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J. Japanese Int. Economies 21 (2007) 365–378 www.elsevier.com/locate/jjie Fragmentation, welfare, and imperfect competition Morihiro Yomogida Faculty of Economics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan Received 1 March 2005; revised 12 March 2006 Available online 3 July 2006 Yomogida, Morihiro—Fragmentation, welfare, and imperfect competition In this paper, we explore the effect of fragmentation of production processes on social welfare in the imperfectly competitive market. We consider a situation in which firms located in a country strategically decide whether they produce at home or move their production overseas. We show that, in such a situation, there exists a Nash equilibrium in which all of the firms move production overseas although domestic production is socially desirable. This implies that “reverse imports” do not necessarily benefit the country. We also discuss the effectiveness of a subsidy for domestic production in improving the social welfare of the country. J. Japanese Int. Economies 21 (3) (2007) 365–378. Faculty of Economics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan. © 2006 Elsevier Inc. All rights reserved. JEL classification: F12; F23 Keywords: Fragmentation; Reverse imports; Production subsidies 1. Introduction In manufacturing industries, production processes that used to be integrated within nations have been disintegrated across countries. Firms in developed countries moved labor-intensive production stages to low-wage countries through foreign direct investment or outsourcing to subcontractors. As a result, the fragmentation of production processes leads to an increase in the so-called reverse imports: goods produced at overseas affiliates or subcontractors are exported * Fax: +81 3 3238 4647. E-mail address: [email protected]. 0889-1583/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jjie.2006.05.001

Fragmentation, welfare, and imperfect competition

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Page 1: Fragmentation, welfare, and imperfect competition

J. Japanese Int. Economies 21 (2007) 365–378

www.elsevier.com/locate/jjie

Fragmentation, welfare, and imperfect competition

Morihiro Yomogida ∗

Faculty of Economics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan

Received 1 March 2005; revised 12 March 2006

Available online 3 July 2006

Yomogida, Morihiro—Fragmentation, welfare, and imperfect competition

In this paper, we explore the effect of fragmentation of production processes on social welfare in theimperfectly competitive market. We consider a situation in which firms located in a country strategicallydecide whether they produce at home or move their production overseas. We show that, in such a situation,there exists a Nash equilibrium in which all of the firms move production overseas although domesticproduction is socially desirable. This implies that “reverse imports” do not necessarily benefit the country.We also discuss the effectiveness of a subsidy for domestic production in improving the social welfare ofthe country. J. Japanese Int. Economies 21 (3) (2007) 365–378. Faculty of Economics, Sophia University,7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan.

© 2006 Elsevier Inc. All rights reserved.

JEL classification: F12; F23

Keywords: Fragmentation; Reverse imports; Production subsidies

1. Introduction

In manufacturing industries, production processes that used to be integrated within nationshave been disintegrated across countries. Firms in developed countries moved labor-intensiveproduction stages to low-wage countries through foreign direct investment or outsourcing tosubcontractors. As a result, the fragmentation of production processes leads to an increase in theso-called reverse imports: goods produced at overseas affiliates or subcontractors are exported

* Fax: +81 3 3238 4647.E-mail address: [email protected].

0889-1583/$ – see front matter © 2006 Elsevier Inc. All rights reserved.doi:10.1016/j.jjie.2006.05.001

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back to developed countries.1 An increase in reverse imports affects the labor markets in devel-oped as well as developing nations. One of recent debates on globalization is concerned aboutthe impact of fragmentation on income distribution within countries. The recent work on inter-national trade examines this issue by using the general equilibrium models that are useful toinvestigate the distributional effect of fragmentation of production processes.2

In addition to its distributional effect, the impact of reverse imports on social welfare is im-portant in the evaluation of the economic aspect of globalization. If a firm decides to move someof its production stages overseas, it must be profitable for the firm to do so. However, the fir-m’s private decision on its production location would not necessarily benefit an economy as awhole. In particular, it is important to examine this issue for developed countries since it is of-ten pointed out that globalization hurts workers in industrialized nations and thus governmentsshould restrict international capital movements and international trade in goods.3 If firms in adeveloped country choose to disintegrate production processes across countries, what is its con-sequence in terms of the social welfare of the country? If fragmentation is not desirable for thecountry as a whole, is it justified for a government to intervene in the firms’ choice of productionlocations?

