Discussion Papers In Economics
And Business

A Welfare Analysis of Global Patent Protection
in a Model with Endogenous Innovation and Foreign Direct Investment
Tatsuro Iwaisako

Hitoshi Tanaka

Koichi Futagami

Discussion Paper 09-24-Rev.

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Welfare Analysis of Global Patent Protection
in a Model with Endogenous Innovation and Foreign Direct Investment
Tatsuro Iwaisako

Hitoshi Tanaka

Koichi Futagami

Discussion Paper 09-24-Rev.
March 2011

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Welfare Analysis of Global Patent Protection
in a Model with Endogenous Innovation and Foreign Direct Investment∗
Tatsuro Iwaisako†

Hitoshi Tanaka‡

Koichi Futagami§
Abstract
This paper constructs a North–South quality-ladder model in which foreign direct investment(FDI) is determined by the endogenous location choice of firms, and examines analytically how
strengthening patent protection in the South affects welfare in the South. Strengthening patent protection increases the South’s welfare by enhancing innovation and FDI, but it also allows the firms
with patents to charge higher prices for their goods, which decreases welfare. However, the modelshows that the former positive welfare effect outweighs the latter negative effect. Moreover, introducing the strictest form of patent protection in the South, that is, harmonizing patent protection in
the South with that in the North, may maximize welfare in the South as well as in the North. Further,a similar result can also be obtained in a nonscale effect model.
Keywords: foreign direct investment, innovation, intellectual property rights protection, welfare analysis
JEL classification: F43, O33, O34∗

An earlier version of this paper was circulated under the title “Dynamic Analysis of Innovation and Foreign Direct Investment: The

Effects of Patent Protection.” The authors are especially grateful to Tetsugen Haruyama and two anonymous referees for their constructive
comments and suggestions. They would like to thank Kyoji Fukao, Shingo Ishiguro, Masamichi Kawano, Hideki Konishi, Jie Li, Toshihiro
Matsumura, Yasusada Murata, Takumi Naito, Masaki Nakabayashi, Tomoyuki Nakajima, Ryoji Ohdoi, Toshihiro Okada, Julen Esteban-Pretel,
Makoto Saito, Yasuhiro Sato, Akihisa Shibata, Tetsuya Shinkai, Etsuro Shioji, Katsuya Takii, Laixun Zhao, and seminar participants at the JEA
Annual Meeting, Fall 2007, the Kansai Macroeconomic Workshop, Hitotsubashi University, Hokkaido University, Kwansei Gakuin University,
Osaka University, RIEB, Tokyo Institute of Technology, and Tokyo Metropolitan University for their helpful comments. This study was partly
supported by a Grant-in-Aid for Young Scientists (No. 18730136, 20730138) from the Ministry of Education, Culture, Sports, and Technology.
Any remaining errors are the authors’ responsibility.
†

Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.

E-mail:iwaisako@econ.osaka-u.ac.jp‡

Faculty of Economics, Hokkai-Gakuen University, 4-1-40, Asahi-machi, Toyohira-ku, Sapporo 062-8605, Japan.

E-mail:tanaka h@hgu.jp§

Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.

futagami@econ.osaka-u.ac.jp

E-mail:1

Introduction

Recently, many developing countries have been encouraged to strengthen intellectual property rights(IPR) protection. An agreement on Trade-Related Aspects of Intellectual Property Rights (the TRIPs
agreement) claims that all World Trade Organization (WTO) member countries should adopt a set ofminimum standards on IPR, including patents and copyrights. Strengthening IPR protection is often
a requirement for developing countries to enter the WTO. However, most developing countries fearthat stronger domestic protection of IPR may damage their economies.1 Empirical studies show thatstrengthening IPR protection in developing countries tends to cause an income transfer from developing
countries that have few or no patents to developed countries, which have many patents.2 However, inorder to judge whether strengthening IPR protection in developing countries is beneficial or harmful inpractice, it is important to examine how strengthening IPR protection in developing countries affects
their welfare, not their income. That is, does strengthening IPR protection in developing countries harm
their welfare?
The present paper examines how strengthening patent protection in a developing country affects its
welfare, considering all the effects through changes in endogenous variables. To do this, we use a North–South quality-ladder model in which both innovation and technology transfers are endogenous. In ourmodel, the main mode of technology transfer is assumed to be foreign direct investment (FDI). There aretypes of technology transfer that occur from a developed country (hereafter referred to as the North) to adeveloping country (hereafter, the South), such as FDI, licensing, illegal imitation, and outsourcing. In
particular, inward FDI is increasing greatly in developing countries. FDI data from the UNCTAD World
Investment Report show that inward FDI stock in developing countries increased at an annual rate of1

A panel data study of the index of patent protection by Park (2008) shows that many developing countries, as well as

developed countries, strengthened patent protection between 1990 and 2005. For instance, Brazil, China, and India strengthened
patent protection within this period to about three times its average 1960–1990 level. However, the indexes of patent protectionof some developing countries in South-east Asia and Latin America remain below those of developed countries such as the U.S.
and Japan.
2
McCalman (2001) estimated the income transfers brought about by patent harmonization as a result of the TRIPs agreement. His results imply that only a few developed countries, including the U.S., could benefit from cross-country income
transfers by strengthening patent protection, whereas all other countries would experience income losses from TRIPs; for instance, the net transfer from Brazil amounts to 28% of GDP. Moreover, Yang and Maskus (2001a) and Park and Lippoldt (2005)
examined how U.S. receipts of royalties and license fees depend on IPR protection in the recipient countries, and showed thatstrengthening IPR protection has statistically significant positive influences on licensing receipts.

–1–about 10% from 1980 to 2007.
The present analysis obtains the following two main results. First, the model shows that strengthening
patent protection in the South enhances FDI and innovation, and raises the wage rate in the South. The
reason for these results is as follows. Strengthening patent protection in the South enhances FDI because
it enables multinationals to charge higher prices and obtain higher profits. Moreover, the enhancementof FDI further promotes innovation in the North by reducing the labor demand of the production sectors
in the North and directing more labor resources to research and development (R&D). On the other hand,strengthening patent protection in the South raises the wage rate in the South.
Second, using the results of the above positive analysis, the present model shows that strengthening
patent protection in the South increases welfare in both the South and the North. That is, we show thatstrengthening patent protection in the South can be a Pareto-improving policy for the North and theSouth. Moreover, we obtain the following important result for an assessment of global patent protection:
harmonizing patent protection policy in the South with that existing in the North— that is, applying
the strictest patent protection—can maximize welfare in the South. This result implies that, in contrast
to the developing countries’ apprehension that stronger IPR protection damages their welfare, patentharmonization is beneficial to developing countries that have few patents.
In our model, strengthening patent protection in the South affects welfare through three channels,
as follows. The first channel is through enhancing innovation: strengthening patent protection promotes
innovation and consequently raises welfare. The second channel is through the change in nominal spending: as mentioned above, strengthening patent protection raises the wage rate in the South and thereby
increases the nominal spending of Southern consumers, which raises welfare in the South. By contrast,
strengthening patent protection lowers the wage rate in the North and thereby lowers the nominal spending of Northern consumers, which reduces welfare in the North. The third channel is through changing
the prices of goods: the sign of this effect is indeterminate because strengthening patent protection affects
the prices of goods positively and negatively. The third channel can be decomposed into the following
three effects. First, there is a welfare effect that occurs through promoting FDI: strengthening patent
protection lowers the prices of some goods by increasing the proportion of goods produced by multinationals in the South, which produce cheaper goods than do the firms located in the North. Therefore, arise in the proportion of FDI firms raises welfare. The second welfare effect caused by the change inprices occurs through raising the wage in the South: strengthening patent protection raises the wage rate–2–

in the South and enables production firms to charge higher prices for their goods by raising the marginal
costs of rival firms, which consequently reduces welfare. The third welfare effect occurs through reducing competition: strengthening patent protection allows multinationals to charge higher prices fortheir goods because it reduces competition with nonpatentees, which reduces welfare. As a result of thisanalysis, we show that the positive welfare effects can outweigh the negative welfare effects.
In the theoretical literature on technology transfer, a number of studies have examined how strengthening IPR protection affects innovation and FDI. Such studies include those of Helpman (1993), Lai(1998), Glass and Saggi (2002), Glass and Wu (2007), Mondal and Gupta (2008), and Dinopoulos andSegerstrom (2010).3 However, with the exception of Helpman (1993), none of these authors conductedcomplete analyses of welfare.4 Unlike these studies, our study analyzes the welfare effect of strengthening patent protection in the South by using a simple model with no transitional dynamics.5 Further, we
also conduct welfare analysis by using the extended model without scale effects; although the extended
model exhibits transitional dynamics, we can conduct a complete analysis of welfare in the same way as
did Helpman (1993), who evaluated the effect on welfare of marginally strengthening IPR protection.
One of the few studies dealing with the welfare effect of IPR protection in developing countries isthat of Helpman (1993), who conducted two welfare analyses: first, a welfare analysis in a North–Southmodel in which the only mode of technology transfer is illegal imitation; and second, a welfare analysis ina model in which the means of technology transfer is FDI.6 The former analysis examined how lowering
the probability of imitation of Northern products by Southern firms, which is achieved by introducing
tighter IPR in the South, affects welfare levels in both the South and the North. The results showed thattighter IPR reduces welfare in the South mainly by hampering innovation. The latter analysis, which ismore relevant to the present paper because it deals with FDI, showed a similar result to the first analysis
3

As can FDI, licensing can play an important role in technology transfer in the development process, as has occurred in,for example, Japan, Korea, and Taiwan. Some studies have constructed North–South growth models in which the mode oftechnology transfer is not FDI but licensing; see, for example, Yang and Maskus (2001b), Tanaka et al. (2007), and Futagami
et al. (2007).
4
Although Dinopoulos and Segerstrom (2010) conducted welfare analysis, theirs was limited to the comparison between
steady states.
5
Although this feature of our model is based on some special assumptions, the policy implications of our model are useful
because few existing studies in this literature deal with the welfare effect of IPR protection.
6
Extending the model of Helpman (1993), Grinols and Lin (2006) analyzed the welfare effect of strengthening patent
protection in the South. However, the equilibrium paths in their model are so complex that they rely on numerical analysis. In
addition, in contrast to the present model, their model does not include FDI.

–3–

without FDI; that is, tighter IPR in the South necessarily reduces welfare in the South.
Why does the result of the present paper contrast with the pessimistic result from the FDI model ofHelpman? The main reason is that the present paper assumes that innovation is determined endogenously,
whereas Helpman’s FDI model assumes for simplicity that innovation is exogenous. By introducing theendogenous determination of innovation, our model can capture an important positive welfare effect ofstrengthening IPR protection, that is, the welfare effect that occurs through enhancing innovation, which
is not taken into account in Helpman’s FDI model. The main result of the present paper implies thatthe negative conclusion regarding the welfare effect of strengthening patent protection in the South may
change significantly when the welfare effect that occurs through innovation is taken into consideration.
We briefly describe how patent protection is incorporated into our model. There are two instrumentsof patent policy: patent length and patent breadth. Patent length refers to the duration for which a patentee can sell the patented product monopolistically. Patent breadth refers to the scope of products thatpatentees can prevent firms without patents from producing and selling. We focus on the effects of extending patent breadth to evaluate analytically the welfare effect of increasing patent protection in theSouth. More concretely, in a quality-ladder model, patent breadth represents the degree of quality thatthe government permits firms other than the patentee to produce and, thus, patent breadth determines
the markup charged by multinationals. Hence, in the present quality-ladder model, broadening patent
breadth operates as would raising the markup of multinationals; that is, broadening patent breadth allows the multinationals to charge higher prices and obtain higher profits, which raises the number ofmultinationals and increases both the labor demand and the wage rate in the South.7
In contrast to the present paper, which deals with optimal patent breadth, and unlike studies that
use the imitation rate as the parameter of IPR protection, some studies analyzed the effects of patent
7

The TRIPs agreement requires WTO member countries to strengthen patent protection not only in regard to patent length

but also in regard to patent breadth. According to Maskus (2000, pp. 21–22), TRIPs mandated that, in adjudicating process
patent infringement cases, the burden of proof is reversed; that is, the defendant must demonstrate that his or her process does
not infringe the plaintiff’s patent. In general, proving process infringement is difficult, and this reduces the scope of productsthat firms without a patent can produce and sell, and the consequence of this is an extension of patent breadth. On the other
hand, TRIPs requires extending the coverage of products that are patentable and the strengthening of patent enforcement; WTO
member countries must extend patent protection to important areas of technology such as chemical products and processes,
pharmaceutical products and processes, and food products and they must make more effort to expose patent infringements. We
can interpret these requirements as strengthening patent protection in regard to patent breadth. See Maskus (2000, Ch. 2) for
details.

–4–

length. Dinopoulos and Kottaridi (2008) focused their analysis on the effect of changing patent length.8
They analyzed the effects of patent harmonization, under which the strength of the South’s patent protection is raised to the level of the North’s patent protection, and obtained the important result that patentharmonization raises the long-run growth rate and improves the relative wage in the South. However,Dinopoulos and Kottaridi (2008) did not evaluate the welfare effects of strengthening patent protection
because of the complexity of their model with a finite patent length.9 Grossman and Lai (2004) also usedpatent length as the policy instrument of patent policy. They analyzed why IPR tends to be better protected in the North than in the South by using a North–South model in which R&D is conducted in bothcountries. However, they assumed quasilinear utility in order to conduct welfare analysis. Furthermore,their model is not a growth model, unlike the present model and that of Dinopoulos and Kottaridi (2008).
The rest of the paper is structured as follows. In Section 2, we describe the model. In Section 3, wederive the equilibrium path of the model and show that strengthening patent protection promotes bothinnovation and FDI. In Section 4, we consider the effect of stronger patent protection on the welfare of
consumers in both the South and the North. In Section 5, we examine how R&D subsidies influence thewelfare effect of strengthening patent protection, and we investigate how the welfare effect of strengthening patent protection would change in a nonscale effect version of the model. In Section 6, we provide
concluding remarks.

