GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.73

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

Hitoshi Tanaka, Tatsuro Iwaisako, and Koichi Futagami

August 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

A Welfare Analysis of Global Patent Protection
in a Model with Endogenous Innovation and Foreign Direct Investment∗
Hitoshi Tanaka†

Tatsuro Iwaisako‡

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 also allows the firms withpatents to charge higher prices for their goods, which decreases welfare. However, the model showsthat the former positive welfare effect overcomes the latter negative one, and introducing the strictest
form of patent protection in the South, that is, harmonizing patent protection in the South with thatin the North, may maximize welfare in the South as well as in the North.
Keywords: foreign direct investment, innovation, intellectual property rights protection, welfare analysis
JEL classification: F43, O33, O34, O40∗

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

ment: The Effects of Patent Protection.” The authors 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, and theTokyo Institute of Technology for their helpful comments. They are especially grateful to Tetsugen Haruyama for his constructive comments. This study was partly supported by a Grant-in-Aid for Young Scientists (No. 18730136) from the Ministry of
Education, Culture, Sports, and Technology. Of course, any remaining errors are the authors’ responsibility.
†
Faculty of Economics, Hokkai Gaku-en 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. E-mail:iwaisako@econ.osaka-u.ac.jp§
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan. E-mail:futagami@econ.osaka-u.ac.jp

1

Introduction

Recently, many developing countries have been pressed 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 of minimum
standards on IPR, including patents, copyrights, etc., and strengthening IPR protection is often a requirement for developing countries to enter the WTO. However, most developing countries seem to be afraidthat stronger domestic protection of IPR may damage their economies. Some empirical studies show thatstrengthening IPR protection in developing countries tends to cause an income transfer from developing
countries that have only a few or no patents to developed countries, which have many patents.1 However,in order to judge whether strengthening IPR protection in developing countries is beneficial or harmful
in reality, it is important to examine how strengthening IPR protection in developing countries affects
their welfare, not their income. Is strengthening IPR protection in developing countries really harmful totheir welfare?
The present paper examines how strengthening patent protection in a developing country affects its
welfare, considering all the effects through changes of 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). Generally,
there are some modes of technology transfers that occur from a developed country (hereafter referred toas the North) to a developing country (hereafter, the South), such as FDI, licensing, illegal imitation,and outsourcing. FDI is one of the most important modes of such technology transfer and accounts forthe largest share of all modes of technology transfer in most developing countries, including China andBrazil.
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 en-

1

McCalman (2001) estimated income transfers brought about by patent harmonization as a result of the TRIPs agreement.

His result implies that only a few developed countries, including the United States (US) could benefit from cross-country
income transfers by strengthening patent protection, whereas all other countries actually lose some of their income as a result;for instance, the net transfer from Brazil amounts to 28% of GDP. Moreover, Yang and Maskus (2001a) and Park and Lippoldt(2005) examined how US receipts of royalties and license fees depend on IPR protection in the recipient countries and showedthat strengthening IPR protection has statistically significant positive influences on licensing receipts.

1hancement of FDI further promotes innovation in the North because it reduces the labor demand of the
production sectors in the North and directs more labor resources to research and development (R&D).
On the other hand, an increase in multinationals resulting from the strengthening of patent protection
causes an increase in labor demand in the South and thus 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 with only a 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 thusincreases the nominal spending of Southern consumers, which raises welfare in the South. Meanwhile,strengthening patent protection lowers the wage rate in the North and thus decreases the nominal spending of Northern consumers, which reduces welfare in the North. The third channel is through changing
prices of goods: the sign of this effect is indeterminate because strengthening patent protection affects theprices of goods positively and negatively. In more detail, the third channel can be decomposed into thefollowing three effects. First, there is a welfare effect that occurs (a) through promoting FDI: strengthening patent protection lowers the prices of some goods by increasing the proportion of goods producedby multinationals in the South, which produce cheaper goods than do the firms located in the North.
Therefore, a rise in the proportion of FDI firms raises welfare. The second welfare effect caused by thechange in prices occurs (b) through raising the wage in the South: strengthening patent protection raises
the wage rate in the South and enables production firms to charge higher prices for their goods because it
raises the marginal cost of rival firms, which consequently reduces welfare. The last effect is the welfare
effect that occurs (c) through reducing competition: strengthening patent protection allows the multinationals to charge higher prices for their goods because it reduces competition with non-patentees, which
reduces welfare. As a result of this analysis, we show that the positive welfare effects can overcome thenegative welfare effects.

2

In the theoretical literature on technology transfer, a number of earlier studies have examined how
strengthening IPR protection affects innovation and FDI. Such studies include Helpman (1993), Lai(1998), Glass and Saggi (2002), Glass and Wu (2007), and Mondal and Gupta (2008).2 However, withthe exception of Helpman (1993), none of the above studies has conducted welfare analyses, mainly
because the equilibrium paths in their models are complicated.3
One of the few studies dealing with the welfare effect of IPR protection in developing countries is
Helpman (1993), which consisted of two welfare analyses: first, a welfare analysis in a North–Southmodel where the only mode of technology transfer is illegal imitation; and second, a welfare analysis ina model where the means of technology transfer is FDI. The former analysis examined how lowering theprobability of imitation by Southern firms of Northern products—which is caused by introducing tighter
IPR in the South—affects welfare levels in both the South and the North. The results showed that tighter
IPR reduces welfare in the South mainly because of the hampering of innovation. The latter analysis,
which is more relevant to the present paper in that it deals with FDI, showed a similar result to the first
analysis 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 this pessimistic result shown in the FDI
model of Helpman? 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 the endogenous determination of innovation, our model can capture the important positive
welfare effect of strengthening 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 results of the present
paper imply that the negative conclusion regarding the welfare effect of strengthening patent protectionin the South may change significantly when the welfare effect that occurs through innovation is taken
into consideration.
We must briefly note the setting of patent protection in the present paper. There are two instruments ofpatent policies: patent length and patent breadth. Patent length refers to the duration for which a patentee
can sell the patented product monopolistically, whereas patent breadth refers to the scope of productsthat patentees can prevent firms without patents from producing and selling. The present paper focuses2

As well as FDI, licensing can play an important role in technology transfer in the development process, as has occurredin Korea, Taiwan, and Japan, for example. Some studies have constructed North–South growth models where the mode oftechnology transfer is not FDI but licensing; see, for example, Yang and Maskus (2001b) and Tanaka et al. (2007, 2008).
3
Extending the model of Helpman (1993), Grinols and Lin (2006) analyzed the welfare effects of strengthening patent
protection in the South. However, the equilibrium paths in their model are so complex that their analysis relies on numericalanalysis. In addition, in contrast to the present model, their model does not include FDI.

3

on the effects of extending patent breadth to evaluate analytically the welfare effect of the stronger patent
protection in the South. In contrast to the present paper and other studies that use the imitation rate asa parameter of IPR protection, Dinopoulos and Kottaridi (2008) focused their analysis on the effect ofchanging patent length.4 They analyzed the effects of patent harmonization, whereby the South’s patent
protection was strengthened to the same level as the North’s patent protection, and obtained the importantresult that patent harmonization raises the long-run growth rate and improves the relative wage in theSouth. However, they did not evaluate the welfare effects of strengthening patent protection because of
the complexity of the model with a finite patent length.5 In contrast, by keeping the model as simple aspossible, we can examine welfare on the equilibrium path fully and obtain clearer results on the welfare
effects of strengthening patent protection through the change in patent breadth.
The rest of the paper is structured as follows. Section 2 describes 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. Section 5 provides concluding remarks.