In this paper, we develop a simple model with imperfect competition to investigate these ques-tions. Firms locate their headquarters in a country and decide whether to produce at home or tomove production overseas by FDI or outsourcing. Fragmentation provides savings in productioncosts for firms, but they must incur an additional fixed cost to coordinate the activities of foreignproduction. In addition to this tradeoff, firms have to incur transport costs to ship their products tothe home market if they produce overseas. In this setting, the firms’ optimal choice of productionlocations may result in an undesirable outcome for the country as a whole. In fact, we show thattwo types of Nash equilibria exist. First, fragmentation is socially desirable but firms choose tointegrate their production at home. Second, firms choose fragmentation but domestic productionis desirable from the social viewpoint of the country. The latter result implies that reverse importsdo not necessarily benefit the country. These results may also provide a rationale for a govern-ment to intervene in the firms’ choice of production locations. We discuss the effectiveness of asubsidy for domestic production in improving the social welfare of the country.4

This paper is closely related to Jones and Kierzkowski (1990) and Jones (2000). They de-velop a simple model to show that a key to fragmentation of production processes is a reductionin communication costs. Fragmentation provides savings in production costs but it requires anadditional cost to coordinate overseas production activities. The development of communication

1 For instance, over the past decade, there was a significant increase in the number of overseas affiliates of Japanesecompanies in the East Asian region. In addition, during this period, there was a noticeable increase in the reverse importsof manufactured goods. “Furthermore, looking at the share of exports to Japan in extra-regional exports in the Asianregion, there is a noticeable increase in the rates of exports to Japan for all industries except iron and steel, which showsthe expanding tendency of the so-called reverse imports (Ministry of Economy, Trade, and Industry, 2003, p. 140).”

2 See Feenstra (1998), Jones (2000), Arndt and Kierzkowski (2001), and Kohler (2004) for the recent development inthe work on this topic.

3 Charles Schumer (the senior Senator from New York state) and Paul Craig Roberts (2004) state: “The question todayis whether the case for free trade made two centuries ago is undermined by the changes now evident in the modern globaleconomy. . . . American jobs are being lost not to competition from foreign companies, but to multinational corporations,often with American roots, that are cutting costs by shifting operations to low-wage countries.”

4 In the literature on industrial organization, it is well known that firms’ optimal investments for process innovation donot necessarily generate a socially desirable outcome. For instance, see Arrow (1962), Dasgupta and Stiglitz (1980), andMills and Smith (1996). Nevertheless, none of them is related to fragmentation of production processes.

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technology is a driving force for fragmentation since it significantly reduces costs to coordinateand/or monitor foreign production activities.5 In addition, Harris (1995) points out that commu-nication costs are fixed costs rather than variable costs for firms. This paper incorporates theidea developed by Jones and Kierzkowski into a model in which firms strategically choose thelocation of production.

There is a recent work on strategic outsourcing and/or foreign direct investment.6 Chen etal. (2004) focus on a domestic firm’s choice of purchasing an intermediate input from a foreignfirm that is the domestic firm’s rival in the final good market. They show that the outsourcinghas a collusive effect that could raise the prices of both intermediate and final goods. Ekholmet al. (2003) point out the importance of export-platform foreign direct investment. They showthat firms in the north make FDI in the south to export their outputs to third countries ratherthan export back to their home countries. This paper complements the existing work in that itexamines the welfare properties of the fragmentation of production processes.7

The rest of this paper is organized as follows. In Section 2, we use a monopoly model to showthat a reduction in a transport cost makes fragmentation more profitable for the monopolist,and there is a range of the transport cost in which the monopolist chooses domestic productiondespite fragmentation being socially desirable. In Section 3, we extend the monopoly model toa duopoly setting in which firms strategically choose the location of production. In contrast tothe monopoly case, we show that both firms strategically choose fragmentation despite domesticproduction being socially desirable. This finding implies that a government can use productionsubsidies to prevent the firms from choosing socially undesirable fragmentation. In Section 4, weintroduce a government into the model so that we can examine the effectiveness of a subsidy fordomestic production in improving the social welfare of the country. In Section 5, we close thispaper with concluding remarks.

2. A monopoly model

In this section, we examine the monopolist’s optimal choice of its production location. Themonopoly model is useful to introduce the basic idea of fragmentation of a production process.It is also a benchmark case with which we shall compare the duopoly setting. The comparisonis useful to clarify the role of strategic interactions between firms in the choice of productionlocations.

Let us consider an economy with two countries, Home and Foreign. There is an industryin which a monopolist produces a product, X. The monopolist locates headquarters at Home,but it can choose the location of its production. Whether it produces X at Home or at Foreigndepends on many factors, such as production costs, transport costs, and government policies.Here, we focus on one aspect: a difference in production costs. If labor costs at Foreign arelower than those at Home, the monopolist may want to move its production to Foreign by FDIor outsourcing.8 However, it would incur an additional cost to coordinate production activities at

5 Long et al. (2004) also explicitly incorporate services into a trade model and show that the growth of the servicesector facilitates fragmentation of production blocks across countries.

6 Another approach to outsourcing and/or foreign direct investment is based on the theory of firms. It emphasizes therole of transaction costs and incomplete contracts. For example, see McLaren (2000), Grossman and Helpman (2002),and Antras (2003) among others.