2

The Model

We develop a dynamic general equilibrium model such that FDI is introduced into a quality-ladder model.
Our model has the same basic structure as that of Grossman and Helpman (1991, Ch. 12).
8

Most of the existing studies dealing with patent protection, such as that of Kwan and Lai (2003), use the imitation rate

as the parameter of patent protection. In contrast to these models that incorporate a constant imitation rate, which depends onthe degree of IPR protection determined by governments, the recent growth model of the endogenous strength of protection
constructed by Eicher and Garcı́a-Peñalosa (2008) assumes that private R&D firms can raise the degree of enforcement by
allocating labor to developing institutions that prevent the infringement of their IPR. They showed that endogenizing IPR
protection generates multiple equilibria; that is, there is a high-growth equilibrium with stronger IPR protection and a lowgrowth equilibrium with weaker IPR protection.
9
In theoretical analyses of patent length, the dynamic properties of the equilibrium paths tend to be complicated. For
example, Futagami and Iwaisako (2007) investigated analytically the characteristics of the equilibrium paths of an economy
incorporating a finite patent length and showed that, even if the production structure is a simple AK type, the equilibrium paths
exhibit oscillations.

–5–Consider an economy comprising two countries, the North and the South, which are denoted by N
and S, respectively. The population size of country i ∈ {N, S} is given by Li , and each agent supplies
one unit of his or her labor inelastically at each point in time. There is a continuum of goods, indexedby ω ∈ [0, 1], that are produced in the North or the South. Each product is classified by a number of“generations” j = 0, 1, 2, · · · and each generation progresses one step ahead if innovation occurs in theindustry. Therefore, product ω of generation j can be produced after the jth innovation in industry ω. As
we explain subsequently, innovation occurs as a result of successful R&D efforts by firms. We assume
that products of different generations have different “qualities”. The quality of product ω of generation
j is given by qj (ω) = λj , where the increment in quality between generation j and j + 1, λ > 1, is
identical for all products. In addition, we assume that one unit of labor produces one unit of output ineach country and industry, irrespective of the generation number j. We choose our units appropriately sothat, at time t = 0, the generation number is zero and quality is unity for all goods.

2.1 Consumers
Consumers living in country i ∈ {N, S} have the following lifetime utility: Ui =R ∞ −ρt
log ui,t dt,
0 e

where ρ is a common subjective discount rate and log ui,t represents instantaneous utility at time t.
hP
i
R1
i
i
We specify the instantaneous utility function as log ui,t = 0 log
j qj (ω)dj,t (ω) dω, where dj,t (ω)
denotes the individual’s consumption of good ω of generation j at time t.10 The representative consumer
maximizes his or her lifetime utility subject to the following budget constraint:
Z ∞R− 0t rs dse

Z ∞Ei,t dt = Ai,0 +0Rte− 0 rs ds wi,t dt,(1)0

where rt is the interest rate that consumers in both countries face at time t, Ai,0 is the initial asset holdingsof a consumer in country i, and wi,t denotes the wage in country i. The term Ei,t represents the flow ofi
R 1 hPi
spending at time t, which is given by Ei,t = 0
j pj,t (ω)dj,t (ω) dω, where pj,t (ω) is the price of
product ω of generation j at time t.
10

In this model, we implicitly assume that the product with a quality level that lies between those of the latest generationand the second-latest generation can be produced and consumed. However, as mentioned below in Subsection 2.2, because of
the pricing behavior of the firms holding the patent on the latest-generation product, only the product of the latest generation is
produced and consumed in each goods sector. Thus, for simplicity, we describe the instantaneous utility as if a product with aquality level that lies between those of the latest generation and the second-latest generation could not be consumed because,in equilibrium, consumers do not consume such a product.

–6–

This consumer’s utility maximization problem can be solved in two stages. In the first stage, theconsumer allocates his or her spending Ei,t to maximize log ui,t , given prices at time t. To solve this static
problem, the consumer allocates identical expenditure shares to all products. Then, for each product,
the consumer chooses the single generation j = Jt (ω) that carries the lowest quality-adjusted pricepj,t (ω)/qj (ω). This implies the following static demand function: Ei,t /pj,t (ω) for j = Jt (ω),
dij,t (ω) =0otherwise.
In the second stage, the consumer chooses the time pattern of spending to maximize his or her lifetime
utility. Such intertemporal utility maximization requires that Ėi,t /Ei,t = rt − ρ. By treating aggregate
spending as the numeraire, we normalize Et ≡ EN,t LN + ES,t LS = 1 for all t so that the interest rate
rt always corresponds to the subjective discount rate ρ.11

2.2

Production

We assume that each economy has a single primary production factor, namely labor. The amounts of
total labor supplied in the North and the South are constant and are denoted by LN and LS , respectively.
As is the case in most related studies, we assume that labor is immobile between the North and theSouth. Labor is devoted to the production of goods in both the North and the South. In addition, in
the North, labor is devoted to innovative activities to develop a higher quality product. We assume thatstate-of-the-art products cannot be invented in the South.
If a Northern firm succeeds in inventing a state-of-the-art good, it can take out a patent for the goodin both countries and supply the good monopolistically. In contrast to the typical setting adopted by, forexample, Grossman and Helpman (1991), we assume that firms in country i ∈ {N, S} other than theinventor of the latest-generation product have the technological capacity to make a product with a levelof quality that lies between those of the latest generation and the second-latest generation by imitating
the product without undertaking R&D if and only if the inventor is located in country i. However, theexistence of the patent legally guards the inventor from imitation. Thus, as mentioned below, the highest
level of product quality that other firms can produce and sell legally depends on the degree of patent
protection in the country.
11

This normalization is convenient for examining the dynamic behavior of the economy. See Grossman and Helpman (1991,

Ch. 12).

–7–

In the present paper, we assume that the inventor of a latest-generation product can select the locationof production; that is, the firm determines whether to produce the good in the North or shift production
to the South by undertaking FDI. In particular, we assume that the Northern firm, which is the inventor
of a latest-generation product, can shift production from the North to the South instantaneously and at
no cost if the firm chooses to undertake FDI.12 If the firm elects to shift production to the South, it canuse Southern labor, which is cheaper than Northern labor. This allows the firm to obtain higher profits ateach point in time. However, a firm that chooses to undertake FDI faces more intense competition frompotential rivals than does a patentee located in the North. This is because patent protection is assumed to
be weaker in the South than in the North. We assume that a firm can freely export its product from one
country to the other without incurring transportation costs or facing tariffs.
Before considering how patentees decide whether to undertake FDI, we must consider how governments protect patents in the North and the South. Generally, there are two policy instruments influencing
the degree of patent protection. One is the patent length, which determines for how long the patentee canproduce and sell the product exclusively. The other is the patent breadth, which determines the scopeof products that the patentee can prevent other firms from producing and selling. In the quality-laddermodel, because products of different qualities within the same product line are perfect substitutes, patent
breadth represents the degree of quality that the government permits other producers to produce.13 In
practice, governments control both policy variables. However, for simplicity, we assume that the patent
length is fixed and infinite and that governments control the degree of patent protection by using only thepatent breadth.14
12

In similar studies of FDI, Lai (1998) and Glass and Wu (2007) make a similar assumption. We can extend the model toinclude the cost of FDI. However, as long as the cost of FDI is small, introducing such a cost into the model would not change
the result that strengthening patent protection in the South can improve the welfare of consumers in the North and the South.
13
Strictly speaking, the concept of patent breadth includes leading breadth and lagging breadth. Leading breadth specifies thelevel of superiority of a product (compared with the patented product) that producers without the patent are legally permitted
to produce and sell. Lagging breadth specifies how inferior a product must be compared with the patented product for the
producers without the patent to legally produce and sell it. The definition of patent breadth used in this paper corresponds tolagging breadth. O’Donoghue and Zweimüller (2004) examined how leading breadth affects innovation and welfare in a closed
economy. On the other hand, similarly to us, Li (2001) analyzed the effect on innovation of lagging breadth in a quality-laddermodel. However, he analyzed a closed economy.
14
Judd (1985), Iwaisako and Futagami (2003), and Futagami and Iwaisako (2007) examined how patent length affects social
welfare. As shown by Futagami and Iwaisako (2007), under the assumption of finite patent length, the equilibrium paths arecomplicated.

–8–In the present paper, we incorporate patent breadth as follows. When the state-of-the-art quality of
product ω is given by qj (ω), firms in country i other than the patentee of the state-of-the-art-quality
product cannot legally produce product ω with a higher quality than qj (ω)/βi , where βi ∈ [1, λ]. Then,βi can be interpreted as representing the patent breadth in country i. In this setting, a higher βi implies abroader patent breadth: if βi is equal to λ, then patent protection in country i is at its maximum; if βi isequal to unity, then patent protection in country i is nonexistent.15
Under the rules of patent policy, the pricing strategy of a firm operating in country i depends on thepatent breadth in that country. The optimal price level for the firm holding the patent for a state-of-theart good is such that the other firms cannot earn positive profit by entering the market for that good.
That is, the leader firm chooses to adopt a limit pricing strategy. More concretely, the patentee of thelatest generation of product ω, the quality of which is equal to qj (ω), adopts a pricing strategy such thatthe quality-adjusted price of the good is no higher than the quality-adjusted price charged by the otherproducers. If the patentee is operating in country i, the other producers can legally produce productω with quality of no more than qj (ω)/βi . Therefore, if the patentee charges a price p that satisfies
p/qj (ω) ≤ p0 /[qj (ω)/βi ], where p0 denotes the price set by the other producers, then the patentee can
exclude the other producers from the market. Because the lowest price that the other producers cancharge is equal to their marginal cost, the limit price of the patentee is given by p = βi M C, where
M C denotes the marginal cost of the other firms. This implies that a greater patent breadth enables thepatentee to charge a higher price; in particular, when βi takes its highest value, λ, the patentee can raise
the price to λM C, whereas, when βi takes its lowest value, unity, the patentee must lower the price tothe level of marginal cost.16
Under the patent breadth policy described above, we derive the optimal pricing strategy and the profitof the patent holders producing in the North and the South. In the rest of the paper, we refer to patent
holders producing in the North as “Northern leaders” and refer to patent holders shifting production
15

We can consider a patent breadth that is broader than λ. However, βi > λ implies that the patent for the state-of-the-art-

quality product prevents the production of the good of the second-latest generation in the same product line; that is, the patent
prevents production of the product invented by the previous innovator. Such a large patent breadth seems unrealistic. Thus, in
our analysis, we assume that the patent breadth implied by βi = λ is the strictest form of patent protection.
16
Gilbert and Shapiro (1990) assumed that the patent authority could raise patentee profits by increasing patent breadth.
Hence, they represented the level of patent breadth by the size of the profit flow. Similarly, Goh and Olivier (2002) assumed
that the patent authority could indirectly raise the legal marginal cost of producing a patented good illegally by increasing patent
breadth. Thus, they represented the level of patent breadth by the scale of this legal cost.

–9–

to the South as “multinationals”. First, let us consider the pricing behavior of Northern leaders. We
assume that patent protection is strictest in the North; that is, patent breadth is at its highest: βN = λ.
Then, Northern firms other than the patent holder of the latest-generation product ω are prohibited fromproducing product ω at a quality level exceeding that of the second-latest generation product. Therefore,
the strongest potential rival to the patent holder of the latest-generation product ω is necessarily the patent
holder of the second-latest-generation product that chooses to operate in the South. This implies that themarginal cost of the strongest rival is equal to the wage in the South, wS,t . Thus, the optimal strategyof the patentees of the latest-generation product that decide to produce their goods in the North is to set
their prices to pN,t = λwS,t . Hence, the instantaneous profit of Northern leaders is:
πN,t = (λwS,t − wN,t )

wN,t
1
=1−
.
λwS,t
λwS,t

(2)

Second, let us consider the pricing behavior of multinationals. If patent protection is strong enoughin the South, as well as in the North, then the optimal price for multinationals in the South, pF,t , is thesame as that of Northern firms: pF,t = λwS,t . However, patent breadth may be lower in the South thanin the North. Suppose that patent breadth in the South βS takes a value of β ∈ [1, λ]. That is, a Southernfirm other than the multinational of industry ω is permitted to produce product ω at a quality of qj (ω)/β
when the quality of the state-of-the-art good produced by the multinational is given by qj (ω). Then,
multinationals are obliged to cut their prices to pF,t = βwS,t (≤ λwS,t ), which is lower than pN,t , unlessthere is maximum patent protection in the South.17 The price that multinationals can charge depends
on the extent of patent breadth in the South, as argued by Goh and Olivier (2002). If the Southerngovernment increases patent breadth, Southern firms other than multinationals can produce only lower
quality products. Consequently, multinationals can charge a higher price the greater patent breadth isextended, that is, when patent protection becomes stricter in the South. From the pricing rule, the profit

17

As mentioned above, production at a quality level beyond the patent breadth specified in each country is assumed to beprohibited effectively in each country. Moreover, we assume that products can be distributed and sold freely in both countries;
this assumption is supported by evidence of parallel imports for many products. Therefore, multinationals cannot charge ahigher price in the North than in the South; if they charge a higher price, the other firms can sell the products that they buy frommultinationals to consumers in the North at a lower price than that charged by multinationals in the North, as a consequence of
which multinationals would lose sales in the North. Thus, multinationals are obliged to cut their price in the Northern market
to the price level prevailing in the South, βwS,t .

– 10 –

flow of multinationals is given by:
πF,t = (βwS,t − wS,t )

1
1
=1−
βwS,t
β

(≥ πN,t ).

(3)

As this equation shows, the higher is β, the greater is the profit flow to multinationals. Consequently, thestronger is patent protection in the South, the greater is the incentive to shift production to the South.

2.3

R&D and FDI

Next, we consider the behavior of R&D firms. Following Grossman and Helpman (1991), we assume
the following R&D process: if a Northern firm devotes aN I˜ units of Northern labor for a time intervalof length dt to research on product ω, it succeeds in developing the next generation product ω with
˜ In other words, I˜ represents the instantaneous probability of success in R&D. Althoughprobability Idt.
R&D firms can choose their levels of R&D, investing in R&D imposes on R&D firms labor costs that are˜ If a firm succeeds in developing the new generation of a good, then it can take out aproportional to I.
patent for that generation of product. For a finite size of R&D activities in equilibrium, the expected gainfrom R&D must not exceed the cost of R&D. Thus, letting vN,t denote the market value of the patent,
we have:
vN,t ≤ wN,t aN

with equality if It > 0,(4)where It denotes the innovation rate in the economy at time t, which is common to all industries.
Once a Northern firm succeeds in inventing a new-generation good, the firm can become a multinational by shifting production to the South at no cost. Therefore, as long as both Northern leader firms
and multinationals exist in equilibrium, the market values of these firms are equal; that is, the following
equality holds at each point in time:
vN,t = vF,t ,(5)where vF,t denotes the market value of multinationals.
Next, we consider no-arbitrage conditions. The shareholders of a Northern leader firm earn dividends
πN,t dt and capital gains v̇N,t dt over a time interval of length dt. Moreover, the Northern leader firm is
exposed to the risk of being leapfrogged by the development of the next-generation good by anotherNorthern firm at the innovation rate It over that time interval. Thus, shareholders face making a capital
loss of vN,t with probability It dt. Therefore, we obtain the following no-arbitrage condition between the– 11 –

stock of the patentee of a state-of-the-art product in the Northern market and a riskless asset:18
rt vN,t = πN,t + v̇N,t − It vN,t .

