FDI and Technology Spillovers under

Vertical Product Differentiation∗

Hodaka Morita†and Xuan Nguyen‡

May 11, 2011

∗This paper is a substantially revised version of Chapter 2 of Nguyen’s PhD thesis, Nguyen (2011).We thank Simon Anderson, Eric Bond, Andrew Daughety, Rod Falvey, Taiji Furusawa, Arghya Ghosh,Jota Ishikawa, Tina Kao, Oliver Lorz, James Markusen, Laura Meriluoto, Larry Qiu, Martin Richardson,Raymond Riezman, Kamal Saggi, Nicolas Schmitt, Frank Stahler, Don Wright, participants of seminarat Hitotsubashi University, Kobe University, University of New South Wales, University of Tokyo, and atAustralasian Economic Theory Workshop 2009, Otago Workshop in International Trade 2009, Asia PacificTrade Seminars 2009, Econometric Society Australasian Meeting 2009, Fall 2010 Midwest International TradeMeeting, and 2010 PhD Conference in Economics and Business for helpful comments. Hiroshi Mukunoki andAlireza Naghavi gave a thorough reading and provided many advice that led to a substantial improvementof the original manuscript.

†Corresponding author: School of Economics, Australian School of Business, University of NewSouth Wales, Sydney 2052 Australia; Tel: (+61) 2 9385 3341; Fax: (+61) 2 9313 6337; Email:H.Morita@unsw.edu.au

‡Deakin Graduate School of Business, Faculty of Business and Law, Deakin University, VIC 3125 Aus-tralia; Tel: (+61) 3 9251 7798; Fax: (+61) 3 9244 5533; Email: Xuan.Nguyen@deakin.edu.au

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FDI and Technology Spillovers under Vertical Product Differentiation

Abstract

This paper explores consequences of technology spillovers that is accompanied by aNorthern firm’s FDI in the South and enhances a Southern firm’s product quality. Tothis end, we explore an international duopoly model of vertical product differentiationin which a Northern firm and a Southern firm compete in the Southern market. Byundertaking FDI, the Northern firm can reduce its production costs and avoid tariff,but its advanced technology spills over to the Southern firm and enhances the Southernfirm’s product quality. We find that, under certain range of parameterizations, theNorthern firm strategically reduces the level of its product quality upon FDI. Insuch cases, FDI can hurt the South and, at the same time, the spillover rate thatmaximizes global welfare could be positive but lower than South-optimal level. Thisresults support the roles played by the World Trade Organization (WTO) in reconcilingthe North-South conflict concerning Intellectual Property Rights.

JEL classification: F12, F13, F21, L13

Keywords: Technology spillovers, Vertical Product Differentiation, Trade, Welfare

1 Introduction

Foreign direct investment (FDI) induces technology spillovers, which often enhances local

firms’ quality standards. That is, if a foreign firm builds its manufacturing plant in a

less developed country, local competitors can enhance their product quality by learning the

foreign firm’s performance, or by employing workers from the foreign firm.1 Throughout

this paper, this phenomenon is referred to as quality-enhancing technology spillovers. For

example, Chery Automobile, a Chinese automaker, hired a number of engineers from the

Nissan-Dongfeng joint venture which was established upon Nissan’s FDI in China. The

resulting technology spillovers through these engineers have significantly improved Chery’s

car quality (Luo, 2005). Similarly, the investment of U.S. software firms in Bangalore since

1984 has also created technological and information externalities to Indian software firms.

Consequently, this has enabled the local firms to produce softwares which meet international

standard (Patibandla, Kapur & Petersen 1999, Pack & Saggi 2006). In section 2, we present

real-world examples of quality-enhancing technology spillovers in more detail.

1In World Investment Report, UNCTAD (1997) argues that transnational corporations (TNCs) are oftenmore cost-efficient and produce higher quality products than domestic firms in developing countries. Tosurvive, domestic firms need to learn or imitate production performance of TNCs. This leads to productionefficiency gains in which domestic manufacturers have to offer less expensive products or improve quality towin consumers back from the TNCs.

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In anticipation of the potential benefits of technology spillovers, Southern governments

often induce FDI in industries where local firms need to learn advanced technology and

know-how from foreign firms. In the case of Chinese automobile industry, Chinese govern-

ment imposed high tariff rates on imports of foreign cars to induce foreign automakers to

undertake FDI in China.2 In a similar move, Indian government promoted FDI in software

sector by enforcing the copyright act. This has strengthened the Intellectual Property Rights

(IPR) protection for both local and foreign firms upon production in India.3 These types

of policy have proved to be sucessful in attracting FDI into a number of industries where

local firms need to learn technologies from foreign firms.

Despite the important interconnections among technology spillovers, FDI, and IPR pro-

tection and trade policy, to the best of our knowledge, no papers have previously explored

theoretical models that capture this interconnection in the context of quality-enhancing

spillovers. We aim to fill this gap in the literature by exploring a model that incorporates

quality-enhancing spillovers in an international duopoly model of vertical product differen-

tiation. We identify conditions under which a Northern firm undertakes FDI in the South,

investigate how spillover and tariff rates affect firms’ profitability, consumer surplus, and

welfare, and discuss policy implications of our analysis.

Our model is based on the standard product-line pricing framework of Mussa and Rosen

(1978), where we focus on two types of consumers as in Waldman (1996, 1997), Glass and

Saggi (1998), and Davis, Murphy, and Topel (2004). In our model, a Northern firm (firm

N) and a Southern firm (firm S) compete in the Southern market which consists of high-

valuation and low-valuation consumers. Each firm chooses its product quality, where the

production cost is increasing in quality level. Firm N has a superior technology in the sense

that firm N does not have binding constraint on its choice of product quality whereas firm

S cannot choose the profit maximizing quality level due to its technological limitation. Firm

S is located in the South, while firm N can locate in the North (home-production) or in the

South (FDI). By undertaking FDI, firm N can avoid tariff.1 However, a certain fraction of

firm N ’s technology spills over to firm S under FDI, and the technology spillover increases

the highest possible level of quality firm S can choose for its product.

The rate of technology spillover, denoted by θ (∈ [0, 1)) and interpreted representing the

2Chinese automobile industry developed quickly in late 1990s and early 2000s following investment offoreign automakers. High levels of trade barrier, evidenced by average tariff rate for complete vehicles ofaround 50% in 1999 and remained around 30% in 2005 even after China became a member of WTO in 2001,have induced foreign automakers to set up their manufacturing plants in China (Gallagher, 2003; Luo, 2005).

3With the enforcement of the copyright act, in 1989-1990 domestic firms launched about 120 new softwareproducts and foreign firms about 160 (Patibandla et al. 1999).

1Qualitative nature of our results would remain unchanged under an alternative setup in which firm N

can also save production costs (such as labor costs) and transport costs by undertaking FDI. See the lastparagraph of subsection 4.1.

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strength of IPR protection in the South, is a key parameter in our model. We find that firm

N undertakes FDI when θ is relatively small and/or the tariff rate is relatively high, and the

resulting technology spillover increases both firm S’s profitability and Southern consumers’

surplus.

When firm N undertakes FDI, it may choose a relatively low quality level for its product

in order to reduce the amount of technology that spills over to firm S. Consequently, the

equilibrium level of firm N ’s product quality can be lower under FDI than under home-

production. We call this phenomenon as firm N ’s strategic quality reduction, which happens

under a broad range of parameterizations in our model. This is a new finding in the analyses

of international oligopoly models, and consistent with real-world observations. For instance,

Gallagher (2003) reports that, Chrysler and Ford brought with them dated technologies to

China and, as a result, the quality of cars they manufactured and sold in China by these

firms was below the quality of cars they manufactured and sold in Japanese or the U.S.

markets (see Section 2 for details).

Firm N ’s strategic quality reduction is the main driving force of the following two welfare

consequences and policy implications in our model. First, FDI may hurt the South in the

sense that Southern welfare can be lower under FDI than under home-production. This find-

ing suggests that, when Southern governments formulate IPR protection and trade policy,

they should carefully assess impacts of quality-enhancing technology spillovers accompanied

by FDI, especially when Northern firms are expected to strategically reduce their product

quality upon FDI. Second, the socially optimal spillover rate, which maximizes the sum of

Northern welfare and Southern welfare, is strictly higher than the North-optimal level but

it can be strictly less than the South-optimal level. This finding suggests that international

organizations such as WTO have an active role to play in reconciling North-South conflicts

regarding IPR protection. See Section 6 for details.

A number of papers have previously studied models of technology spillovers in North-

South trade contexts, where technology spillovers reduce production costs in these models

(see Section 3). We contribute to the literature by exploring quality-enhancing spillovers

under the vertical product differentiation model. As the level of IPR protection decreases,

larger amount of technology spills over to Southern firms but innovating firms have lower

incentives to invest in their R&D activities. Previous papers in the literature analyzed this

important trade-off and explored its welfare consequences and policy implications. In our

analysis, the trade-off arises not from lower R&D incentives but from the Northern firm’s

strategic quality reduction. Our analysis suggests that this new trade-off is also important

when we consider economic impacts and welfare consequences of technology spillovers and

IPR protection in North-South trade contexts.

The rest of the article is organized as follows. Section 2 presents real-world examples of

quality-enhancing technology spillovers, followed by literature review in Section 3. Section

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4 presents our model and undertakes its equililrium characterization. Section 5 explores

economic and welfare consequences of spillover rates and tariff rates, followed by discussions

on policy implications of our findings in Section 6. Section 7 offers some concluding remarks.

2 Quality-enhancing Technology Spillovers: Examples

Recently, UNCTAD (2000) have identified various channels under which technology spillovers

from foreign to domestic firms can take place. These include (i) labor mobility between

foreign firms and local firms, and (ii) proximity between foreign firms and local firms which

leads to the upgrade of technological level in the host country.6 UNCTAD has also argued

that, multinational firms’ entry leads to an increase in product quality, variety and innovation

in host economies, but little evidence that it leads to lower prices. In this section, we consider

real world cases of quality-enhancing technology spillovers that is induced by FDI.

Let us consider first the case of Bangladesh garment industry where Desh (a Bangladesh

firm) and Daewoo (a Korean firm) collaborated in 1980, under which Daewoo trained 130

workers in Desh to manufacture high quality clothing products. Rhee (1990) reported that,

only a few years after this collaboration, 115 workers have left the company to either work

for other competing firms or run their own business.7 As a result, not only could Desh

produce high quality clothes but firms that benefited from these workers were also capable

of manufacturing high quality clothing products. UNCTAD (1992) also discusses this case

and argues that, these 115 workers were major agents for imparting the skills throughout

the whole garment industry in Bangladesh.8

6UNCTAD has also defined FDI which leads to strong links to the domestic economy, such as thatassociated with advanced technology and/or spillovers effects, as “high quality” FDI. See also a discussionon international technology diffusion in Keller (2004).

7Rhee points out that, prior to 1980, the clothing industry in Bangladesh was outdated and could notexport to the world market. In 1979, Desh signed an agreement with Daewoo, which was then a leadingfirm in the world for clothing products, under which Daewoo invested in technical training, plant start-up,and marketing activities for Desh. Desh then produced clothing products under supervision and consultancyfrom Daewoo. Daewoo trained 130 Desh workers in Korea in 7 months which enabled them to produce highquality products, and later sent a team to train other workers in Desh factory in 1980. Consequently, Deshsuccessfully produced high quality clothing products and exported them under Daewoo’s network, whereDesh also learned marketing skills, quality upgrading from Daewoo. Desh experienced significant increase inits product quality: its value per piece increased from $1.3 in 1980 to $2.3 in 1986.

8Along this line, UNCTAD (1992) also reports technology spillovers from Yamaha-Escorts collaborationin India to other local firms through the channel of labor mobility. Similarly, Thompson (2003) finds thatlabor mobility as a channel for quality-enhancing technology spillovers from foreign (mainly Hong Kong)firms to local firms has also been observed in garment industry in China. His survey shows that, localfirms have attempted to copy Hong Kong firms’ production processes and techniques, learn their managerialpractices, and particularly hire Hong Kong firms’ employees. In his survey, about 13,000 workers per annum

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Quality-enhancing technology spillovers from foreign to local firms have not only been

observed in sectors that are labor intensive such as garment and textile, but also in other

sectors such as information technology and manufacturing. Patibandla et al. (1999) doc-

umented that, the investment of Texas Instruments in Bangalore in 1984 and other U.S.

software firms in late 1980s created significant technological and information externalities to

Indian firms. As such, this gave the Indian firms access to the trend in the software market

in the world and enabled them to move to the higher-end market (see also Pack & Saggi

2006).