7 Ishikawa and Komoriya (2004) examine some issues on outsourcing in a model with cost heterogeneity of firms.8 It is an important issue to examine whether firms choose outsourcing or FDI. In this paper, we focus on the firms’

choice of production locations, and thus we abstain from investigating the firms’ choice of organizational structures.

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Foreign. Therefore, there is a tradeoff between low labor costs and high coordination costs. Tomodel this trade-off, let us consider the following cost function:

C(x) ={

cx if X is produced at Home,c∗x + f if X is produced at Foreign,

where c and c∗ are marginal production costs at Home and Foreign, respectively, and f is aconstant fixed cost that represents a coordination cost. We assume that c > c∗ > 0 and f > 0.This implies that a production cost at Foreign could be lower than that at Home due to a differencein variable costs.

Now, we turn to the demand side. Suppose that product X is consumed only at Home. Thus,if its production moves to Foreign, all outputs are exported back to Home. Preferences are quasi-linear and the demand for X is represented by a linear demand function:

p = a − bD,

where p is the price of good X, D is its quantity of demand, and a, b > 0.Given the demand and cost functions, we can derive the profit of the monopolist. If it produces

X at Home, the profit is px − cx. If the monopolist chooses to produce X at Foreign, it has toincur a transport cost as well as a coordination cost. We assume that the monopolist incurs atransport cost t (> 0) to ship one unit of X from Foreign to Home. Then, the profit obtainedfrom Foreign production is px − (c∗ + t)x − f .

We can solve the profit maximization problem backward. For each production location, wederive the optimal output and the market price. Let Π(θ) ≡ maxx(a − bx − θ)x. Substituting theequilibrium output x(θ) = (a − θ)/2b into Π(θ) = bx(θ)2, we obtain

Π(θ) = (a − θ)2

4b.

If X is produced at Home, the profit for the monopolist is Π(c). If it chooses to produce X atForeign, its profit is Π(c∗ + t) − f . Clearly, if t < c − c∗, then Π(c) < Π(c∗ + t). We assumethat this condition, t < c − c∗, is met so that the monopolist could choose to produce at Foreign.Under this condition and Π(c) < Π(c∗) − f , there is a critical value tπ ∈ (0, c − c∗) with

Π(c) = Π(c∗ + tπ ) − f.

If t > tπ , then the monopolist produces X at Home. Thus, the production process of X isintegrated at Home. If t < tπ , then the monopolist moves its production to Foreign, and thefragmentation of the production process takes place.

Now we turn to the evaluation of the welfare property of fragmentation. Foreign productionclearly benefits Home consumers due to a fall in the price of X. At the same time, Home mustincur a coordination cost f . Thus, whether fragmentation benefits Home or not depends on therelative size of these two effects. Consider the following function:

W(θ) ≡x(θ)∫0

(a − bz)dz − θx(θ) = 3(a − θ)2

8b.

If the production of X is integrated at home, the welfare of Home is W(c). If the productionof X moves to Foreign, then the welfare of Home is W(c∗ + t) − f . Since W(·) is monotoni-cally decreasing, W(c) < W(c∗ + t). Thus, if W(c) < W(c∗) − f , then there is a critical value

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tw ∈ (0, c − c∗) with

W(c) = W(c∗ + tw) − f.

If t < tw , then social welfare obtained from Foreign production is higher than that from Homeproduction. If t > tw , domestic production is preferred to foreign production in terms of Homewelfare.

Notice that Π(c) < Π(c∗) − f implies W(c) < W(c∗) − f because W(c∗) − W(c) =CS(c∗) − CS(c) + Π(c∗) − Π(c) > Π(c∗) − Π(c) where CS(θ) is a consumer surplus witha marginal cost θ . In the following analysis, we assume that the demand and cost parameters aresuch that Π(c) < Π(c∗) − f is satisfied. This assumption and t < c − c∗ jointly guarantee theexistence of tπ and tw . In general, tπ is not equal to tw . Thus, there is a possibility that a privatedecision by the monopolist may lead to a socially undesirable outcome as the following resultstates:

Proposition 1. The critical value tπ of transport costs that determines the monopolist’s decisionof production location is smaller than the critical value tw that determines the socially desirablelocation of production. Thus, if t ∈ (tπ , tw), then the monopolist chooses to produce X at Home,although foreign production is socially desirable.

Proof. Note that

CS(c) − CS(c∗ + tw) = Π(c∗ + tw) − f − Π(c).

The left-hand side is negative since the market price is increasing with the marginal cost. Thus,

Π(c∗ + tw) − f − Π(c) < 0.

On the other hand, tπ satisfies Π(c∗ + tπ )−f = Π(c). Substituting this condition into the aboveinequality, we have

Π(c∗ + tw) < Π(c∗ + tπ ).

