Discussion Papers In Economics
And Business

Innovation, Licensing, and Imitation: The Effects ofIntellectual Property Rights Protection and Industrial Policy
Koichi Futagami

Tatsuro Iwaisako
andHitoshi Tanaka

Discussion Paper 07-05

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANInnovation, Licensing, and Imitation: The Effects ofIntellectual Property Rights Protection and Industrial Policy
Koichi Futagami

Tatsuro Iwaisako
andHitoshi Tanaka

Discussion Paper 07-05
February 2007
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Innovation, Licensing, and Imitation: The Effects ofIntellectual Property Rights Protection and Industrial Policy∗
Koichi Futagami†

Tatsuro Iwaisako‡
andHitoshi Tanaka§
Abstract
This paper examines the long-run effects of intellectual property rights (IPR) protection and industrial policies on innovation and technology transfer using a North–Southquality ladder model where licensing is the main mode of technology transfer to developing countries. We show that the governments of developing countries can promote
innovation and technology transfer by strengthening IPR protection, which is enforced
by restricting the imitation of products. Moreover, the results also imply that subsidies on the cost of license negotiation can promote innovation and technology transfer,whereas subsidies on the cost of R&D have no effect.
Keywords: Licensing; Imitation; Innovation; Intellectual property rights;
JEL classification: F43; O33; O34;∗

The authors are especially grateful to Tetsugen Haruyama and Ryoji Ohdoi for their insightful and constructive suggestions. They would like to thank Ryo Arawatari, Takeshi Ikeda, Kazuo Mino, Makoto Mori,
Tetsuya Nakajima, Hideki Nakamura, Noritsugu Nakanishi, attendees at the European Trade Study Group(ETSG) 2006 Vienna Eighth Annual Conference, and seminar participants at Kwansei Gakuin University andOsaka City University for their helpful comments. Of course, all remaining errors are the authors’ responsibility.
†
Faculty of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan. Email: futagami@econ.osaka-u.ac.jp‡
Faculty of Economics, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan. Email: tiwai@ec.ritsumei.ac.jp§
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043,
Japan. E-mail: cg039th@srv.econ.osaka-u.ac.jp

1 Introduction
For developing countries with only limited knowledge of advanced technology, absorption
from abroad is usually essential to promoting economic growth. Historically, for instance,
the Japanese economy following World War II was able to experience high economic growth
by importing knowledge of advanced technologies from the United States and Western Europe. Today, as technologies are continually improved by research and development efforts,
the absorption of advanced knowledge from abroad has become increasingly important fordeveloping countries to catch up with technological progress. For this reason, how developing countries smoothly absorb this knowledge and attain high economic performance has
been a major concern in the field of economic growth theory for at least the past two decades.
Generally speaking, advanced knowledge is considered to be transferred from developed
countries to developing countries through various channels. For example, importing machines and equipment enables firms in developing countries to access the general knowledge
and information embodied in them.1 On the other hand, multinational firms in developed
countries often contribute to the conveyance of knowledge of their refined manufacturing
techniques through their subsidiaries and affiliated partners.2
Local firms in developing countries also play an important role in diffusing knowledgeof advanced technologies in two major ways. First, some local firms aim to make licensing
contracts with patent holders to use their ideas and designs legally or to learn know-how.3
In particular, firms in Japan and Korea made many licensing contracts to help absorb advanced technologies in the national development process after World War II.4 Second, other1

See Coe et al. (1997).
Lai (1998) investigated the long-term effects of intellectual property rights protection in developing countries on the rate of innovation, the rate of international production transfer and world income distribution when
multinational firms transferred their technologies through foreign direct investment.
3
A famous example is the ‘pilgrimage to Montecattini’ where a number of Japanese firms visited Montecattini in Italy—an Italian company that succeeded in converting propylene into a fiber-forming propylene—inorder to obtain a licensing agreement. Other examples of international licensing involving firms of developed
and developing countries are given in Park and Lippoldt (2005, Tables 7 and 8).
4
See Peck (1976), Ozawa (1980), and Enos and Park (1988). One of the reasons why firms in thosecountries made many licensing contracts is that their governments desired the development of domestic firms
2

1

firms often sell products by copying ideas and technologies without the permission of patent
holders in developed countries. These imitation activities are widely observed in developing
countries owing to the weak protection of intellectual property rights (IPR) and are one of
the major ways of disseminating advanced knowledge to developing countries.5
However, excessive risks of imitation induced by weak IPR protection are likely to decrease technology transference through other legal channels, because patent holders feelapprehensive about the imitation of their products and ideas. Indeed, some empirical studies
demonstrate that the strength of IPR protection in the recipient country is a significant determinant of technology transfer toward that country. For example, Yang and Maskus (2001a)found that U.S. receipts of royalties and license fees from unaffiliated firms positively responded to a strengthening of patent rights protection in the recipient country. Likewise,
Smith (2001) simultaneously analyzed the effect of patent rights in foreign countries on
U.S. exports, affiliate sales, and licenses. The results indicated that strengthening foreign
patent rights increased U.S. affiliate sales and licensing if the recipient country had strong
imitative abilities. More recently, using U.S. firm-level data sets, Park and Lippoldt (2005)
explored how royalty and licensing fee payments from unaffiliated firms in foreign countries to U.S. firms were influenced by four IPR indexes of the recipient countries: patentrights, copyrights, trademark rights, and enforcement effectiveness. They concluded that
IPR strength as a whole has statistically significant positive influences on licensing receipts.
The results of these studies imply that stronger IPR protection leading to the restriction ofimitation promotes international technology licensing across countries.
This paper provides a theoretical framework to analyze how strengthening IPR protection, implemented by restricting imitation, affects international technology licensing. We

rather than depending on foreign firms. In addition, Japanese government authorities also feared the outflow
of rents abroad. In fact, the Japanese government restricted foreign direct investment through a law establishedin 1950 (the Foreign Capital Law).
5
Helpman (1993) explored how strengthening IPR in developing countries affected welfare using a dynamic
general equilibrium model, such that technological innovation takes place in developed countries while aninvented product faces the risk of imitation in developing countries at a constant probability through time.

2

construct a product-life-cycle general equilibrium model where local firms in developing
countries pay efforts to win license contracts under circumstances of prevailing imitation. A
key feature of our model is that we explicitly take account of copies of products’ ideas, inaddition to licensing activities, as a means of technology diffusion in developing countries,
and regard the frequency of imitation as a measure of the strength of IPR protection.
By using this model, we investigate the influence of strengthening IPR in developing
countries, the influence of the introduction of subsidies on licensing and R&D processes,
and the influence of changing the rent distribution between licensors and licensees. As aconsequence, we show three main results: (i) strengthening IPR through restricting imitation
unambiguously increases technology transfer and innovation—this is consistent with theempirical results presented earlier; (ii) introducing subsidies for licensing activities promotes
technology transfer and innovation, while subsidizing R&D activities has no effect; and(iii) an increase in the rate of license fees paid to the licensors is an obstacle, not only totechnology transfer, but also to R&D activity.
In spite of the importance of licensing activities in technology transfer, only a few studies
have incorporated it into a general equilibrium model. Yang and Maskus (2001b) initiallyaddressed this issue using a ‘quality ladder’-type product-cycle model developed by Grossman and Helpman (1991, Ch. 12). They concluded that stronger IPR promotes innovationand technology transfer. They also considered that strengthening IPR protection decreases
the cost of licensing (the size effect), and increases the rent distribution of licensor firms thathave patents on advanced technologies (the distribution effect), both of which work positively on technology transfer and innovation. However, because they assumed that firms indeveloped countries use their resources to make licensing contracts, their model does not
suit the Japanese and Korean experience well. In addition, the steady state of their model
is dynamically unstable, so that the model has a problem when the economy cannot approach the steady state.6 Tanaka, Iwaisako, and Futagami (2007) later modified this point
6

A proof is available from the authors on request.