(6)

The shareholders of a multinational earn dividends πF,t dt and capital gains v̇F,t dt over a time interval oflength dt. The multinational is also exposed to the risk of being leapfrogged by a Northern firm at theinnovation rate It . Thus, its shareholders face making a capital loss of vF,t with probability It dt. The
no-arbitrage condition between the stock of a multinational and a riskless asset is:rt vF,t = πF,t + v̇F,t − It vF,t .

(7)

2.4 The Labor Market
First, we consider the labor market in the South. Southern labor is demanded for production by multinationals that have patents for their state-of-the-art products. We let nF,t denote the measure of industries
in which multinationals produce these state-of-the-art products. Because each multinational demands
1/(βwS,t ) units of Southern labor, the aggregate labor demand of multinationals is nF,t /(βwS,t ). Therefore, the labor market clearing condition in the South is:nF,t= LS .
βwS,t(8)

In the North, labor is devoted not only to production but also to R&D activities. Letting nN,t represent
the measure of industries in which Northern firms produce the state-of-the-art-quality products, the labordemand for production in the North is given by nN,t /(λwS,t ). In addition, because R&D firms target all
goods, the labor demand for R&D activities is given by aN It (nF,t + nN,t ). Because nF,t + nN,t = 1,
the labor market clearing condition in the North is:nN,t+ aN It = LN .
λwS,t

3

(9)

Market Equilibrium Paths

In this section, we derive the equilibrium paths of both economies. That is, we explain the determinationof the measure of firms choosing to undertake FDI, nF,t , the wage rates in the South and the North, wS,t
18

If the Northern firm shifts production to the South and becomes a multinational, the gain is (vF,t − vN,t ); however, this iszero from (5). Hence, even if we allow Northern firms to choose their FDI, the no-arbitrage condition remains unchanged.

– 12 –

and wN,t , and the innovation rate, It . As shown in this section, our model has no transitional dynamics
and, thus, these variables are constant over time.
First, we consider the equilibrium determination of FDI. From (5), the market values of Northernleaders and multinationals are equal at each point in time. Therefore, in what follows, we let vt denotethe market value of all firms; that is, vt ≡ vN,t = vF,t . Because (5) holds at each point in time, we obtainv̇F,t /vF,t = v̇N,t /vN,t . Substituting the no-arbitrage conditions (6) and (7) into this equation yields:
πF,t = πN,t .

(10)

Using (2) and (3), the equilibrium condition for FDI, (10) requires the following relationship between
wN,t and wS,t :wS,t =

βwN,t .
λ(11)This means that the relative wage in the South, wS,t /wN,t equals β/λ ∈ [1/λ, 1] and is an increasing
function of β.19 The reason is as follows. Greater patent breadth in the South (a higher β) guarantees
multinationals higher profits, as shown by (3). Moreover, because multinationals and Northern leaders
must earn equal profits, greater patent breadth in the South must also raise the profits of Northern leaders.
In order for the profits of Northern leaders to be higher, the total production cost of Northern leaders must
be lower because their revenue is fixed. The total production cost of Northern leaders, which is equal towN,t /(λwS,t ), is inversely proportional to the relative wage in the South and, hence, the relative wage in
the South must be increasing with β.
Second, from the condition for labor market equilibrium in the South, (8), the relationship between
19

The upper limit of the relative Northern wage rate implied by this model is determined by λ. However, this level isprobably unrealistically low, given a plausible estimate of λ; related literature, such as the study of Şener (2008), suggests that
λ is between 1.05 and 1.4. This is a common feature of quality-ladder North–South models, as explained by Gustafsson andSegerstrom (2010). In the quality-ladder North-South model, the production of goods that have been imitated in the South canmove back to the North due to successful innovation by a Northern firm, and therefore, the price charged by the Northern firm
becomes λwS , which depends on the Southern wage rate. Furthermore, it must not be lower than the Northern wage rate, wN
in order to guarantee positive profit for Northern innovators, and thus this imposes the upper limit of the Northern relative wage
rate: λ > wN /wS . Gustafsson and Segerstrom (2010) released the relative wage from the condition by utilizing a varietyexpansion North-South model, where the production of goods that have been imitated in the South cannot move back to theNorth by Northern firms’ innovation. Moreover, they showed that introducing the differences in R&D technologies between
innovation in the North and imitation in the South into the models, the model can account for an arbitrarily large Northern
relative wage.

– 13 –

the measure of multinationals and the wage rate in the South is positive as follows:
nF,t = βLS wS,t .

(12)This is because a rise in the wage in the South raises the price of the good of a multinational, pF,t =βwS,t , which reduces the demand for the labor used to produce this good, 1/(βwS,t ). The decrease inlabor demand in the South enables more firms to conduct FDI and increases nF,t . In the same way,strengthening patent protection in the South increases the measure of multinationals.
Third, we consider the relationship between the innovation rate, It , and the wage rate in the South,
wS,t . By substituting nF,t + nN,t = 1 and (12) into the condition for the clearing of the Northern labormarket (9), we obtain the innovation rate as follows:It =1 − nF,t
LN
LN + (β/λ)LS
1
−
=
−
.
aN
aN λwS,taNaN λwS,t(13)

These expressions show that the relationship between It and wS,t is positive.
Next, by using the expressions derived so far, we derive the equilibrium value of a firm, vt . As longas the innovation rate is positive, (4) holds with equality: wN,t = vt /aN . By substituting this, (3), (11),
i
h
S
+
ρ
vt − 1.
and (13) into (7), we obtain the following equilibrium dynamics of vt : v̇t = LN +(β/λ)LaN
This differential equation has the unique steady state, v, which is given by:v=

aN.
LN + (β/λ)LS + ρaN(14)This unique steady state v is unstable and, therefore, vt diverges to positive or negative infinity unless vt
is v. Hence, the equilibrium value of vt must immediately jump to v at the initial point in time, because
vt is a jump variable. Because vt is constant over time, we can show that the other variables are also
constant over time; that is, our North–South model economy has no transitional dynamics. However, its
tractability enables us to use the model for welfare analysis.20
20

There are two straightforward ways to extend the model. One is to allow Southern firms to copy the technology ofmultinationals. Assuming this would make the model more realistic because, then, Southern firms other than multinationals
could produce goods. However, this extension injects transitional dynamics into the model because the measure of goods
imitated and produced by Southern firms is a state variable. This complicates the equilibrium path and makes welfare analysis
less tractable. The other possible extension is to introduce a finite patent length as in, for example, Dinopoulos and Kottaridi(2008). The introduction of a finite patent length would affect the welfare effects of raising patent breadth and might change
our welfare results. This would also inject into the model transitional dynamics, perhaps including oscillations, as Judd (1985)
and Futagami and Iwaisako (2007) found. Hence, this extension would make welfare analysis far more difficult.

– 14 –

Note that v depends negatively on β, as shown in (14). This is because strengthening patent protection causes capital losses to rise as leapfrogging by other firms increases because of the promotion of
innovation.
Using the free entry condition, wN,t = vt /aN , and (11), we can compute the following equilibrium
wage rates in the North and South, which are constant over time:
wN =

1
,
LN + (β/λ)LS + ρaN

(15)

wS =

β/λ
,
LN + (β/λ)LS + ρaN(16)

where wN and wS are the equilibrium values of wN,t and wS,t , respectively. In the rest of the paper, thevariables without the subscript “t” represent equilibrium values. From (15) and (16), we can prove thefollowing proposition.
Proposition 1. Strengthening patent protection in the South raises the wage rate in the South and lowers
the wage rate in the North.
Proposition 1 can be interpreted as follows. As shown by (14), strengthening patent protection enhances innovation and therefore reduces the value of Northern firms and multinationals. From the condition for zero profit in R&D, the reduction in the reward for innovation must bring about a decrease in thecost of R&D, which lowers the wage in the North. On the other hand, as shown by (11), strengthening
patent protection in the South raises the relative wage in the South. Because the increase in the relative
wage of the South is sufficiently large to exceed the decrease in the wage in the North, the wage in theSouth must increase.
By substituting (16) into (12) and (13), we can derive the equilibrium values of nF,t and It as follows:(β 2 /λ)LS,
LN + (β/λ)LS + ρaN(17)

β − 1 LN + (β/λ)LS
ρ
− .
β
aN
β

(18)

nF =

I=

Differentiating (17) and (18) with respect to β yields:·¸(β/λ)LSdnF(β/λ)LS
=
2−
> 0,
dβ
LN + (β/λ)LS + ρaN
LN + (β/λ)LS + ρaN– 15 –

dI
1
= 2
dβ
β

µ

¶
LN
LS
+ρ +
> 0.
aN
λaN

(19)

Therefore, we can show that both nF and I are increasing functions of β. Consequently, strengthening
patent protection in the South necessarily promotes FDI and innovation in the North.
Proposition 2. Strengthening patent protection in the South promotes both innovation and FDI.
How can we interpret Proposition 2? As Proposition 1 shows, strengthening patent protection raises
the wage in the South. Therefore, strengthening patent protection raises the price of a good produced bya multinational, pF = βwS , and thereby reduces the demand for the labor used to produce this good,1/(βwS ). Consequently, to keep the Southern labor market in equilibrium, more firms must become
multinationals and shift production to the South than before the policy change. In addition, strengthening
patent protection raises the wage in the South, thereby raising the price of a good produced by a Northernleader, pN = λwS , and thus reducing the demand for the labor used to produce this good, 1/(λwS ).
Because of both the decrease in labor demand by Northern leaders and the increased production shift to
the South, stronger patent protection in the South decreases total demand for the labor used to produce
goods in the North. Consequently, stronger patent protection increases labor demand for R&D activity
and raises the equilibrium innovation rate.21
Our finding that strengthening patent protection in the South enhances FDI is consistent with empirical results. For example, Lee and Mansfield (1996) estimated the relationship between the volume of FDI
flows and the strength of IPR protection, and found that they are positively correlated. A number of theoretical studies contain results similar to ours: Vishwasrao (1994) and Žigić (1998) showed that weakerpatent protection in the South may reduce technology transfers in a partial equilibrium. Lai (1998) andDinopoulos and Segerstrom (2010) obtained this result in a dynamic general equilibrium model.22

21

We implicitly assume the existence of an interior solution, in which 0 < nF < 1 and I > 0. As discussed in Appendix

C, 0 < nF < 1 is guaranteed if the parameters satisfy (λ − 1)LS < LN + ρaN . Further, assuming that β > βmin , wherepβmin ≡ 2−1 (1 − λLN /LS ) + 2−2 (1 − λLN /LS )2 + λ(LN + ρaN )/LS , and (λ − 1)(LN + LS ) > ρaN guarantees
I > 0. In the rest of the paper, we focus on the interior solution by assuming that these parameter conditions are satisfied.
22
In contrast, Glass and Saggi (2002) showed that strengthening IPR protection impedes innovation and FDI in a dynamic
general equilibrium. The dynamic general equilibrium results probably differ because of differences in assumptions about
imitation and IPR protection; like us, Lai (1998) and Dinopoulos and Segerstrom (2010), assume that imitation is costless,whereas Glass and Saggi (2002) assume that imitation is costly and that strengthening IPR protection increases the cost ofimitation.

– 16 –

4

Welfare Analysis

In the previous section, we showed that strengthening patent protection raises the relative wage in theSouth. However, the Southern government’s main concern is the welfare of its consumers: if strengthening patent protection in the South improves the South’s welfare, a Southern government would be keen
to implement the policy. Otherwise, it has an incentive to relax patent protection. Thus, in this section,
we examine the welfare effects of strengthening patent protection in the South.
First, we derive the spending of the representative consumer living in country i ∈ {N, S}. As
mentioned in Subsection 2.1, because we treat total spending as the numeraire, that is, Et = 1 for
all t, the interest rate is equal to the subjective discount rate, rt = ρ. Given the intertemporal utility
maximization of each consumer, the per capita spending of a consumer living in any country is constantover time. Therefore, we let Ei denote the spending of a consumer in country i. Because spending
levels and the wage rate in each country are constant over time, the intertemporal budget constraint (1)is reduced to Ei = ρAi,0 + wi for i ∈ {N, S}. Multiplying both sides of these budget constraints
by the population and adding the constraints yields ρ(AN,0 LN + AS,0 LS ) + wN LN + wS LS = 1,
where we use Et ≡ EN,t LN + ES,t LS = 1. Letting A0 denote the total initial asset holdings, that is,
A0 ≡ AN,0 LN + AS,0 LS , we can derive the value of A0 as follows: A0 = [1 − (wN LN + wS LS )]/ρ.
Because country i’s share of asset holdings must be given as an initial condition, we let ζ ∈ [0, 1] denotethe share of assets held by Northern consumers, that is, ζ ≡ AN,0 LN /A0 .23 By substituting these
relationships into Ei , we obtain the following equilibrium values of EN and ES :EN = ζ

1 − wS LS+ (1 − ζ)wN ,
LN

(20)

1 − wN LN+ ζwS .
LS

(21)

ES = (1 − ζ)

Next, we rewrite the instantaneous utility as follows:Z 1

Z 1
log λJt (ω) dit (ω)dω = (log λ)log ui,t =0

Z 1
log dit (ω)dω.

Jt (ω)dω +
0

(22)

0

Because the latest generation of a product sells for the lowest quality-adjusted price in the product line,
Jt (ω) corresponds to the generation number of the latest generation of product ω. Thus, the first term of
23

When the share of assets held by Southern consumers (1 − ζ) equals (β − 1)(β/λ)LS /(ρaN )(> 0), balanced trade is

obtained; that is, (1 − nF )ES LS = nF EN LN .