Recently, as pointed out by various authors, Chinese car manufacturers have learned from

foreign competitors on how to manufacture high quality cars and/or improve the quality of

cars to be sold in the local market (Gallagher, 2003; Luo, 2005).9 Employing workers with

experience from foreign firms was the practice used by many Chinese automakers. For

instance, Chery Automobile, during its early development time hired engineers from Nissan-

Dongfeng joint venture which was set up upon Nissan’s investment in China, to develop

new products (Luo, 2005). This is a typical example of what has often been observed in

Chinese automobile industry in recent years. That is, on average, the quality of cars made

by Chinese manufacturers has increased sharply as they benefited from foreign automakers’

presence in China. The 2007 survey of J.D. Power in China’s automobile market indicated

that the average number of problems per 100 vehicles produced by local firms in China was

368, compared to 800 in 2000 (Li 2007).

What are the strategies employed by multinationals to deal with the resulting quality-

enhancing technology spillovers upon FDI? It was observed that in many cases, Northern

firms intentionally brought dated technologies to the South to produce goods of lower quality

when compared to similar products they produced at home factories. As such, they could

decrease the amount of technology that spills over to local competitors. Gallagher (2003)

showed that Chrysler and Ford brought dated technologies to China to produce cars which

did not meet quality requirement of Japan, the United States or Europe and thus could only

be sold in China’s market. Ernst & Young (2005) also reported that, Volkswagen initially

brought obsolete models along with factories and engines needed to build them from Europe

to China. Similarly, Japanese firms often brought technologies at their mature period to

Malaysian electronics industry (Praussello, 2005). As these examples reveal, choosing low

quality level for their products is an usual practice that many Northern firms use to cope

with resulting quality-enhancing technology spillovers in the South.

In summary, the Northern firms’ production in the South often creates positive exter-

nalities to local firms and helps improve local firms’ product quality. This paper considers

left Hong Kong firms and many of these workers later worked for local firms.9China only allows foreign automakers to form joint venture with local firms but not wholly owned foreign

company, as the government wants foreign firms to share technologies with local partners (Qiu, 2005).

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a theoretical model that captures these phenomena, and explores policy implications of

quality-enhancing technology spillovers.

3 Relationships to the Literature

This section surveys previous papers that have studied models of technology spillovers in

North-South trade contexts, and discuss our contributions to the literature.10 In a seminal

contribution to this literature, Chin and Grossman (1990) study a Cournot duopoly model in

which a Northern firm competes with a Southern firm in an integrated world market. They

assume that both firms have access to a standard technology, however only the Northern

firm can invest in R&D in order to lower its production costs. The level of spillovers is

interpreted to reflect the strength of IPR protection. Chin and Grossman consider two

polar cases of complete protection or no protection, where the Southern firm can imitate the

Northern firm’s technology under no protection. They find that the interests of the North and

the South generally conflict regarding IPR protection, with the South benefitting from no

protection and the North benefitting from complete protection. Complete protection may or

may not enhance global welfare in their analysis. Zigic (1998) extends Chin and Grossman’s

model by considering a continuum of IPR protection between the two polar cases. Zigic

finds that the North-South conflict regarding IPR protection does not necessarily arise in

this extension, showing the congruence of interests between North and South when the level

of R&D efficiency is relatively high.11

Diwan and Rodrik (1991) consider the incentives of the North and the South to provide

patent protection in a model that allows for a continuum of potential technologies with a

different distribution of preferences over them in the North and the South. The Northern

and Southern markets are segmented and entry into the R&D section in the North is free

in their model. They find that a benevolent global planner which places greater weight on

the South’s welfare would require higher level of IPR protection in the North.12 Deardorff

(1992) studies the impact of extending patent protection from innovating country to another

country. He shows that, if the size of the innovating country is large, this spreads of patent

protection benefits innovating country, harms the other country and the total impact on

10Many authors have empirically investigated technology spillovers from foreign firms to local firms uponFDI, where technology spillovers are often measured by changes in local firms’ productivity. The findingsalong this line are mixed. For instance, Aitken and Harrison (1999) find negative impact of FDI on localfirms’ productivity using data from 4,000 Venezuelan firms; Djankov and Hoekman (2000) find negativespillovers in Czech Republic; while Haddad and Harrison (1993) find positive relationship between FDI andproductivity in manufacturing sector in Morocco. See also Carluccio and Fally (2010) for a survey.

11See also Zigic (2000) and Kim and Lapan (2008) for related analyses.12In their model, to maximize the global welfare (which is the equally weighted sum of the North’s and

the South’s welfare), the levels of IPR protection in the two regions must be identical.

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global welfare is negative. Helpman (1993) examines the debate between the North and the

South about the enforcement of IPR within a dynamic general equilibrium framework in

which the North invents new products and the South imitates them. He finds that tightening

IPR protection in the South hurts the South and may or may not benefit the North. Lai and

Qiu (2003) explore a model in which firms in both the North and the South can innovate, and

IPR protection in each region is represented by the length of patent protection. Comparing

the Nash equilibrium IPR protection standard of the South with that of the North, they

find that the former is weaker than the latter. They also show that both regions can gain

from an agreement that requires the South to harmonize its IPR standards with those of

the North, and the North to liberalize its traditional goods market.13

Papers mentioned above do not address the link between FDI and technology spillovers,

which is a focus of our analysis. Glass and Saggi (1999, 2002) and Naghavi (2007) have

previously explored this link.

Glass and Saggi (2002) construct a Cournot oligopoly model in which a source firm has a

superior technology compared to a host firm, and they compete by producing a homogeneous

good for a market outside the host country. Workers employed by the source firm acquire

knowledge of its superior technology. FDI helps the source firm to save production costs,

but it may induce its workers to work for the host firm. With the knowledge acquired

from the source firm, these workers can produce the product at lower costs. The source

firm may pay a wage premium to prevent the local firm from hisring its workers and thus

gaining access to their knowledge (technology spillovers). Glass and Saggi find that the

host government has an incentive to attract FDI because of technology spillovers to local

firms or the wage premium earned by employees of the source firm. However, when FDI is

particularly attractive to the source firm, the host government has an incentive to discourage

FDI.14

Naghavi (2007) considers a cost-reducing technology spillovers model in which a Northern

firm can choose to either export or undertake FDI in a Southern country, which has a

13See Grossman and Lai (2004) for a related analysis.14Glass and Saggi (1999) develop a dynamic general equilibrium model to examine the impact of FDI on

technology transfer from the North to the South and welfare. Three types of firms are considered: Northernfirm producing in the North; Northern multinationals producing in the South; and Southern firm producingin the South. In this set up, Northern firms and multinationals innovate while Southern firms imitate, and allof them serve consumers in both the North and the South. In steady state, the amount of imitated productsof both Northern firms and multinationals are fully replaced by newly innovated (with quality improvement)products. Glass and Saggi find that, if FDI is the only channel for technology transfer (that is, the Southernfirms only imitate technologies of the multinationals) then the increase in FDI inflows raises the rate ofimitation, innovation North, and improves welfare for both the North and the South. However, if FDI

co-exists with imitation as channels for technology transfer (that is, the Southern firms imitate technologiesof both multinationals and Northern firms in the North) then the increase in FDI does not affect the rateof imitation, innovation, raises Southern welfare and has ambiguous impact on Northern welfare.

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potential competitor. The game consists of five stages, starting with Southern government

choosing its IPR policy, represented by the spillover rate. In the second stage, the Northern

firm chooses its mode of entry. If it chooses export, it will be the monopolist in the Southern

market and the game proceeds to the third stage where the Southern government chooses its

optimal tariff rate. If the Northern firm chooses FDI instead, a Southern firm could emerge

and benefit from the technology spillovers from the Northern firm. In the forth stage, the

Northern firm chooses the level of R&D investment. The final stage is the production stage,

in which the firms compete in quantity. Naghavi finds that stringent IPR regime in the

South induces the Northern firm to undertake FDI. The resulting FDI improves Southern

welfare whenever the Northern firm’s FDI induces entry of the Southern firm. Hence,

the Southern government can maximize Southern welfare by choosing the highest possible

spillover rate that still induces Northern firm to undertake FDI.

The present paper contributes to the literature by studying the link between FDI and

technology spillovers in the context of quality-enhancing spillovers. To this end, we explore a

model that incorporates quality-enhancing technology spillovers in an international duopoly

model of vertical product differentiation. Our paper is the first one, to the best of our

knowledge, to study such a model.15 As in Glass and Saggi (2002), the Northern firm has

technological advantage compared to the Southern firm in our model.16 As mentioned in

Introduction, we identify a new trade-off regarding IPR protection. That is, as the level

of IPR protection decreases, larger amount of technology spills over to the Southern firm

but the level of the Northern firm’s product quality gets further below the socially optimal

level because of strategic quality reduction. We will explore welfare consequences and policy

implications of this trade-off in later sections.

4 Technology Spillovers under Vertical Product Differ-

entiation

In this section, we present an international duopoly model of vertical product differentiation

with quality-enhancing technology spillover. We adopt the standard framework of product-

15Several authors have discussed quality competition in the context of North-South trade. For instance,Das and Donnenfeld (1989) analyze an international duopoly model of vertical product differentiation inwhich two firms in different countries compete against each other by producing products with differentqualities. They show that trade policy influences the firms’s choice of equilibrium quality levels (see alsoFalvey, 1979; Das and Donnenfeld, 1987; Boccard and Wauthy, 2005; Toshimitsu, 2005; Gonzalez and Viaene,2005). In these papers, however, neither the Northern firm’s choice of modes of entry into Southern market,nor technology spillovers have been examined.

16This is often referred to as ownership advantages. See the second last paragraph of subsection 4.1 fordetails.

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line pricing (Mussa and Rosen, 1978) and focus on two-types of consumers. The two-type

consumers approach in this framework has been adopted to analyze durable goods pricing

(Waldman, 1996, 1997), international technology transfer with quality ladders (Glass and

Saggi, 1998), and entry impact on product design (Davis, Murphy, and Topel, 2004). We

then characterize Subgame Perfect Nash Equilibria (SPNEs) of the model, and demonstrate

that strategic reduction of the Northern firm’s product quality occurs when the rate of

technology spillover is relatively small.

4.1 The Model

We consider a Northern firm (firm N) and a Southern firm (firm S) compete in the Southern

market. Firm S is located in the South, while firm N can locate itself in the North (home-

production, denoted HP ) or in the South (FDI). Let qk (≥ 0, k = N , S) denote the quality

of firm k’s product.

On the demand side, there are two groups of consumers, denoted H (type H consumers)

and L (type L consumers), where group j consists of a continuum of nonatomic consumers

of mass mj, j = H, L. A representative individual in group j consumes either zero units or

one unit of the products, and derives a gross benefit of vjqk from the consumption of one

unit of quality qk product, where vH > vL > 0.

We assume that, firm N can choose any quality level for its product, qN .17 Meanwhile,

firm S, using less advanced technology, can only choose a quality level for its product up

to a certain upper bound value. This value differs for FDI and HP . Specifically, when

firm N locates itself in the North, the maximum possible quality level firm S can choose is

given by qS. When firm N undertakes FDI, technology spillovers extend this upper bound

quality level and the maximum quality level firm S can choose for its product is given by

qS(qN) = max(qS + θ(qN − qS), qS), θ ∈ [0, 1). In our model, θ captures the degree of

technology spillovers from firm N to firm S, which can only happen under FDI. Hence,

when firm N undertakes FDI and chooses qN > qS, the higher θ enables firm S to choose a

higher product quality.

Each firm k can produce a product of quality qk at a constant marginal cost of c(qk) with

zero fixed costs, where c(·) is a twice-continuously differentiable function with c′(·) > 0 and

c′′(·) > 0. To derive closed form solutions, we assume that c(qk) = 12q2k. A specific tariff, t

(> 0), is imposed on imports of firm N ’s product.

We consider a three-stage game, described below.

[Stage 1] Firm N determines whether to locate itself in the North (HP ) or in the South

(FDI).