2

The Model

We develop a dynamic general equilibrium model such that FDI is introduced into a quality-ladder model,
in contrast to Lai (1998), where FDI is introduced into a variety-expansion model. Our model has thesame basic structure as Grossman and Helpman (1991, Ch. 12).
Consider an economy consisting of two countries, North and South, which are denoted by N andS, 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 of time. There is a continuum of goods, indexed byω ∈ [0, 1], that are produced in the North or the South. Each product is classified by a countable infinite
number of “generations” j = 0, 1, · · · and each generation progresses one step ahead if innovation occurs
in the industry. Therefore, product ω of generation j can be produced after the jth innovation in industry
ω. As described later, innovation occurs as a result of successful R&D efforts by firms. We assume that4

Most of the existing studies dealing with patent protection, such as Kwan and Lai (2003), have used the imitation rate as aparameter of patent protection.
5
In the theoretical analysis of patent length, the dynamic property of the equilibrium paths tends to become rather complicated. For example, Futagami and Iwaisako (2007) investigated analytically the characteristics of the equilibrium paths of theeconomy with a finite patent length and showed that, even if the production structure is a simple AK type, the equilibrium
paths exhibit oscillations.

4

products of different generations have different “qualities” from each other, and the quality of productω of generation j is provided by qj (ω) = λj , where the increment of quality between generation j andj + 1, λ > 1, is identical for all products. We choose our units appropriately so that the generation
number is zero and the quality is equal to unity for all goods at time t = 0.

2.1

Consumers

Consumers living in country i ∈ {N, S} have the following lifetime utility:
Z ∞
Ui =

e−ρt log ui,t dt,(1)0

where ρ is a common subjective discount rate and log ui,t represents instantaneous utility at time t. We
specify the instantaneous utility function as:
Z 1
log ui,t =


log 

0

X


qj (ω)dij,t (ω) dω,(2)jwhere dij,t (ω) denotes the individual’s consumption of good ω of generation j at time t.6 The representative consumer maximizes his or her lifetime utility (1) under the following budget constraint:
Z ∞R− 0t rs dse

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

(3)

0

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 ofspending at time t, namely:



Z 1 X

Ei,t =
pj,t (ω)dij,t (ω) dω,0jwhere pj,t (ω) is the price of product ω of generation j at time t.
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 thisstatic problem, the consumer allots identical expenditure shares to all products. Then, for each product,
6

In this model, we implicitly assume that the product with a quality level that lies between the latest generation and thesecond-latest generation can be potentially produced and consumed as well as the latest-generation product. However, as
mentioned below in subsection 2.2, owing to the pricing behavior of the firms that possess the patent on the latest-generation
product, only the product of the latest generation is produced and consumed in each goods sector. Thus, we describe theinstantaneous utility as (2) as consumers cannot consume a product with a level of quality that lies between the latest generationand the second-latest generation.

5the consumer chooses the single generation j = Jt (ω) that carries the lowest quality-adjusted pricepj,t (ω)/qj,t (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 (1). This intertemporal utility maximization requires that Ėi,t /Ei,t = rt − ρ. By taking theaggregate spending as the numeraire, we normalize Et ≡ EN,t LN + ES,t LS = 1 for all t so that theinterest rate rt always corresponds to the subjective discount rate ρ.7

2.2

Production

We assume that each economy has a single primary production factor—labor. The amounts of total labor
supplied in the North and the South are constant and given by LN and LS , respectively. As in mostrelated studies, we assume that labor is not mobile between the North and the South. Labor is devoted
to the production of goods in both the North and the South. In addition, in the North, labor is devoted toinnovative activities to develop a higher quality product. We assume that state-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 with the typical setting adopted by,for example, 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 the product of a qualitythat lies between the latest generation and the second-latest generation by imitating the product without
undertaking R&D efforts if and only if the inventor is located in country i. However, the existence of thepatent legally guards the inventor from imitation. Thus, as mentioned below, the highest quality that theother firms can produce depends on the degree of patent protection in the country.
In the present paper, we consider that the inventor of a latest-generation product can select the location of production, i.e., it 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 can shift production
from the North to the South instantaneously without any cost if the firm chooses to undertake FDI.8 If
the firm elects to shift production to the South, the firm can use Southern labor, which is cheaper than
7

This normalization is a convenient method for examining the dynamic behavior of the economy. See Grossman andHelpman (1991, Ch. 12).
8
We can extend the model to include the cost of FDI. However, the results remain almost unchanged.

6Northern labor, which allows the firm to obtain higher profits at each point of time. However, a firm thatchooses to undertake FDI is faced with more intense competition from potential rivals than is a patentee
located in the North 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 any
transportation costs or tariffs.
Before considering how the patentees decide whether to undertake FDI, we must consider how governments protect patents in the North and the South. Generally, there are two instruments influencing
the degree of patent protection. One is the patent length, which represents how long the patentee canproduce and sell the product exclusively. The other is the patent breadth, which refers to the scopeof products that the patentee can prevent other firms from producing and selling. In the quality-laddermodel, products of different qualities within the same product line are perfectly substitutable, and thus
patent breadth represents the degree of quality that the government permits other producers to produce.9
In reality, 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.10
In the present paper, we consider the patent breadth as follows. When the state-of-the-art quality of
product ω is given by qj (ω), firms other than the patentee of the state-of-the-art quality 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 a broader patent breadth:if βi is equal to λ, then patent protection in country i is at its maximum; if βi is equal to one, then patent
protection in country i is nonexistent.11
9Strictly 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; whereas lagging breadth specifies how inferior a product must be compared with the patented productfor the producers without the patent to legally produce and sell it. The definition of patent breadth that we use in the present
paper corresponds to lagging breadth. O’Donoghue and Zweimuller (2004) examined how a change of leading breadth affects
innovation and welfare in a closed economy. On the other hand, similarly to the present paper, Li (2001) analyzed the effect oninnovation of changing lagging breadth in a quality-ladder model. However, he focused on the analysis of a closed economy.
10
Judd (1985), Iwaisako and Futagami (2003), and Futagami and Iwaisako (2007) examined how changing patent length
affects social welfare. As shown by Futagami and Iwaisako (2007), the equilibrium paths under finite patent length become
more complicated.
11
We can consider a patent breadth that is broader than λ. However, βi > λ means that the patent of the state-of-the-art
quality excludes even the production of the good of the second-latest generation on the same product line, that is, the productinvented by the previous innovator. Such a broad patent breadth seems to be somewhat unrealistic. Thus, we assume that thepatent breadth, βi = λ, is the strictest patent protection in our analysis.