– 17 –

(22) is equal to log λ multiplied by the total number of innovations obtained in all industries by time t.
Because the rate of innovation is constant over time in our model, we can rewrite this term as:
Z 1
Jt (ω)dω = (log λ)It.

(log λ)(23)

0

The second term of (22) can be rewritten as follows:

R1

i
i
i
0 log dt (ω)dω = nF log dF,t + (1 − nF ) log dN,t ,where diF,t and diN,t denote the demand for goods produced by multinationals and Northern leaders,
respectively. By using diF,t = Ei /pF = Ei /(βwS ) and diN,t = Ei /pN = Ei /(λwS ), we obtain:Z 1

log dit (ω)dω = log Ei − log wS − (log β)nF − (log λ)(1 − nF ).

(24)

0

As shown above, Ei , wS , nF , and I are all constant on the equilibrium path. Hence, from (22)–(24),(log λ)I represents the utility growth rate. Substituting (22)–(24) into the lifetime utility function, we
obtain the welfare of each consumer in country i ∈ {N, S} as follows:·¸
1 log λUi (β) =I + log Ei − log wS − (log β)nF − (log λ)(1 − nF ) ,
ρ
ρ

(25)

where Ui (β) denotes the welfare of each consumer in country i when patent breadth in the South is β.
This shows that the welfare of an individual depends on the innovation rate, nominal spending, the wage
in the South, which in turn determines the prices of goods, the measure of multinationals, and patent
breadth in the South. The welfare levels of a Northern individual and a Southern individual differ only
because their nominal spending, Ei , differs.
To determine whether increasing patent breadth in the South raises welfare, we differentiate (25)with respect to breadth β. The derivative of Ui (β) is given by:dUi (β)
dβ

1n
ρ

=

h
+

log λ dI
1 dEi
+
ρ dβ
Ei dβ
| {z }| {z}innovation-enhancing effect nominal spending effect(+)(+) or (–)
io
dnF
1 dwS
nF
(log λ − log β)−−. (26)dβ
w dβ
β|| S{z }
| {z }{z}
FDI-promoting effect marginal cost effect competition-reducing effect
(+)
(–)
(–)

As shown on the right-hand side (RHS) of (26), an increase in patent breadth in the South affects thewelfare of both countries through the following three channels. The first channel is the welfare effectthat occurs through enhancing innovation, which is indicated by the first term on the RHS of (26). As
shown in Proposition 2, increasing patent breadth promotes innovation and raises welfare. We refer to– 18 –

this effect as the innovation-enhancing effect. This effect has a positive influence on the welfare of bothcountries. The second channel is the welfare effect that occurs through the change in nominal spending,which is indicated by the second term on the RHS of (26). As shown by (20), (21), and Proposition
1, increasing patent breadth raises nominal spending in the South, but reduces nominal spending in the
North. Thus, it affects the welfare of both countries. We refer to this effect as the nominal spending
effect. The third channel is the welfare effect that occurs through changing the prices of goods, which isindicated by the three terms in square brackets on the RHS of (26).
The sign of the sum of the three terms in the square brackets is indeterminate because increasing
patent breadth has both positive and negative effects on the prices of goods in the following ways. First,
extending patent breadth increases the proportion of goods that multinationals produce, as shown in
Proposition 2. Because patent breadth is smaller in the South than in the North, the price of the goods
produced by multinationals (βwS ) is lower than the price of the goods produced by Northern leaders(λwS ). This means that an increase in patent breadth improves the welfare of both countries by increasing the proportion of FDI firms, nF . We refer to this positive welfare effect as the FDI-promoting effect,
which is indicated by the first term in the square brackets. Second, from (16), increasing patent breadthraises the wage rate in the South. This causes a rise in the marginal costs of followers, which allows
Northern leaders and multinationals to charge higher prices, and this reduces the welfare of both countries. We refer to this negative effect as the marginal cost effect, which is indicated by the second termin the square brackets. Third, increasing patent breadth in the South enables multinationals to raise theprice of their goods directly, which reduces welfare. This is because increasing patent breadth permits
Southern firms other than multinationals to produce only goods of lower quality. This means that multinationals can outcompete other firms even if multinationals charge a higher price for their goods. For
this reason, increasing patent breadth reduces the welfare of both countries. We refer to this negative
effect, which is shown by the last term in the square brackets, as the competition-reducing effect.
If the positive welfare effects outweigh the negative welfare effects, then strengthening patent protection in the South raises welfare. As shown in the subsequent subsections, whether this is the casedepends on the values of the parameters.

– 19 –

4.1

The Effect on the South’s WelfareFirst, we explore the effect of strengthening patent protection on the South’s welfare. We determine
the parameter values that cause the strictest patent protection to maximize the welfare of Southern consumers. In the rest of this subsection, as a benchmark, we focus on the case in which consumers in theSouth have no assets at the initial point in time; that is, ζ = 1. In Subsection 4.3, we analyze the generalcase in which ζ 6= 1.
We can summarize the results of our analysis of the South’s welfare in the case of ζ = 1 as follows.24
Proposition 3. Suppose that consumers in the South have no assets at the initial point in time. Then, thestrictest patent protection in the South (βS = λ) maximizes the welfare of consumers in the South if andonly if the parameters satisfy (log λ)(LN + λLS + ρaN )/(λ2 ρaN ) ≥ LS / (LN + LS + ρaN ).
Proof. If ζ = 1, we obtain the following equality from (21) and (26) in the range of β ∈ (βmin , λ]:dUS (β)/dβ = [f (β) + (log λ − log β) (dnF /dβ)] /ρ, where f (β) ≡ [(log λ) /ρ] (dI/dβ) − (nF /β).
It is straightforward to show that f 0 (β) < 0 from (17) and (19), and therefore f (β) ≥ 0 for all β ∈(βmin , λ] if f (λ) ≥ 0. Because (log λ − log β) (dnF /dβ) ≥ 0, this implies that dUS (β)/dβ ≥ 0 for
all β ∈ (βmin , λ] if f (λ) ≥ 0. Meanwhile, if f (λ) < 0, then dUS (λ)/dβ < 0. This is because(log λ − log β) (dnF /dβ) = 0 when β = λ. As a result, the strictest patent protection (βS = λ)maximizes the welfare of consumers in the South if and only if f (λ) ≥ 0. By rewriting f (λ) ≥ 0, we
obtain (log λ)(LN + λLS + ρaN )/(λ2 ρaN ) ≥ LS / (LN + LS + ρaN ).
If ζ = 1, then dUS (β)/dβ is simplified to the sum of the innovation-enhancing effect, the FDIpromoting effect, and the competition-reducing effect because ES = wS from (21). The innovationenhancing effect necessarily offsets the competition-reducing effect for all β ∈ (βmin , λ] if and only if
the parameters satisfy the condition in Proposition 3. The FDI-promoting effect is necessarily nonnegative and is zero when β = λ. Therefore, the strictest patent protection maximizes welfare in the South if
and only if the condition in Proposition 3 holds.
24

For Propositions 3–5, we assume that the degree of patent protection in the South is no weaker than the level of protection

below which Northern R&D activities cease; that is, β ∈ (βmin , λ]. For some set of parameter values, a low value of β thatprevents innovation could maximize welfare. However, if the cost of innovation is sufficiently low, there is no such set ofparameter values. For instance, by assuming aN < (λ − 1)(LN + LS )2 / {[(λ + 1)(LN + LS ) + λLS ] ρ}, we can showthat any low value of β that prevents innovation will maximize neither the welfare of Southern consumers nor that of Northern
consumers. The proof is given in Appendix D.

– 20 –

Clearly, the larger is Northern labor, LN , the more likely is the condition in Proposition 3 to hold.
Therefore, Proposition 3 implies that the strictest patent protection improves the welfare of consumers
in the South if labor is more abundant in the North. Why might strengthening patent protection raise
the welfare of Southern consumers in such a case? An increased abundance of labor in the Northintensifies the promotion of the innovation effect of strengthening patent protection, dI/dβ, which isrepresented by the left-hand side (LHS) of the condition in Proposition 3. Moreover, an increased abundance of Northern labor decreases the proportion of multinationals, nF , and, consequently, weakens
the competition-reducing effect of strengthening patent protection, −nF /β, which is represented by the
RHS of the condition in Proposition 3. Thus, the more abundant is labor in the North, the more intensiveis the positive welfare effect of strengthening patent protection.
In addition, the condition in Proposition 3 necessarily holds irrespective of the amount of labor in
the North, as long as LS /aN is sufficiently large that LS /aN ≥ λρ/ [(log λ)(2λ − 1)].25 Therefore,
Proposition 3 shows that the strictest patent protection improves the welfare of consumers in the Southif labor is more abundant in the South and if the productivity of R&D is higher in the North. The reason
is as follows. The more abundant is labor in the South and the higher is the productivity of R&D in the
North, the larger is the innovation-enhancing effect of strengthening patent protection, dI/dβ. However,higher R&D productivity and Southern labor abundance increase the proportion of multinationals, nF ,the consequence of which is an intensification of the competition-reducing effect of strengthening patent
protection. Thus, increased labor abundance in the South and increased productivity of R&D in the
North have two opposing effects on welfare. However, if LS /aN is sufficiently large to satisfy LS /aN ≥λρ/ [(log λ)(2λ − 1)], the former positive effect outweighs the latter negative effect.
Proposition 3 is important in the following two respects. First, it seems widely supposed thatstrengthening patent protection, particularly by equating levels of protection in the North and South,
lowers welfare in the South. However, our result contradicts this intuitive supposition, and shows that,far from being harmful, strengthening patent protection in the South, even to the extent that its level ofprotection matches that of the North, may benefit the South.26 In other words, this paper provides a ratio25
26

The proof is given in Appendix E.
A possible explanation for the intuitive supposition is that the benefits conferred by the innovation-enhancing effect areunderestimated because this effect is difficult to discern in practice. In addition, as mentioned in the conclusion, incorporating
enforcement costs to implement patent protection, which we ignore in this paper, into the analysis may reduce the probability
that the strictest protection of patent maximizes the welfare in the South.

– 21 –

nale for strengthening patent protection, which is a policy implemented in many developing countries.27
Second, our result contrasts with that of Helpman (1993), the seminal paper that examines the effectof strengthening IPR protection on welfare. Helpman examined the welfare effect of strengthening IPR
protection both in an endogenous innovation model, in which the only mode of technology transfer
is illegal imitation, and in an exogenous innovation model, in which FDI is the mode of technology
transfer. Helpman concluded from both models that stronger IPR protection in the South necessarily
damages welfare in the South. We obtain important implications from our results that contrast with theresults of Helpman’s two models. First, comparing our model with Helpman’s model in which imitationis the only mode of technology transfer suggests that the effect of strengthening IPR protection on theSouth’s welfare depends on the main mode of technology transfer: when the main mode of technology
transfer is FDI, strengthening IPR protection is likely to raise the South’s welfare. Second, comparing ourmodel with Helpman’s model incorporating FDI suggests that taking the innovation-enhancing effect into
account may reverse the sign of the total welfare effect of strengthening IPR protection: if the positiveeffect on innovation of strengthening IPR protection is taken into account, increasing patent protection
might raise the South’s welfare.

4.2

The Effect on the North’s Welfare

Next, we examine how strengthening patent protection in the South affects the North’s welfare. To
do this, we first show that the effect on the North’s welfare of increasing patent breadth is independent of the initial distribution of assets, ζ. From (15), (16), and (20), EN /wS becomes EN /wS =[1 + (ζρaN /LN )] (λ/β). Then, the effect of increasing patent breadth on log(EN /wS ) is given by:
1 dEN
1 dwS
1
−
= − < 0.
EN dβ
wS dβ
β

(27)

This shows that the effect of increasing patent breadth on log(EN /wS ), that is, the sum of the nominal
spending effect and the marginal cost effect, is independent of the initial distribution of assets, ζ. Because
the innovation rate, I, and the measure of multinationals, nF , are independent of ζ, the magnitudes of
the innovation-enhancing effect, the FDI-promoting effect, and the competition-reducing effect do notdepend on ζ. Thus, the effect on the North’s welfare, dUN (β)/dβ, is independent of ζ.
27

Park’s (2008) panel data on the index of patent protection show that many developing countries strengthened patent

protection between 1990 and 2005.

– 22 –

As shown in the following proposition, dUN (β)/dβ is positive for all β ∈ (βmin , λ] if the parameterssatisfy an inequality.
Proposition 4. The strictest patent protection in the South (βS = λ) maximizes the welfare of consumers
in the North if the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .
Proof. By substituting (27) into (26), we can rewrite dUN (β)/dβ as follows:·¸
dUN (β)1 log λ dI
nF
1
dnF
=
−
− + (log λ − log β)
.
dβ
ρ
ρ dβ
β
β
dβ

(28)

If [(log λ) /ρ] (dI/dβ)−(nF /β)−(1/β) > 0, then dUN (β)/dβ > 0 because (log λ − log β) (dnF /dβ) ≥0. From (17) and (19), we find that the following relationship holds:nF
1
log λ dI
−
−
ρ dβ
β
β

=
>
=

·µ
¶
¸
log λ
LN
1
LS
(β/λ)LS
1
+ρ
+
−
−
ρ
aN
β 2 λaN
LN + ρaN + (β/λ)LS
β
·µ
¶
¸
log λ
LN
1
(β/λ)LS
1
LS
+ρ
−
−
+
2
ρ
aN
β
λaN
LN + ρaN
β
·
¸·
¸
2
β
log λ
1
1
LN + ρaN + LS
−
.
(29)
β
λ
ρaN β LN + ρaN

If LN ≥ [λ/(log λ) − 1] ρaN , then the parameters satisfy (log λ) / (ρaN β) ≥ 1/ (LN + ρaN ) for allβ ∈ [1, λ]. Therefore, from (28) and (29), we can conclude that dUN (β)/dβ > 0 for any value ofβ ∈ (βmin , λ] if the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .
The strictest patent protection maximizes Northern welfare when the quantity of Northern labor isrelatively large for the same reasons as given in the interpretation of Proposition 3. That is, an increased
abundance of Northern labor enhances the innovation-enhancing effect of strengthening patent protection
and, thus, the positive welfare effects outweigh the negative welfare effects.
The condition in Proposition 4 is stricter than the condition in Proposition 3.28 Hence, we can showthat when ζ = 1, strengthening patent protection makes both the South and the North better off as longas the parameters satisfy the condition in Proposition 4. In other words, as long as labor resources in
the North are sufficiently abundant or as long as the productivity of R&D is sufficiently high to satisfy

28

The LHS of the inequality in Proposition 3 is an increasing function of LN and the RHS is a decreasing function of

LN . Substituting LN = [λ/(log λ) − 1]ρaN into the inequality in Proposition 3 reveals that the inequality holds if LN =[λ/(log λ) − 1]ρaN . Thus, the inequality in Proposition 3 holds whenever LN ≥ [λ/(log λ) − 1]ρaN .