17All our results would remain unchanged under an alternative assumption that firm N can choose anyqN satisfying qN ≤ qN , where qN is a constant satisfying qN ≥ vH

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[Stage 2] Firm N chooses quality level qN for its product. Having observed qN , firm S

chooses quality level qS, subject to qS ≤ qS(qN).

[Stage 3] Firms N and S simultaneously set prices for their own product, and consumers

make their purchase decisions.

Notice that the game described above has two stage 2 subgames, one is HP subgame in

which firm N locates itself in the North, while the other is FDI subgame in which firm N

locates itself in the South.

We end this subsection by presenting two remarks. First, a basic assumption of our

model is that firm N has a superior technology compared to firm S in the sense that firm

N can choose any quality level for its product, qN (or it can choose qN ≤ qN where qN ≥vH ; see footnote 17). This assumption is consistent with Markusen’s (1995) discussion on

the theory of the multinational enterprise, which is based on Hymer (1976) and Dunning

(1981). Markusen points out that, if foreign multinational enterprises are exactly identical to

domestic firms, they will not find it profitable to enter the domestic market because there are

added costs of doing business in another country including communications and transport

costs, higher costs of stationing personnel aborad, and barriers due to language and customs.

Therefore, he argues, the multinational enterprise must arise due to the fact that it possesses

some special advantage such as superior technology or lower costs due to scale economies.

Dunning (1981) labels this type of advantage as ownership advantage. In their theoretical

analysis of multinational firms and technology transfer, Glass and Saggi (2002) assume that

a multinational firm has a superior technology compared to local firms because of ownership

advantages.

Second, we focus on the case in which there is no cost of production (so that the firms

only incur costs associated with quality development and tariffs). In reality, production cost

is positive and depends on where the firm is located. For instance, with HP , there are

transport costs that the Northern firm has to incur when exporting its output to the South.

With FDI, the Northern firm can save on transport costs and at the same time exploit the

lower wages in the South. These factors potentially make Southern production relatively

attractive for the Northern firm, even though it might also need to pay additional costs due

to the operation in an unfamiliar environment. It is thus straightforward to assume that,

beside tariff t, there is an extra cost disadvantage of Northern production per unit of output,

w. In this case, the total disadvantages of Northern production is captured by t + w, rather

than t as presented above. Analyzing the model with the inclusion of w, however, would

leave all of our results unchanged, so that we have ignored w in this paper to focus the

attention of readers on welfare consequences of tariff and spillver rates.18

18Detailed analysis for the inclusion of w in our model is available upon requests by interested readers.

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4.2 Equilibrium Characterization

Throughout our analysis we assume that qS < vL holds. If qS ≥ vL holds, then qS does not

impose a binding constraint on firm S’s choice of quality level, since firm S can choose its

profit-maximizing quality level, vL, without technology spillovers as shown later in this sec-

tion. Hence, by assuming qS < vL, we focus on cases in which quality-enhancing technology

spillover can play a role.

We derive Subgame Perfect Nash Equilibria of the model described above. We focus

on a range of parameterizations in which firm N sells its product to all type H consumers

and firm S sells its product to all type L consumers in the equilibrium. Following Davis

et al. (2004) and Glass and Saggi (1998), we call this type of equilibrium as a separating

equilibrium. Note that all proofs are presented in the Appendix.

Proposition 1. There exists an unique value mH > 0 such that the game has a separating

equilibrium if and only if mH > mH . Furthermore, if mH > mH , the separating equilibrium

is the unique equilibrium of the game.

To understand the logic behind Proposition 1, let us first consider the case in which the

spillover rate, θ, is equal to zero. This implies that, technology does not spill over from firm

N to firm S even when firm N chooses to locate itself in the South. In this case, firm N ’s

optimal choice in Stage 1 is to locate itself in the South to avoid the tariff.

Suppose that the game has a separating equilibrium when θ = 0. In equilibrium, firm

N sells its product with quality qN at a price of pN to mH type H consumers, while firm S

sells its product with quality qS at a price of pS to mL type L consumers. We find that

pN = vHqN − (vH − vL)qS, (3.1)

pS = vLqS, (3.2)

where qN > qS.19 Firm S extracts all surplus from type L consumers by charging pS =

vLqS. If a type H consumer purchases firm S’s product at pS, the consumer’s net benefit is

vHqS −pS = (vH − vL)qS. Then, in order for firm N to sell its product to type H consumers,

it must leave the same amount of surplus, (vH − vL)qS, to be captured by the consumers,

and hence pN = vHqN − (vH − vL)qS. Then, the equilibrium profits of firms N and S are

πN(qN) and πS(qS) respectively, where

πN(qN) = mH [pN − c(qN)] = mH [vHqN − (vH − vL)qS −1

2q2N ], (3.3)

19Market separating constraints are: vHqN − pN ≥ vHqS − pS ⇒ pN − pS ≤ vH(qN − qS) and vLqS − pS ≥vLqN − pN ⇒ pN − pS ≥ vL(qN − qS). Combining these and given one constraint must hold with strictinequality, we have vL(qN − qS) < vH(qN − qS) ⇒ qN > qS .

12

πS(qS) = mL[pS − c(qS)] = mL[vLqS −1

2q2S]. (3.4)

When θ = 0, firm S’s maximum possible quality level is not affected by firm N ’s quality level

qN , and hence qS(qN) = qS for all qN . Given qS < vL, firm S chooses qS = qS to maximize

πS(qS) whereas firm N chooses qN = vH to maximize πN(qN), at stage 2 in equilibrium.20

Proposition 1 tells us that the number of type H consumers, mH , must be greater than

a threshold value mH for the game to have a separating equilibrium. This is because, if mH

is lower than the threshold, ignoring type L consumers is no longer firm N ’s optimal choice,

and firm N is strictly better off by selling its product to both types of consumers.

In the case of θ > 0, the positive spillover rate can negatively affect firm N ’s profitability.

This is because technology spillover can increase firm S’s product quality by increasing its

maximum possible quality level. This in turn increases the amount of surplus, (vH − vL)qS,

that firm N must offer to type H consumers to ensure their purchase of firm N ’s product,

resulting in the reduction of firm N ’s profitability. Firm N continues to undertake FDI

when the value of θ is relatively small, but may switch to home-production when θ becomes

higher. In any case, Proposition 1 again tells us that mH must be greater than a threshold

for the game to have a separating equilibrium, because, otherwise, firm N will be strictly

better off by selling its product to both types of consumers.

Next we turn to Proposition 2, which tells us that if mH > mH , the unique equilibrium

of the game is an FDI equilibrium if θ is relatively small, and it is an HP equilibrium

otherwise.

Proposition 2. Suppose mH > mH . There exist a value θ∗ ∈ (0, 1] such that the equilibrium

of the game is an FDI equilibrium if θ ≤ θ∗, and it is an HP equilibrium if θ > θ∗.

Furthermore, there exists a value t ≥ 0 such that θ∗(< 1) is strictly increasing in t if t < t,

and θ∗ = 1 otherwise.

As mentioned above, firm N chooses to undertake FDI if θ = 0, and an increase in

θ reduces firm N ’s profitability. Firm N ’s disadvantage of home-production is that it has

to pay the specific tariff t. Proposition 2 tells us that if the tariff rate is relatively low,

there exists a threshold θ∗ < 1 such that firm N chooses home-production over FDI if θ

is greater than θ∗. The threshold θ∗ is increasing in t, because firm N ’s disadvantage of

home-production is increasing in t. And, when t exceeds the threshold t, firm N undertakes

FDI for all θ ∈ [0, 1) (that is, θ∗ = 1).

We now establish Proposition 3, which tells us that strategic reduction of firm N ’s product

quality occurs when θ is relatively small.

20Notice that if qS ≥ vL, firm S’s maximum possible quality level would not impose a binding constrainton firm S’s choice of quality, where firm S would choose qS = vL to maximize πS(qS) at stage 2.

13

Proposition 3. Suppose mH > mH , and let q∗k denote the equilibrium level of firm k’s

product quality. There exists a threshold θ, θ ∈ (0, θ∗], such that (i) and (ii) below hold in

the equilibrium of the game.

(i) Firm N chooses q∗N = (1− θ)vH + θvL (< vH) if θ ≤ θ and q∗N = vH if θ > θ.

(ii) Firm S chooses q∗S = qS((1− θ)vH + θvL) if θ ≤ θ, q∗S = vL if θ ∈ (θ, θ∗], and q∗S = qS if

θ > θ∗.

If the spillover rate θ is high enough satisfying θ > θ∗, firm N chooses home-production

to avoid technology spillovers. Since there is no spillover, firm S chooses q∗S = qS as in the

case of θ = 0 explained above. Firm N then chooses q∗N = vH , which maximizes its profit

mH [vHqN−(vH−vL)qS− 12q2N−t]. Notice that the profit-maximizing level of firm N ’s product

quality under home-production, q∗N = vH , coincides with the socially optimal quality level,

because the net social benefit associated with the consumption of firm N ’s product by type

H consumers is mH [vHqN − 12q2N ].

Proposition 3 (i) tells us that firm N chooses q∗N = vH when θ > θ, and it chooses

a lower quality level (1 − θ)vH + θvL when θ ≤ θ. This result, referred to as strategic

reduction of firm N ’s product quality, can be explained as follows. Consider the equilibrium

of the FDI subgame. Given firm N ’s quality choice qN , firm S chooses qS to maximize

πS(qS) = mL[vLqS − 12q2S] subject to qS ≤ qS(qN) ≡ max(qS + θ(qN − qS), qS). Let q∗S(qN)

denote firm S’s best response function. By anticipating firm S’s response to qN , firm N

chooses qN to maximize its profit in the subsequent equilibrium, which is

πN(qN) ≡ mH [vHqN − (vH − vL)q∗S(qN)− 1

2q2N ]. (3.5)

We find that the candidates for the profit-maximizing level of firm N ’s product quality

are qN = vH and qN = (1−θ)vH +θvL. If the level of qN does not impose a binding constraint

on firm S’s choice of qS then firm N chooses q∗N = vH that maximizes [vHqN − 12q2N ]. In

contrast, if the level of qN imposes a binding constraint, firm N chooses q∗N = (1−θ)vH +θvL,

which is lower than vH , to reduce the amount of technology spillovers from firm N to firm

S.

Notice that, without the constraint qS ≤ qS(qN), firm S would choose qS = vL to maximize

its profit mL[vLqS− 12q2S]. If the spillover rate θ is large enough so that vL < qS((1−θ)vH+θvL)

⇔ θ > vL−qS

vH−vLholds, then the constraint is not binding at both candidates qN = (1−θ)vH+θvL

and qN = vH . In this case, firm N chooses q∗N = vH in equilibrium. In contrast, if θ is small

enough so that vL ≥ qS(vH) ⇔ θ ≤ vL−qS

vH−qS, then the constraint is binding at both candidates

qN = (1 − θ)vH + θvL and qN = vH . In this case, firm N chooses q∗N = (1 − θ)vH + θvL in

equilibrium. We find that there exists a unique value θ ∈ (0, 1) such that, in the equilibrium

of the FDI subgame, firm N chooses q∗N = vH if θ > θ and q∗N = (1 − θ)vH + θvL if θ ≤ θ.

14

Finally, we define θ ≡ min{θ, θ∗} in order to state this result in terms of the equilibrium of

the entire game, leading to Proposition 3.

Finally, the following lemma will be useful when we explore welfare consequences of IPR

protection in the next section.

Lemma 1. θ < θ∗ = 1 if t ≥ t, and θ = θ∗ < 1 otherwise.

If t ≥ t, firm N chooses FDI for all θ ∈ [0, 1) (that is, θ∗ = 1) by Proposition 2. Lemma 1

tells us that firm N chooses q∗N = vH if θ is relatively large satisfying θ > θ, and strategically

reduces its product quality to q∗N = (1− θ)vH + θvL if θ ≤ θ.