3and constructed a technology licensing model. In their model, firms in developing countries
are assumed to use their own resources to win licensing contracts. However, they did not
examine the effects of IPR protection policies.
Our study extends the models of both Yang and Maskus (2001b) and Tanaka, Iwaisako,
and Futagami (2007) by formalizing the possibility that the design of a licensed product iscopied by another firm. This extension is meaningful in the following three respects. First,
our model better reflects actual observations on technology diffusion than either of the above
studies. This is because the imitation of products is fairly prevalent in developing countries,
and, as stated previously, is one of the main channels of technology diffusion. Second, ourmodel better describes the trade-off that a patent holder faces by granting a license to an
outside firm located in a low-wage country with weak IPR protection: the patented idea or
product is exposed to a greater risk of imitation in exchange for the income accruing fromlicense fees.
Third, and most importantly, our setting enables us to obtain richer implications forthe policy of IPR protection. Yang and Maskus (2001b), for example, abstracted away thenotion of the length and the breadth of patents and the procedures used for enforcement of
IPR protection policy with the intention of analytical simplicity. As a result, they did not
specify how government authorities control the strength of IPR protection. Instead, they
indirectly analyzed the effects of stronger IPR protection by assuming that a fall in licensing
costs and an increase in the licensor’s share of rents are a consequence of strengthening IPR
protection policy. However, it is likely to be difficult to derive the direct implications ofsuch a practical policy as the strict enforcement of IPR protection through the restriction ofimitation without some additional settings. This is because the model leaves unformulated
the connection between IPR protection policy and both licensing costs and rent shares. In
contrast, our model can directly draw conclusions about a restrictive policy on imitation
since we explicitly introduce imitation into the model with an index of the degree of IPR
protection. Moreover, our results give support to the global tide of intellectual property
4reform in the direction of strict protection following the World Trade Organization’s (WTO)
Trade-Related Aspects of Intellectual Property Rights Agreement in terms of promoting
innovation and technology transfer.
The remainder of this paper is structured as follows. Section 2 introduces the model
where both licensing and imitation coexist. Section 3 shows that a unique steady state exists. Section 4 conducts comparative statics of the steady state. Section 5 provides someconcluding remarks.

2 The Model
This paper constructs a quality ladder-type dynamic North–South model in which licensing
is the main mode of technology transfer to a developing country in order to examine theeffects of governmental policies on innovation and technology transfer. In this model, we
consider that imitation of products prevails in the developing country because of incomplete
IPR protection. We regard this speed of imitation as an index reflecting the level of IPR
protection in the developing country. Our model is mainly based on work by Yang and
Maskus (2001b) and Tanaka, Iwaisako, and Futagami (2007).
Consider an economy consisting of two regions, North and South, labeled N and S,
respectively. A continuum of goods indexed by ω ∈ [0, 1] exists in the economy and goods
are produced in either the North or the South. Each product ω is classified by a countableinfinite number of qualities j = 0, 1, · · ·. The product with one-grade higher quality than thecurrent top-of-the-line quality of the product becomes available if innovation occurs in theindustry. Therefore, product ω with quality j can be produced after the jth innovation in theindustry ω. We assume that the quality is provided by qj (ω) = λj , where the increment ofquality, λ > 1, is identical for all products. As described below, research and development
conducted by firms brings this quality improvement. We choose units appropriately so thatthe quality at time t = 0 is equal to unity in all industries.
52.1 Consumer’s Optimization
Consumers living in both regions have identical preferences:
U=

 ∞
0

e−ρt log u(t)dt,(1)

where ρ is a common subjective discount rate and log u(t) represents instantaneous utility
at time t. We specify the instantaneous utility function in Cobb-Douglas form as:log u(t) =

 1
0

⎡

log ⎣



⎤

qj (ω)dj,t (ω)⎦ dω,jwhere dj,t (ω) denotes consumption of good ω with quality j at time t. The representative
consumer maximizes his or her utility (1) under an intertemporal budget constraint:
 ∞
0

t

e− 0 r(s)ds Et dt = A0,

where rt is the interest rate consumers in both countries face at time t and A0 is the sum of
initial asset holdings and discounted total labor income. The term Et represents the flow ofspending at time t, namely:
⎡
⎤
 1 
⎣
pj,t (ω)dj,t (ω)⎦ dω,
Et =
0

j

where pj,t (ω) is the price of product ω with quality j at time t.
We can solve this representative consumer’s problem in two steps. In the first step, we
think of the intratemporal maximization problem by computing the allocation of spending
Et to maximize log u(t) given prices at time t. As a result of the static maximization, theconsumer allots identical expenditure shares to all products and chooses a single quality
j = Jt (ω) of each product that carries the lowest quality-adjusted price pj,t (ω)/qj,t (ω). This6

implies the static demand function:

dj,t (ω) =⎧⎪⎪⎨ Et /pj,t (ω)

for j = Jt (ω),⎪⎪⎩

otherwise.

0

In the second step, we compute the time pattern of spending to maximize the consumer’sutility (1) subject to the dynamic budget constraint. This intertemporal utility maximization
requires Ėt /Et = rt − ρ. By taking the aggregate spending as the numeraire, we normalize
Et = 1 for all t so that the interest rate rt is always equal to the subjective discount rate ρ.

2.2 Production
We now consider the production side. We assume that each economy has a single primary
production factor, labor. The total labor supply is assumed constant and depends on the
country. We also assume that one unit of output requires one unit of labor input. In addition, research activities and license negotiations to win a license from a patent holder also
require labor inputs, while imitation is assumed to progress exogenously without any labor,
described below.
Two types of firm are assumed to exist in the economy, ‘leaders’ and ‘followers’. Leaders
are firms that have the ability to produce the current highest quality of each good, while
followers are the remaining firms. As a general feature of this kind of model, industrial
leaders are assumed not to intend to further research their products until the products arecopied. Therefore, the quality gap between leaders and their closest rivals never exceeds
one step.
A firm is also distinguished in terms of its location; that is, whether it is in the Northor in the South. We assume that only Northern firms have the ability to conduct R&D andbring state-of-the-art products to the market. When succeeding in innovation, a Northernfirm can acquire the patent on the design of a product in the North. In addition, the firm can7also export the good to the South without any transportation costs or tariffs.
On the other hand, to acquire the exclusive rights to produce and sell a Northern firm’s
product that has not yet been imitated, a Southern firm must propose a license contract to theNorthern patent holder. Granted the license, the Southern firm can receive the blueprint of
the product and acquire enough knowledge to manufacture it. Moreover, the firm can legally
make a monopoly of the product in the entire world. However, Southern licensees must keep
paying a part of the rents from the sale to their licensors as a license fee, until the products are
imitated or replaced by the next highest quality product. We assume that Southern licensees
pay the exogenously determined share proportion of profits δ ∈ (0, 1), which reflects thebargaining power between a licensee and a licensor.7 All Southern licensees are forbiddenby their licensors to copy the blueprint and to break the license contracts so as to avoid
paying the license fee.
When a product license is granted to a Southern firm, the design of the product becomes
the target of imitation by other Southern firms.8 For tractability, we assume that imitation occurs exogenously and that every licensee firm operating in the developing country is equally
exposed to the threat of imitation.9 In more detail, we assume that in an infinitesimal timeinterval dt, imitation occurs randomly in each industry with probability mγdt, where m is
an exogenous parameter determined by imitation technology or other factors such as cultural
climate, while 0 ≤ γ ≤ 1 is a policy parameter that reflects the degree of IPR protection
chosen by the Southern authority. Smaller γ therefore means stronger IPR protection in theSouth: when γ is equal to zero, patent enforcement in the South is perfect so that no imita7