Since Π(·) is decreasing, tπ < tw . �The intuition for this result is straightforward. The foreign production benefits Home con-

sumers since cost savings in production lead to the lower market price. The monopolist doesnot take into account this effect when it decides the location of its production. Thus, there is therange of the transport cost, at which fragmentation is socially desirable, but it is more profitablefor the monopolist to integrate the production process domestically.

3. Strategic fragmentation

Now let us extend the previous model to a setting with two Home firms. Firms with identicalcost structures produce a homogeneous good. In the first stage, they simultaneously determinethe location of production. In the second stage, they choose their outputs in Cournot fashion.Using this extended model, we examine strategic interactions between firms in the choice ofproduction locations.

Solving the firm’s problem backward, the profit of each firm can be represented as a functionof marginal costs. Let x(θ, θ ′) denote the equilibrium output of the firm with its own marginal

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cost θ and its rival’s marginal cost θ ′. It can be shown that

x(θ, θ ′) = 2(a − θ) − (a − θ ′)3b

.

Then, each firm’s surplus, when its marginal cost is θ and the rival’s is θ ′, is represented as

Π(θ, θ ′) ≡ [p(x(θ, θ ′) + x(θ ′, θ)

) − θ]x(θ, θ ′).

Consider the following game:

I F

I Π(c, c), Π(c, c) Π(c, c∗ + t), Π(c∗ + t, c) − f

F Π(c∗ + t, c) − f , Π(c, c∗ + t) Π(c∗ + t, c∗ + t) − f , Π(c∗ + t, c∗ + t) − f

Here, I denotes “integration” and F denotes “fragmentation.” If Π(c∗ + t, c) − Π(c, c) > f ,then it is optimal for the firm to choose fragmentation given the rival’s choice of integration.Similarly, if Π(c∗ + t, c∗ + t) − Π(c, c∗ + t) > f , then the firm prefers fragmentation to in-tegration given the rival’s choice of fragmentation. Figure 1 shows the Nash equilibrium of thefirms’ choice of a location. Since a reduction in the transport cost makes fragmentation moreprofitable, yFI (t) = Π(c∗ + t, c) − Π(c, c) and yFF (t) = Π(c∗ + t, c∗ + t) − Π(c, c∗ + t)

are drawn as downward sloping curves in Fig. 1. Notice that for each t ∈ [0, c − c∗), we have

Fig. 1. The effects of t and f on the firm’s strategic choice of a production location.

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Π(c∗ + t, c)− Π(c, c) > Π(c∗ + t, c∗ + t)− Π(c, c∗ + t).9 This means that it is more profitableto switch to F from I if the rival still chooses integration than if it already chooses overseasproduction. Suppose that the fixed cost is greater than Π(c∗, c)− Π(c, c). Then, it is never prof-itable for any firms to produce X overseas. Thus, both firms would choose integration at a Nashequilibrium. If the fixed cost is smaller than Π(c∗, c) − Π(c, c), then firms’ optimal strategiesdepend on transport costs as well as fixed coordination costs.

As in Fig. 1, let tL and tH be such that Π(c∗ + tL, c∗ + tL) − Π(c, c∗ + tL) = f andΠ(c∗ + tH , c) − Π(c, c) = f . If the transport cost is high enough in the sense that t > tH ,then it is optimal for both firms to choose integration. As the transport cost declines, it is moreprofitable for one firm to switch to fragmentation. There is a range of the transport cost in whichasymmetric Nash equilibrium appears. If t ∈ (tL, tH ), then one firm optimally chooses fragmen-tation given the other one choosing integration. In this range, it is not profitable for one firmto switch to fragmentation if the rival has already produced overseas. Then, (F, I ) and (I,F )

are Nash equilibria. If the transport cost is much smaller and t < tL, then both firms optimallychoose fragmentation. These observations are summarized in the next lemma.

Lemma 1. If t < c− c∗, then the Nash equilibrium choices of firms’ production locations dependon t and f in the following manner:

(1) if f > Π(c∗ + t, c) − Π(c, c), then both firms optimally choose to produce X at Home;(2) if Π(c∗ + t, c∗ + t) − Π(c, c∗ + t) < f < Π(c∗ + t, c) − Π(c, c), then one firm chooses to

move the production of X overseas and the other firm chooses to integrate the production ofX at Home;

(3) if f < Π(c∗ + t, c∗ + t) − Π(c, c∗ + t), then both firms choose fragmentation and produceX overseas.

3.1. The welfare properties of strategic fragmentation

In this section, we shall evaluate the welfare properties of strategic fragmentation. In themonopoly case, the monopolist might choose domestic production even though fragmentation isdesirable from the social viewpoint of Home. The similar result is obtained in the duopoly modelmainly because firms do not take into account the positive effect of fragmentation on consumersurplus. In addition to this result, in the duopoly model, both firms might choose fragmentationeven though domestic production is still desirable from the social viewpoint of Home. This iscaused by strategic interactions between firms, and thus the monopoly setting does not have sucha feature.

