depends on the parameter set of theoutsourcing firms’ bargaining power β and the relative intensity of inputs η, we examine the caseof (β, η) ∈ {0.05, 0.10, .., 0.95}2 .
[Table 2 about here]
Within these parameters, we obtain the solutions for an appropriate set of organizational costsfH|O , fH|V , f M|O , f M|V , as follows. Proposition implies that condition (4) is a necessary condition

but not a sufficient condition for the existence of an equilibrium. Thus, if we set an erroneous
parameter set of fl|k , we cannot obtain the set of θl|k that satisfies condition (6). Moreover, it
would become more challenging to solve the equations. Therefore, by exogenously setting θl|k tosatisfy condition (6), we determine the set of fl|k in the appropriate order in the numerical analysis.
By using this method, we set fH|O = 0.5, fH|V = 10, f M|O = 1, and f M|V = 20, and with theseorganizational costs, we obtain a unique solution for all the cases of (β, η) ∈ {0.05, 0.10, .., 0.95}2 .
20

We use GAMS for the numerical analysis here.

Their setting on α is consistent with the estimates using the plant-level U.S. manufacturing data in Bernard,
Eaton, Jensen, and Kortum (2003).
21

The value of δ is justified as follows. Because a firm’s revenue, R, is a power function of the firm’s productivity,
R is also a Pareto distributed and G(R) = 1 − (b∗ /R)δ(1−α)/α , where b∗ is the revenue of the least productive firm. Melitz
and Redding (2013) and existing empirical analyses suggest that the firms’ size distribution defined by the firms’
revenue is well approximated by a Pareto distribution, with a shape parameter δ (1 − α) /α close to one. In addition,a firm’s revenue is required to have a finite mean. Therefore, we are required to have δ (1 − α) /α > 1. These two
conditions are satisfied when δ = 4.25. For δ = 4.25, we have δ (1 − α) /α = 1.42 > 1.
22

22

For the analysis of comparative statics, we compare these equilibrium outcomes with those for thecase of f M|O = 0.9; namely, the organizational cost for foreign multinational outsourcing decreases
by 10 percent.

5.2

Comparative statics

We first explore how multinational entry affects the amount of domestic vertical integration NH|V ,which is captured by a change in θH|V . We obtain the following result.
Result 1. A decrease in the organizational cost of the multinational firms engaged in outsourcing
f M|O increases the amount of domestic vertical integration NH|V for the following environments:
1. The sector is intensive in the firm’s investments: η is high.
2. Firms have sufficiently weak bargaining power: β is low.

Figure 5 summarizes Result 1. As with the fraction of domestic vertical integration φH|V ,multinational entry increases the amount of domestic vertical integration NH|V for a higher η and alower β. As per the result of Proposition 2, this result can essentially be expressed by a change inψO .
We hereafter compare the amount of domestic vertical integration captured by θH|V , with afraction of domestic vertical integration φH|V . The comparison results are summarized as follows.
Result 2. The parameter region of (β, η), in which the amount of domestic vertical integration
increases, is narrower than the region in which a fraction of vertical integration increases. Therefore, a region exists where the amount of domestic vertical integration decreases, but a fraction ofdomestic vertical integration increases.
Figure 6 describes the change in φH|V . A comparison of Figures 5 and 6 demonstrates thatthe parameter region of (β, η), in which domestic vertical integration is facilitated in terms of the23amount, is narrower than that in terms of the fraction. This phenomenon can be explained bychanging the sector’s aggregate production index X, which reduces the possibility that multinational entry increases domestic vertical integration. Therefore, the amount of domestic vertical
integration can decrease, even when the fraction of domestic vertical integration increases.
[Figures 5 and 6 about here]
We finally explore how multinational entry impacts the amount of domestic outsourcing. We
obtain the following results.
Result 3. A decrease in the organizational cost of the multinational firms engaged in outsourcing
f M|O increases the amount of domestic outsourcing NH|O and that of the active domestic firms (θH|O
decreases) in the following environments:
1. The sector is intensive in intermediate inputs: η is sufficiently low.
2. Firms have sufficiently strong bargaining power: β is sufficiently high.