It may be more natural to consider that the rent sharing between licensors and licensees is determined
endogenously according to their bargaining power. We can endogenize rent sharing, if we assume that licensors
and licensees decide the rent share δ through Nash bargaining. However, to simplify the analysis, we regard
share proportion δ as exogenously given, following Yang and Maskus (2001b) and Tanaka, Iwaisako, andFutagami (2007).
8
We exclude the possibility that Northern follower firms imitate a patented product by assuming perfectprotection of IPR in the North. In equilibrium where the Southern wage rate is lower than the Northern wage
rate, even if a Northern follower firm were to copy a licensed product, the Northern firm could not operatebecause of the limit-pricing strategy of the Southern official licensee. Therefore, in equilibrium, a Northernfollower firm would not engage in imitation activities of a licensed product.
9
The assumption of exogenous imitation following the technology transfer is also found in Lai (1998).

8

tion occurs; when γ is equal to one, IPR are not protected in the South at all. Throughout
this paper, we assume that mγ > ρ/(1 − δ) to ensure the local stability of the steady state.
The exogenous imitation rate mγ can be also interpreted from another point of view.
In the above formulation, the average time up to imitation after licensing in an industry
is a random variable that follows the exponential distribution with parameter mγ, whose
expectation is given by the reciprocal of the parameter, 1/(mγ). Hence, one can regard
1/(mγ) as the expected patent life in the South. Namely, in this model, the patent of alicensed product ‘expires’ in the South after a time interval of length 1/(mγ) on average.10
According to this interpretation, a smaller γ corresponds to longer patent protection in therecipient country of the technology license.
Once imitation occurs in an industry, perfect competition prevails in the industry andthe product is sold at unit cost wS , where wS is the wage rate in the South. Therefore, theSouthern licensee loses its monopoly rent and its stock becomes of no value in the market. In
addition, the Northern licensor can no longer receive the license fee. On the other hand, we
posit state-of-the-art products manufactured in the North possess confidentiality, so that forfollower firms, they are technologically or economically impractical to copy. Namely, we
assume that no imitation occurs in an industry where the Northern leader firm manufactures
the product in the North.
To maximize profits, each leader firm whose product has not yet been imitated sets prices
at the upper limit to exclude rival firms from the market. Assuming that the patents of all
products whose qualities are inferior to each state-of-the-art product are in the public domain, and that the Southern wage rate is less than the Northern wage rate, the strongest
rivals of each leader firm whose product has not yet been imitated are always Southern followers who have the ability to produce the second-highest quality of each product. As aleader firm can exclude rival firms by setting the lowest quality-adjusted price on its prod-

10

A similar interpretation of the expected value of patent protection length in the South is also used in Kwan
and Lai (2003) and Grinols and Lin (2006).

9

uct, the optimal price setting of each Northern producer and each Southern licensee is themarginal cost of the strongest rival firm multiplied by the increment in quality:p = λwS .
The price setting of each leader then yields a demand per product of 1/(λwS ). Hence, eachNorthern patent holder earns a flow of profits:
πN = (λwS − wN )

1
wN
=
1
−
,
λwS
λwS

(2)

where wN is the wage rate in the North, which must be restricted below λwS so that theNorthern leaders can earn strictly positive profits. On the other hand, the profits of Southernlicensees are:πL = (λwS − wS )

1
1
=1− .
S
λw
λ

(3)

2.3 Research Activities and License Negotiations
We describe the random success of innovation as a Poisson process. That is, aN I˜i units of labor input into research activities during an infinitesimal time interval dt lead an entrepreneur
i to success of innovation with probability I˜idt, where aN is a parameter. We assume theproductivity of research aN is the same in all firms, so that follower firms can compete with
the incumbent leaders in regard to research and development of the next-higher-quality product. Let VN be the market value of a Northern leader, which is the reward for innovation. In
any moment, each entrepreneur decides the labor input to maximize his or her instantaneous
profit: (VN − wN aN )I˜i . Hence, the following zero-profit condition in research activities issatisfied:
VN,t ≤ wtN aN

with equality if I˜i > 0.

(4)

Similarly, we assume that a Southern firm and a Northern patent holder can stochasti10

cally reach agreement on a license contract according to the degree of negotiation effort by
the Southern firm. We assume that the Southern firm i hoping to reach a licensing agreement with instantaneous probability ι̃i must throw aL ι̃i units of labor per unit of time into
negotiation activities, where aL is a parameter that satisfies aL < aN .11 Let VL denote theexpected present value of profits earned by an incumbent licensee firm. For Southern firms,
the expected gain obtained by winning a license is equal to (1 − δ)VL . Therefore, such firms
optimally choose the intensity of license negotiation in order to maximize their instantaneous profit [(1 − δ)VL − wS aL]ι̃i . In the equilibrium, since the level of license negotiationmust be positive but finite, the following zero-profit condition in the license negotiation issatisfied:
VL,t ≤ wtSaL
1−δwith equality if ι̃i > 0.

(5)

While we posit in the above that patent holders are always willing to comply with theoffer of license contracts, we need to consider the possibility that patent holders may refuse
these offers. Northern patent holders will allow Southern firms to manufacture their products only when the market value after licensing exceeds the current value, VN,t ; otherwise
they will not admit licensing. Reaching agreement on a license, the Northern patent holder
acquires a claim on a fraction of the Southern licensee’s profit as the license fee. Since a
Northern licensor can receive 100 × δ percent of the licensee’s profit in any moment, theexpected value of that claim is expressed as δVL,t. Assuming that a licensor is obliged tocompete with its licensee in a Bertrand fashion if it also produces the product, no licensor
has an incentive in equilibrium to continue to sell the product after the license agreement.
Therefore, the market value of a licensor firm is also δVL,t. As a result, the equilibrium with

11

In our setting, Southern firms only incur license negotiation costs and Northern firms enjoy the benefitof licensing agreements without any effort. Perhaps, it may be more realistic to assume that not only theSouthern firms but also the Northern firms incur negotiation costs. However, to make the analysis tractable
and more contrastive to existing studies, we assume that only Southern firms throw their resources into license
negotiation and bear all of the negotiation cost.

11

positive licensing requires the condition:
δVL,t ≥ VN,t.

2.4 Equilibrium Conditions
In the equilibrium, there exist three possible categories of industry in the market: (i) the
Northern patent holder produces the state-of-the-art variety; (ii) the Southern licensee produces the highest-quality product under a license; and (iii) Southern imitators produce thehighest-quality product under perfect competition. We represent the measure of industries
belonging to each category by nN,t, nL,t , and nM,t, respectively. Because the measure of allindustries is unity, we have nN,t + nL,t + nM,t = 1. In the following part of this paper, we
focus only on the symmetric equilibrium such that all industries in the same category are
symmetric.
In the symmetric equilibrium, the intensities of innovation and licensing are common
to all industries. Let I denote this aggregate innovation intensity in each industry, namely,I =˜ Then, investment to innovation targeted at any industries yields the same ex-

i Ii .

pected payoff because the patents of a second-highest-quality product are always in the public domain. As a consequence, the research efforts of entrepreneurs range over all ω equallyand innovation occurs in every industry with equal probability. Meanwhile, Southern firms
negotiate license contracts with Northern state-of-the-art patent holders whose products areneither licensed nor imitated. In the symmetric equilibrium, Southern firms choose equal
efforts of negotiation among the industries. As a result, each Northern leader firm whose
product is neither licensed nor imitated receives such offers with equal intensity in the equilibrium. Let ι denote the aggregate intensity of license negotiation targeting at each industry,
namely, ι =i ι̃i .