It is possible to derive the social welfare of Home as a function of marginal costs. For eachpair θ, θ ′ ∈ {c, c∗ + t}, let

CS(θ, θ ′) ≡ (2a − θ − θ ′)2

18b,

W (θ, θ ′) ≡ CS(θ, θ ′) + Π(θ, θ ′) + Π(θ ′, θ).

If firms choose to integrate the production process at Home, then the welfare of Home is W (c, c).Similarly, if one firm chooses fragmentation and the other still produces at Home, then the social

9 See Appendix A for the proof.

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Fig. 2. The welfare properties of strategic fragmentation.

welfare of Home is W (c∗ + t, c)−f . If both firms choose fragmentation, then the social welfareof Home is W (c∗ + t, c∗ + t) − 2f . A change in the home welfare caused by fragmentationcrucially depends on the transport cost and the coordination cost. If W (c∗ + t, c)− W (c, c) > f ,then fragmentation by one firm, when the other one choosing domestic production, raises thesocial welfare of Home. Similarly, for the given choice of foreign production by one firm, frag-mentation by the other firm benefits Home if W (c∗ + t, c∗ + t) − W (c∗ + t, c) > f .

Figure 2 shows a change in Home welfare caused by fragmentation. Since a reduction in thetransport cost increases gains from fragmentation for Home, wFI (t) = W (c∗ + t, c) − W (c, c)

and wFF (t) = W (c∗ + t, c∗ + t)− W (c∗ + t, c) are drawn as downward sloping curves. Observethat for each t ∈ [0, c − c∗), we have W (c∗ + t, c)− W (c, c) > W(c∗ + t, c∗ + t)− W (c∗ + t, c).This implies that gains from fragmentation for Home is larger when only one firm starts produc-ing abroad than those when one firm has already chosen fragmentation and the other one movestheir production overseas.10

10 A switch in the production regime from (F, I ) to (F,F ) provides a larger increase in consumer surplus than thatfrom (I, I ) to (F, I ) because a reduction in the price is greater and the level of output is larger in the former than in thelatter. Contrary to this, the negative effect of fragmentation on the profit of the firm remaining at home is greater if theproduction regime shifts from (F, I ) to (F,F ) than if it does from (I, I ) to (F, I ). The overall effect of fragmentationon W depends on the relative size of these two effects. See Appendix A for the proof.

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Figure 2 also shows that firms’ optimal choice of production locations is not necessarily bestfrom the viewpoint of the social welfare of Home. As in Fig. 2, let t ′L and t ′H be such thatW (c∗ + t ′L, c∗ + t ′L) − W (c∗ + t ′L, c) = f and W (c∗ + t ′H , c) − W (c, c) = f . If t ∈ (tH , t ′H ),then firms could optimally choose to produce at Home even though fragmentation is sociallydesirable. The intuition for this result is similar to that obtained in the monopoly model. Firmsdo not take into account the positive effect of fragmentation on consumer surplus.11

If the transport cost falls further more, then both firms move production overseas. Ift ∈ (t ′L, tL), then both firms could optimally choose fragmentation despite domestic productionbeing socially desirable. That is, the socially best production regime for Home is (F, I ), but bothfirms choose fragmentation at the unique Nash equilibrium.

This result originates from strategic interactions between firms. In the Cournot setting, thefirm switching to fragmentation always gains at the expense of the rival. The reduction in therival’s profit has a negative impact on the social welfare of Home. However, the firm switchingto fragmentation from integration does not take into account this negative effect on the rival’sprofit. This strategic effect is a cause for the outcome in which the firm’s choice of a productionlocation might be socially undesirable.

Such fragmentation has three effects on the welfare of Home: a positive effect on consumersurplus, a positive effect on the profit of the firm switching to fragmentation, and a negative effecton the profit of the firm already choosing fragmentation. The reason for socially undesirablefragmentation can be seen as follows. When one firm has already chosen fragmentation, the otherfirm’s choice of fragmentation shifts production from the more efficient firm to the less efficientone. Since the more efficient firm has the higher markup, a fall in its output may reduce producersurplus in the industry. This negative effect in producer surplus can dominate the positive effectin consumer surplus.12 Therefore, socially undesirable fragmentation can arise. This result canbe stated as follows. (See Appendix A for the proof.)

Proposition 2. When one firm has already chosen fragmentation, the other firm’s choice of frag-mentation may not be socially desirable.

Proposition 2 implies that reverse imports do not necessarily benefit Home. If t ∈ (tL, tH ),then one firm has already chosen fragmentation but the other has stayed at home. The equilibriumis desirable in the social viewpoint of Home. When the transport cost falls and t ∈ (t ′L, tL), thefirm that used to stay at home moves production overseas and thus there is an increase in reverseimports. This change in the volume of imports does not benefit Home since (F, I ) is better than(F,F ) in terms of the social welfare.