Figures 7 and 8 summarize Result 3. To understand the result, note that the fraction of domestic
outsourcing is defined by φH|O = 1 − φH|V . This implies that the parameter region of (β, η), in which
the fraction of domestic outsourcing increases, coincides with the region in which the fraction ofdomestic vertical integration decreases (see Figure 6). Because an increase in aggregate production
has the effect of discouraging less productive firms from being active, the parameter region of (β, η),in which the amount of domestic outsourcing increases, is narrower than the region in which thefraction of domestic outsourcing increases.23[Figures 7 and 8 about here]
We determine that the parameter region of (β, η), in which the amount of domestic outsourcing increases, becomes far narrower for the case of smaller organizational costs under domestic outsourcing. For example, there is no
parameter region of (β, η), in which the amount of domestic outsourcing increases for the case of fH|O = 0.02. See
Appendix A.
23

24

6

Conclusion

This study explores the domestic firms’ vertical organizational change when they encounter increased openness to new foreign multinational entry. Although the effect of multinational activities
on the host country’s economy can occur through many different channels, this study provides asimple analysis by emphasizing a two-sided hold-up problem. We find that the two-sided hold-up
problem plays a vital role in explaining the changes in each organizational form’s share in a market. If the number of firms increases through multinational entry and it increases the suppliers’ revenue share at the ex-post bargaining, outsourcing is more likely to be widespread in intermediateinput intensive sectors. Conversely, vertical integration is more likely to be widespread in a firm’s
investment-intensive sector.
To further understand the organizational changes, this study may imply that some entry deterrence of the foreign multinational firms and some additional exit of the domestic outsourcing firms
may occur when vertical integration becomes more widespread than before in a firm’s investmentintensive sectors. Such outcomes are due to an indirect effect of the increased vertically integrated
firms in a host country. This indirect effect may be derived from comparing the case in which thenumber of domestic vertical integration firms would be fixed even after a new entry. Our framework may elucidate the difference in the number of multinational entrants across the countries andsectors to a certain extent.
From this perspective, our study may provide an analysis of not only the organizational change
but also the indirect effects on some entry barriers. If policymakers disregard these indirect effectsof organizational restructuring, it may misevaluate some effects of new foreign multinational entry
in developing countries (for example, the spillover effect on the domestic productivity or labor).
Thus, it can be essential to analyze domestic firms’ organizational changes when experiencing new
foreign multinational entry.
The analysis in this study captures the relationship between an intermediate-input supplier and25

a final-good producer. We can also apply our model to capturing a firm’s relationship with a distributor or a retailer instead of an intermediate-input supplier. Vertical integration with a distributor
or a retailer may make it possible for a firm to access customer information further. Such verticallinkage may assist a firm in surviving in the competitive market environment. From this perspective, the application of our model for the relationship between a firm and a distributor/retailer may
also provide important implications.
Despite these contributions of this study, there remain some recommendations for further research. One of them is that this model may be applied to the analysis of domestic vertical integration’s entry deterrence effect against foreign multinational entry. The increase in the numberof domestic vertical integration firms may demonstrate a cross-sectoral distinction in the numberof foreign multinational entrants. In the business literature, several studies report that strengthening the vertical relation effectively works as a survival strategy of the domestic firms to protect
their markets from multinational entry (Dawar and Frost, 1999; Venugopal, 2010; Sanotos andWilliamson, 2015).24 We hope that this study assists researchers in addressing this type of entry
deterrence phenomenon.

Appendix A

Numerical results under the lower organizational
cost for domestic outsourcing

This appendix provides the numerical results when domestic outsourcing’s organizational cost fH|O
is sufficiently low. Other parameters do not change with the parameter set summarized in Table 2.
We set fH|O = 0.02 in this appendix instead of fH|O = 0.05 in Section 5. In this setting, we obtainthe following results.
Result 4. When the organizational cost of domestic outsourcing fH|O decreases, the relationshipbetween multinational entry and the organizational forms of the domestic firms is summarized as24

One can consult, for example, Kitamura, Matsushima, and Sato (2021), who consider a local firm’s survival strategy to protect a local market from multinational entry via exclusive dealing by employing a game-theoretic approach.