How does the measure of products in each category change over time? In an infinitesimal
time interval of length dt, Northern entrepreneurs succeed in upgrading It (nL,t + nM,t)dt
12

products that Southern licensees or imitators manufacture, whereas ιt nN,tdt products are
newly licensed and come to be manufactured in the South (see figure 1). Therefore, themeasure of products manufactured in the North follows the equation of motion:ṅN,t = It(nL,t + nM,t) − ιt nN,t .

(6)

On the other hand, measure mγnL,tdt licensed products are newly copied in the time interval, while ItnM,t dt imitated products revert to Northern leaders because of success ininnovation. Hence, we obtain the following equation of motion for the measure of imitatedproducts:
ṅM,t = mγnL,t − ItnM,t.

(7)

Because nN,t + nL,t + nM,t = 1, the measure of licensed products changes over time according to the following equation:ṅL,t = −ṅN,t − ṅM,t .

Now we consider how the market value of each firm varies over time. First, we consider
the stock of a Northern patent holder that has not yet achieved a license for its product. During an infinitesimal time interval of length dt, each Northern incumbent leader is exposed tothe hazard of replacement by a higher-quality product with probability Itdt. If innovation
occurs, the incumbent Northern patent holder suffers capital loss VN,t . In the same time interval, the patent holder can reach a license agreement with a Southern firm with probability
ιt dt. The Northern leader then acquires δVL,t instead of the current market value VN,t. If neither innovation nor licensing occurs in the industry during the time interval, the patent holder
can earn the profits πN,tdt and capital gain V̇N,tdt. The total sum is the expected earnings ofthe shareholders in a Northern leader firm. Provided that the idiosyncratic risks arising fromholding a stock are diversified away by all investors, a stock should yield exactly the same13

expected rate of return as the risk-free interest rate, rt . The no-arbitrage condition between
the stock and a risk-free asset is then:
rtVN,t = πN,t + V̇N,t − ItVN,t + ιt (δVL,t − VN,t).

(8)

In the same manner, we can consider the total market value of a Southern firm operating
under license. A Southern licensee suffers a capital loss VL,t if innovation occurs in theindustry. In addition, a licensee firm is also faced with the risk of imitation by other Southernfirms. Since a product is imitated by follower firms with instantaneous probability mγ,
a Southern licensee loses the monopolistic position with probability (It + mγ)dt in theinfinitesimal time interval of length dt. If neither innovation nor imitation occurs in theindustry during the time interval, the licensee firm can earn profits πL,tdt and capital gain
V̇L,t dt. Since the sum of these risky rates of returns must be identical to the risk-free interest
rate, we obtain the following no-arbitrage condition:
rt VL,t = πL,t + V̇L,t − (It + mγ)VL,t.

(9)

We finally consider the labor market equilibrium conditions. Let LN and LS denote thefixed labor supply in the North and the South, respectively. For analytical tractability, we
assume that LS is equal to or greater than (aL/aN )LN . On the demand side, entrepreneurs
who make an effort in R&D and Northern leader firms require labor in the North, while firms
under negotiation with a Northern patent holder and Southern manufacturers (licensees andcompetitive firms) demand labor in the South. Entrepreneurs in the North conduct R&D at
the same aggregate intensity It over all industries, so they employ aN It(nN,t + nL,t + nM,t)units of labor at each moment. In addition, each manufacturing firm in the North sells
1/(λwtS ) units of the product at time t, so that Northern manufactures employ nN,t/(λwtS )14

units of labor at the time. Thus, the labor market-clearing condition in the North is:
aN It(nN,t + nL,t + nM,t) +1
nN,t = LN .
λwtS

(10)

In the South, follower firms employ aL ιt nN,t units of labor for license negotiation at time t.
Moreover, for production, licensee firms require nL,t/(λwtS ) units of labor, while competitive firms that manufacture imitated products need nM,t/wtS units of labor. In consequence,
the labor market-clearing condition in the South is:aL ιt nN,t +1
1
n + S nM,t = LS .
S L,t
λwt
wt

(11)

3 Steady State Equilibrium
In the following part of this paper, we pay attention to only the steady state equilibrium inwhich innovation and licensing keep taking place at some constant speed over time.12 In thesteady state, the fraction of each type of industry, the market values of firms, and the wage
¯ denote therates of both regions are constant over time. Let variables with upper bar, e.g., I,
steady state values of the corresponding variables.
In the steady state, the market value of a firm is equal to the expected present value of
profits. From equations (3) and (9), the value of a licensee firm is given by:(λ − 1)/λ.
V̄L = ¯I + mγ + ρ(12)Moreover, the zero-profit condition in licensing activities (5) implies that:w̄S =(1 − δ)V̄L
.
aL

12

(13)

We can verify that the equilibrium path converging to the steady state exists and is locally unique if the¯ satisfies the condition (19) as stated below. The proof isaggregate innovation intensity in the steady state, I,
given in the appendix.

15

Similarly, using the relation that:
w̄N =

V̄N
,
aN

(14)

which is derived from the zero-profit condition in innovation (4), together with equations(2), (8), and (13), we obtain:
1 + δῑV̄L
V̄N = ¯aL
1 .
I + ῑ + ρ + aN (1−δ)λ
V̄L

(15)

For the sake of seeking the steady state values, we first rewrite the condition on the
Northern labor market. Combining equations (10), (12), and (13), we can derive pairs of I¯and n̄N that are consistent with Northern labor market clearing as follows:n̄N =(1 − δ)(λ − 1) ¯Φ(I; γ),aL(16)¯ γ) ≡ (LN − aN I)/(¯ I¯ + mγ + ρ). This relationship is drawn as a downwardwhere Φ(I;¯ n̄N ) plane (see figure 2). We name this curve NL. The NL curve
sloping curve on the (I,means that the ratio of products manufactured in the North to all products must decrease with¯ otherwise the Northern labor market is never cleared owing to the excess
an increase in I;
demand for labor by incumbent leaders and firms researching higher-quality products.
To determine I¯ and n̄N , we need another equation with respect to these variables. We
can derive this relationship from the Southern labor market-clearing condition. First, fromequations (6) and (7), the following relations are satisfied in the steady state:mγI¯¯ − n̄N ), n̄L =ῑn̄N = I(1(1−n̄(1 − n̄N ).
),
and
n̄
=
N
M
I¯ + mγI¯ + mγ(17)

Substituting (12), (13), and (17) into (11), we have:n̄N = 1 −(1 − δ)(λ − 1)LS ¯Ψ(I; γ),
aL

16

(18)

¯ γ) ≡ (I¯+mγ)/[(I¯+mγ+ρ)(I¯+mγλ)+(1−δ)(λ−1)I(¯ I¯+mγ)]. Note that thewhere Ψ(I;right-hand side of equation (18) is increasing with I¯ under the assumption mγ > ρ/(1 − δ).
We describe the combinations of I¯ and n̄N that satisfy equation (18) by the SL curve infigure 2. The interpretation of the SL curve is similar to that of the NL curve. Namely, theproportion of products manufactured in the South to all products, 1 − n̄N , must fall with a¯ since the additional labor demand of leader firms manufacturing the products andrise of I,
of follower firms engaged in license negotiation prevent the Southern labor market clearing
without such a reduction.
Since the SL curve is upward-sloping under the above assumptions, there is at mostone crossing point of the two curves in the region where both I¯ and n̄N are positive. To
ensure that the unique and attainable steady state and the locally unique equilibrium pathconverging to this steady state exist, we focus our attention on the case in which I¯ satisfies
the following inequality:LS
max 0, λ
− mγ
aL