– 23 –

the condition, then raising patent protection in the South to the level enjoyed in the North is a Paretoimproving policy.29
With respect to the effect on the welfare of consumers in the North, the results of the present paper are consistent with those of Helpman’s FDI model. In his exogenous innovation model, Helpman
concluded that tightening IPR protection when the main mode of technology transfer is FDI benefits theNorth if the imitation rate in the South is sufficiently low. Our endogenous innovation model implies thatmaximum patent protection in developing countries is globally optimal for the consumers in the North
if labor resources in the North are sufficiently abundant or if the productivity of R&D is sufficiently
high. This result implies that Helpman’s conclusion about Northern welfare is robust to incorporating
the innovation-enhancing effect of strengthening IPR protection. In that sense, our Proposition 4 complements Helpman’s conclusion about Northern welfare.

4.3

Generalizing the Initial Distribution of Assets

In order to generalize the result described in Proposition 3, we show that the strictest patent protection
can maximize the welfare of consumers in the South even when ζ 6= 1. When ζ 6= 1, the nominal
spending effect and the marginal cost effect do not cancel each other out. Thus, one must consider thesewelfare effects of strengthening patent protection. From (16) and (21), ES /wS becomes ES /wS =1 + [(1 − ζ)λρaN / (βLS )] . Hence, the effect of strengthening patent protection on log(ES /wS ) is:
1 dwS
1−ζ
1
1 dES
−
=−
< 0.
ES dβ
wS dβ
βLS /(λρaN ) + 1 − ζ β(30)This means that the higher is the initial level of assets held by Southern consumers (the larger is (1 − ζ)),the greater is the negative effect of strengthening patent protection on log(ES /wS ). Therefore, the total
effect of strengthening patent protection on the welfare of Southern consumers is more likely to be
negative the higher is the initial level of assets held by Southern consumers. However, we can show
29

The RHS of the inequality in Proposition 4 is a U-shaped function of λ, and the restriction for the other parameters becomes

stringent when λ takes extremely large or small values. However, unless λ is an extreme value, the ranges of values for LN , aN ,and ρ that satisfy the inequality are sufficiently broad. We assess the stringency of the inequality by using a numerical example.
Following the numerical analysis of Şener (2008), we use the range [1.05, 1.4] for λ so that the value of λ − 1 representing themarkup in this model can be consistent with empirical data. Assuming that ρ is 0.05, if LN /aN > 1.02604, the inequality in
Proposition 4 holds. Further, LN /aN must satisfy the conditions that (λ − 1)LS < LN + ρaN and (λ − 1)(LN + LS ) > ρaN ,which are assumed in Section 3. However, as long as LS /aN is less than 21.5207, values of LN /aN that exceed 1.02604
satisfy the two conditions. Thus, the parametric restrictions are not particularly stringent.

– 24 –

that the strictest patent protection maximizes the welfare of Southern consumers for any ζ ∈ [0, 1] if
the parameters satisfy the condition given in Proposition 4. Combining this result with that stated in
Proposition 4 enables us to state the following proposition.
Proposition 5. The strictest patent protection in the South (βS = λ) maximizes the welfare of consumers
in both the South and the North for any initial asset distribution between the North and the South if theparameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .
Proof. The proof relating to the welfare of Northern consumers is given in Proposition 4. Therefore, it
is sufficient for this proof to show that dUS (β)/dβ > 0 for any values of β ∈ (βmin , λ] and ζ ∈ [0, 1]
if the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN . We can rewrite dUS (β)/dβ for any ζ ∈ [0, 1] asfollows:
dUS (β)
dβ

=
>

·
µ
¶
¸
1 log λ dI
nF
1 dES
1 dwS
dnF
−
+
−
+ (log λ − log β)
ρ
ρ dβ
β
ES dβ
wS dβ
dβ
·
¸
1 log λ dI
nF
1
dnF
−
− + (log λ − log β)
,
ρ
ρ dβ
β
β
dβ

(31)

where the inequality holds because (1/ES ) (dES /dβ) − (1/wS ) (dwS /dβ) > −1/β from (30). Notethat the RHS of (31) is equal to dUN (β)/dβ. Therefore, using the same proof as in Proposition 4, we
can show that dUS (β)/dβ > dUN (β)/dβ > 0 for any values of β ∈ (βmin , λ] and ζ ∈ [0, 1] if theparameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .
Proposition 5 shows that as long as labor resources in the North are sufficiently abundant or as
long as the productivity of innovation is sufficiently high to satisfy the condition, then raising patent
protection in the South to the level enjoyed in the North is a Pareto-improving policy irrespective ofthe distribution of assets between the North and the South. To establish Proposition 3, we assumed
that Southern consumers initially held no assets. As shown by (21), holding no initial assets implies
that no assets are ever held, which appears to imply that the proposition is dependent on restricting the
distribution of assets. However, if the inequality in Proposition 5 holds, the strictest patent protection in
the South is optimal, regardless of the distribution of assets between countries. That is, even if Southern
consumers hold assets, the strictest patent protection in the South can maximize the welfare of Southern
consumers.
The result given in Proposition 5 differs from that obtained by Grossman and Lai (2004). They
showed that maximum patent protection tends to be suboptimal for the South. The difference between– 25 –

their results and ours is largely attributable to the difference in the size of the dynamic benefit of strengthening patent protection in the South. By using a quality-ladder type model, we assume that innovation
occurs through the improvement of existing goods. In our model, the invention of a latest-generation
good generates permanent social benefit by providing fundamental knowledge that is freely available to
the R&D of that industry even after obsolescence. Having assumed that the invention of a good has noinfluence on other R&D, Grossman and Lai (2004) ignore this “shoulders-of-giants” effect in the R&D
process. Taking this effect into account implies that strengthening patent protection in the South can generate dynamic benefits supplementary to those identified by Grossman and Lai because patent protection
increases the fundamental knowledge available for future R&D by promoting innovation. Thus, in ourmodel, stronger patent protection in the South can improve the welfare of the South if R&D resourcesin the North are sufficient and if R&D is sufficiently productive. Moreover, even patent harmonization,
which requires maximum patent protection in the South, can improve welfare of the South.30

5

Discussion

5.1

R&D Subsidies and Patent Protection in the SouthIn Proposition 5, we concluded that, provided a certain parameter condition is satisfied, the strictest
patent protection in the South can maximize welfare in both the North and the South. In this subsection,
we briefly consider the possibility that the strictest patent protection is suboptimal for the South. Supposethat the Southern government implements patent protection that is weaker than the maximum, and does
not cooperate with the Northern government. Can the Northern government implement a policy thatinduces the Southern government to maximize its patent protection in this case?
One policy option is for the North to raise R&D productivity, perhaps by improving higher education. Higher education is important for training researchers who develop new products. Improvements
in higher education that successfully raise researchers’ abilities to do R&D will increase the produc30

If one introduces into our model imitation by Southern firms of multinationals’ technology, our welfare results mightchange for the following three reasons. First, in such a model, strengthening patent protection in the South would affect welfare
through channels other than (26) because it would be bound to affect the progress of imitation and the measure of imitatedproducts. Second, imitation by Southern firms would change the magnitudes of the five welfare effects derived in our model.
Third, introducing imitation into our model would generate transitional dynamics, as explained in footnote 20. Thus, if imitation
activities are sufficiently pervasive and convergence to the steady state is sufficiently slow, our welfare results might change.

– 26 –

tivity of R&D in the economy. According to our model, an improvement in the productivity of R&D,
which is represented by a decrease in aN , reinforces the innovation-enhancing effect. Hence, such an
improvement can reduce the stringency of the parameter constraint that must be satisfied if the strongest
patent protection is to maximize the welfare of Southern consumers, as shown in Proposition 5. Therefore, a policy that increases R&D productivity, including an improvement in higher education, gives theSouthern government an incentive to maximize its patent protection.
Another policy option to induce the South to enact maximum patent protection is to subsidize R&D.
We can analyze the effect of an R&D subsidy by somewhat modifying our model.31 Suppose that theNorthern government subsidizes entrepreneurs by 100 × sR percent of R&D costs, where sR ∈ [0, 1).
We assume that the subsidies are financed by a lump-sum tax levied on Northern consumers, and assume
that the Northern government runs a balanced budget at each point in time. Under these assumptions,strengthening patent protection in the South still affects the welfare of the South through the five channels shown in (26). Among those channels, the innovation-enhancing effect tends to be represented byan inverted U-shaped function of sR : the effect strengthens as sR increases up to a certain point, after
which it weakens. In addition, the R&D subsidy exacerbates the negative competition-reducing effect.
However, subsidizing R&D mitigates the negative effect of the combined nominal spending and marginal
cost effects, and also increases the positive FDI-promoting effect. Thus, if the positive effects of introducing an R&D subsidy on dUS (β)/dβ outweigh the negative effects, then introducing an R&D subsidy
may make the strongest patent protection optimal for the South.

5.2 Reexamination in a Nonscale Effect ModelIn this subsection, we introduce population growth into the model and examine how our basic results
would change. In practice, population grows in many countries. However, so far, we have assumed thatthe quantity of labor supplied is constant over time. In addition, the model developed in the preceding
sections exhibits a scale effect; that is, an increase in the size of the labor force raises the innovation rate
and the growth rate of utility. Therefore, in line with the settings used by Segerstrom (1998), who developed a closed economy quality-ladder model without a scale effect, we incorporate positive population
growth into our model and examine the robustness of our main results.
We first describe the settings of the nonscale effect model and derive the effects of strengthening
31

In Appendix F, we analyze the effect of an R&D subsidy in our model.

– 27 –

patent protection on innovation and FDI. We retain the notation used and the assumptions made in theoriginal model if possible. Following earlier studies, which use two-country nonscale effect models, suchas Dinopoulos and Segerstrom (2010), we assume that the labor population grows at the same constantrate, n, in both the North and South, and that 0 < n < ρ. We let L̄N and L̄S denote the initial levelsof population in the North and South, respectively. Letting Lt denote the total world population at timet, we can represent Lt as Lt = (L̄N + L̄S )ent . Further, we define L̃i as the ratio of the populationof country i ∈ {N, S} to the world population; that is, L̃i = L̄i /(L̄N + L̄S ). Suppose that the initial
measure of members of each household in country i ∈ {N, S} is unity; in other words, the measure ofhouseholds in country i ∈ {N, S} equals L̄i . We assume that the number of members of each household
grows at the constant rate n in both countries. Then, the lifetime utility of each representative householdR∞
in country i ∈ {N, S} is given by Ui = 0 e−(ρ−n)t log ui,t dt. The modified budget constraint is
R ∞ − R t (r −n)ds
R ∞ − R t (r −n)ds
0 s
0 s
e
E
dt
=
A
+
wi,t dt. Thus, the demand for each product and the
i,t
i,0
0
0 e
Euler equation for each household are the same as those in Section 2.1. We let ct denote per capita global
spending; that is, ct ≡ Et /Lt . In Section 5.2, unlike in the original model, we use the per capita global
spending as the numeraire and normalize ct = Et /Lt = EN,t L̃N +ES,t L̃S = 1 for all t so that rt always
equals ρ. Hence, the per capita spending of households in country i, Ei,t , is constant for all t.
In order to remove the scale effect from the original model, we need to change an assumption on
the cost of R&D. Following Segerstrom (1998), we assume that R&D costs increase with the aggregate
volume of R&D over time. Concretely, we replace the cost of R&D, aN , with aN Xt (ω), where Xt (ω)
represents the difficulty of doing R&D in industry ω, which is assumed to evolve as follows:Ẋt (ω)= µIt (ω),
Xt (ω)(32)

where µ is a parameter that affects the growth rate of the difficulty of doing R&D: an increase in µ implies
an increase in the growth rate of the difficulty of doing R&D. Under this assumption, the innovation rate
and the growth rate of the utility level do not depend on the population level in the long run as shown
below.32
Under the assumption of increasing difficulty of R&D, the free entry condition for R&D, (4), changes
to vN,t (ω) = wN,t aN Xt (ω), where vN,t (ω) means that the stock values are not necessarily symmetricalamong industries ex ante. However, assuming that the R&D difficulty index, Xt (ω), is symmetricalacross industries at the initial point in time makes the innovation rate It (ω) symmetrical across industries
32

The earlier nonscale effect models including Segerstrom (1998) exhibit this property.

– 28 –

and, thus, vN,t (ω) is also symmetrical because of the no-arbitrage condition. As a result, no variable
depends on ω in equilibrium. Therefore, we henceforth omit ω from the equilibrium conditions, including
the free entry condition for R&D:
vN,t = wN,t aN Xt .