4. Production subsidies

Proposition 2 suggests that the home government should use subsidy policies to induce thefirms to choose the socially ideal locations of production. There are some policy options. Let usexamine the simplest policy scheme: lump-sum subsidies.

11 This fragmentation has three different effects on the social welfare of Home: a positive effect on consumer surplus, apositive effect on the profit of the firm switching to fragmentation, and a negative effect on the profit of the firm remainingat home. The sum of the positive effect on consumer surplus and the negative effect on the profit of the firm choosingintegration is positive. This net positive effect makes a social welfare gain greater than a firm’s profit increase, and thisdifference is not taken into account by the firm in its decision of switching to fragmentation.12 This explanation draws on Lahiri and Ono (1988).

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4.1. Lump-sum production subsidies

Suppose that the home government provides a lump-sum subsidy for the firm if it chooses toproduce X at Home. Let s (> 0) be the fixed size of the lump-sum subsidy. Then, the firm hasto incur opportunity costs of losing the subsidy as well as the fixed coordination cost if it movesits production overseas. Given the rival’s choice of the production location, the firm gains fromfragmentation if

Π(c∗ + t, θ ′) − Π(c, θ ′) > f + s,

where θ ′ ∈ {c, c∗ + t}. Figure 3 shows the effects of the lump-sum subsidy on the firms’ choice ofproduction locations. As in Fig. 3, let t ′′L and t ′′H be such that Π(c∗+ t ′′L, c∗+ t ′′L)−Π(c, c∗+ t ′′L) =f + s and Π(c∗ + t ′′H , c) − Π(c, c) = f + s. If t ∈ [0, t ′′L), then the unique Nash equilibrium is(F,F ). The subsidy reduces this range of the transport cost. Since it is financed by a lump-sumtax, Home incurs the same size of the fixed cost f as before the subsidy. Thus, the critical valuest ′L and t ′H remain the same.

These observations imply that the subsidy reduces the possibility of socially undesirablefragmentation. Without the production subsidy, the undesirable fragmentation would occur ift ∈ (t ′L, tL). After the subsidy scheme is implemented at Home, the range shrinks to (t ′L, t ′′L).

Fig. 3. The effects of the lump-sum subsidies on the firm’s strategic choice of a production location.

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The subsidy scheme might be effective to prevent the firms from choosing socially undesirablefragmentation.

Nonetheless, the subsidy for domestic production is not necessarily welfare improving. Ift ∈ (t ′′H , t ′H ), then (F, I ) and (I,F ) are socially desirable choices of production locations, but theNash equilibrium is (I, I ). The implementation of the production subsidy might worse the situa-tion by increasing the possibility of this outcome being obtained. For instance, if t ∈ (t ′′H , tH ) andthere is no production subsidy, then the resulting Nash equilibria (F, I ) and (I,F ) are sociallydesirable. After the production subsidy, the Nash equilibrium turns out to be (I, I ), which isclearly not an social optimum. Using the production subsidy, the home government might try toprevent firms from choosing socially undesirable fragmentation. However, as this example sug-gests, there is a risk of inducing the firms to choose the socially undesirable domestic production.

5. Concluding remarks

In this paper, we examine the welfare properties of fragmentation of a production process inthe imperfectly competitive market. The firm’s optimal choice of production locations does notnecessarily result in the best outcome for the economy as a whole. In the monopoly setting, thefirm does not take into account the positive effect of fragmentation on consumer surplus, andas a result, the firm chooses to integrate its production process at Home despite the desirabilityof overseas production in terms of the social welfare of Home. In the duopoly setting, the firmgains from fragmentation at the expense of the rival. The negative impact of fragmentation on thedomestic rivals’s profit reduces the social welfare of Home, but its effect is not taken into accountby the firm in choosing to move production overseas. As a result, there is Nash equilibrium inwhich all of the firms choose fragmentation but the equilibrium outcome is not desirable fromthe social viewpoint of Home. This result also implies that an increase in reverse imports due tothe fragmentation does not necessarily raise the welfare of Home.

These results would provide a rationale for a government to intervene in the firm’s privatechoice of production locations. In the duopoly setting, the government of Home can use the lump-sum subsidy for domestic production to achieve the socially desirable equilibrium outcome. Onthe other hand, the subsidy may induce all of the firms to produce at Home despite the socialdesirability of fragmentation by one firm. This can be caused by the policy maker’s lack ofinformation about the firms’ cost structures. In this sense, policymakers should be cautious aboutintervening in the firm’s choice of production locations.