26

follows:
1. The parameter of (β, η) in which the fraction of domestic vertical integration φH|V increases
or decreases does not change.
2. The parameter of (β, η) in which the amount of domestic vertical integration NH|V increases
becomes narrower.
3. The parameter region of (β, η) in which the amount of the active domestic firms NH decreases
becomes wider. For fH|O = 0.02, NH always decreases.
4. The parameter region of (β, η) in which the amount of domestic outsourcing NH|O decreases
becomes wider. For fH|O = 0.02, NH|O always decreases.

Figures 9, 10, 11, and 12 summarize Result 4. Note that Figures 6 and 10 coincide; that is, adecrease in organizational cost of domestic outsourcing does not affect the organizational form ofdomestic firms in terms of the fraction of the domestic firms. The basic direction of φH|V ’s change
is determined by the sign of ∂ψO /∂βO . Because equation (22) is determined by α and η, the levelof the organizational cost does not affect the change in ψO ; therefore, the first property of Result 4
holds.
Conversely, a decrease in domestic outsourcing’s organizational cost affects the domestic firms’organizational form in terms of the amount. Note that a decrease in fH|O increases the amount ofactive firms N, affecting bargaining under outsourcing. Because ∂σ(N)/∂N = τe−τN > 0 and∂2 σ(N)/∂N 2 = −τ2 e−τN < 0, multinational entry does not considerably decrease the revenue shareof the outsourcing firms βO for a lower value of fH|O . Equation (21) implies that this effect reduces
the level of φH|V ’s change, as compared with the case of the higher value of fH|O . Therefore,a change in the aggregate production X becomes more dominant. Because a change in X may
discourage domestic vertical integration, the amount of vertical integration decreases. Moreover,27

a change in X reduces the domestic firms’ profit, which decreases the amount of active firms and,hence, the amount of domestic outsourcing.
[Table 2 about here][Figures 9, 10, 11, and 12 about here]

Appendix B
B.1

Proof of All Results

Proof of Lemma 1

The first-order conditions under vertical integration satisfyRy yl|V (i) , zl|V (i) = Rz yl|V (i) , zl|V (i) = c.
Note that yl|V (i) and zl|V (i) are the optimal input production levels under the joint profit maximization problem. The input production levels under outsourcing yl|O (i) and zl|O (i) satisfyβO Ry yl|O (i) , zl|O (i) = (1 − βO ) Rz yl|O (i) , zl|O (i) = c.
By comparing (7) and (11), we have ψV R ψO if and only if πV (θ, f ) R πO (θ, f ). Because πV (θ, f )is the maximized value, πV (θ, f ) ≥ πO (θ, f ) must hold for all θ > 0 by definition. However, weshow that πV (θ, f ) = πO (θ, f ) never holds. Suppose that in negation, there exists a case in which
πV (θ, f ) = πO (θ, f ). Because we have a unique solution, yl|O (i) = yl|V (i) and zl|O (i) = zl|V (i). Thus,
we have βO Ry yl|V (i) , zl|V (i) = c. However, this contradicts first-order condition (B.1). Thus, wehave ψV > ψO .
Q.E.D.

B.2

Proof of Proposition 1

Assume that for all l ∈ {H, M}, 0 < θl|O < θl|V holds in an equilibrium. Subsequently, fromequations (14) and (15), N and X can be determined; thus, βO and ψO can be determined. Because
28every firm under monopolistic competition is small, a single firm’s decision on organizational form
does not affect the levels of N and X. Given N and X exogenously, the firms’ profits πk (θ, fl|k ),where k ∈ {O, V}, are summarized in Figure 3, which shows that for sufficiently large flV , we have0 < θlO < θlV for all l ∈ {D, M}.
Q.E.D.