If t < t, firm N chooses FDI if θ is relatively small satisfying θ ≤ θ∗, and choose home-

production otherwise (Proposition 2). Lemma 1 tells us that θ = θ∗ holds in this case. This

means that, whenever firm N chooses FDI in the equilibrium (that is, whenever θ ≤ θ∗

holds), firm N strategically reduces its product quality (that is, θ ≤ θ holds). To see why

θ = θ∗ holds in this case, suppose θ < θ∗ < 1 holds. For any θ ∈ (θ, θ∗], firm N prefers FDI

to home-production (because θ ≤ θ∗), and q∗N = vH and q∗S = vL hold in the equilibrium

(because θ > θ). Firm N ’s equilibrium profit is then constant for all θ ∈ (θ, θ∗], and is strictly

greater than its profit under home-production. Then, since firm N ’s equilibrium profit in

the home-production subgame is constant for all θ, firm N should be strictly better off by

choosing FDI over home-production for all θ > θ, and hence θ∗ = 1 should hold instead of

θ∗ < 1. This in turn means that, if θ∗ < 1, then θ = θ∗ must hold.

In summary, we have shown that the game has a separating equilibrium if and only if the

population of type H consumers is relatively large. The separating equilibrium is the unique

equilibrium, which is an FDI equilibrium if the spillover rate θ is relatively low and it is an

HP equilibrium otherwise. We have also found that FDI reduces the equilibrium quality of

firm N ’s product from the socially optimal level vH to a suboptimal level (1 − θ)vH + θvL

when θ is relatively low. This is because, by reducing its product quality, firm N can reduce

the amount of technology that spills over to firm S, and this in turn increases firm N ’s

profitability.

5 Impacts of quality-enhancing technology spillovers

In this section we will investigate impacts of quality-enhancing technology spillovers on

firms’ profits, Southern consumers, Southern welfare, and global welfare. To this end, we

will undertake comparative statics exercises concerning the spillover rate θ, and identify and

compare optimal spillover rates θS and θW that respectively maximize Southern welfare and

global welfare. We will then present an outline of comparative statics results concerning

tariff rates. Finally, given that Firm N ’s strategic quality reduction is a central result of our

model, we ... .

15

5.1 Economic and welfare consequences of spillover rates

We undertake comparative statics exercises concerning the spillover rate θ, focusing on the

cases in which the equilibrium of the game is a separating equilibrium for all θ ∈ [0, 1).21

Let πN(θ), πS(θ), CS(θ), WS(θ), and W (θ) denote the profit of the Northern firm and the

Southern firm, consumer surplus, Southern welfare, and global welfare in the equilibrium of

the game, respectively. We present our results under two cases; the case of t ≥ t (Case I)

and t < t (Case II). See Proposition 2 for the definition of t.

Case I: t ≥ t

Recall that θ < θ∗ = 1 holds if t ≥ t by Lemma 1. That is, firm N undertakes FDI for

all θ ∈ [0, 1) and strategically reduces its product quality by choosing q∗N = (1− θ)vH + θvL

if and only if θ ≤ θ.

Proposition 4.

(i) πN(θ) is strictly decreasing in θ for all θ ∈ [0, θ] and πN(θ)|θ∈(θ,1) = πN(θ) hold.

(ii) πS(θ), CS(θ) and WS(θ) are strictly increasing in θ for all θ ∈ [0, θ]. Furthermore,

πS(θ)|θ∈(θ,1) > πS(θ), CS(θ)|θ∈(θ,1) > CS(θ) and WS(θ)|θ∈(θ,1) > WS(θ) hold, where πS(θ),

CS(θ) and WS(θ) are constant for all θ ∈ (θ, 1).

When θ ∈ [0, θ], firm N undertakes FDI and imposes a binding constraint on firm

S’s quality choice by choosing q∗N = (1 − θ)vH + θvL. Holding else constant, an increase

in θ extends firm S’s upper bound quality level. Firm N partially offsets this effect by

reducing its product quality (that is, q∗N = (1 − θ)vH + θvL decreases as θ increases), but

firm S’s equilibrium quality q∗S = qS + θ(q∗N − qS) is still increasing in θ for all θ ∈ [0, θ].

That is, the direct (positive) impact of an increase in spillover rate on firm S’s equilibrium

quality outweighs the indirect (negative) impact of firm N ’s strategic reduction of its product

quality. Firm N ’s equilibrium profit πN(θ) is strictly decreasing in θ for all θ ∈ [0, θ]. In

the equilibrium, firm S captures all surplus from type L consumers by charing p∗S = vLq∗Sto them, whereas firm N leaves a rent of (vH − vL)q∗S to be captured by type H consumers.

Hence the equilibrium consumer surplus is given by CS(θ) = mH(vH − vL)q∗S. Then, since

q∗S is strictly increasing in θ, both πS(θ) and CS(θ) are also strictly increasing in θ for all

θ ∈ [0, θ].

When θ = θ, firm N is indifferent between choosing qN = (1− θ)vH + θvL and qN = vH .

And, once θ exceeds θ, it becomes too costly for firm N to impose a binding constraint on

firm S’s quality choice, and hence firm N chooses q∗N = vH while firm S chooses q∗S = vL

for all θ ∈ (θ, 1). Hence q∗S|θ=θ < q∗S|θ∈(θ,1) = vL for all θ ∈ (θ, 1), which implies that

21The condition can be written as mH > limθ→θ∗

mH , see the proof of Proposition 1.

16

πS(θ)|θ∈(θ,1) > πS(θ) and CS(θ)|θ∈(θ,1) > CS(θ) hold, where πS(θ) and CS(θ) are constant

for all θ ∈ (θ, 1).

Concerning Southern welfare, notice that Southern government receives no tariff revenue

for all θ ∈ [0, 1) in the equilibrium, because firm N undertakes FDI for all θ ∈ [0, 1) in case

I. Equilibrium Southern welfare is then given by WS(θ) = πS(θ) + CS(θ), and hence WS(θ)

shares the same properties with πS(θ) and CS(θ) as Proposition 4 (ii) tells us.

Next we turn to global welfare, which is the sum of the net social benefit associated with

the consumption of firm N ’s product, mH [vHqN − qN2

2], and of firm S’s product, mL[vLqS −

qS2

2]. Hence qN = vH and qS = vL are global welfare-maximizing levels of firm N ’s product

quality and firm S’s product quality, respectively. This leads us to Proposition 5.

Proposition 5. For any given θ′ ∈ (θ, 1), W (θ′) > W (θ) holds for all θ ∈ [0, θ], where W (θ′)

is constant for all θ′ ∈ (θ, 1).22

As mentioned above, firm N chooses q∗N = vH and firm S chooses q∗S = vL in the

equilibrium for all θ ∈ (θ, 1). In contrast, if θ ∈ [0, θ], firm N strategically reduces its

product quality to (1− θ)vH + θvL, which in turn reduces firm S’s product quality as well.

Hence equilibrium global welfare achieves the maximum possible level when θ ∈ (θ, 1).

Finally, Propositions 4 (ii) and 5 together imply the following corollary.

Corollary 1. Let θS and θW respectively denote the optimal spillover rates for Southern

welfare and global welfare. Then θS ∈ (θ, 1) and θW ∈ (θ, 1) hold.

In case I considered here, the strategic reduction of firm N ’s product quality reduces

Southern welfare as well as global welfare. Hence, Southern welfare and global welfare are

both maximized when θ exceeds θ so that it is too costly for firm N to strategically reduce

its product quality in order to impose a binding constraint on firm S’s choice of product

quality.

Case II: t < t

Recall that θ = θ∗ < 1 holds if t < t by Lemma 1. That is, firm N undertakes FDI and

strategically reduces its product quality by choosing q∗N = (1− θ)vH + θvL if θ ≤ θ∗, whereas

it chooses HP and q∗N = vH if θ > θ∗.

Proposition 6.

(i) πN(θ) is strictly decreasing in θ for all θ ∈ [0, θ∗], and πN(θ) = πN(θ∗) for all θ ∈ (θ∗, 1).

22For the interval [0, θ], we find that there exists a value θ ∈ [0, θ] such that W (θ) is strictly increasing inθ for all θ ∈ [0, θ] and strictly decreasing in θ for all θ ∈ [θ, θ]. See Proposition 8 for an analogous propertyin case II.

17

(ii) πS(θ) and CS(θ) are strictly increasing in θ for all θ ∈ [0, θ∗], and πS(θ∗) > πS(θ)|θ∈(θ∗,1)

and CS(θ∗) > CS(θ)|θ∈(θ∗,1) hold, where πS(θ) and CS(θ) are constant for all θ ∈ (θ∗, 1).

Given θ∗ = θ, properties of πN(θ), πS(θ), and CS(θ) in the interval [0, θ∗] are same as the

ones presented in Proposition 4 for case I. That is, when θ ∈ [0, θ∗], firm N undertakes FDI

and imposes a binding constraint on firm S’s quality choice by choosing q∗N = (1−θ)vH +θvL,

but q∗S is still increasing in θ for all θ ∈ [0, θ∗]. Consequently, for all θ ∈ [0, θ∗], πN(θ) is

strictly decreasing in θ whereas πS(θ) and CS(θ) are strictly increasing in θ.

When θ = θ∗, firm N is indifferent between choosing FDI with qN = (1−θ)vH +θvL and

HP with qN = vH . And, once θ exceeds θ∗, it becomes too costly for firm N to undertake

FDI, and it chooses HP . This is the key difference between Cases I and II. Since the tariff

rate t is relatively small in case II, home production becomes firm N ’s optimal choice when

θ exceeds θ∗. Since there is no technology spillover under HP , firm S’s equilibrium quality

level q∗S is reduced discontinuously from qS + θ∗(q∗N − qS) to qS once θ exceeds θ∗. Then,

πS(θ) and CS(θ) are both discontinuously reduced when firm N switches from FDI to HP ,

because πS(θ) and CS(θ) are increasing in the level of firm S’s product quality. Therefore we

have that πS(θ∗) > πS(θ)|θ∈(θ∗,1) and CS(θ∗) > CS(θ)|θ∈(θ∗,1) hold, where πS(θ) and CS(θ)

are constant for all θ ∈ (θ∗, 1).

Now we turn to Southern welfare. When θ ∈ [0, θ∗], we have that WS(θ) = πS(θ)+CS(θ)

since Southern government receives no tariff revenue when firm N chooses FDI. Proposition

6 (ii) then tells us that WS(θ) is strictly increasing in θ for all θ ∈ [0, θ∗] and so is maximized

when θ = θ∗. Pick any θ = θ′ ∈ (θ∗, 1) and compare WS(θ∗) and WS(θ′). Notice that, when

θ = θ′, firm N chooses home production and hence Southern government receives tariff

revenue. That is, WS(θ′) = πS(θ′) + CS(θ′)+tariff revenue. Hence the comparison between

WS(θ∗) and WS(θ′) is not obvious even though we know πS(θ∗) > πS(θ′) and CS(θ∗) >

CS(θ′) by Proposition 6 (ii).

Notice that the comparison between WS(θ∗) and WS(θ′) is equivalent to the comparison

between W (θ∗) and W (θ′) because global welfare is Southern welfare plus firm N ’s profit

where firm N is indifferent between θ = θ∗ and θ = θ′ (that is, W (θ) = WS(θ)+πN(θ) where

πN(θ∗) = πN(θ′)). Recall that qN = vH and qS = vL are global welfare-maximizing levels of

firm N ’s product quality and firm S’s product quality, respectively. When θ = θ∗, firm N

chooses FDI and strategically reduces its product quality level to (1− θ∗)vH + θ∗vL (< vH)

but firm S’s product quality q∗S = qS + θ∗(q∗N − qS) is greater than qS because of technology

spillover (but still less than vL). In contrast, when θ = θ′, firm N chooses HP with q∗N = vH

and firm S chooses q∗S = qS since there is no technology spillover.

Under θ = θ∗, firm N ’s strategic reduction of its product quality reduces the net social

benefit associated with the consumption of firm N ’s product, whereas technology spillover

increases the net social benefit associated with the consumption of firm S’s product. We

18

find that, when the population of type H consumers mH is relatively large, the former effect

dominates the latter effect so that W (θ∗) < W (θ′) and hence WS(θ∗) < WS(θ′) hold, as

formally stated in Proposition 7 below.

Proposition 7. WS(θ) is strictly increasing in θ for all θ ∈ [0, θ∗], and there exists a value

m∗ such that WS(θ∗) < (=, >) WS(θ)|θ∈(θ∗,1) if mH > (=, <) m∗, where m∗ > limθ→θ∗

mH holds

under a range of parameterizations and WS(θ) is constant for all θ ∈ (θ∗, 1).