(33)

The other equilibrium conditions are as follows. Because of the change in the normalization, theprofits of Northern firms and multinationals, respectively, change to πN,t = [1 − wN,t /(λwS,t )] Lt andπF,t = (1 − 1/β) Lt . The no-arbitrage conditions for the stocks of Northern leaders and multinationals,(6) and (7), respectively, remain unchanged. Thus, the equilibrium condition for FDI, (10), holds, and wethereby obtain the equilibrium wage rate in the South as (11). The labor market equilibrium conditionsin the South and the North are nF,t Lt /(βwS,t ) = LS,t and nN,t Lt /(λwS,t ) + aN Xt It = LN,t .
Although incorporating increasing R&D costs purges the model of the scale effect, it also introducestransitional dynamics into the model. This complicates analysis of the effects of policy changes because
one must consider their effects on the transition. However, by linearizing the market equilibrium patharound the balanced growth path (BGP), we can show that strengthening patent protection does raiseinnovation and the growth rate on the transitional path, while it does not affect them in the long run.
Proposition 6. We consider the nonscale effect model. Suppose that the economy is initially on the BGP.
Strengthening patent protection marginally in the South promotes innovation in the short run, although
the positive effect approaches zero in the long run. Moreover, strengthening patent protection marginallyin the South promotes FDI in both the short run and the long run.
Proof. See Appendix A.
Using the results of the positive analysis, we now conduct welfare analysis in the nonscale effectmodel. To examine analytically how strengthening patent protection affects welfare, we adopt an approach similar to the one used by Helpman (1993). We assume that, when patent breadth is changed, theeconomy is on the BGP. We then evaluate the effect on welfare of Northern and Southern households ofa marginal increase in β. The instantaneous utility of any household in each country remains unchanged
Rt
as in the original model: log ui,t = (log λ) 0 Iτ dτ + log Ei − log wS,t + (log λ − log β) nF,t − log λ.
Because instantaneous utility comprises five parts, we can decompose the total welfare effect into the– 29 –

following five parts as we did in the original model:
dUi (β)
dβ

h
+

Z ∞
=

¶
µZ t
d
d log Ei+
(log λ)Iτ dτdβdβ| {z }|{z 0}
innovation-enhancing effect nominal spending effect(+) or (–)(+)
iod log wS,t
nF,t
−
−
dt.
dβ
β
|
{z
}
| {z }
marginal cost effect competition-reducing effect(+) or (–)(–)−(ρ−n)te
0dnF,t(log λ − log β)
dβ
|
{z
}
FDI-promoting effect
(+)

n

(34)

Each of these effects corresponds to a welfare effect in the original model which exhibits scale effects,(26). As proved in Appendix B, the signs of some of the welfare effects are determinate as shown in(34).
As was the case for the original model, by showing that the innovation-enhancing effect outweighs
the competition-reducing effect and the combined negative effect of the nominal spending and marginal
cost effects, we can show that strengthening patent protection improves the welfare of Northern andSouthern households. The following proposition summarizes the results of our welfare analysis of thenonscale effect model.33
Proposition 7. We consider the nonscale effect model. Suppose that the economy is initially on the
BGP. Strengthening patent protection marginally in the South raises the welfare of households in both
North and South for all β ∈ (1, λ], if the parameters satisfy either (i): nρ logµ λ > Ω, or (ii): L̃S <ihi−1
hn log λλ n log λ−ΩΩ−Ω−1 , where Ω ≡ λ+µ[(ρ/n)−1]λ−1 ρ µρ µ1+µ[(ρ/n)−1] .
Proposition 7 implies that when the South’s population share is lower (and the North’s is higher),strengthening patent protection in the South tends to improve the welfare of the Northern and Southernhouseholds. The reason is similar to that in the original model; the higher is the North’s share of thelabor population, the more likely is the positive innovation-enhancing welfare effect to outweigh thenegative competition-reducing welfare effect. This implies that the welfare effects of patent protectionin the South are robust to the incorporation of a nonscale effect.34
33
34

See Appendix H for the proof.
As Şener (2008) pointed out, the policy results may depend on how the scale effect is purged from the model. According toŞener (2008), there are three main approaches to removing scale effects: incorporating diminishing technological opportunities,
as undertaken by Segerstrom (1998); incorporating rent protection activities, as proposed by Dinopoulos and Syropoulos (2007);and incorporating variety expansion, as undertaken by, for example, Dinopoulos and Thompson (1998). We adopt the first of– 30 –

6

Conclusion

We developed a North–South quality-ladder model, in which foreign direct investment (FDI) is the main
channel of technology transfer. We then conducted not only a positive analysis but also a welfare analysis.
Despite the fact that welfare analysis is crucial for assessing policies, few previous theoretical studies
on intellectual property rights (IPR) protection in developing countries have conducted such an analysis.
However, by focusing our analysis on patent breadth, we examined analytically how strengthening patent
protection in the South affects welfare in the South. We showed that strengthening patent protection canraise welfare not only in the North but also in the South.
This result contrasts with that of Helpman (1993), whose pioneering study examined the effect ofstronger IPR protection on welfare. Helpman concluded that stronger IPR protection in the South necessarily damages welfare in the South, regardless of whether the mode of technology transfer is illegal
imitation or FDI. However, our results differed markedly from Helpman’s in this respect. Thus, our result
provides a theoretical basis for strengthening patent protection in the South.
To simplify the analysis and obtain clearer results, we abstracted from two factors whose incorporation would make the model more realistic. The first is the costs of enforcing patent protection. In
practice, resources are required to enforce patent protection. For instance, the government must allocate
labor to institutions applying laws dealing with patent infringements. Hence, increasing patent breadth
requires more labor resources. Incorporating the costs associated with patent protection might result in
our finding that strengthening patent protection improves Southern welfare being subject to more stringent restrictions. The second factor is trade barriers between North and South. Trade barriers, in the formof tariffs, for example, are expected to affect both the benefits and costs of stronger patent protection in
the South. For example, the existence of tariffs might induce tariff-jumping FDI from the North andmight intensify the positive FDI-promoting welfare effect of strengthening patent protection. Moreover,increasing the number of multinationals by strengthening patent protection might reduce the South’s tariff revenue, thereby reducing the welfare of Southern consumers. Incorporating tariffs into the model
might also have other effects that are not easily predictable or obvious.35 Although these extensions arethese approaches. Adopting either of the other two approaches is beyond the scope of the present paper. However, examining
the effect of these other approaches on the results is worthwhile.
35
Related studies examined the effect of trade liberalization using a North–South quality-ladder model. By extending thesymmetric North–North model of Dinopoulos and Segerstrom (1999) to a North–South model, Grieben (2005) examined how
Northern and Southern tariffs affect wage inequality in the North. Grieben and Şener (2009) examined how tariff reductions– 31 –

beyond the scope of the present paper, they are worth examining.

Appendix A: Proof of Proposition 6
In this appendix, we prove Proposition 6.
To describe the equilibrium path, we define the following two variables: zt ≡ Lt /(aN Xt ) andyt ≡ Lt /vt , each of which is constant on the BGP. Note that zt is a state variable, whereas yt is a jump
variable. From (11) and (33), the wage rates in the North and the South are represented by using zt andyt :wN,t =ztyt

andwS,t =

β zt
.
λ yt

(35)

In addition, from (35) and the labor market equilibrium conditions, the innovation rate and the measureof multinationals in the market equilibrium are expressed by using zt and yt as follows:
1
yt ,
β
β2
zt
nF,t =
L̃S ,λyt

It = L̃(β)zt −

(36)
(37)

where L̃(β) ≡ L̃N + (β/λ)L̃S . Given (7), (32), (36), and (37), the market equilibrium path in thisnonscale effect model can be characterized by the dynamic system for zt and yt as follows:
·
¸
żt
1
= n − µ L̃(β)zt − yt ,ztβẏt= −L̃(β)zt + yt − (ρ − n).
yt

(38)
(39)

All of the other endogenous variables are determined by the values of zt and yt . From (38) and (39), zt
and yt are constant on the BGP and satisfy:
µ
¶
βn
1
z=
+ρ−n
(β − 1)L̃(β) µ

and

β
y=
β−1

µ

¶
n
+ρ−n ,µ(40)

where z and y are the values on the BGP. As in the original model, terms without the subscript “t”
represent values on the BGP.
By conducting comparative statics, we can derive the long-run effects of an increase in β on It andnF,t . Suppose that the economy is on the BGP until patent protection is changed at time 0. From (36) andaffect Northern innovation and Southern imitation in a North–South model in which Northern monopolists engage in rentprotection activities, which were originally proposed by Dinopoulos and Syropoulos (2007).

– 32 –

(40), on the BGP, we obtain I = n/µ, which is independent of β. Thus, strengthening patent protection
does not affect the long-run innovation rate. Meanwhile, differentiating (40) with respect to β yields:
zβ ≡
yβ ≡

dz
y
L̃S
=−
−
z < 0,dββ(β − 1)L̃(β) λL̃(β)
dy
y
=−
< 0.
dβ
β(β − 1)

(41)
(42)

By using (37), (41), and (42), we obtain the effect of strengthening patent protection on nF as follows:ondnF /dβ = nF L̃N /[β L̃(β)] + n/[µ(β − 1)L̃(β)z] > 0, where we use the relationship that y =β L̃(β)z − (βn/µ) on the BGP from (38). Hence, strengthening patent protection in the South increases
the measure of multinationals in the long run.
Unlike the original model, the nonscale effect model has transitional dynamics because zt is a statevariable. Therefore, we must take the effects on the transition into consideration to evaluate the overall
effects of a policy. To do so, we derive the linearized system of zt and yt in the neighborhood of the BGP
and compute the transition paths of It and nF,t . The linearized system of (38) and (39) is given by:


  
zt − zżt−µL̃(β)z βµ z

.
 =
(43)
−L̃(β)yyyt − yẏt
Let J denote the Jacobian matrix of the dynamic system on the RHS of (43). The determinant of J isnegative as follows: det J = −(β − 1)µL̃(β)zy/β < 0. Therefore, one characteristic root is negative
and the other is positive and, thus, the BGP is a saddle point. Because yt is a jump variable, whereas
zt is a state variable, the market equilibrium path is uniquely determined in this nonscale effect model.
Moreover, we can show that the negative root of the characteristic equation is smaller than −n. We
let ν denote the negative characteristic root and we let h = [1, Λ]T denote the characteristic vector
corresponding to ν. Solving Jh = νh for Λ yields Λ = β[ν/(µz) + L̃(β)]. Using the characteristicroot and vector, we obtain the market equilibrium path, including the transition, as follows: zt = z +(z0 − z) eνt and yt = y + (z0 − z) Λeνt . By differentiating these expressions with respect to β, we candescribe the responses of zt and yt to a marginal increase in β as the following functions of time t:
dzt
dβ
dyt
dβ

¡
¢
= zβ 1 − eνt ,(44)= yβ − zβ Λeνt ,(45)

where z0 = z is used because we assume that the economy is on the BGP at the initial point in time andthat zt is not jumpable.
– 33 –

Finally, we derive the complete paths of the effects of a change in β on It and nF,t from the paths ofzt and yt . By using (36), (44), and (45), we obtain: dIt /dβ = (L̃S z/λ) + L̃(β)zβ + (y/β 2 ) − (yβ /β) +hi−L̃(β) + (Λ/β) zβ eνt . By substituting (41), (42), and Λ = β[ν/(µz) + L̃(β)] into this equation, we
obtain:−zβ νtdIt= (−ν)
e > 0.
dβµz(46)This shows that a rise in β enhances innovation in the short run, although the positive effect vanishes in
the long run because ν < 0. Likewise, by using (37), (38), (41), (42), (44), and (45), we obtain:"#−zβ νt
dnF,t
L̃N
n
= nF
+
+ (y − zΛ)
e
.
dβ
zy
β L̃(β) µ(β − 1)L̃(β)z(47)

The first two terms on the RHS of (47) represent the long-run effect on nF,t , which is positive. Moreover,from Λ = β[ν/(µz)+ L̃(β)] and (40), we obtain y −zΛ = −β(ν +n)/µ. Because ν < −n as mentioned
above, y − zΛ > 0 holds. This implies that the last term on the RHS of (47) is positive, and thus, a risein β promotes FDI in the short run as well as in the long run.

Appendix B: The Welfare Effects in the Nonscale Effect ModelIn this appendix, we evaluate each of the constituent welfare effects in (34).
First, we can derive the magnitude of the welfare effect through enhancing innovation from (46) as
h ³R
´
i
R∞
t
follows: 0 e−(ρ−n)t (log λ) d 0 Iτ dτ /dβ dt = {[1/(ρ−n)]−1/(ρ−n−ν)}(log λ)(−zβ )/(µz) >0. An increase in β enhances innovation in the short run. Thus, the innovation-enhancing effect is positive in the nonscale effect model, as in the original model.
Second, we evaluate the welfare effect through nominal spending. Because per capita spending
is constant over time in each country, the intertemporal budget constraint can be reduced to Ei =R∞
(ρ − n) (Ai,0 + Wi ), where Wi = 0 e−(ρ−n)t wi,t dt for i ∈ {N, S}. Global total initial asset holdings,
A0 , equal the total volume of stocks at the initial point in time: A0 = v0 × (nN,0 + nF,0 ) = L0 /y0 . By
using ζ ≡ AN,0 L̄N /A0 , which denotes the share of assets held by Northern households at the initial time
period, the initial asset holdings of a consumer in the North and South are given by AN,0 = ζ/(L̃N y0 )and AS,0 = (1−ζ)/(L̃S y0 ), respectively. By substituting these expressions into Ei and then differentiating with respect to β, we obtain the following expression for the change in log Ei caused by an increase– 34 –

in β:
µ
¶
1 dEi
1 dy0
1 dWi
= (1 − φi ) −
,
+ φi
Ei dβ
y dβ
Wi dβ

(48)

where φi ∈ [0, 1] denotes the ratio of labor income to total household wealth in country i; that is,φi = Wi /[Ei /(ρ − n)]. In (48), we use y0 ' y because the change in the level of a variable following amarginal increase in β is infinitesimal. Because the change in log Ei is constant over time, the magnitudeof the nominal spending effect is given by the RHS of (48) multiplied by 1/(ρ − n), the sign of which is
ambiguous.
Third, we evaluate the welfare effect through promoting FDI. Given (47), a rise in β increases nF,tat each point in time from period 0. Therefore, the FDI-promoting effect is clearly nonnegative.
Fourth, we evaluate the welfare effect through raising marginal cost. By using (35), (41), (42), (44),and (45), we obtain: (1/wS )(dwS,t /dβ) = (1/β) + (zβ /z) − (yβ /y) + [(y − zΛ)(−zβ )/(zy)]eνt ={λL̃N − µ [(ρ/n) − 1] L̃S }{β + µ [(ρ/n) − 1]}−1 (λL̃N + β L̃S )−1 + [(y − zΛ) (−zβ )/(zy)]eνt . The
first term on the RHS of this equation represents the long-run effect on wS,t , the sign of which is
ambiguous. The sign of the second term is positive. Therefore, the sign of dwS,t /dβ is ambiguR∞ous. The welfare effect through raising marginal cost is given by 0 e−(ρ−n)t (−d log wS,t /dβ)dt =R∞−(1/wS ) 0 e−(ρ−n)t (dwS,t /dβ)dt = −1/[(ρ − n)WS ](dWS /dβ). The sign of this effect is ambiguous.
Finally, we can derive the welfare effect through reducing competition simply as follows:

R ∞ −(ρ−n)t
0 e(−nF,t /β)dt = −nF /[β(ρ − n)] < 0. We have used nF,t = nF because the change in nF,t following amarginal increase in β is infinitesimal. Thus, the competition-reducing effect is negative.