We focus on strategic interactions between firms that locate their headquarters in the samecountry. In addition, firms compete only in their home market, and thus, all of the outputs pro-duced overseas are exported back to the home market. Empirical evidences suggest that firms indeveloped nations move their production to low-wage countries and export the outputs producedthere to other developed countries as well as their home countries. For the investigation of thisaspect, we need to develop a model in which firms locating headquarters in different countrieschoose whether to produce at their home nations or to move production to low-wage countries.In this situation, governments may want to intervene strategically in the firms’ choice of produc-tion locations. It is a future research agenda to analyze strategic government policy for the firms’choice of production locations.

In this paper, we use a partial equilibrium setting with imperfect competition. This allows usto focus on the effect of fragmentation on the efficiency of resource allocation within an industry.To examine the effect of fragmentation on inter-industry resource allocation, we need to extendthe present model to a general equilibrium setting. Recently, Neary (2003) introduces a tractable

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376 M. Yomogida / J. Japanese Int. Economies 21 (2007) 365–378

model of oligopoly in general equilibrium. Integrating the present model to his framework is apromising way to examine the welfare effect of strategic fragmentation in a general equilibriummodel. However, it is beyond the scope of this paper and left for our future work.

Acknowledgments

I thank Kenzo Abe, Richard Baldwin, Reiko Aoki, Toru Hokari, Jota Ishikawa, Ngo Van Long,Michihiro Ohyama, Takao Okawa, and Laixun Zhao for their valuable comments. I also thankanonymous referees for their useful suggestions.

Appendix A

First, we prove the following claim stated in Section 3:

Claim. If t < c − c∗, then Π(c∗ + t, c) − Π(c, c) > Π(c∗ + t, c∗ + t) − Π(c, c∗ + t).

Proof. Recall that for each pair θ, θ ′ ∈ {c, c∗ + t},

x(θ, θ ′) = 2(a − θ) − (a − θ ′)3b

,

Π(θ, θ ′) = bx(θ, θ ′)2.

Thus,

yFI (t) = [2(a − c∗ − t) − (a − c)]2

9b− (a − c)2

9b,

yFF (t) = (a − c∗ − t)2

9b− [2(a − c) − (a − c∗ − t)]2

9b.

Note that for all t ∈ (0, c − c∗),dyFI (t)

dt= −4

3x(c∗ + t, c) < 0,

dyFF (t)

dt= −4

3x(c, c) < 0.

Since x(·,·) is strictly decreasing in the first argument, we have∣∣∣∣dyFI (t)

dt

∣∣∣∣ �∣∣∣∣dyFF (t)

dt

∣∣∣∣,where equality holds if and only if t = c∗ − c. Note that yFI (c − c∗) = yFF (c − c∗). Thus, ift < c − c∗, then

Π(c∗ + t, c) − Π(c, c) = yFI (t) > yFF (t) = Π(c∗ + t, c∗ + t) − Π(c, c∗ + t). �Next, we provide the proof of Proposition 2.

Proof of Proposition 2. We show that if t < c − c∗, then wFI (t) > yFI (t) > yFF (t) > wFF (t).Let θ, θ ′ ∈ {c, c∗ + t}. Substituting the explicit formula of x(θ ′, θ) + x(θ, θ ′) into the in-

verse demand p = a − b(x(θ, θ ′)+ x(θ, θ ′)), we derive the equilibrium market price, p(θ, θ ′) ≡

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M. Yomogida / J. Japanese Int. Economies 21 (2007) 365–378 377

(a + θ + θ ′)/3. Then, the consumer surplus is

CS(θ, θ ′) = [a − p(θ, θ ′)]2

2b.

Let vFI (t) ≡ CS(c∗ + t, c)− CS(c, c) and vFF (t) ≡ CS(c∗ + t, c∗ + t)− CS(c, c∗ + t). Note thatfor all t ∈ (0, c − c∗),

dvFI (t)

dt= −x(c∗ + t, c) + x(c, c∗ + t)

3< 0,

dvFF (t)

dt= −4x(c∗ + t, c∗ + t)

3− dvFI (t)

dt< 0.

It can be easily shown that∣∣∣∣dvFF (t)

dt

∣∣∣∣ −∣∣∣∣dvFI (t)

dt

∣∣∣∣ = x(c∗ + t, c∗ + t) − x(c, c)

3> 0.

This implies that fragmentation provides the larger benefits for consumers if the productionregime changes to (F,F ) from (F, I ) than if it switches to (F, I ) from (I, I ).

Next, we derive a change in the profit of the firm when its rival switches to fragmentation. LetzFI (t) ≡ Π(c, c∗ + t) − Π(c, c) and zFF (t) ≡ Π(c∗ + t, c∗ + t) − Π(c∗ + t, c). Then, for allt ∈ (0, c − c∗),

dzFI (t)

dt= 2x(c, c∗ + t)

3> 0,

dzFF (t)

dt= 2[2x(c∗ + t, c) − x(c∗ + t, c∗ + t)]

3> 0.

It can be easily shown that

dzFI (t)

dt<

dzFF (t)

dt.