< I¯ <

LN
.
aN

(19)

If both curves cross once in the first quadrant, n̄N takes a value that is between zero andone. Then, n̄L , n̄M , and ῑ are given by equations (17). Furthermore, V̄L , V̄N , w̄S , and w̄N
are determined by equations (12)–(15).
However, we must impose two additional conditions on the parameters to assure theexistence of the steady state. The first is a condition about the incentive of patent holders tolicense. As stated above, a patent holder has no incentive to grant a license of its product if
the expected value of the license fee is below the current market value. Therefore, the steadystate with strictly positive licensing requires δ V̄L ≥ V̄N . The second condition is concernedwith the wage rates in both regions. Our analysis presumes that the Northern wage rate
is higher than the Southern wage rate. Moreover, the Northern wage rate wN is restricted
below λwS in the equilibrium; otherwise Northern leaders would cease to operate because17

of negative profits. From equations (13), (14), and (15), we can restate these conditions as:

1 + δῑV̄L
aN (1 − δ)λaN (1 − δ)< ¯< min δ,.
aL
aL
(I + ῑ + ρ)V̄L + aN (1−δ)λaL

4 Comparative Statics
In this section, we consider how the intensities of innovation and licensing are affected by
the stronger protection of intellectual property rights, subsidy policies for license negotiation
and research activities, and changes in the profit division rule.

4.1 Effects of Strengthening IPR Protection
In Section 2, we have assumed the imitation speed is affected by the IPR protection policyof the Southern authorities. That is, we have thought of γ as a policy parameter on IPR protection by the Southern government. Thus, in this subsection, we first conduct comparative
statics with respect to γ.
First, totally differentiating equation (16), we obtain:dn̄N = −(1 − δ)(λ − 1)  N¯ + m(LN − aN I)dγ
¯
(L
+
a
mγ
+
a
ρ)d
I
.
N
N
aL(I¯ + mγ + ρ)2(20)

Because LN − aN I¯ > 0 from equation (10), equation (20) means that n̄N is required to increase with a fall of γ, if I¯ were unchanged, in order to maintain equilibrium in the Northernlabor market. In other words, the NL curve in figure 2 rotates clockwise in response to a fallin γ induced by tightening IPR protection. This is because, for any given I¯ and n̄N , a lower
γ raises the Southern wage rate through an increase in V̄L (see equations (12) and (13)).
The higher Southern wage rate enables each Northern patent holder to set a higher price.
This leads to lower product demand, which thereby gives a lower each incumbent Northernleader’s demand for Northern labor. Therefore, the Northern labor supply can afford to re-18

tain more producers in the North, that is, n̄N must be higher than before to clear the excess¯ is unchanged by the Southernlabor supply, if the labor demand of the research sector, aN I,
policy change.
Next, the total differential of equation (18) is expressed as follows:dn̄N =¯ γ) 2 (1 − δ)(λ − 1)LS Ψ(I;
aL






AdI¯ + Bdγ ,


(21)


¯
− 1)/(I¯ +where A = δ + λ(1 − δ) − mγρ(λ − 1)/(I¯ + mγ)2 > 0 and B = m λ + Iρ(λ
mγ)2



> 0. Equation (21) shows that n̄N is required to decrease with a fall of γ, if I¯ were

unchanged, in order to maintain equilibrium in the Southern labor market. Thus, the SL
curve in figure 2 moves downward with a decrease in γ.
Intuitively, if both I¯ and n̄N were unchanged, restrictions on imitation by the Southern government would decrease Southern labor engaging in manufacturing for two reasons.
First, using the same argument as with Northern labor demand, the increase in the Southern
wage rate through an increase in V̄L due to a reduction in the threat of imitation decreases
each incumbent leader’s demand for Southern labor with the fall of γ. Second, from equation (17), a reduction of the proportion of imitated industries to licensed industries in theSouth, n̄M /n̄L , as induced by the policy modification, has a negative effect on labor demandin the South because licensee firms behaving as monopolists employ less Southern laborthan a comparable competitive firm. The redundant labor originating from these two effects
must be absorbed by follower firms under license negotiation to restore equilibrium to theSouthern labor market. As a consequence, tightening IPR protection leads more Southernfollower firms to reach an agreement of a license contract with a patent holder, which is described by an increase in ῑn̄N , at each moment. From equation (17), this means that n̄N must
decrease with the strengthening of IPR protection for any given I¯ in order for the Southernlabor market to clear.
Because tightening IPR protection shifts both the NL and SL curves simultaneously up19

wards, modification of the IPR protection policy moves the intersection from E to E  infigure 2. Since the new intersection after the policy change is located rightward of the original, we can confirm that tightening IPR protection in the South unambiguously increases
Ī.
However, the figure provides no information about whether n̄N increases or not. Therefore, we next compute ∂ n̄N /∂γ to examine its sign. Using equations (20) and (21), we caneliminate the term dI¯ and obtain:
⎡
⎢
⎣1 +

=

⎤

L + aN mγ + aN ρ⎥2 ⎦ dn̄N¯ γ)
LS A(I¯ + mγ + ρ)2 Ψ(I;N
(1 − δ)(λ − 1)  N
N
¯
(L
+
a
mγ
+
a
ρ)B
−
m(L
−
a
dγ.
I)A
N
N
N
AaL (I¯ + mγ + ρ)2(22)¯ is positive, we can confirm that ∂ n̄N /∂γ >Because (LN +aN mγ+aN ρ)B−m(LN −aN I)A
0 from equation (22). This result and equation (17) imply that both ∂ῑ/∂γ and ∂(ῑn̄N )/∂γ
are negative. In other words, license activities are stimulated by a strengthening IPR protection.
Hence, the above analysis is summarized in the next proposition.
Proposition 1 Strengthening intellectual property rights protection through restrictions on
imitation promotes innovation and technology licensing to developing countries.
This proposition enhances Yang and Maskus’ (2001b) result regarding the strengtheningof IPR protection. Instead of assuming a policy parameter of the Southern government
authorities, Yang and Maskus (2001b) have indirectly regarded both a rise in the probabilityof success in license negotiations under the same labor inputs (the cost-reducing effect) and arise in royalty payments to the licensor (the distribution effect) as the effects of strengthening
IPR protection. Based on such a formulation, they concluded that stronger IPR protection
promotes innovation and licensing through two effects. In contrast, our model explicitly
takes into account the possibility of imitation by other firms, and interprets the lower speed
20

of exogenous imitation as the result of stronger IPR protection by the Southern government.
As a result, we obtain proposition 1 which implies that the developing country’s authoritythat aims to encourage licensing of state-of-the-art products should regulate copies targeting
licensed products.13
We can also show that restrictions on imitation raise the Southern wage rate in the steadystate. From equation (13), ∂ w̄S /∂γ satisfies the following equation:




∂ w̄S
∂ I¯
(1 − δ)(λ − 1)
m
+
< 0.
=−
∂γ
aL λ(I¯ + mγ + ρ)2
∂γ

(23)

To interpret this equation, recall that the Southern wage rate relates closely to profitability
in the negotiation activities of the license because of free entry. This equation then showsthat a rise of γ causes the Southern wage rate to change through two channels. First, tighter
enforcement of IPR protection (a fall in γ) mitigates the threat of imitation by other firms,
so that a licensee can enjoy the longer expected duration of the monopoly. This causes thestock value of a licensee firm that has a one-to-one correspondence to the Southern wage
rate to increase directly. However, since strengthening IPR protection activates innovationin the North as stated in proposition 1, the higher frequency of innovation shortens the
expected duration of the monopoly. In consequence, this second indirect effect induces theSouthern wage rate to decrease and depresses the first effect. However, we can verify that thefirst positive effect dominates the second negative effect under restriction (19). Substituting
equation (21) into (22) and rearranging the terms, we have:¯ γ) 2¯ + LS (B/m)(I¯ + mγ + ρ)2 Ψ(I;
(LN − aN I)∂ Ī
= −m × .
∂γ¯ γ) 2(LN + aN mγ + aN ρ) + LS A(I¯ + mγ + ρ)2 Ψ(I;We can show that the numerator of the fraction on the right-hand side is smaller than the13

Another feature of our model is to confirm the local stability of the steady state. We prove in the appendix
that the steady state of our model has a unique converging path. However, and as mentioned in the Introduction,
the steady state in Yang and Maskus (2001b) is totally unstable.