7

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 with the patent of a state-of-the-art
good is such that the other firms cannot earn any positive profit by entering the market for the good.
That is, the leader firm chooses to adopt a limit pricing strategy. To put it concretely, the patentee of thelatest generation of product ω, the quality of which is equal to λj , adopts a pricing strategy such thatthe quality-adjusted price of the good is not higher than the quality-adjusted price charged by the otherproducers. If the patentee is operating in country i, the other producers can legally produce product ωwith quality λj /βi at most. Therefore, if the patentee charges a price p that satisfies p/λj ≤ p0 /(λj /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 can charge 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 theother firms. This implies that a broader patent breadth enables the patentee to charge a higher price; inparticular, when βi takes the highest value, λ, the patentee can raise the price to λM C, whereas when βitakes the lowest value, 1, the patentee must lower the price to the level of marginal cost.12
Under the patent breadth policy mentioned above, we derive the optimal pricing strategy and the
profit of the patent holders producing in the North and the South, respectively. In the rest of the paper,
we refer to the patent holder firms producing in the North and the patent holder firms shifting production
to the South as “Northern leaders” and “multinationals”, respectively. First, let us consider the pricing
behaviors of Northern leaders. We assume that patent protection is strictest in the North; that is, thepatent breadth is broadest, βN = λ, in the North. Then, the Northern firms other than the patent holderof the latest-generation product ω are prohibited from producing product ω above the quality level ofthe second-latest generation product. Therefore, the strongest potential rival of the patent holder of thelatest-generation product ω is necessarily the patent holder of the second-latest-generation product thatchooses to operate in the South. Letting wS denote the wage in the South, the marginal cost of thestrongest rival is equal to wS . Thus, patentees of the latest-generation products that decide to produce
their good in the North set their prices to pN = λwS as a result of the optimal strategy. Thereby, theinstantaneous profit of Northern leaders becomes:
πN = (λwS − wN )
12

1
wN
=1−
,
λwS
λwS

(4)

Originally, Gilbert and Shapiro (1990) assumed that the patent authority could raise the profit yielded by the patentee by

widening the patent breadth and, hence, they identified the size of the profit flow with the extent of the patent breadth. Similarly,
Goh and Olivier (2002) assumed that the patent authority could indirectly raise the legal marginal cost of producing a patented
good illegally by widening patent breadth, and they identified the extent of this legal cost with the extent of the patent breadth.

8where wN denotes the wage of Northern labor.
Second, let us consider the pricing behaviors of multinationals. If the patent protection is strong
enough in the South as well as in the North, then the optimal price for multinationals in the South, pF ,is the same as that of Northern firms: pF = λwS . However, the patent breadth may be narrower in theSouth than in the North. Suppose that the patent breadth in the South βS takes a value of β ∈ [1, λ]. That
is, Southern firms other than the multinationals are permitted to produce the product with a quality λj /βwhen the state-of-the-art quality that the multinationals produces is given by λj . Then, multinationals
are obliged to cut their prices to pF = βwS (≤ λwS ), which is lower than pN except in the case of
maximum patent protection. Note that the price that multinationals can charge depends on the extent
of the patent breadth in the South, as in Goh and Olivier (2002). If the Southern government extends
the patent breadth, the other Southern firms can produce only lower quality products. In consequence,
multinationals can charge a higher price when the patent breadth is extended, that is, when the patent
protection becomes stricter in the South. From the pricing rule, the profit flow of multinationals is givenby:πF = (βwS − wS )

1
1
=1−
βwS
β

(≥ πN ).

(5)

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

2.3

R&D and FDI

Next, we consider the behaviors of R&D firms. Following Grossman and Helpman (1991), we assume
an R&D process as follows: 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˜
probability Idt.
If a firm succeeds in developing the new generation of a good, then it can take out apatent 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 whenever It > 0,(6)where It denotes the innovation rate in the entire economy at time t, which is common to every industry.
Once a Northern firm succeeds in inventing a new-generation good, the firm can become a multinational by shifting production to the South without any cost. Therefore, as long as both Northern leader

9firms and multinationals exist in equilibrium, the market values are equal for the Northern leader firms
and the multinational firms; that is, the following equality holds at each point of time:
vN,t = vF,t ,(7)

where vF,t denotes the market value of the multinationals.
Finally, we turn our attention to the no-arbitrage conditions. Shareholders of a Northern leader firm
earn dividends πN dt and capital gains v̇N dt over a time interval of length dt. Moreover, the Northernleader firm is exposed to the risks of being leapfrogged by development of the next-generation goodby another Northern firm at the innovation rate It over the time interval. Thus, shareholders are facedwith a capital loss of amount vN with a probability It dt. Therefore, we obtain the no-arbitrage condition
between the stocks of the patentee of a state-of-the-art product in the Northern market and a riskless asset
as follows:13
rt vN,t = πN,t + v̇N,t − It vN,t .

(8)

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

(9)

2.4 Labor Market
First, we consider the labor market in the South. Southern labor is demanded for production by multinationals that have patents for the state-of-the-art products. We let nF,t denote the measure of industries
in which multinationals produce the state-of-the-art products. As each multinational demands 1/(βwS,t )units of Southern labor, the aggregate labor demand of the multinationals is given by nF,t /(βwS,t ).
Therefore, the labor market clearing condition in the South becomes:
nF,t= LS .
βwS,t(10)

Next, we consider the labor market in the North. Northern 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 the13

If the Northern firm shifts production to the South and becomes a multinational, the gain is given by (vF,t −vN,t ); however,this is zero from (7). Hence, even if we consider the choice of FDI by the Northern firms, the no-arbitrage condition remains
unchanged.

10state-of-the-art quality products, the labor demand for production in the North is given by nN,t /(λwS,t ).
In addition, because R&D firms target all of the goods, the labor demand for R&D activities is given by
aN It (nF,t + nN,t ). Noting that nF,t + nN,t = 1, the labor market clearing condition in the North is:nN,t+ aN It = LN .
λwS,t

3

(11)

Market Equilibrium Paths

In this section, we derive the equilibrium path of the economies. In subsection 3.1, we show how themeasure of firms that elect to undertake FDI, nF,t , the wage rate in the South, wS,t , and the innovation
rate, It , are determined when the market value of firms, vN,t (= vF,t ), is given. Then, in subsection 3.2,
we show how the equilibrium value of vN,t is determined and, consequently, how innovation and FDI
are determined in the market equilibrium.

3.1 The Determination of FDI and Innovation for Given Market Values of Firms
First, the labor market equilibrium in the South, (10), determines the wage rate in the South, wS,t , asfollows:
wS,t =

nF,t
.
βLS

(12)

This shows that, as more multinationals produce in the South, the labor demand in the South becomeslarger, and thus the wage rate in the South rises.
Next, we consider the equilibrium determination of FDI. As (7) holds at each point of time, we obtainv̇F,t /vF,t = v̇N,t /vN,t . Substituting the no-arbitrage conditions (8) and (9) into this equation yields:
πF = πN,t .

(13)

From (7), the market values are equal between the Northern leaders and the multinationals at each pointof time and, therefore, we let vt denote the market value of firms, that is, vt ≡ vN,t = vF,t in the restof the paper. As long as the innovation rate is positive, (6) holds with equality, that is, wN,t = vt /aN .
Substituting this and (12) into (4), the profit of the Northern leader is given by:
πN,t = 1 −

vt
β
LS
.
λ aN nF,t(14)

Substituting (5) and (14) into (13), we obtain the equilibrium measure of multinationals as follows:
nF,t =

β2
LS vt ,
λaN
11

(15)

Profit flows ofmultinationals and Northern leaders
πF , πN,t1
Profit flow of Nothern leadersπN,tβProfit flow of multinationalsβ
1 − β −1πF