This implies that a loss for the firm caused by the rival’s choice of F is greater if the firm choosesfragmentation than if it chooses integration.

Now, it is ready to examine a change in the social welfare in response to a shift in the produc-tion regime. Note that for all t ∈ (0, c − c∗),

dwFI (t)

dt= dvFI (t)

dt+ dyFI (t)

dt+ dzFI (t)

dt

= −1

3

[x(c∗ + t, c) − x(c, c∗ + t)

] + dyFI (t)

dt< 0.

It can be shown that if t � c − c∗, then x(c∗ + t, c) � x(c, c∗ + t). Thus, for all t ∈ (0, c − c∗],∣∣∣∣dwFI (t)

dt

∣∣∣∣ �∣∣∣∣dyFI (t)

dt

∣∣∣∣,where equality holds if and only if t = c−c∗. This result with wFI (c−c∗) = yFI (c−c∗) impliesthat

(A.1)wFI (t) > yFI (t) if t < c − c∗.

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378 M. Yomogida / J. Japanese Int. Economies 21 (2007) 365–378

Similarly, note that for all t ∈ (0, c − c∗),dwFF (t)

dt= dvFF (t)

dt+ dyFF (t)

dt+ dzFF (t)

dt

= 1

3

[x(c∗ + t, c∗ + t) − x(c, c)

] + dyFF (t)

dt

= −[x(c, c∗ + t) + x(c, c)

3

]< 0.

It can be easily shown that if t � c − c∗, then x(c∗ + t, c∗ + t) � x(c, c). Thus, for allt ∈ (0, c − c∗],∣∣∣∣dwFF (t)

dt

∣∣∣∣ �∣∣∣∣dyFF (t)

dt

∣∣∣∣,where equality holds if and only if t = c − c∗. This result with wFF (c − c∗) = yFF (c − c∗)implies that

(A.2)yFF (t) > wFF (t) if t < c − c∗.

As shown in the previous proof, if t < c − c∗, then yFI (t) > yFF (t). Using this result togetherwith (A.1) and (A.2), it can be shown that if t < c − c∗, then

wFI (t) > yFI (t) > yFF (t) > wFF (t). �References

Antras, P., 2003. Firms, contracts, and trade structure. Quart. J. Econ. 118, 1375–1418.Arndt, S., Kierzkowski, H., 2001. Fragmentation: New Production and Trade Patterns of the World Economy. Oxford

Univ. Press, Oxford, UK.Arrow, K.J., 1962. Economic welfare and the allocation of resources for invention. In: Nelson, R. (Ed.), The Rate and

Direction of Inventive Activity: Economic and Social Factors. Princeton Univ. Press.Chen, Y., Ishikawa, J., Yu, Z., 2004. Trade liberalization and strategic outsourcing. J. Int. Econ. 63, 419–436.Dasgupta, P., Stiglitz, J., 1980. Industrial structure and the nature of innovative activities. Econ. J. 358, 266–293.Ekholm, K., Forslid, R., Markusen, J., 2003. Export-platform foreign direct investment. NBER Working Paper No. 9517.Feenstra, R., 1998. Integration of trade and disintegration of production in the global economy. J. Econ. Perspect. 12,

31–50.Grossman, G., Helpman, E., 2002. Integration versus outsourcing in industry equilibrium. Quart. J. Econ. 117, 85–120.Harris, R., 1995. Trade and communication costs. Canad. J. Econ. 28, S46–S75.Ishikawa, J., Komoriya, Y., 2004. Reverse import and hollowing out: The case of heterogeneous firms. Mimeo. Hitotsub-

ashi University.Jones, R., 2000. Globalization and the Theory of Input Trade. MIT Press, Cambridge, MA.Jones, R., Kierzkowski, H., 1990. The role of services in production and international trade: A theoretical framework. In:

Jones, R., Krueger, A. (Eds.), The Political Economy of International Trade. Basil Blackwell, Oxford, pp. 31–48.Kohler, W., 2004. International outsourcing and factor prices with multistage production. Econ. J. 114, C166-85.Lahiri, S., Ono, Y., 1988. Helping minor firms reduce welfare. Econ. J. 98, 1199–1202.Long, N.V., Riezman, R., Soubeyran, A., 2004. Fragmentation and services, unpublished working paper.McLaren, J., 2000. Globalization and vertical structure. Amer. Econ. Rev. 90, 1239–1254.Mills, D., Smith, W., 1996. It pays to be different: Endogenous heterogeneity of firms in an oligopoly. Int. J. Ind. Org. 14,

317–329.Ministry of Economy, Industry, and Trade in Japan, 2003. White Paper on International Trade.Neary, J.P., 2003. Globalization and market structure. J. Europ. Econ. Assoc. 1, 245–271.Schumer, C., Roberts, P.C., 2004. Second thoughts on free trade. New York Times.