21denominator from condition (19), and ∂ Ī/∂γ is larger than −m. Thus, from equation (23),
we can conclude that the Southern wage rate w̄S is decreasing with γ (that is, increasing
with the degree of IPR protection).

4.2 Effects of Subsidy Policies
In this subsection, we explore the effects of industrial policies through subsidies on R&D
and technology transfer. In the previous subsection, we confirmed that the Southern government can encourage innovation and technology transfer by restricting imitation activities.
In addition, government authorities are probably also concerned with subsidizing license
negotiations and R&D for the sake of more directly promoting innovation and technology
transfer. Hence, we examine whether or not governments can promote such activities bypartly bearing the cost of license negotiations and R&D. Throughout the analysis in thissection, the subsidies are assumed to be financed by lump-sum taxes.
4.2.1

Subsidies on license negotiation

We first consider the effects of subsidies on license negotiations by the Southern government. Let sL ∈ [0, 1) be the subsidy rate on the cost of license negotiations. The subsidy
improves the profitability of Southern follower firms under license negotiation. That is, byengaging in license negotiations, a Southern follower firm i can earn the instantaneous expected profit [(1− δ)VL − (1− sL )wS aL ]ι̃i . Therefore, the introduction of subsidies modifies
the zero-profit condition and yields the following relation:w̄S =(1 − δ)V̄L.
(1 − sL )aL(24)

If sL is equal to zero, this equation reduces to equation (13). Moreover, this equation showsthat an increase in the rate of subsidy, other things being equal, pushes the Southern wage
rate up because Southern follower firms wish to negotiate harder license contracts with the22Northern patent holder owing to a reduction in the cost of negotiation.
To determine a new pair of I¯ and n̄N , we compute new NL and SL curves. From equations (10), (12), and (24), we have the following new NL curve:n̄N =(1 − δ)(λ − 1) ¯Φ̂(I; sL),
aL

(25)

¯ sL ) ≡ (LN − aN I)/[(1¯
where Φ̂(I;− sL )(I¯ + mγ + ρ)]. Similarly, substituting (12), (17),and (24) into (11), we obtain the new SL curve as follows:n̄N = 1 −(1 − δ)(λ − 1)LS ¯Ψ̂(I; sL ),
aL

(26)

¯ I¯ + mγ)].
¯ sL ) ≡ (I¯ + mγ)/[(1 − sL)(I¯ + mγ + ρ)(I¯ + mγλ) + (1 − δ)(λ − 1)I(
where Ψ̂(I;The labor market clearing of both countries requires I¯ and n̄N to satisfy both equations (25)and (26).
Next, we totally differentiate equations (25) and (26) and examine the effects of thesubsidies on license negotiation. Totally differentiating equation (25) implies that:(1 − δ)(λ − 1)
LN + aN mγ + aN ρ ¯¯ sL )dsL .
dn̄N =−
dI + Φ̂(I;aL (1 − sL )(I¯ + mγ + ρ)2(27)This equation shows that n̄N must increase with an increase in the subsidy rate sL for agiven I¯ to maintain equilibrium in the Northern labor market. Namely, the NL curve rotatesclockwise with an increase in the subsidy rate as shown in figure 2. This is because anincrease in sL enables each Northern leader to set higher prices through the increase in theSouthern wage rate and leads to lower labor demands by incumbent leaders for any given I¯and n̄N . As a result, n̄N must be higher than before to clear the Northern labor market, if¯ is unchanged.
the labor demand of the R&D sector, aN I,

23

Meanwhile, from equation (26), we have:dn̄N =

¯ sL ) 2(1 − δ)(λ − 1)LS Ψ̂(I;
aL





(I¯ + mγ + ρ)(I¯ + mγλ)dsL . (28)× [(1 − sL )A + sL (1 − δ)(λ − 1)]dI¯ −I¯ + mγThis equation shows that n̄N must decrease with an increase in the subsidy rate sL for agiven Ī to maintain equilibrium in the Southern labor market. Thus, the SL curve moves
downwards as in figure 2. This is due to the same reasoning as shown in the Northern labormarket: namely, an increase in sL decreases the labor demands of incumbent producers
through an increase in the Southern wage rate for any given I¯ and n̄N , so that ῑn̄N , which is¯ − n̄N ) from equation (17), must be higher than before. Therefore, 1 − n̄N must
equal to I(1increase with the increase in the subsidy rate in order to clear the Southern labor market if I¯is unchanged by the policy modification.
An increase in the subsidy rate moves the intersection in figure 2 from E to E  . Asa consequence, we can immediately confirm that innovation intensity increases in the newsteady state. However, whether n̄N increases or not is again unclear from the figure, so wenext compute ∂ n̄N /∂sL . For tractability, we suppose that the initial subsidy rate is set equal
to zero and examine the effect of a marginal increase in the rate. Substituting equation (28)
into (27) and applying sL = 0, we obtain:
⎡
⎢
⎣1 +

⎤

L + aN mγ + aN ρ⎥2 ⎦ dn̄N¯ 0)
ALS (I¯ + mγ + ρ)2 Ψ̂(I;N

(1 − δ)(λ − 1) (LN + aN mγ + aN ρ)(I¯ + mγλ)¯ 0) dsL .
− Φ̂(I;=−aL
A(I¯ + mγ)(I¯ + mγ + ρ)¯¯I+This equation implies that ∂ n̄N /∂sL |sL =0 < 0 because (LN +aN mγ+aN ρ)(I+mγλ)/[A(¯ γ) = Φ̂(I;¯ 0) from condition (19) and from the assumptionmγ)(I¯ + mγ + ρ)] > Φ(I;that LS ≥ (aL/aN )LN . Thus, from equation (17), we can conclude that ∂ῑ/∂sL |sL =0 and24∂(ῑn̄N )/∂sL |sL =0 are positive: that is, a marginal increase in the subsidies on license negotiation from zero can also promote licensing. These results are summarized as follows.
Proposition 2 Suppose that the initial rate of a subsidy on license negotiation is zero. Then,a marginal subsidy on license negotiation can promote innovation and licensing.
How does the subsidy on license negotiation affect the Southern wage rate w̄S ? The
subsidy has an effect on the Southern wage rate w̄S through two channels:
∂ w̄S
1−δ
1 − δ ∂ V̄L
=
V̄L +
2
∂sL
(1 − sL ) aL
(1 − sL )aL ∂sL(1 − δ)(λ − 1)
∂ I¯
I¯ + mγ + ρ=−.
(1 − sL )aL λ(I¯ + mγ + ρ)2
1 − sL∂sL(29)

The first term represents a direct effect, whereas the second term is an indirect effect throughV̄L . Since an increase in sL , other things being equal, reduces negotiation costs, the Southern
wage rate must be higher than before to attain zero profits in the negotiation activities. On the¯ so that it lowers the stock value
other hand, the higher sL also raises innovation intensity I,
of licensee firms V̄L through increasing the danger of being replaced by a higher-quality
product. This second effect has a negative influence on the Southern wage rate.
Although the two effects have different signs to each other, the direct positive effectalways dominates the indirect negative effect if the initial subsidy rate is zero and condition(19) is satisfied. Substituting (27) into (28) and applying sL = 0, we have:∂ I¯ 

∂sL 

sL =0



=



¯ + LS (I¯ + mγλ)(I¯ + mγ + ρ)2 Ψ̂(I;¯ 0)(I¯ + mγ + ρ) (I¯ + mγ)(LN − aN I)¯ 0)(I¯ + mγ)(LN + aN mγ + aN ρ) + LS A(I¯ + mγ)(I¯ + mγ + ρ)2 Ψ̂(I;

2

2 

.