B.3

Proof of Lemma 2

By partially differentiating φH|V with respect to ψO , we have# δ(1−α)−α
"
α
∂φH|V
δ (1 − α) ψV fH|O (ψV − ψO ) fH|O
=− 2

< 0.

∂ψO
αψO fH|V − fH|O ψO fH|V − fH|O
Q.E.D.

B.4

Proof of Lemma 3

From Assumption 1 and equation (8), we have ∂βO /∂N = −γα σ0 (N) < 0.
Q.E.D.

B.5

Proof of Lemma 4

By solving ∂ψO /∂βO R 0 with respect to βO , we have βO Q β∗O (η), which satisfies β∗O (0) = 0 andβ∗O (1) = 1. For η = 1/2, we can use L’Hôpital’s rule, which leads to limη→1/2 β∗ (η) = 1/2. Finally,
we show that ∂β∗O (η) /∂η > 0. By differentiating β∗O (η) with respect to η, we have√√ 
λ (1 − α (1 − 2η (1 − η))) (1 − 2αη (1 − η)) − 2 λ∂β∗O (η)=,∂η
2 (1 − 2η)2 λwhere λ = η (1 − η) (1 − αη) (1 − α (1 − η)). Note that ∂β∗O (η) /∂η > 0 if and only if 1−2αη (1 − η) >√2 λ. Because we have (1 − 2αη (1 − η))2 − 4λ = (1 − 2η)2 > 0, ∂β∗O (η) /∂η > 0 holds for η , 1/2.
For η = 1/2, by using L’Hôpital’s rule, we have limη→1/2 β∗O (η) /η = 1/ (2 − α) > 0. Thus, wealways have ∂β∗O (η) /∂η > 0.
Q.E.D.
29

B.6

Proof of Proposition 2

By applying Assumption 2 and the results in Lemmas 2, 3, and 4 to equation (21), condition (23)can easily be shown to hold.
Q.E.D.

B.7

Proof of Lemma 5

By partially differentiating πk with respect to X, we have
1−µ
1−µ
∂πV
α − µ − 1−α
α − µ − 1−α
∂πO
α
α
=−
X
ψV θ 1−α < −X
ψO θ 1−α =
< 0.
∂X
1−α
1−α
∂X

for ψO < ψV .
Q.E.D.

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32

Variable
X
θH|O
θH|V
θ M|O
θ M|V
φH|O
φH|V
N
NH|O
NH|V
ψO
ψV
βO
βV
πO
πV
σ(·)
α
δ
b
c
µ
τ
γ
β
η
fH|O
fH|V
f M|O
f M|V
p(i)
x(i)
y(i)
z(i)
R(i)

Definition
aggregate production (consumption)
cutoff productivity for domestic outsourcing
cutoff productivity for domestic vertical integration
cutoff productivity for foreign multinational outsourcing
cutoff productivity for foreign multinational vertical integration
fraction (relative prevalence) of domestic outsourcing
fraction (relative prevalence) of domestic vertical integration
total amount of operating firms (including foreign multinational subsidiaries)
amount of domestic firms under outsourcing
amount of domestic firms under vertical integration
degree of two-sided hold-up problem under outsourcing
profit parameter under vertical integration
revenue share under outsourcing
revenue share under vertical integration
profit under outsourcing
profit under vertical integration
revenue share at outside option under outsourcing
degree of product differentiation
shape parameter of Pareto distribution
scale parameter of Pareto distribution
unit labor costshare of consumption spends of each sector
shape parameter of σ(·)
fraction of loss at outside option under outsourcing
bargaining power
firm’s investment intensity
organizational cost of domestic outsourcing
organizational cost of domestic vertical integration
organizational cost of foreign multinational outsourcing
organizational cost of foreign multinational vertical integration
price of final goods for firm iquantity of final goods for firm iquantity of firm’s investments (firm’s inputs) for firm iquantity of intermediate inputs for firm irevenue of firm iTable 1: Variable Definitions

33

Parameter
α
δ
b
c
µ
τ
γ
β
η
fH|O
fH|V
f M|O (before)f M|O (after)
f M|V

Value
0.75
4.25
1
1
0.5
50
0.5
{0.05, 0.10, .., 0.95}{0.05, 0.10, .., 0.95}
0.5
10
1
0.9
20

Table 2: Parameter Values

34

Stage 1

Stage 2

Stage 3

Stage 4

Firms observe  anddecide whether to be
active.