Notice that θ = θ∗ is the highest possible spillover rate under which firm N undertakes

FDI, and hence FDI is most likely to benefit the South in equilibrium when θ = θ∗.

Proposition 7 tells us that, even when θ = θ∗, FDI still hurts the South if the population

of type H consumers is relatively large (that is, WS(θ∗) < WS(θ)|θ∈(θ∗,1) if mH > m∗). The

main driving force of this result is firm N ’s strategic quality reduction, which reduces the net

social benefit associated with the consumption of firm N ’s product, leading to the negative

welfare effect of FDI when mH is relatively large. See the last paragraph of this subsection

on details.

Next we turn to global welfare W (θ). Proposition 8 tells us that W (θ) can be a non-

monotone function of θ in the interval [0, θ∗].

Proposition 8. There exists a value θ ∈ (0, θ∗] such that W (θ) is strictly increasing in

θ for all θ ∈ [0, θ] and strictly decreasing in θ for all θ ∈ [θ, θ∗], and W (θ) > W (θ)|θ∈(θ∗,1)

holds where W (θ) is constant for all θ ∈ (θ∗, 1). Furthermore, there exists a value m∗∗ such

that θ < θ∗ holds if and only if mH > m∗∗, where m∗∗ > limθ→θ∗

mH holds under a range of

parameterizations.

Recall that, when θ = 0, firm N chooses FDI with q∗N = vH and firm S chooses q∗S = qS

since there is no technology spillover. As the spillover rate increases from θ = 0, firm

N ’s equilibrium product quality q∗N = (1 − θ)vH + θvL decreases because of the strategic

quality reduction, and firm S’s equilibrium product quality increases because of spillover.

Consequently, as θ increases, q∗N gets further away from the socially optimal level vH and this

reduces the net social benefit associated with type H consumers’ consumption, whereas q∗Sgets closer to the socially optimal level vL and this increases the net social benefit associated

with type L consumers’ consumption. Proposition 8 tells us that, when θ is relatively small,

the latter effect dominates the former effect so that W (θ) is increasing in θ. It also says that,

when mH is relatively large, former effects starts to dominate the latter when θ exceeds a

threshold θ so that W (θ) is decreasing in θ for all θ ∈ [θ, θ∗]. Once θ exceeds θ∗, firm N

chooses HP with q∗N = vH and firm S chooses q∗S = qS. Notice that these equilibrium quality

choices are identical to those when θ = 0, implying that the equilibrium global welfare is the

same under θ = 0 and θ ∈ (θ∗, 1) (W (0) = W (θ) for all θ ∈ (θ∗, 1)). This in turn implies

that W (θ) is maximized when θ = θ.

19

We can now compare the optimal spillover rates for Southern welfare and global welfare.

We have that θW = θ ∈ (0, θ∗] by Proposition 8. If mH > m∗, we have that θS is any θ in

the interval (θ∗, 1), implying θW < θS. Suppose instead that mH ≤ m∗, so that θS = θ∗.

Proposition 8 then tells us that θW = θ < θ∗ = θS if mH > m∗∗, and θW = θS = θ∗ otherwise.

Hence we have Corollary 2.

Corollary 2. 0 < θW < θS holds if mH > min{m∗, m∗∗}, and 0 < θW = θS holds otherwise.

Corollay 2 says that, when the population of type H consumers mH is relatively large, the

globally optimal spillover rate is strictly lower than Southern optimal spillover rate. Recall

also that FDI always hurts, rather than benefits, the South (even when θ = θ∗) when mH

is relatively large (Proposition 7).

The main driving force of these two welfare consequences of quality-enhancing technology

spillover in our analysis is firm N ’s strategic quality reduction. To see this, suppose that firm

N cannot strategically reduce its product quality and must choose qN = vH for any given θ.

We then find that there exists a value θ∗∗ ∈ (0, 1] such that firm N undertakes FDI if and

only if θ ≤ θ∗∗, where θ∗∗ < 1 holds when t is relatively small. If θ∗∗ < 1, firm S’s equilibrium

product quality is strictly increasing in θ for all θ ∈ [0, θ∗∗] because of technology spillover.

This implies that equilibrium global welfare is maximized when θ = θ∗∗. Then, since firm

N is indifferent between θ = θ∗∗ and any θ ∈ (θ∗∗, 1), equilibrium Southern welfare is also

maximized when θ = θ∗∗. That is, FDI benefits the South when θ is equal to or sufficiently

close to θ∗∗, and θW = θS = θ∗∗ holds, and hence neither of the two welfare consequences

summarized in the previous paragraph does not hold in the absence of the strategic quality

reduction.23

5.2 Economic and welfare consequences of tariff rates

In this subsection, we present an outline of comparative statics exercises concerning the tariff

rate t, focusing on the cases in which the equilibrium of the game is a separating equilibrium

for all t > 0.24 Let πN(t), πS(t), CS(t), WS(t), and W (t) denote the profit of the Northern

firm and the Southern firm, consumer surplus, Southern welfare, and global welfare in the

equilibrium of the game, respectively. For expositional convenience, in this subsection we

make a tie-breaking assumption that firm N chooses HP if it is indifferent between HP and

FDI.

When t is relatively large, firm N chooses FDI to avoid tariff payment, whereas, when t

is relatively small, firm N chooses HP to avoid technology spillovers. This is formalized in

23See Appendix for the proof of the results presented in this paragraph.24The condition can be written as mH > lim

t→tmH , see the proof of Proposition 1.

20

Proposition 9.

Proposition 9. For any given θ ∈ [0, 1), there exists a value t(θ) ≥ 0 such that firm N

chooses HP if t ≤ t(θ) whereas it undertakes FDI if t > t(θ) in the equilibrium of the game.

Furthermore, t(0) = 0, t(θ) is strictly increasing in θ for all θ ∈ (0, θ), and t(θ) is constant

for all θ ∈ [θ, 1), where θ is as defined in Proposition 3.

When the spillover rate θ is zero, firm N is strictly better off by undertaking FDI for

all t > 0, implying t(0) = 0. As θ increases, FDI becomes less attractive option for firm N ,

and this implies that the threshold t(θ) is increasing in θ.

When t ∈ [0, t(θ)], firm N chooses HP and q∗N = vH whereas firm S chooses q∗S = qS

because no technology spills over from firm N to firm S under HP . Notice that equilibrium

quality levels q∗N and q∗S are constant for all t ∈ [0, t(θ)], implying that the equilibrium global

welfare W (t) = mH(vHq∗N −q∗N

2

2)+mL(vLq∗S−

q∗S2

2) is constant for all t ∈ [0, t(θ)]. Also, πN(t)

is strictly decreasing in t and WS(t) is strictly increasing in t for all t ∈ [0, t(θ)] because

firm N pays more tariff to the Southern government as t increases, and firm N is indifferent

between HP and FDI when t = t(θ). The equilibrium Southern welfare WS(t) is therefore

maximized when t = t(θ).

Once t exceeds t(θ), firm N switches from HP to FDI, and further increase in t does not

affect equilibrium profits and welfare. Given this, take any t′ > t(θ) and compare Southern

welfare and global welfare under t = t(θ) and t = t′. We obtain the following result.

Proposition 10.

(i) If θ > θ, W (t′) > W (t(θ)) and WS(t′) > WS(t(θ)) hold.

(ii) If θ ≤ θ, there exists a value m∗ such that W (t′) > (=, <) W (t(θ)) and WS(t′) >

(=, <) WS(t(θ)) hold if mH < (=, >) m∗, where m∗H > lim

t→tmH holds under a range of

parameterizations.

Suppose θ > θ. Proposition 3 tells us that q∗N = vH and q∗S = vL under FDI with t = t′,

whereas q∗N = vH and q∗S = qS under HP with t = t(θ). That is, the level of firm N ’s product

quality is at the socially optimal level under both HP and FDI and the level of firm S’s

product quality is also at the socially optimal level under FDI, but the level of firm S’s

product quality is below socially optimal level under HP . Hence we have W (t′) > W (t(θ)),

which implies WS(t′) > WS(t(θ)) because firm N is indifferent between t = t′ and t = t(θ).

Next suppose θ ≤ θ. Proposition 3 tells us that q∗N = (1 − θ)vH + θvL and q∗S =

qS + θ(q∗N − qS) (< vL) under FDI with t = t′, whereas q∗N = vH and q∗S = qS under HP

with t = t(θ). The level of firm N ’s product quality is below the socially optimal level under

FDI due to its strategic quality reduction, whereas the level of firm S’s product quality is

below the socially optimal level under both FDI and HP , but the quality level is higher

21

under FDI because of technology spillover. Given that firm N ’s product is consumed by

high valuation consumers and firm S’s product by low valuation consumers, this implies that

global and Southern welfare are both higher under HP when mH is relatively large, implying

Proposition 10 (ii).

Proposition 10 tells us that FDI induced by a higher tariff rate hurts the South when the

spillover rate is relatively low and the population of high valuation consumers is relatively

large. It can be shown, as in the previous subsection, that the strategic quality reduction is

the driving force of this negative welfare effect of FDI.

5.3 Quality-enhancing versus cost-reducing technology spillovers

In our model of quality-enhancing technology spillovers, we have demonstrated that the

Northern firm strategically reduces its product quality under a broad range of parameteriza-

tions when it undertakes FDI in the South. And the strategic quality reduction is a driving

force of our two main welfare and policy implications.

Would Northern firms choose strategy analogous to the strategic quality reduction when

technology spillovers result in a reduction of Southern firms’ production costs rather than

an enhancement of their product quality? In order to provide an answer to this question,

Nguyen (2011) has analyzed an international duopoly model with cost-reducing technology

spillovers outlined as follows.

Firms N and S, respectively Northern firm and Southern firm, compete in the Southern

market with a homogenous good. Firm N has better technology so that it incurs a lower

level of marginal cost compared to firm S, holding other things constant. In addition, firm N

can choose its supply strategy between home production (HP ) or undertaking FDI in the

South, whereas firm S only produces in the South. A spillover rate, θ ∈ [0, 1), represents the

strength of IPR protection in the South and captures the amount of knowledge spilled over

from firm N to firm S if firm N undertakes FDI in the South. Specifically, when firm N

undertakes FDI in the South, the marginal cost for firm S is reduced from c0 (the marginal

cost facing firm S if firm N chooses HP ) to min(c0 − θ(c0 − cfN), c0), where cf

N is firm N ’s

marginal cost. With these specifications, θ plays a similar role to the spillover rate presented

in subsection 4.1. A specific tariff, t, is imposed on import of firm N ’s product.

Nguyen (2011) finds that, firm N undertakes FDI if the spillover rate is relatively low

and it chooses HP otherwise. However, regardless of its supply strategy, firm N always

chooses the lowest marginal cost for its production. The logic behind this result goes as

follows. Under FDI, firm N chooses zero marginal cost if the spillover rate is zero. When θ

is positive, consider a small increase in firm N ’s marginal cost by δ. On one hand, this reduces

firm N ’s profitability, keeping other things constant. On the other hand, this reduces firm

S’s marginal cost by δθ, which reduces cost difference between the two firms and intensifies

22

competition. Thus, increasing marginal cost always hurts firm N so that it chooses the lowest

possible marginal cost. Applying this result to the case of linear demand, Nguyen (2011)

finds that when the spillover rate is set such that firm N is indifferent between HP and FDI,

FDI always raises the level of Southern welfare and global welfare. The reason is that while

firm N keeps its marginal cost plan the same under either supply strategies, firm S enjoys

lower marginal cost if firm N undertakes FDI. Finally, global welfare-maximizing level of

spillover rate is found to be either zero or the same as the South-optimal level, depending

on tariff rate, t.

To compare between quality-enhancing and cost-reducing spillovers, we assume that the

strategic reduction of Northern firm’s product quality under quality-enhancing spillovers

framework is equivalent to the intentional increasing of Northern firm’s marginal cost under

cost-reducing spillovers framework. In other words, if the Northern firm does not bring its

best technology to the South then it either produces the product with lower quality, or at a

higher marginal cost. It then follows that the analogous “strategic” reduction of Northern

firm’s product quality does not arise in the comparable model of cost-reducing technology

spillovers. This also explains why FDI might hurt the South in the presence of quality-

enhancing spillovers whereas it always benefits the South in the presence of cost-reducing

spillovers. Note that, the result of Nguyen (2011)’s cost-reducing spillovers model concern-

ing that FDI always benefits the South is consistent with Naghavi (2007) who analyzes

technology spillovers which comes as a consequence of both FDI and R &D.