Using this equation and condition (19), we can show that ∂ Ī/∂sL |sL =0 < I¯+ mγ + ρ. Thus,
from equation (29), ∂ w̄S /∂sL |sL =0 > 0, namely, the marginal rise of the subsidy rate fromzero raises the Southern wage rate w̄S .

25

4.2.2

Subsidies on R&D

We now turn our analysis to the effects of subsidies on R&D by the Northern government.
Let sR ∈ [0, 1) denote a subsidy rate on R&D chosen by the Northern government. As inthe subsidies on license negotiation, subsidies on R&D improve the profitability of Northernfirms engaging in R&D. Namely, a Northern follower firm i that undertakes R&D can earn
the instantaneous expected profit [VN − (1 − sR )wN aN ]I˜i. Hence, introduction of subsidies
alters the zero-profit condition and replaces equation (14) with the following:
w̄N =

V̄N
.
(1 − sR )aN

However, this modification does not bring any change in both the NL and SL curves because the labor market-clearing conditions in both countries are independent of the Northern
wage rate (see equations (10) and (11)). Thus, neither I¯ nor ῑ are influenced at all by subsidies on R&D. We can summarize this result as the following proposition.
Proposition 3 Subsidies on R&D have no influence on innovation and licensing.
In addition, because innovation intensity is not influenced by the policy modification, thestock value of Southern licensee firms, V̄L , is also unchanged. As a result, a subsidy on
the cost of R&D has no influence on the Southern wage rate. Hence, the subsidy policy on
R&D, which is intended for promoting innovation in this model, can only affect the wage
gap between the North and the South.

4.3 Effects of a Change in Profit Division
The determination of a profit division rule between a licensor and a licensee has been assumed to be dependent on the bargaining power between the licensor and a licensee. The
bargaining power may be affected by a change in the contracting environment, for example,
the revision of commercial law and a change in the enforcement of patent law. Hence, in26

this subsection, we examine how an alteration of the rate of license fee influences innovationand licensing.
Consider that the licensors’ share of profit δ increases marginally from the initial value.
Because the lower expected return induced by the higher license fee is insufficient to pay thenegotiation cost, a higher licensors’ share deteriorates the profitability of Southern firms engaging in negotiation. Therefore, to restore zero profits in negotiation activities, the Southern
wage rate w̄S must fall to a new equilibrium if I¯ were to be left unchanged. Because of thelimit-pricing strategy, the decrease of the Southern wage rate leads to higher labor demandby each incumbent leader. Hence, the improvement of licensors’ share of profit makes thefraction of products manufactured in the North, n̄N , impossible to retain at the same level¯ so the NL curve is pressured to rotate counterclockwise. In fact, by
as before for a given I,
totally differentiating the NL curve (16), we obtain:

λ − 1 (1 − δ)(LN + aN mγ + aN ρ) ¯¯ γ)dδ .
dn̄N = −dI + Φ(I;aL(I¯ + mγ + ρ)2(30)

From this relationship, we can confirm that n̄N must fall with a rise of δ for any given I¯ to
be consistent with equilibrium in the Northern labor market.
A similar argument to the NL curve is also applied to the SL curve. Totally differentiating the SL curve (18) gives the following relation:
dn̄N =¯ γ) 2 LS (λ − 1) Ψ(I;aL

(I¯ + mγ + ρ)(I¯ + mγλ)dδ .
(1 − δ)AdI¯ +Ī + mγ(31)

Because of the pricing rule, the fall of the Southern wage rate generates additional labordemand by each Southern firm to manufacture the product. Therefore, the rise of δ makes
the fraction of products manufactured in the South, n̄L + n̄M , inevitably to decrease for a¯ In consequence, the SL curve is required to shift upwards.
given I.
Figure 3 describes how a rise of δ affects the two curves and the intersection. As the27

figure shows, a rise in the rate of the license fee δ induces the intersection to move leftwards and the innovation intensity I¯ to unambiguously decrease. However, figure 3 does
not explain whether the change raises n̄N or not. Therefore, we must compute ∂ n̄N /∂δ todetermine the signs of ∂ῑ/∂δ and ∂(ῑn̄N )/∂δ.
¯ we have:
Substituting equation (31) into (30) to eliminate the term of dI,
⎡
⎢
⎣1 +

⎤

(L + aN mγ + aN ρ)⎥2 ⎦ dn̄N¯ γ)
ALS (I¯ + mγ + ρ)2 Ψ(I;N(λ − 1) (LN + aN mγ + aN ρ)(I¯ + mγλ)¯ γ) dδ.
− Φ(I;=aLA(I¯ + mγ)(I¯ + mγ + ρ)¯ γ) from
Recall that (LN + aN mγ + aN ρ)(I¯ + mγλ)/[A(I¯ + mγ)(I¯ + mγ + ρ)] > Φ(I;condition (19) and from the assumption that LS ≥ (aL /aN )LN . Hence, this equation implies
that ∂ n̄N /∂δ > 0. Moreover, from the result and equation (17), we obtain ∂ῑ/∂δ < 0 and∂ (ῑn̄N ) /∂δ < 0. Namely, a higher license fee rate δ reduces licensing activities.
We can summarize these results into the following proposition.
Proposition 4 A higher rate of license fee becomes an obstacle to both innovation and theconclusion of license agreements.
This proposition contains a seemingly counterintuitive assertion: that is, the higher licensor’s share of profit deters not only licensing, but also innovation. However, in fact, theresult is fairly natural in this model. A higher licensor’s share of profit, other things being
equal, raises the stock value of a Northern leader owing to an improvement in the expected
payoff the leader can obtain by reaching license agreement. This effect on the stock value
must be exactly offset by a change of the Northern wage rate since innovators always attain
zero profits. However, these changes do not have any influence on the degree of innovation
because innovation intensity depends neither on the stock value of a Northern leader nor on
the Northern wage rate (see equation (10) and (11)). In addition, more Northern labor is devoted to manufacturing by incumbent leaders than before for two reasons. First, incumbent
28

leaders become less likely to reach license agreement because of a reduction in negotiation
efforts by Southern follower firms. In consequence, more leaders operate in the North than
before. Second, a rise in δ forces the Southern wage rate down, as later verified. As pointed
out earlier, a decrease in the Southern wage rate leads to higher labor demand by each incumbent leader. Thus, less labor can engage in R&D activities than before, and the economy
incurs the situation of less innovation, despite the favorable change to the licensors.
We now examine how an increase in the licensor’s profit share δ affects the Southern
wage rate. As discussed previously, this change lowers the Southern wage rate. We computethe partial derivative of w̄S with respect to δ to verify it:V̄L 1 − δ ∂ V̄L(1 − δ)(λ − 1)
I¯ + mγ + ρ ∂ Ī
∂ w̄S
+
.
=−
=−
+
∂δ
aL
aL ∂δ
aLλ(I¯ + mγ + ρ)2
1−δ
∂δ