– 35 –

Appendix C: The Conditions for 0 < nF < 1 and I > 0
In this appendix, we show that we can guarantee 0 < nF < 1 when (λ − 1)LS < LN + ρaN holds, andthat I > 0 when β > βmin holds. Moreover, we show that λ > βmin if (λ − 1)(LN + LS ) > ρaN .
First, we consider a parameter condition to exclude the equilibrium in which all firms possessing
patents move to the South. If patent protection is sufficiently strong in the South, that is, if β is sufficiently
high (or close to λ), all firms that succeed in innovation may choose to become multinationals and shift
their production to the South. In this case, no firm engages in production in the North, so that the
proportion of multinationals, nF,t , is equal to unity. In order to exclude such an extreme case, we assume
that (λ − 1)LS < LN + ρaN . Once we assume that the values of the parameters satisfy this inequality,
nF is less than unity even under the strictest patent protection in the South (β = λ) from (17).
By contrast, when patent protection is sufficiently weak in the South, that is, when β is sufficiently
low, no firm can conduct R&D (It = 0). Specifically, from (18), innovation rate I takes a value of zero
if and only if:β ≤ βmin ≡ 2−1 (1 − λLN /LS ) +p

2−2 (1 − λLN /LS )2 + λ(LN + ρaN )/LS .

Furthermore, if βmin > λ, no firm conducts R&D even under the strictest patent protection in theSouth. In order to exclude such an extreme case, we assume that the values of the parameters satisfy(λ − 1)(LN + LS ) > ρaN . Once we assume that the values of the parameters satisfy this inequality, I
is positive, at least under β = λ from (18).

– 36 –

Appendix D: Proof of Footnote 24
In this appendix, we prove the assertion in footnote 24. It is sufficient for the proof to show that Ui (λ) ishigher than Ui (β̄) for any β̄ ∈ [1, βmin ] if aN < (λ − 1)(LN + LS )2 / {[(λ + 1)(LN + LS ) + λLS ] ρ}.
To verify this, we first compute the welfare of each consumer when there is no innovation; that is,
Ui (β̄) for β̄ ∈ [1, βmin ]. If It = 0, then nF,t = 1 − λLN wS,t holds from (9). Substituting this equation
into (8), we obtain wS = 1/(λLN + β̄LS ) and nF = β̄LS /(λLN + β̄LS ) for β̄ ∈ [1, βmin ]. This implies
that wN = λ/[β̄(λLN + β̄LS )] for β̄ ∈ [1, βmin ] because (11) holds even if It = 0. By substituting wSand wN into (20) and (21), we have:
EN =

ES =

ζ(β̄ − 1)(λLN + β̄LS ) + λLN,
β̄LN (λLN + β̄LS )(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS,
β̄LS (λLN + β̄LS )for β̄ ∈ [1, βmin ]. Thus, from these equations and (25), we can compute Ui (β̄) for β̄ ∈ [1, βmin ] asfollows:
UN (β̄) =1
ρUS (β̄) =1ρ

½
ζ(β̄ − 1)(λLN + β̄LS ) + λLN
log
β̄LN
¾
¡
¢
β̄LS
+
log λ − log β̄ − log λ ,λLN + β̄LS½(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS
log
β̄LS
¾
¡
¢
β̄LS
+
log λ − log β̄ − log λ .
λLN + β̄LS

Next, we derive the welfare of each consumer when β = λ; that is, Ui (λ). Substituting (15) and (16)
into (20) and (21) yields the equilibrium values of each consumer’s spending when β = λ:
¶
ζρaN
+1 ,
LN

(49)

¸
(1 − ζ)ρaN
+1 .
LS

(50)

1
EN =
LN + LS + ρaN

ES =1
LN + LS + ρaN·µ

Therefore, substituting (16)–(18) and (49) into (25) yields:
UN (λ) =

1
ρ

½

·
¸
µ
¶
¾
log λ λ − 1 LN + LS
ζρaN
ρ
+ log
−
+ 1 − log λ .
ρ
λ
aN
λ
LN
– 37 –

Likewise, from (16)–(18), (25), and (50), we obtain:
¸
¾
½
·
¸
·
1 log λ λ − 1 LN + LSρ
(1 − ζ)ρaN
US (λ) =−+ 1 − log λ .
+ log
ρ
ρ
λ
aN
λ
LS
Next, we compare Ui (β̄) with Ui (λ). By subtracting UN (β̄) from UN (λ), we have:
½
·
¸
µ
¶
1 log λ λ − 1 LN + LSρζρaN
UN (λ) − UN (β̄) =
−
+ log
+1
ρ
ρ
λ
aN
λ
LN
¾
¡
¢
β̄LS
ζ(β̄ − 1)(λLN + β̄LS ) + λLN−
log λ − log β̄ . (51)
− log
β̄LN
λLN + β̄LS
Note that the sum of the second and third terms in (51) satisfies the following inequality:µ¶ζρaN
ζ(β̄ − 1)(λLN + β̄LS ) + λLNlog+ 1 − log
LN
β̄LN
ζρaN β̄ + β̄LN= log
ζ(β̄ − 1)(λLN + β̄LS ) + λLN£¤ζ(β̄ − 1)(λLN + β̄LS )β̄/λ + β̄LN≥ log
ζ(β̄ − 1)(λLN + β̄LS ) + λLN= log β̄ − log λ,where the inequality on the third line uses the fact that ρaN ≥ (β̄ −1)(λLN + β̄LS )/λ must hold because(β − 1)[LN + (β/λ)LS ]/ (βaN ) − (ρ/β) ≤ 0 for β ≤ βmin from (18). Thus, UN (λ) − UN (β̄) mustsatisfy the following inequality for any β̄ ∈ [1, βmin ]:½·¸
ρ
1 log λ λ − 1 LN + LS−
+ log β̄ − log λUN (λ) − UN (β̄) ≥
ρ
ρ
λ
aN
λ
¾
¡
¢
β̄LS
−
log λ − log β̄
λLN + β̄LS½·¸
λ − 1 LN + LS1β̄LS1(log λ)
− −1−
=
ρ
λ
ρaN
λ
λLN + β̄LS
µ
¶¾
β̄LS
+(log β̄) 1 +λLN + β̄LS
> 0,where the last inequality uses the condition that aN < (λ−1)(LN +LS )2 / {[(λ + 1)(LN + LS ) + λLS ] ρ}.
Therefore, the welfare of each Northern consumer is higher when β = λ than when there is no innovation
if aN < (λ − 1)(LN + LS )2 / {[(λ + 1)(LN + LS ) + λLS ] ρ}.
We can also show that US (λ) − US (β̄) is positive if the condition is satisfied. Subtracting US (β̄)
from US (λ) yields:·¸·¸log λ λ − 1 LN + LS
(1 − ζ)ρaN
ρ
+ log
−
+1
ρ
λ
aN
λ
LS
¾
¡
¢
(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS
β̄LS
− log
−
log λ − log β̄ . (52)β̄LS
λLN + β̄LS

1
US (λ) − US (β̄) =ρ½– 38 –

The sum of the second and third terms in (52) satisfies the following inequality:·¸(1 − ζ)ρaN(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LSlog
+ 1 − logLSβ̄LS
(1 − ζ)ρaN β̄ + β̄LS
= log
(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS£¤
(1 − ζ)(β̄ − 1)(λLN + β̄LS )β̄/λ + β̄LS
≥ log
(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS
> log β̄ − log λ,where the first inequality uses the fact that ρaN ≥ (β̄ − 1)(λLN + β̄LS )/λ must hold because (β −1)[LN + (β/λ)LS ]/ (βaN ) − (ρ/β) ≤ 0 for β ≤ βmin from (18). Thus, US (λ) − US (β̄) must satisfy
the following inequality for any β̄ ∈ [1, βmin ]:US (λ) − US (β̄) >=·¸log λ λ − 1 LN + LSρ−
+ log β̄ − log λ
ρ
λ
aN
λ
¾
¡
¢
β̄LS
−
log λ − log β̄
λLN + β̄LS½·¸
λ − 1 LN + LS1β̄LS1(log λ)
− −1−
ρ
λ
ρaN
λ
λLN + β̄LS
¶¾
µ
β̄LS
+(log β̄) 1 +λLN + β̄LS
1
ρ

½

> 0,
where the last inequality uses the condition that aN < (λ−1)(LN +LS )2 / {[(λ + 1)(LN + LS ) + λLS ] ρ}.
Thus, the welfare of each Southern consumer is higher when β = λ than when there is no innovation, if
aN < (λ − 1)(LN + LS )2 / {[(λ + 1)(LN + LS ) + λLS ] ρ}.
We have confirmed that when the value of β is so low that no R&D is undertaken, consumer welfare
is not maximized if aN < (λ − 1)(LN + LS )2 / {[(λ + 1)(LN + LS ) + λLS ] ρ}.

– 39 –

Appendix E: The Sufficient Condition of LS for Proposition 3
In this appendix, we show that the condition given in Proposition 3 holds irrespective of LN , if LS¯
dI ¯satisfies LS ≥ λρaN /[(log λ)(2λ − 1)]. From (17) and (19), we can show that f (λ) = logρ λ dβ
−
β=λ
h ³
´
i
log λ 1nF
LNLS
+ ρ + λa
− LN +LLSS+ρaN is an increasing function of (LN /aN ) + ρ. Because
λ = ρ
λ2 aN
N
we focus on the equilibrium in which nF < 1, it follows that (LN /aN ) + ρ > (λ − 1)LS /aN necessarily
holds. Therefore, if f (λ) ≥ 0 when (LN /aN ) + ρ = (λ − 1)LS /aN , then f (λ) is necessarily positive
for any value of (LN /aN ) + ρ. Substituting (LN /aN ) + ρ = (λ − 1)LS /aN into f (λ), we find thatf (λ) ≥ 0 holds if LS ≥ λρaN / [(log λ)(2λ − 1)] .

– 40 –

Appendix F: Analysis of the Effects of an R&D Subsidy
In this appendix, we analyze how an R&D subsidy influences the welfare effect of strengthening patent
protection in the South. To do this, we modify our model by incorporating the following three assumptions, as stated in the text. First, the Northern government subsidizes entrepreneurs by 100 × sR percent
of R&D costs, where sR ∈ [0, 1). Second, the subsidies are financed by a lump-sum tax levied on Northern consumers. Third, the Northern government runs a balanced budget at each point in time. Taxationby the government changes the intertemporal budget constraint of the consumers in country i as follows:
Z ∞ R
Z ∞ R
Z ∞ R
t
− 0t rs ds− 0t rs ds
e
Ei,t dt = Ai,0 +
ewi,t dt −e− 0 rs ds Ti,t dt,
(53)
0

0

0

where Ti,t is the amount of tax levied in country i at time t. Note that TS,t is equal to zero because
Southern consumers are not taxed. To achieve the balanced budget, the Northern government must
equalize its revenue and expenditure:
LN TN,t = sR wN,t aN It ,(54)

where the LHS represents tax revenues and the RHS represents the subsidy payment, which is equal tosR times the wage paid to workers engaging in R&D.
The subsidy influences the profitability of R&D because it decreases the costs of R&D for entrepreneurs. As a result, the following condition, which is a generalized version of (4), must be satisfied
in equilibrium to ensure nonpositive profit in the R&D process:vN,t ≤ (1 − sR )wN,t aN

with equality if It > 0,(55)

where the LHS represents the expected gain from R&D and the RHS represents the cost of R&D.
Because the zero-profit condition in the R&D sector is influenced by the subsidy, the values of theendogenous variables also depend on the subsidy rate. Hereafter, we focus on the equilibrium, in which
the innovation rate, It , and production in the North, nN,t = 1 − nF,t , are strictly positive. From thezero-profit condition (55), the Northern wage is equal to wN,t = vt /[(1 − sR )aN ]. Substituting thisexpression, (11), (12), and nN,t = 1 − nF,t into (9) yields:
It =LN + (β/λ)LS
1 − sR.
−aN
βvt

From (3), (7), and (56), the dynamic equation for vt is:·¸
LN + (β/λ)LS
sR
v̇t =
− 1.
+ ρ vt +aNβ– 41 –(56)(57)

Because vt is a jump variable, equation (57) shows that vt must jump at the initial time period to thefollowing steady-state value:v=(β − sR )aN.
β[LN + (β/λ)LS + ρaN ](58)

Therefore, from (11), (12), (55) and (56), the other endogenous variables immediately jump to theirsteady-state values, as is the case when sR = 0. The steady-state values of wN,t , and wS,t are:wN =β − sR,(1 − sR )β[LN + (β/λ)LS + ρaN ]

(59)

wS =

(β − sR )/λ,(1 − sR )[LN + (β/λ)LS + ρaN ](60)

which reduce respectively to (15) and (16) if sR = 0. Furthermore, by substituting (58) and (60) into(12) and (56), we have the steady-state values of nF,t and It :(β − sR )(β/λ)LS,(1 − sR )[LN + (β/λ)LS + ρaN ](61)

β − 1 LN + (β/λ)LS(1 − sR )ρ
−,β − sRaN
β − sR

(62)

nF =

I=

which are equal to (17) and (18) if sR = 0.
Next, we compute the equilibrium value of spending, Ei . From (53) and rt = ρ, Ei satisfies thefollowing relationship:
Ei = ρAi,0 + wi − Ti ,(63)

where TS = 0 and TN = sR wN aN I/LN , both of which are constant over time. Summing the spendingof all consumers yields:
E ≡ EN LN + ES LS = ρA0 + (LN wN + LS wS ) − LN TN = 1,(64)

where A0 ≡ AN,0 LN + AS,0 LS , and the last equality holds because of the normalization that Et = 1
for all t. By substituting (64) into (63), we can represent Ei as follows:
EN = ζ

1 − wS LS+ (1 − ζ)(wN − TN ),LN

ES = (1 − ζ)