6 Policy implications

Stronger IPR protection in the South reduces the rate of technology spillovers, and this can

induce Northern firms to undertake FDI in the South. Higher tariff rates in the South can

also induce Northern firms to undertake FDI. Does Northern firms’ FDI benefit the South?

FDI can potentially benefit Southern firms and consumers through technology spillovers,

but the Southern government loses its tariff revenue under FDI. The total effect of FDI on

the South is therefore not immediately obvious in general. Our analysis demonstrates that

the Northern firm may strategically reduce its product quality upon FDI, and, because of the

strategic quality reduction, the Northern firm’s FDI hurts the South when the population

of high-valuation consumers is relatively large. In contrast, under an alternative assumption

that the Northern firm cannot strategically reduce its product quality, the Northern firm’s

FDI benefits the South if the Southern government can optimally set the rate of technology

spillovers in order to maximize Southern welfare in our model. Our analysis therefore suggests

that the strategic quality reduction, which is often observed in reality (see Section 2), is an

important issue to be considered when one accesses welfare impacts of FDI and technology

spillovers in the contexts of quality-enhancing spillovers.

23

An equally important policy implication of our analysis is that we have identified the

cases in which the spillover rate that maximizes global welfare is positive but lower than the

level which maximizes Southern welfare. Suppose there is a social planner, who can set the

spillover rate in the South. If Northern welfare is the only concern, the social planner would

set the spillover rate equal to zero, whereas if Southern welfare is the only concern then she

would choose the spillover rate that maximizes Southern welfare (which is positive). Should

the social planner support the North by choosing zero spillover rate or support the South

by choosing a positive spillover rate if she was to maximize total surplus of the North and

the South? We demonstrate that, there are certain cases in which the social planner should

neither support the North nor the South. This is because global-welfare maximizing level of

spillovers could be positive but lower than South-optimal level (that is, 0 < θW < θS), due

to the Northern firm’s strategic reduction of its product quality when it undertakes FDI in

the South, as detailed in the previous subsection.

In practice, TRIPS agreement, administered by WTO, is by far the most influential

agreement that is related to international IPR issues. The objective of the TRIPS agreement

was to enforce the level of IPR protection in Southern countries to the level accepted globally,

normally those proposed by Northern countries.25 The agreement also aims to “contribute to

promotion of technological innovation and to the transfer and dissemination of technology...

in a manner conducive to social and economic welfare.” As pointed out by Lai and Qiu

(2003) and other authors, for the purpose of maximizing global welfare, the level of IPR

protection in Southern countries should be set equal to or even stronger than that adopted in

Northern countries (see also Diwan and Rodrik 1991). In contrast, our analysis suggests that,

WTO should take into account the costs and benefits associated with technology spillovers

in Southern countries as a consequence of Northern firms’ FDI. In doing so, WTO might

allow the presence of positive spillovers in the South to some degree but require that the

level of spillovers is lower than what Southern countries desire. This result, which is unique

to quality-enhancing spillovers, suggests the active roles to be played by WTO in reconciling

the North-South conflict concerning the level of IPR protection in the Southern countries.

7 Conclusion

Technology spillovers induced by FDI usually improves performance of the local firms at

the cost of the foreign firms. This has become an important issue in the international

trade literature. Various papers have analyzed technology spillovers from Northern firms

to Southern firms that reduce the latter’s marginal cost (Chin & Grossman, 1990, among

others). Incorporating FDI in such cost-reducing technology spillovers framework, previous

25The U.S., Japan and European Nation were most active players in the negotiation for TRIPS.

24

authors have found that, Northern FDI usually benefits the South (Glass & Saggi, 2002;

Naghavi 2007).

The present paper departs from this literature by exploring an international duopoly

model of vertical product differentiation with technology spillovers. We have shown that,

the conventional argument that FDI accompanied by technology spillovers benefits the

South does not necessarily hold in the presence of quality-enhancing technology spillovers.

The driving force of this result is the strategic reduction of the Northern firm’s product

quality under FDI, which happens in a range of parameterizations. This strategic quality

reduction reduces the net social benefits associated with the consumption of Northern firm’s

product, and thus it hurts the South. We have also found that, the global welfare-maximizing

level of spillovers is positive but could be lower than the South-optimal level. These finding

lends a support to the WTO in that, through TRIPS agreement, WTO can reconcile the

North-South conflict concerning the level of IPR protection in the Southern countries.

Similar implications for trade policy are also embodied in our analysis. Particularly,

since FDI could hurt the South, implementing a high trade barrier to attract FDI with

technology spillovers might not be a good choice for Southern countries. This suggests that

Southern governments should carefully assess the impact of spillovers, especially those are

associated with product quality.

In summary, this paper contributes to international trade and FDI literature in a number

of ways. First, we have constructed an international duopoly model of vertical product

differentiation with technology spillovers to study the location choice of a Northern firm

between home-production and FDI. We then analyzed the equilibrium quality levels the

Northern firm and the Southern firm would choose for their product. By exploring these

strategic choices of product quality, we have discovered novel policy implications of quality-

enhancing technology spillovers, which are also consistent with reality.

Appendix

Proof of Proposition 1.

Let us denote by pik and qi

k respectively price and quality levels chosen by firm k(= N,S) in subgamei(=HP, FDI). Also, let qi

k∗ be equilibrium quality level of firm k in subgame i. The proof goes as

follows. First, we assume that the separating SPNE of the game exists to find the level of qualityeach firm chooses in the separating SPNE. We then focus on HP subgame only (that is, withoutconsidering FDI subgame) to characterize necessary conditions for such separating SPNE withinHP subgame (Claim 1 and 2). We then repeat this step but focus on FDI subgame only (Claim3 and 4). Finally, sufficient conditions for separating SPNE of the whole game are examined inClaim 5 and 6 where we consider off-equilibrium credible threat (that is when firm N deviates byselling to consumers in the other subgame).

25

Let us now find the values of qik∗. First, consider the HP subgame. In the separating equilibrium

of this subgame, the pricing constraints are given by:

vHqHPN − pHP

N ≥ 0 (A.1)

vLqHPS − pHP

S ≥ 0 (A.2)

vHqHPN − pHP

N ≥ vHqHPS − pHP

S (A.3)

vLqHPS − pHP

S ≥ vLqHPN − pHP

N . (A.4)

From (A.2) and (A.3), it follows that vHqHPN − pHP

N ≥ vHqHPS − pHP

S ≥ 0. So that (A.1) holdsand can be excluded. Next, if (A.2) does not hold with equality, we can increase both pHP

S andpHP

N by some small amount without affecting any other constraints, a contradiction, so that (A.2)should hold with equality. Then, if (A.3) does not hold with equality, we can increase pHP

N by asmall amount without affecting any other constraints, a contradiction. So (A.3) holds with equality.Lastly, plug pHP

N from (A.3) to (A.4), we see that (A.4) always holds and can be excluded. So thatwe end up with only two constraints being held with equality, (A.2) and (A.3). Thus, pHP

S = vLqHPS ,

and pHPN = vLqHP

S + vH(qHPN − qHP

S ).

Note that qHPN > qHP

S holds because from (A.3) and (A.4), we have vH(qHPS −qHP

N ) ≤ pHPS −pHP

N ≤vL(qHP

S − qHPN ) ⇒ vH(qHP

S − qHPN ) ≤ vL(qHP

S − qHPN ) ⇒ qHP

N ≥ qHPS and the equality can not hold

(when both firms choose same product quality then they engage in Bertrand pricing game and eachmakes a zero profit). Therefore, qHP

N > qHPS .

The problem facing firm S becomes:

maxqHPS

mL[vLqHPS −

qHPS

2

2] (A.5)

subject to: qHPS ≤ qS .

Firm N takes firm S’s product quality as given to solve his problem:

maxqHPN

mH [vLqHPS + vH(qHP

N − qHPS )−

qHPN

2

2− t]. (A.6)

The solutions are given by: qHPS

∗ = qS and qHPN

∗ = vH . The profits accrued to firm N and firm S

in the separating equilibrium of HP subgame are respectively given by πHPN

∗ = mH [vLqS + v2H2 −

vH qS − t], and πHPS

∗ = mL[vLqS −q2S2 ].

26

Now, let us explore the FDI subgame. In the separating equilibrium of this subgame, the pricingconstraint will be similar to that of HP subgame. Since firm S sells to type L consumers, it has theresponse function qFDI

S = vL if qS(qFDIN ) = qS + θ(qFDI

N − qS) ≥ vL, and qFDIS = qS + θ(qFDI

N − qS)otherwise. Anticipating this, firm N solves its problem:

maxqFDIN

mH [vLqFDIS + vH [qFDI

N − qFDIS ]−

qFDIN

2

2]. (A.7)

There are two relevant options for firm N . The first option is to make the constraint qS(qFDIN ) =

qS + θ(qFDIN − qS) bind by choosing qFDI

N∗ = q′N = (1− θ)vH + θvL so that firm S chooses qFDI

S∗ =

qS(q′N ). The second option is to choose qFDIN

∗ = vH , allowing firm S to choose qFDIS

∗ = vL. Notethat the possibility in which firm N chooses qFDI

N∗ = vH and firm S chooses qFDI

S∗ = qS(vH) < vL

does not arise because it is then more profitable for firm N to choose qFDIN

∗ = q′N . Similarly, thepossibility in which firm N chooses qFDI

N∗ = q′N and firm S chooses qFDI

S∗ = vL does not arise

because it is then more profitable for firm N to choose qFDIN

∗ = vH .

qFDIN

∗ = vH gives firm N ’s profit πFDIN

∗ = mH [v2H2 + v2

L − vHvL] and firm S obtains profit

πFDIS

∗ = mL[v2L2 ], whereas qFDI

N∗ = (1−θ)vH +θvL gives firm N profit πFDI

S∗ = mH [−(1−θ)(vH −

vL)qS + ((1−θ)vH+θvL)2

2 ] and firm S obtains profit πFDIS

∗ = mL[vL(1− θ)qS + θ[(1− θ)vH + θvL]−((1−θ)qS+θ[(1−θ)vH+θvL])2

2 ]. Simple comparison suggests that if θ > θ = vH−qS−√

(vH−qS)2−2(vH−vL)(vL−qS)

vH−vL

then firm N chooses qFDIN

∗ = vH , and it chooses qFDIN

∗ = q′N = (1− θ)vH + θvL otherwise.

We can now focus on HP subgame to find the necessary conditions for separating SPNE withinthis subgame to exist, as formalized in Claim 1 and 2.

Claim 1. Consider HP subgame. Assume that firm N chooses qHPN

∗ = vH , then firm S only sells

to type L consumers in this subgame if and only if mH < mH1, where mH1 ≡ mLqS(vL−vH)+

v2H2−t

−(vH−qS)2

2+t

if (vH−qS)2

2 + vLqS −q2S2 > t > (vH−qS)2

2 , mH1 ≡ 0 if t ≥ (vH−qS)2

2 + vLqS −q2S2 , and mH1 ≡ +∞

otherwise.

Proof. Consider the outcome in which firm S deviates from separating SPNE of HP subgame tosell to type H consumers under HP . Then its [quality, price] menu, [qHP

S , pHPS ], satisfies:

vHqHPS − pHP

S ≥ v2H − pHP

N (A.8)

That is, firm S will choose pHPS = vHqHP

S − v2H + pHP

N . Then, since vHqHPS − v2

H + pHPN <

vLqHPS −vLvH +pHP

N ⇒ vLqHPS −pHP

S > vLvH −pHPN , type S consumers still purchase from firm S,

so that it sells to all consumers and firm N sells nothing. Since firm N never chooses a price belowits average cost, v2

H2 + t, for firm S to sell to all consumers then pHP

N = v2H2 + t must hold. Firm S

then chooses pHPS = vHqHP

S − v2H2 + t, obtaining profit πHP ′

S = (mH +mL)(t− (vH−qHPS )2

2 ) which can

27

be maximized at qHPS = qS and thus πHP ′

S = (mH + mL)(t− (vH−qS)2

2 ). If t ≤ (vH−qS)2

2 this profit

is non-positive so that firm S will not deviate. If t > (vH−qS)2

2 , for firm S to be better off under

separating equilibrium, we need πHP ′S < πHP

S∗, or (mH + mL)(t− (vH−qS)2

2 ) < mL(vLqS − qS2

2 ) ⇒

mH < mLvLqS−

qS2

2+

(vH−qS)2

2−t

t− (vH−qS)2

2

≡ ¯mH1, which also requires t < (vH−qS)2

2 + vLqS −q2S2 .