10Measure of multinationals
nF,tFigure 1: The determination of the measure of multinationals

when vt is given. The mechanism by which the measure of multinationals is determined is illustrated in
Figure 1. The profit of the multinationals, πF , does not depend on nF,t and, therefore, is represented by
the horizontal line. On the other hand, the profit of the Northern leader, πN,t , is an increasing functionof nF,t and is represented by an upward curve in Figure 1. The reason for this is because an increase in
the measure of multinationals raises the wage rate in the South, as shown in (12). A rise in the wage ratein the South causes a rise in the marginal cost of the nearest rivals of the Northern leaders. It enables theNorthern leaders to raise the prices of their goods, pN,t (= λwS,t ), which in turn raises their profit flow,
πN,t . The equilibrium measure of the multinationals, nF,t , is determined by the intersection of the two
curves.
By using this figure, we find that strengthening patent protection—that is, a rise in β—affects thedetermination of nF,t in the following two ways. First, strengthening patent protection raises the profit
flow of the multinationals and shifts the πF line upward. Second, strengthening patent protection reduces
the labor demand in the South and lowers the wage in the South, as shown in (12). A fall in the wage
in the South causes a fall in the marginal cost of the nearest rival of the Northern leaders and, thus, theNorthern leaders have to lower the prices of their goods. As a result, strengthening patent protection
shifts the πN curve downward. Because both of these effects raise nF,t , strengthening patent protectionin the North promotes multinationalization.
At the same time that the measure of the multinationals is determined, the wage rate in the South is12determined as follows:
wS,t =

β
vt ,
λaN

(16)

where we use (12) and (15). According to this equation, strengthening patent protection (higher β)raises the wage rate in the South. This is because tighter patent protection increases the measure ofmultinationals, as shown in (15). An increase in the measure of multinationals raises labor demand for
production in the South. Although the stronger patent protection in the South has a negative effect on theSouthern wage as a result of the decrease in the labor demand by each multinational, the positive effectoccurring through the increase in the measure of multinationals overcomes this negative effect. Thus,
stronger patent protection raises the wage in the South.
Finally, we consider the determination of the innovation rate, It . The wage rate in the South determines the price of a good produced by the Northern leader, as pN,t = λwS,t = βvt /aN by using (16).
Then, the quantity and the labor demand of this good is given by xN,t = 1/pN,t = aN /βvt . Substituting
this and (15) into the Northern labor market clearing condition (11), we obtain the innovation rate as
follows:
It =1
LN + (β/λ)LS
−
,
aN
βvt

(17)

when vt is given. This equation shows that, given vt , strengthening patent protection (an increase in β)raises the innovation rate. The reason for this is as follows: as mentioned above, strengthening patent
protection raises the profit flow of the multinationals and reduces that of the Northern leaders. These
effects induce more firms to shift production to the South. In addition, strengthening patent protection
raises the wage in the South and the good price, which allows the Northern leaders to charge higher prices
and, consequently, reduces the labor demand of each good sector, xN,t . Because of these two effects,
stronger patent protection in the South decreases the total demand for labor in the Northern productionof goods, (1 − nF,t )xN,t . This leads to an increase in the labor devoted to R&D in the North, so that theequilibrium innovation rate rises.

3.2 The Equilibrium Path of FDI and Innovation
So far, we have derived the equilibrium values of nF,t and It for a given value of vt . Finally, using thesevalues, we derive the equilibrium dynamics of the market value of a firm, vt . Substituting (17) into (8)or (9), we obtain the equilibrium dynamics of vt as follows:·¸
LN + (β/λ)LSv̇t =+ ρ vt − 1.
aN

13This differential equation has the unique steady state, v, which is given by:v=

aN.
LN + (β/λ)LS + ρaN(18)This unique steady state v is unstable, thus vt diverges to positive or negative infinity if vt takes any
value except v. Then, the equilibrium value of vt must immediately jump to v at the initial point of time,
because vt is jumpable. Because vt becomes constant over time, we can show that the other variables arealso constant over time; that is, the present North–South economy has no transitional dynamics and has
tractable features that enable an examination of the effects of policies. Note that v depends negatively on
β, as shown in (18). This is because strengthening patent protection causes capital losses to rise, owing
to leapfrogging by other firms, which occurs as a result of the promotion of innovation.
By substituting the equilibrium value of v into (15) and (17), we can derive the equilibrium values ofnF,t and It as follows:(β 2 /λ)LS,
LN + (β/λ)LS + ρaN
β − 1 LN + (β/λ)LS
ρ
It =
− .
β
aN
β
nF,t =

Differentiating these with respect to β yields:
·
¸
dnF,t
(β/λ)LS(β/λ)LS
=
2−
> 0,
dβ
LN + ρaN + (β/λ)LS
LN + ρaN + (β/λ)LS
dIt
1
= 2
dβ
β

µ

¶
LS
LN
+ρ +
> 0.
aN
λaN

(19)

(20)

From (19) and (20), we can show that both nF,t and It are increasing functions of β. Because boththe measure of the multinationals and the innovation rate depend positively on v, as shown in (15) and(17), a rise in β has negative effects on FDI and innovation through the decrease in v. However, thedirect positive effects of a rise in β, shown in (15) and (17), overcome these indirect negative effects.
Consequently, strengthening patent protection in the South necessarily promotes FDI and innovation in
the North.
Although we implicitly assume that the equilibrium is an interior solution in the above analysis, wemust also consider the case of a corner solution where either nF,t = 1 or It = 0 holds.14 First, weconsider the equilibrium where all firms possessing patents move to the South. If the patent protection
is sufficiently strong in the South, that is, if β is sufficiently high (or close to λ), all firms that succeed
14

An equilibrium with no multinationals (nF,t = 0) is not possible because the Southern labor market cannot clear.

14

in invention 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 measure of multinationals, nF,t , is equal to one.
In order to exclude such an extreme case, we assume that (λ − 1)LS < LN + ρaN . If the values of theparameters satisfy this inequality, nF,t is less than one even under the strictest patent protection in theSouth (βS = λ).
By contrast, when the patent protection is sufficiently weak in the South, that is, β is sufficiently low,
no firm may conduct R&D (It = 0). Specifically, innovation intensity It takes a value of zero if:β ≤ βmin ≡ 2−1 (1 − λLN /LS ) +p

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

As there is no innovation, the Northern labor market equilibrium (11) becomes (1 − nF )/(λwS ) = LN .
As there are both Northern leaders and multinationals in this case, (13) continues to hold. Using these
relations and the Southern labor market equilibrium, we obtain the equilibrium values of the measureof multinationals and the Southern and the Northern wage rates as follows: nF = βLS /(λLN + βLS ),wS = (λLN + βLS )−1 , and wN = λ/[β(λLN + βLS )]. Furthermore, if βmin > λ, no firm conducts
R&D even under the strictest patent protection in the South. In order to exclude such an extreme case,
we assume that the values of the parameters satisfy (λ − 1)(LN + LS ) > ρaN .
Taking into account the possibility of the corner solution such that It = 0, we obtain the equilibrium
values of nF,t and It as follows:(β 2 /λ)LS

nF = LN + (β/λ)LS + ρaN

βLS


,
λLN + βLS
β − 1 LN + (β/λ)LS
ρ


−
β
a
β
N
I=


0

if βmin ≤ β ≤ λ,(21)
if 1 ≤ β ≤ βmin ,if βmin ≤ β ≤ λ,(22)

if 1 ≤ β ≤ βmin ,where nF and I are the equilibrium values of nF,t and It , respectively. In the rest of the paper, thevariables without subscript “t” represent the values at the equilibrium.
From (21) and (22), we can summarize the results about the effects of strengthening patent protection
on innovation and FDI in the following proposition:
Proposition 1 Suppose that parameters are in the region where innovation is positive, that is, β > βmin .
Then, strengthening patent protection promotes both innovation and FDI.

15

The result that strengthening patent protection in the South enhances FDI accords with the results of
empirical studies; for instance, Lee and Mansfield (1996) estimated the relation between the volume of
FDI flows and the strength of IPR protection and found that they are positively correlated.15
Moreover, we can derive the equilibrium wage rates wS,t and wN,t as follows:

β/λ


if βmin ≤ β ≤ λ,
wS = LN + (β/λ)LS + ρaN

1


,
if 1 ≤ β ≤ βmin ,λLN + βLS





1
wN = LN + (β/λ)LS + ρaN

λ/β


λLN + βLS

(23)

if βmin ≤ β ≤ λ,(24)
if 1 ≤ β ≤ βmin .