1 − (wN − TN )LN+ ζwS ,
LS
– 42 –(65)

where ζ ≡ AN,0 LN /A0 .
In this extended model, as in the original model, strengthening patent protection in the South affects the welfare of the South through the five channels shown in (26). First, increasing patent breadth
increases welfare through enhancing innovation. The magnitude of this innovation-enhancing effect isgiven by:·µ¶¸log λ dI
1 − sRLN
log λLS (β − sR )(β − 1) + β(1 − sR )
> 0.
= 2
+ρ +
ρ2 dβ
ρ
(β − sR )2 aN
λaN(β − sR )2(66)

Note that the magnitude of the innovation-enhancing effect tends to be an inverted U-shaped function ofsR . This can be shown by partially differentiating dI/dβ with respect to sR as follows:∂2I−sR [(2β − 1)LS + λ(LN + ρaN )] + βLS + (2 − β)λ(LN + ρaN )=.
∂sR ∂βλaN (β − sR )3

(67)

2

I
Because β < 2β − 1 and 2 − β < 1, ∂s∂R ∂β
is positive if and only if sR is less than a critical value:ŝR ≡ [βLS + (2 − β)λ(LN + ρaN )]/ [(2β − 1)LS + λ(LN + ρaN )]. Therefore, dI/dβ is increasing
with sR if sR < ŝR , and is decreasing with sR if sR > ŝR .
Second, increasing patent breadth raises the welfare of the South through raising nominal spending.
Third, increasing patent breadth decreases welfare through raising the marginal cost of production. To
examine the magnitude of the sum of these two effects, it is useful to compute ES /wS . By substituting(54), (59), (60), and (62) into (65), we obtain:ES(1 − ζ)λρaN= 1 + (1 − sR )
.
wS
βLS

(68)

Therefore, differentiating the logarithm of (68) with respect to β yields the sum of the nominal spending
effect and the marginal cost effect as follows:
µ
¶
1
1 dES
1 dwS
(1 − sR )(1 − ζ)
−
=−
< 0.
ρ ES dβwS dβ[βLS /(λρaN ) + (1 − sR )(1 − ζ)]βρ
³
´
1 dwS
S
Equation (69) shows that ρ1 E1S dE−
is increasing with sR :
dβ
wS dβ
¶¸
· µ
∂
1 ∂ES
1 ∂wS
(1 − ζ)LS /(λρaN )
1
−
=
> 0.
∂sR ρ ES ∂βwS ∂β[βLS /(λρaN ) + (1 − sR )(1 − ζ)]2 ρ

(69)

(70)

Fourth, increasing patent breadth raises welfare through promoting FDI. By differentiating (61) withrespect to β, we can derive the magnitude of the FDI-promoting effect:·¸(log λ − log β) dn̄F(log λ − log β)(β/λ)LS(β/λ)LS + (sR /β)(LN + ρaN )
=
2−
ρ
dβ
(1 − sR )[LN + (β/λ)LS + ρaN ]ρ
LN + (β/λ)LS + ρaN
≥ 0.

(71)
– 43 –

By partially differentiating dn̄F /dβ with respect to sR , we obtain:·¸∂ 2 n̄F(β/λ)LS(β/λ)LS + (1/β)(LN + ρaN )
> 0.
=
2−
∂sR ∂β(1 − sR )2 [LN + (β/λ)LS + ρaN ]LN + (β/λ)LS + ρaN(72)

Therefore, the FDI-promoting effect is increasing with sR .
Fifth, increasing patent breadth lowers welfare through the competition-reducing effect. From (61),the magnitude of the competition-reducing effect is given by:−

nF(β − sR )(1/λ)LS
=−
< 0.
βρ
(1 − sR )[LN + (β/λ)LS + ρaN ]ρ

This equation shows that the competition-reducing effect is decreasing with sR :µ¶∂nF
(β − 1)(1/λ)LS
−
=−
< 0.
∂sR
βρ
(1 − sR )2 [LN + (β/λ)LS + ρaN ]ρ

(73)

(74)

In summary, the effect of strengthening patent protection on welfare in the South is represented bysubstituting (66), (69), (71), and (73) into (26).
The marginal effect of the R&D subsidy on the welfare effect of stronger patent protection is rather
complex and not necessarily monotonic. As shown in (67), the R&D subsidy increases the positive
innovation-enhancing effect for sR < ŝR , but decreases it for sR > ŝR . In addition, as shown in (70)and (72), the R&D subsidy lessens the combined nominal spending and marginal cost effects, which
are negative, but also increases the positive FDI-promoting effect. However, the subsidy exacerbates thenegative competition-reducing effect, as shown in (74). The total marginal effect of the R&D subsidy isgiven by the net effect of these changes.
According to our numerical analysis, whether the introduction of an R&D subsidy gives the Southan incentive to raise its patent protection to the maximum is ambiguous. For some parameter values,
the introduction of an R&D subsidy might increase the marginal welfare effect of strengthening patent
protection. For example, suppose that aN = 103, λ = 1.4, LN = 1, LS = 12, ρ = 0.05, andS (λ)ζ = 0.6. In this case, dUdβ
< 0 and the South’s optimal patent breadth is less than λ if sR = 0 (Figure
¯
2
(β) ¯
1). However, because ∂∂sURS∂β> 0 in this case, the Northern government can induce the South
¯

sR =0

to strengthen its patent protection indirectly by introducing an R&D subsidy. In fact, if the Northern
S (λ)
government subsidizes R&D by 10 percent of costs (sR = 0.1), the sign of dUdβ
becomes positive andmaximum patent protection becomes optimal for the South (Figure 2). By contrast, if aN = 85, λ = 2,
S (λ)
LN = 4, LS = 0.5, ρ = 0.05, and ζ = 0.7, dUdβ
< 0 for any sR ∈ [0, 1) (see Figure 3). Therefore, inthis case, the strongest patent protection is suboptimal for the South no matter what the subsidy rate.
– 44 –

-3.5142
Welfare of the South (=US(β))-3.51421-3.51422-3.51423-3.51424-3.51425-3.51426-3.51427-3.51428

Patent breadth in the South (=β)

Figure 1: Patent breadth and the welfare of the South: the case of aN = 103, λ = 1.4, LN = 1, LS = 12,
ρ = 0.05, ζ = 0.6, sR = 0. Note that βmin ' 1.397 in this case.

– 45 –

Welfare of the South (=US(β))

-3.27
-3.28
-3.29
-3.3
-3.31
-3.32
-3.33

Patent breadth in the South (=β)

Figure 2: Patent breadth and the welfare of the South: the case of aN = 103, λ = 1.4, LN = 1, LS = 12,
ρ = 0.05, ζ = 0.6, sR = 0.1. Note that βmin ' 1.365 in this case.

– 46 –

0
Marginal effects of strengthening
patent protection (=dUS(λ)/dβ)

-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Subsidy rate (=sR)

Figure 3: Subsidy rates and the marginal effects of changing patent breadth at the maximum patent
protection β = λ: the case of aN = 85, λ = 2, LN = 4, LS = 0.5, ρ = 0.05, ζ = 0.7. It is required thatsR < 0.939 for nF < 1.

– 47 –

Appendix G: Proof of ν < −nIn this appendix, we show that ν < −n. The characteristic equation of the Jacobian matrix, J, of the
dynamic system (43) is given by the following quadratic equation:
h

µ

i

1
F (x) ≡ x − −µL̃(β)z + y x − 1 −β2¶µL̃(β)zy = 0.

By the definition of F , we have:
h

i

µ

1
F (−n) = n + −µL̃(β)z + y n − 1 −β2¶µL̃(β)zy.

From (38), µL̃(β)z = n + (µy/β) holds on the BGP. Substituting this and (40) into (75) yields:·

F (−n) =
=
=
=
=

¸
µ
¶µ
¶
1
1
1
n + −n − µy + y n − 1 −n + µy y
β
β
β
¶¸
·
µ
1
1
y
− (µ − β)n + (β − 1) n + µy
β
β
·
¸
β−1
1
− (µ − 1)n +
µy
y
β
β
·
µ
¶¸
n
n
1
− n− +
+ρ−n
µy
µ
µ
β
1
−ρ µy
β
2

< 0.
This result proves that ν < −n because ν is the negative root of the quadratic equation F (x) = 0.

– 48 –(75)

Appendix H: Proof of Proposition 7
In this appendix, we prove Proposition 7 by deriving the parameter values at which the total welfare
effect is positive.
For that purpose, we first decompose the sum of the nominal spending effect and the marginal
cost effect into parts that can each be signed. Because WS = βWN /λ holds from (35), we obtain(1/WS ) (dWS /dβ) = (1/WN ) (dWN /dβ) + (1/β). Using this and (48), we can rewrite the sum of thenominal spending effect and the marginal cost effect for Northern households as follows:
Z ∞³ d log E
d log wS,t ´Ne−(ρ−n)t
−
dt
dβ
dβ
0
µ
¶
1
1 dy0
1 dWN
1
=
(1 − φN ) −
−
−
,
ρ−n
y dβ
WN dβ
β(ρ − n)(76)

where 0 ≤ 1 − φN ≤ 1 by the definition of φi . Likewise, the corresponding expression for Southernhouseholds is:
Z ∞0³ d log E

d log wS,t ´
dt
dβ
dβ
¶
1 dy0
1 dWN
1
1
(1 − φS ) −−− (1 − φS )
,
=
ρ−n
y dβ
WN dβ
β(ρ − n)e−(ρ−n)t

S

−
µ

(77)

where 0 ≤ 1 − φS ≤ 1. The second terms on the RHS of (76) and (77) are negative. Meanwhile, we cancompute (1/WN ) (dWN /dβ) in the first terms on the RHS of (76) and (77) as follows:Z
1 dWN
ρ − n ∞ −(ρ−n)t dwN,t
=
dt
e
WN dβ
wN 0
dβ
·
¸
Z ∞
¡
¢
¢
y
z ¡
−(ρ−n)t zβνtνt= (ρ − n)e
1 − e − 2 yβ − zβ Λe
dt
z 0
y
y
µ
¶
yβ
zβ
zβ
ρ−n
ρ−n
=
1−
−
+ Λ
,
z
ρ−n−ν
y
y ρ−n−νwhere the second equality uses (35), (44) and (45). From this and (45), we have:
µ
¶
zβ
yβ
zβ
1 dy0
1 dWN
1
ρ−n
ρ−n
−
−
= − (yβ − zβ Λ) −
1−
+
− Λ
y dβ
WN dβ
y
z
ρ−n−ν
y
y ρ−n−νµ¶−zβ
ρ−n= (y − zΛ)
1−
zy
ρ−n−ν
> 0,
where the inequality holds because y − zΛ = −β(ν + n)/µ > 0 and ν < 0. Consequently, the firstterms on the RHS of (76) and (77) are positive. This implies that the sum of the nominal spending effectand the marginal cost effect is necessarily greater than or equal to −1/[β(ρ − n)].
– 49 –

If the innovation-enhancing effect outweighs the sum of the competition-reducing effect and 1/[β(ρ−n)], the total welfare effect for Northern households is positive. This is because the FDI-promoting effect is nonnegative. Further, in this case, the total welfare effect for Southern households is also positivefrom (34) and (77). Hence, a rise in β improves welfare in both the North and the South if the following
inequality holds:
µ
¶µ
¶µ
¶
−zβ
1
log λ
1
>
−
ρ−n ρ−n−ν
µ
z
{z
}
|

nF
β(ρ − n)| {z }
competition-reducing effectinnovation-enhancing effectBecause −n − ν > 0 as shown in Appendix G, (78) holds if1β(ρ−n) . This inequality can be rewritten as:

nF + 1n log λ
>
ρ µ
β

µ

z
−zβ

³

1
β(ρ − n)| {z }+11
ρ−n − ρ. (78)

the negative part in the sumof nominal spending effectand marginal cost effect

´³

log λ
µ

´³

−zβ
z

´

nF
> β(ρ−n)
+

¶
.

(79)

Substituting (37), (40), and (41) into the RHS of (79) yields:

"
#−1 
µ
¶ 

z
(β/λ)L̃S
nF + 1= 1 − β + (β − 1)
Ω(β)
Ω(β),


β
−zβ
L̃(β)
where Ω(β) = β+µ[(ρ/n)−1]1+µ[(ρ/n)−1] . Because Ω(β) is an increasing function of β, the RHS of (79) is anincreasing function of β. Therefore, if inequality (79) holds at β = λ, inequality (79) holds for allβ ∈ (1, λ]. Consequently, we can show that a rise in β improves welfare in both the North and the Southif (79) holds at β = λ.
Substituting β = λ into (79) and then rewriting the resultant expression yields:Ω(λ)
n log λ,> Ω(λ) −ρ µ
λ + (λ − 1) L̃S Ω(λ)(80)

where we use L̃(λ) = L̃N + L̃S = 1. This implies that inequality (79) holds irrespective of L̃S if
n log λ> Ω(λ).
ρ µ
If the parameters do not satisfy (81), we can rewrite (80) as follows:·¸·¸
λ n log λn log λ −1L̃S <− Ω(λ) Ω(λ) −[Ω(λ)]−1 .
λ−1ρ µ
ρ µ

(81)

(82)

The set of values of L̃S that satisfies (82) becomes empty if λ, n/ρ, and µ do not satisfy λn(log λ)/ [(λ − 1) ρ] >µΩ(λ). However, assuming that µ is sufficiently low ensures that λn(log λ)/ [(λ − 1) ρ] > µΩ(λ) beλ−1cause µΩ(λ) = µ + (1/µ)+(ρ/n)−1
is an increasing function of µ.

– 50 –

Thus, if λ, n/ρ, and µ satisfy (81), or if L̃S satisfies (82), strengthening patent protection in the South
improves the welfare of Northern and Southern households.
The result shows that the inequality is more likely to hold the lower is L̃S . Why is this? From (46),the smaller is L̃S , the weaker is the positive effect on innovation in the short run. This is because adecrease in L̃S lowers −zβ /z from (40) and (41). Thus, the lower is L̃S , the weaker is the innovationenhancing effect. On the other hand, from (37) and (40), the smaller is L̃S , the lower is the measureof multinationals, nF and, thus, the weaker is the competition-reducing effect. Despite the fact thatthe smaller is L̃S , the weaker are the positive and negative welfare effects, the weakening of the latter
outweighs the weakening of the former. This can be verified by the fact that the RHS of (79) is anincreasing function of L̃S . Hence, the lower is L̃S , the more the positive welfare effect outweighs thenegative welfare effect.

– 51 –

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– 54 –