Q.E.D.

Claim 2. Consider HP subgame. In this subgame, firm N only sells to type H consumers if

and only if mH > mH1, where mH1 = mL

(vL−qS)2

2−t

v2H2−qS(vH−vL)− (vL−qS)2

2

if t < (vL−qS)2

2 , and mH1 = 0

otherwise.

Proof. Assume firm N deviates from separating equilibrium of HP subgame, choosing qHPN 6= vH ,

to sell to type L consumers under HP . Then, vLqHPN − pHP

N ≥ vLqHPS − pHP

S holds, so thatpHP

N = vLqHPN − vLqHP

S + pHPS and since vLqHP

N − vLqHPS + pHP

S < vHqHPN − vHqHP

S + pHPS ⇒

vHqHPN − pHP

N > vHqHPS − pHP

S , type H consumers still purchase firm N ’s product. It then sells

to all consumers and firm S sells nothing. Firm S’s reservation price is qHPS

2

2 , so that deviationimplies firm N chooses a [quality, price] menu, [qHP

N , pHPN ], satisfying:

vLqHPN − pHP

N ≥ max(vLqHPS −

qHPS

2

2) (A.9)

Firm S’s profit, vLqHPS − qHP

S2

2 , is concave in qHPS and since vL > qS , firm S’s profit is maximized at

qHPS = qS . This in turn implies that for firm N to sell to all consumers then pHP

N = vLqHPN −vLqS +

qS2

2 must hold. The profit of firm N under such a deviation will be πHP ′N = (mH + mL)(vLqHP

N −

vLqS + qS2

2 − qHPN

2

2 − t), which could be maximized at qHPN = vL, and firm N obtains profit πHP ′

N =

(mH + mL)( (vL−qS)2

2 − t). If t ≥ (vL−qS)2

2 , this profit is non-positive and firm N will not deviate. If

t < (vL−qS)2

2 , for firm N to be better off under separating equilibrium, we need πHP ′N < πHP

N∗, or

(mH + mL)( (vL−qS)2

2 − t) < mH [v2H2 − qS(vH − vL)− t] ⇒ mH > mL

(vL−qS)2

2−t

v2H2−qS(vH−vL)− (vL−qS)2

2

≡ mH1.

Note that v2H2 − qS(vH − vL)− (vL−qS)2

2 = (vH−qS)2

2 − (vL−qS)2

2 + vLqS + q2S2 > 0.

Q.E.D.

Claim 3. Consider FDI subgame. Assume that firm N chooses qFDIN

∗ (=vH or q′N ), then in thissubgame firm S always sells to type L consumers only.

Proof. Assume that firm S deviates from this separating equilibrium by selling to type H consumersin separating equilibrium of FDI subgame. It then chooses a [quality, price] menu, [qFDI

S , pFDIS ],

satisfying equation (A.10) below:

vHqFDIS − pFDI

S ≥ vHqFDIN

∗ − pFDIN (A.10)

28

That is, firm S will choose pFDIS = vHqFDI

S −vHqFDIN

∗+pFDIN . However, since vHqFDI

S −vHqFDIN

∗+pFDI

N < vLqFDIS − vLqFDI

N∗ + pFDI

N ⇒ vLqFDIS − pFDI

S > vLqFDIN

∗ − pFDIN , firm S then sells to all

consumers and firm N sells nothing. Note that firm N never charges price below qFDIN

∗2

2 , its unit

cost, thus, for firm S to sell to all consumers then pFDIS = vHqFDI

S − vHqFDIN

∗ + qFDIN

∗2

2 must hold,

and firm S’s profit is π′S = (mH + mL)(− (q∗N−qFDIS )(2vH−qFDI

N∗−qFDI

S )2 ) < 0. Therefore, firm S will

not deviate.Q.E.D.

Claim 4. Consider FDI subgame. In this subgame, firm N only sells to type H consumers

if and only if mH > mH2, where mH2 = mL

(1−θ)(vL−qS)2

2(1+θ)

v2H2−vHvL+v2

L−(1−θ)(vL−qS)2

2(1+θ)

if θ ≥ θ, and mH2 =

mL

(1−θ)(vL−qS)2

2(1+θ)

−(1−θ)(vH−vL)qS+((1−θ)vH+θvL)2

2− (1−θ)(vL−qS)2

2(1+θ)

otherwise, and θ = vH−qS−√

(vH−qS)2−2(vH−vL)(vL−qS)

vH−vL.

Proof. Assume firm N deviates from the separating equilibrium of FDI subgame by selling to typeL consumers under FDI. Then, firm N chooses a [quality, price] menu, [qFDI

N , pFDIN ], satisfying:

vLqFDIN − pFDI

N ≥ max(vLqFDIS −

qFDIS

2

2) (A.11)

That is, firm N will choose pFDIN = vLqFDI

N − max(vLqFDIS − qFDI

S2

2 ). Since vLqFDIS − qFDI

S2

2

is concave in qFDIS , its maxima is obtained at qFDI

S = min(qS(qFDIN ), vL). Can firm S choose

qFDIS = vL if firm N deviates from the separating equilibrium of FDI subgame? If this happens

then pFDIN = vLqFDI

N − v2L2 , so that profit of firm N from deviation will then be πN = (mH +

mL)(vLqFDIN − v2

L2 − qFDI

N2

2 ) ≤ 0, contradiction. Therefore, if firm N deviates then qFDIS = qS(qFDI

N )

must hold. In such a deviation, firm N chooses pFDIN = vLqFDI

N − vLqS(qFDIN ) + q2

S(qFDIN )2 . Then,

vHqFDIN − pFDI

N > vHqFDIS − qFDI

S2

2 , so that firm N sells to all consumers and firm S sells nothing.

The profit of the firm N from deviation will be πFDI′N = (mH + mL)(vLqFDI

N − vLqS(qFDIN ) +

qS2(qFDI

N )2 − qFDI

N2

2 ), which is maximized at qFDIN = vL+θqS

1+θ . Thus, πFDI′N = (mH +mL) (1−θ)(vL−qS)2

2(1+θ) .

Then, qS(qFDIN ) = qS+θvL

1+θ < vL.

• If θ > θ, for firm N to be better off under separating equilibrium, we need πFDI′N < πFDI

N∗|θ>θ,

or (mH + mL) (1−θ)(vL−qS)2

2(1+θ) < mH [v2H2 − vHvL + v2

L] ⇒ mH > mL

(1−θ)(vL−qS)2

2(1+θ)

v2H2−vHvL+v2

L−(1−θ)(vL−qS)2

2(1+θ)

=

mH2. Note that v2H2 − vHvL + v2

L − (1−θ)(vL−qS)2

2(1+θ) >v2

H2 − vHvL + v2

L − (vL−qS)2

2 > 0 ⇔(vH−vL)2

2 + v2L2 − (vL−qS)2

2 > 0, which always holds.

• If θ ≤ θ, πFDI′N < πFDI

N∗|θ≤θ ⇔ (mH + mL) (1−θ)(vL−qS)2

2(1+θ) < mH [−(1 − θ)(vH − vL)qS +

29

((1−θ)vH+θvL)2

2 ] ⇒ mH >mL

(1−θ)(vL−qS)2

2(1+θ)

−(1−θ)(vH−vL)qS+((1−θ)vH+θvL)2

2− (1−θ)(vL−qS)2

2(1+θ)

= mH2. Note that the

denominator of mH2 is positive because following its deviation from separating SPNE, firmN reduces its quality from qN = (1− θ)vH + θvL to qN = qS+θvL

1+θ so that per-consumer profitdeclines for two reasons: (i) it reduces its quality from separating equilibrium level, and (ii)once reaching qN = qS+θvL

1+θ , it even has to reduce its price further to preempt firm S fromselling. The denominator of mH2 simply captures this per-consumer profit reduction.

Q.E.D.

Claim 5. Assume θ > θ. Then,(i) the separating SPNE is an FDI equilibrium if t ≥ t ≡ (vH − vL)(vL − qS) and mH >

max(mH2, mH3), where mH3 = mL

(vL−qS)2

2−t

v2L−vHvL−

q2S2

+vH qS+tif t < (vL−qS)2

2 and mH3 = 0 otherwise,

and(ii) the separating SPNE of the game is an HP equilibrium if t < t and mH > max(mH1, mH4),

where mH4 = mL

(1−θ)(vL−qS)2

2(1+θ)

vLqS+v2H2−vH qS−

(1−θ)(vL−qS)2

2(1+θ)−t

.

Proof. Let us compare firm N ’s profit in the separating SPNE of HP and FDI subgames whenθ > θ. It follows that FDI is better for firm N if πFDI

N∗|θ>θ ≥ πHP

N∗ ⇒ mH [v2

L + v2H2 − vHvL] ≥

mH [vLqS + v2H2 − vH qS − t] ⇒ t ≥ (vH − vL)(vL − qS) = t. In other cases, HP makes firm N better

off.

• For the separating SPNE of the game to be an FDI equilibrium, beside condition t ≥ t, weneed firm N ’s profit if it deviates to sell to all consumers in HP subgame is lower than itsprofit in such an SPNE, πHP ′

N < πFDIN

∗|θ>θ ⇒ (mH +mL)( (vL−qS)2

2 −t) < mH [v2L+ v2

H2 −vHvL],

which is always true if t ≥ (vL−qS)2

2 . If t < (vL−qS)2

2 , we need mH > mL

(vL−qS)2

2−t

v2L−vHvL−

q2S2

+vH qS+t≡

mH3. Note that v2L− vHvL−

q2S2 + vH qS + t > v2

L− vHvL−q2S2 + vH qS +(vH − vL)(vL− qS) =

vLqS −q2S2 > 0. Claim 4 then provides sufficient condition.

• For the separating SPNE of the game to be an HP equilibrium, beside condition t < t, weneed firm N ’s profit if it deviates to sell to all consumers in FDI subgame is lower than itsprofit in such an equilibrium, πFDI′

N < πHPN

∗ ⇒ (mH + mL) (1−θ)(vL−qS)2

2(1+θ) < mH [vLqS + v2H2 −

vH qS − t] ⇒ mH > mL

(1−θ)(vL−qS)2

2(1+θ)

vLqS+v2H2−vH qS−

(1−θ)(vL−qS)2

2(1+θ)−t≡ mH4. Note that the denominator of

mH4 is positive since firm Ns’ per-consumer profit in SPNE of HP subgame is higher thanthat in SPNE of FDI subgame which is higher than per-consumer profit it gets by deviation(see similar logic in the proof of Claim 4). The sufficient condition is then given by Claim2. Note that, (vH−qS)2

2 > (vH − vL)(vL − qS), so condition mH < mH1 = +∞ in Claim 1 isalways satisfied.

30

Q.E.D.

Claim 6. Assume θ ≤ θ. Then,(i) the separating SPNE of the game is an FDI equilibrium if t ≥ t and mH > max(mH2, mH5),

where mH5 = mL

(vL−qS)2

2−t

−(vH−vL)qS(1−θ)+((1−θ)vH+θvL)2

2− (vL−qS)2

2+t

if t < (vL−qS)2

2 and mH5 = 0 otherwise,

and t ≡ θ(vH − vL)[vH − qS − θ vH−vL2 ], and

(ii) the separating SPNE of the game is an HP equilibrium if t < t and mH > max(mH1, mH4).

Proof. Let us compare profit of firm N under separating SPNE of FDI and HP subgames whenθ ≤ θ. It follows that FDI is better for firm N if πFDI

N∗|θ≤θ ≥ πHP

N∗ ⇔ mH [−(vH − vL)qS(1− θ)+

((1−θ)vH+θvL)2

2 ] ≥ mH [vLqS + v2H2 − vH qS − t], or similarly, t ≥ θ(vH − vL)[vH − qS − θ vH−vL

2 ] ≡ t(θ).