We can summarize the results about the wage rate in the South and that in the North in the following
proposition:
Proposition 2 Suppose that parameters are in the region where innovation is positive, that is, β > βmin .
Then, strengthening patent protection raises the wage rate in the South and lowers the wage rate in the
North.
The reason for the results is as follows: an increase in the measure of multinationals, induced bystrengthening patent protection in the South, raises the demand for labor in the South, and consequently
raises the wage in the South. On the other hand, strengthening patent protection enhances innovation andtherefore reduces the value of the Northern firms and multinationals. From the zero profit condition in
R&D, the reduction in the reward for innovation must bring about a decrease in the cost of R&D, which
lowers the wage in the North.

4

Welfare Analysis

In the previous section, we show that strengthening patent protection raises the relative wage in the South.
However, the most important concern for the Southern government is the domestic consumers’ welfare:
if strengthening patent protection in the South improves the South’s welfare, the Southern government
will be eager to carry the policy into action. If not, it has an incentive to relax patent protection. Thus, inthis section, we examine the welfare effects of strengthening patent protection in the South.
15

Some theoretical studies obtained a similar result to ours: Vishwasrao (1994) and Zigic (1998) showed that weaker protec-

tion of patents in the South may lead to reductions in technology transfers in a partial equilibrium; and Lai (1998) showed thistendency in a dynamic general equilibrium.

16

First, we derive the aggregate spending of the representative consumer living in country i ∈ {N, S}.
As mentioned in subsection 2.1, because we take the total spending as the numeraire, that is, Et = 1 for
all t, the interest rate is equal to the subjective discount rate, rt = ρ. Then, the per capita spending ofa consumer living in each country is constant over time from the intertemporal utility maximization ofeach consumer. 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 (3)is reduced to:
Ei = ρAi,0 + wi ,i ∈ {N, S}.

(25)

Multiplying both sides of these budget constraints by the population and adding them, we obtain 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 thetotal 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

(26)

Because country i’s share of asset holdings must be given as the initial conditions, we let ζ ∈ [0, 1]
denote the share of the asset holdings by Northern consumers, that is, ζ ≡ Ai,0 LN /A0 . Substituting (26)
into (25), we can derive the equilibrium values of EN and ES as follows:
EN = ζ

1 − wS LS+ (1 − ζ)wN ,
LN

(27)

1 − wN LN+ ζwS .
LS

(28)

ES = (1 − ζ)

Next, we rewrite the instantaneous utility as follows:Z 1
log λJt (ω) dit (ω)dωZ 1
Z 1= (log λ)Jt (ω)dω +log dit (ω)dω.

log ui,t =

0

0

(29)

0

Because the latest generation of a product is always set at the lowest quality-adjusted price in the productline, Jt (ω) corresponds to the generation number of the latest generation of product ω. Thus, the firstterm of (29) is equal to log λ times the total number of innovations obtained in all industries by time t.
In the present model, the rate of innovation is constant over time and thus we can rewrite this term easily
as follows:
Z 1(log λ)Jt (ω)dω = (log λ)It.
0

17

(30)

The second term of (29) can be rewritten as follows:
Z 1
log dit (ω)dω = nF log diF,t + (1 − nF ) log diN,t ,0where diF,t and diN,t denote the demand for the good produced by multinationals and the Northern leaders,
respectively. Moreover, 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 ).

(31)

0

From (1) and (29) - (31), the welfare of each consumer in country i(= N, S) is given by:·¸
1 log λUi (β) =I + log Ei − log wS − (log β)nF − (log λ)(1 − nF ) ,
ρ
ρ

(32)

where Ui (β) denotes the welfare of each consumer in country i when the patent breadth in the South isequal to 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, andthe patent breadth in the South. The difference between the welfare levels of a Northern individual and aSouthern individual is only the difference in nominal spending, Ei .
In order to examine whether extending patent breadth in the South raises welfare, we differentiate(32) 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
1
(log λ − log β)−− nF. (33)dβ
wS dββ| {z }|{z}| {z }
FDI-promoting effect marginal cost effect competition-reducing effect
(+)
(-)
(-)

As shown on the right-hand side (RHS) of (33), extending patent breadth in the South affects the welfare
of both countries through the following three channels. The first channel is the welfare effect that occurs
through enhancing innovation, which is indicated by the first term on the RHS of (33). As shown in
Proposition 1, extending patent breadth promotes innovation and raises welfare. We refer to this effectas the innovation-enhancing effect. This effect has a positive influence on the welfare of both countries.
The second channel is the welfare effect that occurs through the change in nominal spending, whichis indicated by the second term on the RHS of (33). As shown later, extending 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 last channel is the welfare18effect that occurs through changing the prices of goods, which is indicated by the three terms in square
brackets on the RHS of (33).
The sign of the sum of the three terms is indeterminate because extending 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 1. Because patent
breadth is narrower in the South than in the North, the price of the goods that multinationals produce(βwS ) is cheaper than the price of the goods that the Northern leaders produce (λwS ). This means that
extending patent breadth improves the welfares of both countries through a rise in 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 (23), extending patent breadth raises the wage rate in theSouth. This causes a rise in the marginal cost of followers, which allows the Northern leaders and themultinationals to charge higher prices and thus reduces the welfare of both countries. We refer to thisnegative effect as the marginal cost effect, which is indicated by the second term in the square brackets.
Finally, extending patent breadth in the South enables the multinationals to raise the price of their goods
directly, which reduces welfare. This is because extending patent breadth permits the Southern firms
other than the multinationals to produce only goods of lower quality. This means that the multinationals
can out-compete the other firms even if the multinationals charge a higher price for their goods. For thisreason, extending 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, we can show that strengthening patent protectionin the South raises welfare. As shown in the subsequent subsections, whether this is the case depends onthe values of the parameters.

4.1 The Effect on the South’s WelfareFirst, we explore the effect of strengthening patent protection on the South’s welfare and derive thevalues of the parameters that cause the strictest patent protection to maximize the welfare of Southern
consumers. In the rest of this subsection, we focus our analysis on the case where consumers in theSouth have no assets at the initial point of time, that is, ζ = 1, as a benchmark case. In the final part, weanalyze the generalized case where ζ 6= 1.
From (28), we obtain ES = wS when ζ = 1 and thus the nominal spending effect and the marginal
cost effect, which are shown by the second and fourth terms on the RHS of (33), respectively, cancel each19other. Then, the derivative of US (β) becomes a simpler form as follows:dUS (β)
dβ

=

1£
ρ

log λ dIρ dβ
| {z }
innovation-enhancing effect
(+)
¤
dnF
1
+ (log λ − log β)
− nF
.
dβ
β
| {z }|{z}
FDI-promoting effect competition-reducing effect
(+)
(-)

(34)