Active firms decideorganizational forms
and contract with
suppliers.

Firms and suppliers supply
inputs.

Firms produce final
products.

Under outsourcing, ex-postbargaining occurs.

Figure 1: Timing of gameR
  (1 −  ( N )) R

 (1 −   ) R(1 −  )(1 −   ) R



1− 

Firm’s outside option
earnings

  ( N ) R
Supplier’s outside
option earnings

O R(1 −  O ) R

Firm’s revenue

Supplier’s revenue

Figure 2: Bargaining over revenue under outsourcing.

35𝜋𝑉 (𝜃, 𝑓𝐻|𝑉 )𝜋𝑂 (𝜃, 𝑓𝐻|𝑂 )𝜋𝑉 (𝜃, 𝑓𝑀|𝑉 )𝜋𝑂 (𝜃, 𝑓𝑀|𝑂 )0−𝑐𝑓𝐻|𝑂−𝑐𝑓𝐻|𝑉−𝑐𝑓𝑀|𝑂−𝑐𝑓𝑀|𝑉

Figure 3: Equilibrium

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 4: Properties of β∗O (η)

36

0.9

1.0

𝛽

𝜃𝐻|𝑉 decreases (𝑁𝐻|𝑉 increases) when 𝑓𝑀|𝑂 decreases.

𝜂𝜃𝐻|𝑉 increases (𝑁𝐻|𝑉 decreases) when 𝑓𝑀|𝑂 decreases.

Figure 5: Changes of θH|V when f M|O decreases.

𝛽𝜙𝐻|𝑉 increases when 𝑓𝑀|𝑂 decreases.
𝜙𝐻|𝑉 decreases when 𝑓𝑀|𝑂 decreases.

Figure 6: Changes of φH|V when f M|O decreases.

37

𝜂

𝛽

𝜃𝐻|𝑂 decreases when 𝑓𝑀|𝑂 decreases.

𝜂𝜃𝐻|𝑂 increases when 𝑓𝑀|𝑂 decreases.

Figure 7: Changes of θH|O when f M|O decreases.

𝛽

𝑁𝐻|𝑂 decreases when 𝑓𝑀|𝑂 decreases.
𝑁𝐻|𝑂 increases when 𝑓𝑀|𝑂 decreases.

Figure 8: Changes of NH|O when f M|O decreases.

38

𝜂

𝛽

𝜃𝐻|𝑉 decreases (𝑁𝐻|𝑉 increases) when 𝑓𝑀|𝑂 decreases.

𝜂𝜃𝐻|𝑉 increases (𝑁𝐻|𝑉 decreases) when 𝑓𝑀|𝑂 decreases.

Figure 9: Changes of θH|V when f M|O decreases ( fH|O = 0.02).

𝛽𝜙𝐻|𝑉 increases when 𝑓𝑀|𝑂 decreases.

𝜂𝜙𝐻|𝑉 decreases when 𝑓𝑀|𝑂 decreases.

Figure 10: Changes of φH|V when f M|O decreases ( fH|O = 0.02).

39

𝛽𝜃𝐻|𝑂 decreases when 𝑓𝑀|𝑂 decreases.

𝜂𝜃𝐻|𝑂 increases when 𝑓𝑀|𝑂 decreases.

Figure 11: Changes of θH|O when f M|O decreases ( fH|O = 0.02)

𝛽𝑁𝐻|𝑂 decreases when 𝑓𝑀|𝑂 decreases.

𝜂

𝑁𝐻|𝑂 increases when 𝑓𝑀|𝑂 decreases.

Figure 12: Changes of NH|O when f M|O decreases ( fH|O = 0.02).

40