Note that, by defining θ∗ = vH−qS−√

(vH−qS)2−2t

vH−vL, θ∗ ∈ [0, 1), then it can be established that if

θ ≤ θ∗ then firm N chooses FDI, and it chooses HP otherwise.26

• For the separating SPNE of the game to be an FDI equilibrium, beside condition t ≥t, we need firm N ’s profit by deviating from this SPNE to sell to all consumers underHP will be lower, πHP ′

N < πFDIN

∗|θ≤θ ⇒ (mH + mL)( (vL−qS)2

2 − t < mH [(vH − vL)qS(1 −θ) + ((1−θ)vH+θvL)2

2 ], which is always true if t ≥ (vL−qS)2

2 . If t < (vL−qS)2

2 , we need mH >

mL

(vL−qS)2

2−t

−(vH−vL)qS(1−θ)+((1−θ)vH+θvL)2

2− (vL−qS)2

2+t

≡ mH5. Note that the denominator of mH5 is

positive thanks to per-consumer profit firm N obtains under SPNE of FDI subgame is higherthan that in HP subgame and higher than per-consumer profit it gets from deviation (seemore on this logic in proof of Claim 4 and 5). Claims 4 then provides sufficient condition.

• For the separating SPNE of the game to be an HP equilibrium, beside condition t < t, weneed firm N ’s profit by deviating from this SPNE to sell to all consumers under FDI islower than the profit it reaps in such an SPNE, πFDI′

N < πHPN

∗ ⇒ (mH + mL) (1−θ)(vL−qS)2

2(1+θ) <

mH [vLqS + v2H2 − vH qS − t] ⇒ mH > mH4 (where the denominator of mH4 is positive as in

the proof of Claim 5). The sufficient condition is then given by Claim 2. Note that, thecondition of mH < mH1 in Claim 1 is always satisfied in this case, since (i) if t < (vH−qS)2

2

then mH1 = +∞, and (ii) if t ≥ (vH−qS)2

2 > t then θ∗ > θ and by defining θ∗ = 1, theseparating SPNE is then an FDI equilibrium.

Q.E.D.

With the help of Claims 1-6, the proof of Proposition 1 is constructed as we define:

26Note that for expositional convenience, we assume that firm N chooses HP if t ≤ t(θ) or if θ > θ∗, andit chooses FDI if t > t(θ) or if θ ≤ θ∗.

31

mH =

max(mH2, mH3) if θ > θ and t ≥ t

max(mH1, mH4) if θ > θ and t < t

max(mH2, mH5) if θ ≤ θ and t ≥ t

max(mH1, mH4) if θ ≤ θ and t < t

Finally, since mH2 and mH4 are weakly decreasing in θ, mH1 and mH3 are independent of θ whilemH5 is weakly increasing in θ ∈ [0, θ∗], if mH > lim

θ→θ∗mH then the game has a separating equilibrium

for all θ ∈ [0, 1). Similarly, since mH1 and mH3 are decreasing in t, mH2 and mH5 are independentof t while mH4 is increasing in t ∈ [0, t], if mH > lim

t→tmH then the game has a separating equilibrium

for all t ≥ 0.Q.E.D.

Proof of Proposition 2.

If t ≥ t, for all θ in (0, θ), from the proof of Claim 6 above, θ∗ = vH−qS−√

(vH−qS)2−2t

vH−vL≥ θ =

vH−qS−√

(vH−qS)2−2(vH−vL)(vL−qS)

vH−vLso that the separating SPNE of the game is an FDI equilibrium

for all θ ∈ (0, θ]. Furthermore, for all θ ∈ (θ, 1), following the proof of Claim 5 above, the separatingSPNE of the game is an FDI equilibrium. Hence, we can re-define θ∗ = 1 to formalize the proof ofProposition 2. If t < t, since t ≤ (vH−qS)2

2 , it follows that θ∗ < θ as proof of Claim 6 stated. Then,

θ∗ = vH−qS−√

(vH−qS)2−2t

vH−vLis increasing in t.

Q.E.D.

Proof of Proposition 3.The proof comes directly from proof of Proposition 1. Q.E.D.

Proof of Lemma 1.

The proof comes directly from proof of Proposition 1 and Proposition 2 for the case in which t ≥ t.In the case of t < t, since θ∗ < θ, defining θ ≡ θ∗ leads to Lemma 1. Q.E.D.

Proof of Proposition 4, 5.If θ > θ then under separating equilibrium of FDI subgame, firm N chooses qFDI

N∗ = vH while

firm S chooses qFDIS

∗ = vL, so that πN (θ), πS(θ), CS(θ), WS(θ) are all independent of θ.If θ ≤ θ then in the separating equilibrium of FDI subgame (see also proof of Claim 3), it follows

that sign[∂πS(θ)∂θ ] = sign[∂CS(θ)

∂θ ] = sign[∂WS(θ)∂θ ] = sign[∂qFDI

S∂θ ] = vH − qS − 2θ(vH − vL) > 0

since θ < vH−qS

2(vH−vL) ⇔ 3(vH − qS)2 > 8(vH − vL)(vL − qS) always holds; whereas sign[∂πFDIN∂θ ] =

sign[∂qFDIN∂θ ] = vL − vH < 0.

If θ increases from θ = θ to θ′ > θ then global welfare is maximized which in turn implies WS(θ′) >

WS(θ) (since firm N ’s profit evaluated at θ = θ and at θ = θ′ are the same). Furthermore, sincefirm S chooses higher product quality at θ = θ′, CS(θ′) > CS(θ) and πS(θ′) > πS(θ) hold. Q.E.D.

Proof of Proposition 6.

32

If θ > θ∗, the separating SPNE of the game is an HP equilibrium where firm N chooses qHPN

∗ = vH

and firm S chooses qHPS

∗ = qS , so that πN (θ), πS(θ), CS(θ), WS(θ) are all independent of θ.If θ ≤ θ∗ then the separating SPNE of the game is an FDI equilibrium, and firm N chooses qFDI

N∗ =

q′N while firm S chooses qFDIS

∗ = qS(q′N ). Hence, sign[∂πFDIS (θ)∂θ ] = sign[∂CS(θ)

∂θ ] = sign[∂WS(θ)∂θ ] =

sign[∂qFDIS∂θ ] = vH − qS − 2θ(vH − vL) > 0 as θ∗ = θ < vH−qS

2(vH−vL) (see more in proof of Proposition

4,5), whereas sign[∂πFDIN (θ)∂θ ] = sign[∂qFDI

N∂θ ] = vL − vH < 0

If θ increases from θ = θ∗ to θ′ ≥ θ∗, by Proposition 3 and Lemma 1, firm S chooses lower productquality, thus CS(θ′) < CS(θ∗) and πS(θ′) < πS(θ∗) hold. Q.E.D.

Proof of Proposition 7.

An increase in θ from θ∗ to θ′ > θ∗ switches the equilibrium of the game from FDI to HP , so

that global welfare changes from W (θ∗) = mH(q′′NvH − q′′N2

2 ) + mL(qS(q′′N )vL −qS(q′′N )2

2 ) to W (θ′) =

mH(v2H2 ) + mL(vLqS −

q2S2 ), where q′′N = (1− θ∗)vH + θ∗vL. Therefore, W (θ′) > W (θ∗) ⇔ mH(v2

H2 −

(vH − vL)qS − t) + mL(vLqS −q2S2 ) + mH(vH − vL)qS + mHt > mH(q′′NvH − q′′N

2−(vH−vL)qS(q′′N )2 ) +

mL(qS(q′′N )vL −qS(q′′N )2

2 ) + mH(vH − vL)qS(q′′N ). The first three terms in the LHS of the equationrespectively represent firm N ’s profit, firm S’s profit, and consumer surplus under HP , whereasthree terms in the RHS of the equation respectively represent firm N ’s profit, firm S’s profit, andconsumer surplus under FDI at θ = θ ≡ θ∗. Firm N ’s profit is the same in both LHS and RHS.

Thus, W (θ′) > W (θ∗) requires mH >(vH−vL)(qS(q′′N )−qS)+(vLqS(q′′N )− qS(q′′N )

2

2)−(vLqS−

q2S2

)

t ≡ m∗. Letm∗ = +∞ in the case of t = 0 leads to Proposition 7. Note that, for small enough t, m∗ > lim

θ→θ∗mH .

Q.E.D.

Proof of Proposition 8.

When θ ≤ θ then W (θ) = mH

(qFDIN vH−

qFDIN

2

2

)+mL

(qFDIS vS−

qFDIS

2

2

), so that ∂W (θ)

∂θ = −mHθ(vH−vL)2 + mL(vL − qS(q′N ))∂qS(q′N )

∂θ , which is positive when θ = 0. Furthermore, ∂2W (θ)∂θ2 = −mH(vH −

vL)2−mL

((∂qS(q′N )

∂θ )2 +(vL− qS(q′N )(vH −vL))

< 0, hence W (θ) is concave in θ for all θ ∈ [0, θ] andcan be maximized at some θ ≤ θ, where θ = θ makes ∂W (θ)

∂θ = 0. Note that when mH is relativelyhigh then θ ≈ 0 < θ. Formally, when ∂W (θ)

∂θ (θ = θ) < 0 then θ < θ holds, which happens when

mH > mL[vL−(qS+θ(vH−vL))][vH−qS−2θ(vH−vL)]

θ2(vH−vL)2≡ m∗∗. Note that, we can always restrict parameters

such that the denominator of m∗ becomes small so that m∗ > limθ→θ∗∗

mH .Finally, since either at θ = 0 (FDI) or at any θ = θ′ > θ∗ (HP ), firm N chooses qN = vH whilefirm S chooses qS = qS , it follows that W (θ = 0) = mH

v2H2 + mL(vLqS −

q2S2 ) = W (θ = θ′). This

implies that θ = θ maximizes global welfare for all θ ∈ [0, 1). Q.E.D.

Proof of the case firm N is required to choose qN = vH under FDI.

Under FDI equilibrium, given firm N chooses q∗N = vH , firm S chooses q∗S = min{vL, qS(vH)}.Assume first that vL ≥ qS(vH) = qS + θ(vH − qS) then q∗S = qS + θ(vH − qS). Then comparing

33

profit for firm N under HP (πN = mH(v2H2 − (vH − vL)qS − t)) and under FDI (πN = mH(v2

H2 −

(vH − vL)qS)), it follows that firm N chooses FDI if t ≤ (vH − vL)(qS − qS) (which is less than t =(vH−vL)(vL−qS). If vL < qS(vH) = qS+θ(vH−qS) then q∗S = vL so that if t ≥ (vH−vL)(vL−qS) = t

firm N chooses FDI. Combining two cases, we have that if t ≥ t, firm N chooses FDI for all θ

and consequently the analysis of Case I (subsection 5.1) still holds.If t < t then since firm S chooses q∗S = qS + θ(vH − qS) under FDI, firm N chooses FDI ift ≤ (vH −vL)(qS− qS) ⇔ θ ≤ t

(vH−vL)(vH−qS) . Under FDI, it follows that W (θ) = CS(θ)+πS(θ)+

πN (θ) = mHq∗S(vH−vL)+mL[vLq∗S−q∗S

2

2 ]+mH [v2H2 −(vH−vL)q∗S ]. Thus, ∂W (θ)

∂θ = (vL−q∗S)vH > 0.Also, ∂WS(θ)

∂θ = (vH − q∗S)vH > 0. Q.E.D.

Proof of Proposition 9.

For the case of θ ≤ θ, the proof comes from Claim 6 in which the threshold t(θ) has been defined,where ∂t(θ)

∂θ = (vH − vL)((vH − qS)− θ(vH − vL)) > 0 for all θ ∈ [0, 1). If θ > θ, by defining t(θ) = t

forms the proof for Proposition 9. Q.E.D.

Proof of Proposition 10.

If θ > θ, since firms N and S choose their socially optimal quality under FDI, it is obvious

that W (t′) > W ((θ)). If θ ≤ θ, W (t′) = mH(vHq′N − q′N2

2 )+mL(vLqS −q2S2 ), and W (t(θ)) =

mH(v2H2 )+mL(vLqS −

q2S2 ). Thus, W (t′) > W (t) ⇔ mH < mL

(q′N−qS)(2vL−qS−qS)

θ(vH−vL)2≡ m∗

H . Note thatfor θ small then m∗

H becomes large and can exceed mH . Q.E.D.

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