As discussed in Appendix A, we can show that the innovation-enhancing effect, which is indicatedby the first term on the RHS in (34), necessarily overcomes the competition-reducing effect, which isindicated by the third term of the equation, for all β ∈ [βmin , λ] if and only if the parameters satisfy(log λ)λ−2 (LN + λLS + ρaN )(ρaN )−1 ≥ LS (LN + LS + ρaN )−1 . Therefore, we can guarantee thatthe strictest patent protection maximizes welfare in the South if and only if that inequality holds because
the second term on the RHS in (34) is necessarily nonnegative and becomes zero when β = λ. We cansummarize the results of the welfare analysis as follows:16
Proposition 3 Suppose that consumers in the South have no assets at the initial point of time, that is,ζ = 1. Then, the strictest patent protection in the South (βS = λ) maximizes the welfare of consumers in the South if and only if the parameters satisfy (log λ)λ−2 (LN + λLS + ρaN )(ρaN )−1 ≥LS (LN + LS + ρaN )−1 .
As can be seen easily, when the Northern labor, LN , is larger, the condition in Proposition 3 tends
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 can strengthening patent protection
raise the welfare of Southern consumers in such a case? More abundant labor in the North intensifies thepromotion of the innovation effect of strengthening patent protection, dI/dβ, which is indicated by the
LHS of the condition in Proposition 3. In addition, the factor decreases the proportion of multinationals, nF , and, consequently, weakens the competition-reducing effect of strengthening patent protection,
16

In Propositions 3–5, we suppose that the degree of patent protection in the South is not weaker than the level of protection

below which Northern R&D activities cease, that is, β ∈ [βmin , λ]. For some values of parameters, a low value of β thatprevents innovation could maximize welfare. However, if the cost of innovation is sufficiently low, such a case is impossible.
For instance, assuming aN < (λ − 1)(LN + LS )2 [(λ + 1)(LN + LS ) + λLS ]−1 ρ−1 , we can show that any low value of βthat prevents innovation will not maximize the welfare of the Southern consumer nor that of the Northern consumer. The proof
is available on request.

20

dnF /dβ, which is indicated by the RHS of the condition in Proposition 3. Thus, more abundant labor in
the North intensifies the positive welfare effect of strengthening patent protection.
In addition, as proved in Appendix A, the condition in Proposition 3 necessarily holds irrespectiveof the size of labor in the North, as long as LS /aN is so large that LS /aN ≥ λ [(log λ)(2λ − 1)]−1 ρ.
Therefore, Proposition 3 shows that the strictest patent protection improves the welfare of consumers in
the South if labor is more abundant in the South and if the productivity of R&D is higher. The reason is asfollows. More abundant labor in the South and higher productivity of R&d intensify the promotion of theinnovation effect of strengthening patent protection, dI/dβ, while they also increase the proportion ofmultinationals, nF , and consequently, intensify the competition-reducing effect of strengthening patent
protection. Thus, more abundant labor in the South and higher productivity of R&D have two opposing
effects on welfare. However, if LS /aN is so large as to satisfy LS /aN ≥ λ [(log λ)(2λ − 1)]−1 ρ, theformer positive effect overcomes the latter negative one.
The result obtained in Proposition 3 is important in the following two aspects. First, it seems to
be widely recognized that stronger patent protection lowers welfare in the South. However, our result
contrasts with this intuitive recognition and shows that, far from being harmful, stronger patent protection is beneficial to the South. In other words, this paper provides a rationale for strengthening patent
protection, which is a policy implemented in reality in many developing countries.
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, where the only mode of technology transfer was
illegal imitation, and in an exogenous innovation model, where FDI was the mode of technology transfer.
Helpman concluded that stronger IPR protection in the South necessarily damaged welfare in the Southin both models. We obtain some important implications from our results that contrast with the resultsof Helpman’s two models. First, comparing our model and Helpman’s result from his model where
imitation is the only mode of technology transfer, we can infer that the effect of strengthening IPR
protection on the South’s welfare depends on what the main mode of technology transfer is: when themain mode of technology transfer is FDI, strengthening IPR protection is likely to raise the South’s
welfare. Second, by comparing our model and Helpman’s result from his model that includes FDI,
we can show that taking the innovation-enhancing effect into account may reverse the sign of the total
welfare effect from strengthening IPR protection: endogenizing innovation in the model is essential toan appropriate assessment of the welfare effect of strengthening IPR protection.

21

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 dothis, we first show that the effect on the North’s welfare of extending patent breadth is independent of theinitial distribution of assets, ζ, by examining the nominal spending effect and the marginal cost effect.
From (23), (24), and (27), EN /wS becomes:
EN
=
wS

µ
1+ζ

ρaN
LN

¶

λ
,
β

and the effect of extending patent breadth on log(EN /wS ) is given by:
1 dEN
1 dwS
1
−
= − < 0.
EN dβ
wS dβ
β

(35)

This shows that the effect of extending patent breadth on 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 magnitudesof the innovation-enhancing effect, the FDI-promoting effect, and the competition-reducing effect are
determined without regard to ζ. Thus, we find that the effect on the North’s welfare, dUN (β)/dβ, is
independent of ζ.
Using (33) and (35), we find the effect of strengthening patent protection on the North’s welfare as
follows:
dUN (β)
dβ

=

1£
ρ

log λ dI1−
ρ dββ
| {z }|{z}innovation-enhancing effectnominal spending effect(-)(+)
and marginal cost effect (-)¤
dnF
1+ (log λ − log β)
− nF
.
dβ
β
| {z }|{z}
FDI-promoting effectcompetition-reducing effect(+)(-)

If we verify that this is positive, we can show that strengthening patent protection in the South necessarilyraises the North’s welfare. As shown in Appendix B, dUN (β)/dβ is positive for all β ∈ [βmin , λ] aslong as the parameters satisfy an inequality. We can summarize the results of the analysis of the North’s
welfare as the following proposition:
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 .

22

The condition in Proposition 4 is stricter than the condition imposed in Proposition 3.17 Hence, we
can show that strengthening patent protection in the case where ζ = 1 makes both the South and theNorth better off as long as the parameters satisfy the condition in Proposition 4. In other words, as longas labor resource in the North is abundant enough to satisfy the condition, or as long as the productivityof R&D is sufficiently high to satisfy the condition, then harmonizing the Southern standard of patent
protection with the Northern one by strengthening patent protection in the South is a Pareto-improving
policy.
With respect to the effect on the welfare of consumers in the North, the results of the present paper
agree with that of Helpman’s FDI model. In his exogenous innovation model, Helpman concluded thattightening IPR protection when the main mode of technology transfer is FDI benefits the North if theimitation rate in the South is sufficiently small. Meanwhile, our endogenous innovation model implies
that maximum patent protection in developing countries is globally optimal for the consumers in the
North if the labor resource of the North is sufficiently large and the productivity of R&D is sufficiently
high. This result implies that Helpman’s conclusion on the welfare of the North will not change even
if one takes into account the innovation-enhancing effect of strengthening IPR protection. In that sense,
the result obtained in Proposition 4 complements Helpman’s conclusion on the welfare of the North.

4.3

The Generalization of the Initial Distribution of Assets

Finally, in order to generalize the result obtained in Proposition 3, we show that the strictest patent
protection can maximize the welfare of consumers in the South even in the case where ζ 6= 1. When
ζ 6= 1, the nominal spending effect and the marginal cost effect do not cancel each other out and wehave to consider these welfare effects of strengthening patent protection. From (23) and (28), ES /wS
becomes:ES
λρaN= 1 + (1 − ζ)
,
wS
LS β
and the effect of strengthening patent protection on log(ES /wS ) is given by:
1 dES
1 dwS
1−ζ
1
−
=−
< 0.
ES dβ
wS dβ
βLS /(λρaN ) + 1 − ζ β
17

(36)

By substituting LN = [λ/(log λ) − 1]ρaN into the inequality in Proposition 3, we can confirm that the inequality holds

necessarily if LN = [λ/(log λ) − 1]ρaN . Thus, the inequality in Proposition 3 holds whenever LN > [λ/(log λ) − 1]ρaN ,because the LHS of the inequality of the condition in Proposition 3 is an increasing function of LN and the RHS is a decreasing
function of LN . That is, if the parameters satisfy the inequality in Proposition 4, then the parameters also satisfy the inequality
in Proposition 3.

23

This means that when the initial asset level of the Southern consumer is larger, that is, (1 − ζ) is larger,
the negative effect of strengthening patent protection on log(ES /wS ) becomes larger. Therefore, thetotal effect of strengthening patent protection on the welfare of the Southern consumer is more likely tobe negative as the initial asset level of the Southern consumer is larger. However, as shown in Appendix
C, we can show that the strictest patent protection maximizes the welfare of the Southern consumer forany ζ ∈ [0, 1] if the parameters satisfy the condition given in Proposition 4. Combining this result withthe result that we obtained in Proposition 4, we can obtain the following proposition.
Proposition 5 The strictest patent protection in the South (βS = λ) maximizes the welfare of consumers
both in the South and in the North for any initial asset distribution between the North and the South if
the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .
Proposition 5 shows that as long as labor resource in the North is abundant enough to satisfy thecondition, or as long as the productivity of innovation is high enough to satisfy the condition, thenharmonizing the Southern standard of patent protection with the Northern one by strengthening patent
protection in the South is a Pareto-improving policy irrespective of the distribution of assets between the
North and the South. In Proposition 3, we suppose that the consumer in the South has no assets initially.
As seen in (28), holding no assets initially means that no assets are held at each point of time, and theresult of the proposition seems to be dependent on the restriction of the distribution of assets. However,if the inequality in Proposition 5 holds, we can show that the strictest patent protection in the South isoptimal, regardless of the distribution of assets among countries. That is, even if the consumer in theSouth holds some assets, the strictest patent protection in the South can maximize the welfare of eachconsumer in the South.

5

Conclusion

The present paper constructs a North–South quality-ladder model, where FDI is the main channel oftechnology transfer, and conducts not only a positive analysis but also a welfare analysis. Despite thefact that welfare analysis is the most important factor for assessing policies, few previous theoreticalstudies on IPR protection in developing countries have conducted such an analysis, mainly because
the equilibrium paths are so complex that they cannot evaluate the welfare effect of strengthening IPR
protection. However, by focusing the analysis on patent breadth, the present paper examines analytically
how strengthening patent protection in the South affects welfare in the South. As a result of the analysis,24we have shown that strengthening patent protection can raise welfare not only in the North but also in
the South.
This result stands in contrast to Helpman (1993), the pioneering study that 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 analysis differed markedly from Helpman’s result in this respect. Thus,
our result provides a theoretical basis for strengthening patent protection in the South.

Appendix A: Proof of Proposition 3
In this appendix, we prove Proposition 3 by showing that dUS (λ)/(dβ) ≥ 0 if and only if the parameterssatisfy (log λ)λ−2 (LN + λLS + ρaN )(ρaN )−1 ≥ LS (LN + LS + ρaN )−1 . Additionally, we prove that(log λ)λ−2 (LN + λLS + ρaN )(ρaN )−1 ≥ LS (LN + LS + ρaN )−1 holds necessarily if the parameterssatisfy LS ≥ λ[(log λ)(2λ − 1)]−1 ρaN .
Substituting the derivatives of I and nF into (33), we obtain the following equality in the range ofβ ∈ [βmin , λ]:dUS (β)
dβ

(

· µ
¶
¸
log λ 1 LN
LS
=
+ρ +
ρ
β 2 aN
λaN|{z}innovation-enhancing effect (+)·¸(β/λ)LS(β/λ)LS+ (log λ − log β)
2−
LN + ρaN + (β/λ)LS
LN + ρaN + (β/λ)LS{z}|
FDI-promoting effect (+))(β/λ)LS−.
L + ρaN + (β/λ)LS| N{z}
competition-reducing effect (-)
1
ρ

(37)

We define f (β) as the sum of the first term and the third term in the curly bracket of (37):f (β) ≡=log λ dI
1
− nF
ρ dβ β· µ¶¸log λ 1 LN
LS(β/λ)LS
+ρ +
−
.
2
ρ
β
aN
λaN
LN + ρaN + (β/λ)LS

If f (β) is positive, then the RHS of (37) is also positive because the second term is always nonnegative.
As it is straightforward to show that f 0 (β) < 0, it is ensured that f (β) ≥ 0 for all β ∈ [βmin , λ] if f (λ) ≥0. Because the second term in the RHS of (37) is always nonnegative, this implies that dUS (β)/dβ isnonnegative for all β ∈ [βmin , λ], that is, the strictest patent protection (βS = λ) maximizes the welfare
25

of the consumer in the South if f (λ) ≥ 0. On the other hand, if f (λ) < 0, the strictest patent protection(βS = λ) does not maximize the welfare of the consumer in the South, because the second term in the
RHS of (37) is zero when β = λ, and consequently dUS (λ)/dβ is negative. As a result, the strictest
patent protection (βS = λ) maximizes the welfare of the consumer in the South if and only if f (λ) ≥ 0.
By the definition, f (λ) is given by:
f (λ) =

log λ
ρλ2

µ

LN
LS
+ρ+λ
aN
aN

¶
−

LS
.
LN + ρaN + LS

(38)

Rewriting f (λ) ≥ 0, we obtain the condition in Proposition 3, (log λ)λ−2 (LN +λLS +ρaN )(ρaN )−1 ≥LS (LN + LS + ρaN )−1 .
Finally we show that the condition given in Proposition 3 holds irrespective of the size of labor in
the North if labor in the South satisfies LS ≥ λ[(log λ)(2λ − 1)]−1 ρaN . Note that f (λ) is an increasing
function of (LN /aN + ρ). Because we focus our analysis on the equilibrium where nF < 1, LN /aN +ρ > (λ − 1)LS /aN necessarily holds. Therefore, if f (λ) > 0 when LN /aN + ρ = (λ − 1)LS /aN , thenf (λ) is necessarily positive. Substituting LN /aN + ρ = (λ − 1)LS /aN into (38) yields the following
inequality:
LS ≥

λ
ρaN .
(log λ)(2λ − 1)

Appendix B: Proof of Proposition 4
In this appendix, we prove Proposition 4 by showing that dUN (β)/dβ is positive for any value of β ∈[βmin , λ] if the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .
Using f (β) that is defined in Appendix A, we can rewrite dUN (β)/dβ as follows:·¸
1 log λ dI
1dnF
1dUN (β)=− + (log λ − log β)
− nF
dβ
ρ
ρ dβ β
dβ
β
·
¸
1
1
dnF
=
f (β) − + (log λ − log β)
.
ρ
β
dβ

(39)

The last term on the RHS of (39) is necessarily positive and thus dUN (β)/dβ > 0 if f (β) − β −1 ispositive. By the definition of f (β), we find that the following relation must hold:
·µ
¶
¸
1
log λ
LN
LS
1
(β/λ)LS1f (β) −
=
+
+ρ
−
−
2
β
ρ
aN
β
λaN
LN + ρaN + (β/λ)LS
β
·µ
¶
¸
LN
LS
log λ
1
(β/λ)LS
1
+
>
+ρ
−
−
2
ρ
aN
β
λaN
LN + ρaN
β
·
¸·
¸
2
1
β
log λ
1
=
LN + ρaN + LS−.
βλρaN β LN + ρaN
26

(40)

If we assume that LN ≥ [λ/(log λ) − 1] ρaN , then the parameters satisfy the following relation for allβ ∈ [1, λ]:
log λ
1
−
≥ 0.
ρaN β LN + ρaN
Therefore, from (39) and (40), we can conclude that dUN (β)/dβ > 0 for any value of β ∈ [βmin , λ] if
the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .

Appendix C: Proof of Proposition 5
In this appendix, we prove Proposition 5, which states that the strictest patent protection in the Southmaximizes the welfare of consumers both in the South and in the North for any initial asset distribution
if LN ≥ [λ/(log λ) − 1] ρaN is satisfied. Because the proof on the welfare of the Northern consumer
is given in Appendix B, it is sufficient for the proof to show that dUS (β)/dβ > 0 for any values ofβ ∈ [βmin , λ] and ζ ∈ [0, 1] if the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .
Using f (β) that is defined in Appendix A, we can rewrite dUS (β)/dβ for any ζ ∈ [0, 1] as follows:·µ¶¸
dUS (β)1 log λ dI
1 dES
1 dwS
dnF
1
=
+
−
+ (log λ − log β)
− nF
dβ
ρ
ρ dβ
ES dβ
wS dβ
dβ
β
·
µ
¶
¸
1 dES
1 dwS
dnF
1
f (β) +−+ (log λ − log β)
=
ρ
ES dβ
wS dβ
dβ
·
¸
1
1
dnF
>
f (β) − + (log λ − log β)
,
(41)
ρ
β
dβ
1 dwS
−1
S
where the last inequality holds because E1S dE
dβ − wS dβ is larger than −β , which can be shown

directly from (36). Note that the RHS of (41) is equal to dUN (β)/dβ. Therefore, using the same proof
as in Appendix B, we can show that dUS (β)/dβ > dUN (β)/dβ > 0 for any values of β ∈ [βmin , λ]and ζ ∈ [0, 1] if the parameters satisfy LN ≥ [λ/(log λ) − 1] ρaN .

27

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28

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29

Appendix D (Not Intended for Publication): Proof of the Assertion in Footnote 16
In this appendix, we prove the assertion in footnote 16. 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 ]−1 ρ−1 .
To verify this, we first compute the welfare of each consumer in the case of no innovation, that is,
Ui (β̄) for β̄ ∈ [1, βmin ]. Substituting (23) and (24) into (27) and (28), we have:ζ(β̄ − 1)(λLN + β̄LS ) + λLN
β̄LN (λLN + β̄LS )(42)(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS
β̄LS (λLN + β̄LS )

(43)

EN =
and
ES =

for β̄ ∈ [1, βmin ]. Thus, from (21) – (23), (32), and (42), we can compute UN (β̄) for β̄ ∈ [1, βmin ] asfollows:1ρUN (β̄) =½
ζ(β̄ − 1)(λLN + β̄LS ) + λLN
log
β̄LN
¾
¡
¢
β̄LS
log λ − log β̄ − log λ .
+λLN + β̄LS

Similarly, from (21)–(23), (32), and (43), US (β̄) for β̄ ∈ [1, βmin ] can be derived as follows:½
1(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS
US (β̄) =
log
ρ
β̄LS
¾
¡
¢
β̄LS
+
log λ − log β̄ − log λ .
λLN + β̄LS
Next, we derive the welfare of each consumer in the case where β = λ, that is, Ui (λ). By substituting(23) and (24) into (27) and (28), the equilibrium values of each consumer’s spending in the case whereβ = λ are given as follows:
1
EN =
LN + LS + ρaN

µ

ζρaN
+1
LN

¶
(44)

and
1
ES =
LN + LS + ρaN·¸(1 − ζ)ρaN+1 .
LS

Therefore, substituting (21)–(23) and (44) into (32) yields:
½
·
¸
µ
¶
¾
ζρaN
1 log λ λ − 1 LN + LSρ
+ log
UN (λ) =−+ 1 − log λ .
ρ
ρ
λ
aN
λ
LN
i

(45)

In a similar way, from (21)–(23), (32), and (45), we obtain:
¸
¾
½
·
¸
·
1 log λ λ − 1 LN + LSρ
(1 − ζ)ρaN
US (λ) =−+ log+ 1 − log λ .
ρ
ρ
λ
aN
λ
LS
Now, we compare Ui (β̄) with Ui (λ) to confirm the assertion in footnote 16. By subtracting UN (β̄)
from UN (λ), we have:·¸µ¶log λ λ − 1 LN + LS
ρ
ζρaN
−
+ log
+1
ρ
λ
aN
λ
LN
¾
¡
¢
β̄LS
ζ(β̄ − 1)(λLN + β̄LS ) + λLN−− log
log λ − log β̄ . (46)β̄LN
λLN + β̄LS1UN (λ) − UN (β̄) =ρ½Note that the sum of the second term and the third term in (46) 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
ζλ−1 (β̄ − 1)(λLN + β̄LS )β̄ + β̄LN≥ log
ζ(β̄ − 1)(λLN + β̄LS ) + λLN= log β̄ − log λ,where the inequality of the third line uses the relation that ρaN ≥ λ−1 (β̄ − 1)(λLN + β̄LS ) must hold−1 < 0 for β ≤ βbecause (β − 1)β −1 [LN + (β/λ)LS ]a−1
min from (22). Thus, UN (λ) − UN (β̄)
N − ρβmust satisfy the following inequality for any β̄ ∈ [1, βmin ]:½·¸
1 log λ λ − 1 LN + LSρUN (λ) − UN (β̄) ≥−+ log β̄ − log λ
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 ]−1 ρ−1 .
Therefore, we can conclude that the welfare of each Northern consumer in the case where β = λ is higher
than the welfare in the case of no innovation, if aN < (λ−1)(LN +LS )2 [(λ + 1)(LN + LS ) + λLS ]−1 ρ−1 .
In the same way, we can show that US (λ)−US (β̄) is positive if the condition is satisfied. Subtracting
US (β̄) from US (λ), we obtain:
½
·
¸
·
¸
(1 − ζ)ρaN
1 log λ λ − 1 LN + LSρ
+ log
US (λ) − US (β̄) =
−
+1
ρ
ρ
λ
aN
λ
LS
¾
¡
¢
(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS
β̄LS
− log
−
log λ − log β̄ . (47)β̄LS
λLN + β̄LS
ii

The sum of the second term and the third term in (47) 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)λ−1 (β̄ − 1)(λLN + β̄LS )β̄ + β̄LS
≥ log
(1 − ζ)(β̄ − 1)(λLN + β̄LS ) + β̄LS
> log β̄ − log λ,where the first inequality uses the relation that ρaN ≥ λ−1 (β̄ − 1)(λLN + β̄LS ) must hold because−1 < 0 for β ≤ β(β − 1)β −1 [LN + (β/λ)LS ]a−1
min from (22). Thus, US (λ) − US (β̄) mustN − ρβsatisfy the following inequality for any β̄ ∈ [1, βmin ]:½·¸
1 log λ λ − 1 LN + LSρUS (λ) − US (β̄) >−+ log β̄ − log λ
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
¶¾
µ
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 ]−1 ρ−1 .
That is, the welfare of each Southern consumer in the case where β = λ is also higher than the welfare
in the case of no innovation, if aN < (λ − 1)(LN + LS )2 [(λ + 1)(LN + LS ) + λLS ]−1 ρ−1 .
Thus, we have been able to confirm that when the value of β is so low that no R&D is undertaken, thisdoes not maximize the welfare of each consumer if aN < (λ−1)(LN +LS )2 [(λ + 1)(LN + LS ) + λLS ]−1 ρ−1 .

iii