(32)

This equation shows that an increase in δ brings about two effects on the profitability oflicense negotiation. First, other things being equal, higher δ directly impinges on licensees’
profitability, which is expressed by the first term of equation (32). On the other hand, theindirect effect through the value of a licensee firm improves profitability, as represented by
the second term. This is due to an increase in the licensee’s stock value induced by thedecrease in the risk of replacement by a new invention. As a result, increase in δ causes two
conflicting effects. However, by computing ∂ Ī/∂δ, we can confirm that the second positiveeffect is insufficient to compensate for the first negative effect. Substituting (30) into (31)and eliminating the term dn̄N , we have:¯ γ) 2¯ + LS (I¯ + mγλ)(I¯ + mγ + ρ)2 Ψ(I;I¯ + mγ + ρ(I¯ + mγ)(LN − aN I)
∂ I¯
=−
.

¯ γ) 2∂δ1−δ
(I¯ + mγ)(LN + aN mγ + aN ρ) + LS A(I¯ + mγ)(I¯ + mγ + ρ)2 Ψ(I;¯ 0) = Ψ(I;¯ γ), we can show that ∂ Ī/∂δ > −(I¯ + mγ + ρ)/(1 − δ) in
Noting that Ψ̂(I;¯ L |s =0 < I¯ + mγ + ρ. Thus, we can conclude that thethe same way as the proof of ∂ I/∂s
L
Southern wage rate is decreasing with the profit share of licensors from equation (32), thatis, ∂ w̄S /∂δ < 0.

29

5 Concluding Remarks
Licensing of patents has played an important role in the introduction of high technologies
and development processes in Japan and Korea following World War II. In this paper, weconstructed a dynamic North–South model to investigate the effects of governments’ policies on innovation and technology transfer in an economy where the main channel of transfer
is licensing activities. From the comparative statics analysis of the model, we obtained thefollowing three results. First, the Southern government can promote innovation and technology transfer by restricting imitation activities. Second, an increase in subsidies on the costof license negotiations also promotes innovation and technology transfer, while subsidies on
the cost of R&D have no effect. Third, policy changes that induce higher license fee rates
reduce innovation and technology transfer.
A key feature of our model is that the production of copies is assumed to prevail in
the South because of the imperfect enforcement of IPR protection often observed in actual
developing countries. As a result, the model well describes firms in developing countries
that make an effort at negotiating licenses with patent holders in developed countries inan environment of imperfect IPR protection. This assumption enables us to draw richer
implications concerning IPR protection policy as enforced by restricting imitation activities
than existing studies because these simplified the IPR protection policy setting.
However, our model is constructed on the following two assumptions in order to maintainsimplicity. First, imitation of products is assumed to be an exogenous process. However,it may be more realistic to consider copying as a profit-maximizing activity of follower
firms.14 Second, no alternative channel of technology transfer save licensing is incorporated
in the model. In practice, not only licensing but also FDI is a primary channel of technology
transfer to developing countries.15 Therefore, one direction for future research would be to
14

Glass and Saggi (2002b) pointed out that strengthening IPR protection in the South decreases FDI flows
to the South using a model that endogenizes imitation activities as well as FDI.
15
For example, Glass and Saggi (2002a) constructed a symmetric two-country model that includes the firm’s
choice of market mode: either establishing a local subsidiary company or licensing technology to a local firm.

30

develop a model that takes account of these limitations.

A Appendix: A Proof of Local Stability of the Steady StateIn this appendix, we show that the steady state of the economy is a saddle point whose stablemanifold is a hyperplane of dimension two. Because our model has two state variables (andtwo jump variables), it ensures the steady state to be saddle-point stable and the equilibrium
path to be (locally) determinate.
To show it, we first derive an autonomous system of differential equations that describes
the dynamics of the model. Because the system of this economy is completely describedby four variables, nN,t, nL,t , VL,t , VN,t , we compute dynamic equations with respect tothose variables. Substituting equations (5), (10), and (11) into (6) yields the first differential
equation with respect to nN,t as:!

LS(λ − 1)nM,t
1
aL
LN
+
+
+
1−
nN,t
ṅN,t = −aL
(1 − δ)λVL,taN(1 − δ)λVL,taN"(1 − nN,t).

(33)

Similarly, eliminating nL,t from equation (7) by using the relation nN,t + nL,t + nM,t = 1
and substituting (5) and (10) into (7), we have the second differential equation with respect
to nM,t as follows:ṅM,t = mγ(1 − nN,t) − nM,t

LN
aL nN,t−+ mγ .
aN
aN (1 − δ)λVL,t(34)

These two variables are state variables since the measure of products belonging to eachcategory, which is determined as a result of past innovation, licensing, and imitation, cannot
adjust immediately.
The other two equations are derived from no-arbitrage conditions (8) and (9). From
Antràs (2005) developed a North–South model in which the Northern researcher can choose the mode of
production between licensing and multinationalizing.

31

equations (3), (5), (9), and (10), and rt = ρ, we obtain the third differential equation withrespect to VL,t :

LN
V̇L,t = ρ + mγ +
aN





!

aL nN,t1+ 1−
VL,t −aN (1 − δ)λ
λ

"

.

(35)

Moreover, substituting equations (2), (4), (5), and rt = ρ into (8), we have the last differential equation with respect to VN,t :

V̇N,t =

aL
+ It + ιt + ρ VN,t − 1 − διtVL,t ,aN (1 − δ)λVL,t(36)

where It and ιt are given by equations (10) and (11) according to the values of nN,t, nL,t,and VL,t . Note that the stock values of firms, VL,t and VN,t , are jumpable.
The four equations give an autonomous system of differential equations and completely
characterize the dynamics of the model. The values of the other endogenous variables are
determined from the four variables.
Next, we derive a characteristic equation associated with a Jacobian matrix of a systemof equations linearized around the steady state. From equations (33) – (36), the system of
linearized equations is given by:
⎛

⎞

⎛

⎞⎛

⎜ ṅN,t ⎟⎜ −J11
⎜
⎟
⎜
⎜
⎟
⎜
⎜ ṅ
⎟
⎜ J
⎜ M,t ⎟
⎜ 21
⎜
⎟=⎜
⎜
⎟
⎜
⎜ V̇
⎟
⎜ −J
⎜ L,t ⎟
⎜
31
⎜
⎟
⎜
⎝
⎠
⎝

V̇N,t

J41

J12

−J13

−J22 −J23
0

J33

J42

J43

⎞

0 ⎟ ⎜ nN,t − n̄N ⎟

⎟⎜
⎟
⎟⎜
⎟
⎟
⎜
0 ⎟ ⎜ nM,t − n̄M ⎟
⎟
⎟⎜
⎟,
⎟⎜
⎟
⎟
⎜
0 ⎟ ⎜ VL,t − V̄L ⎟
⎟
⎟⎜
⎟
⎠⎝
⎠

J44

VN,t − V̄N

where
J11 = −∂ ṅN,t1
aL(1 − n̄N )= I¯ ++> 0,∂nN,t(1 − δ)λV̄L aN (1 − δ)λV̄L

32

(37)

J12 =∂ ṅN,t
λ−1
=
> 0,
∂nM,t
(1 − δ)λV̄L!

∂ ṅN,t(λ − 1)n̄M(1 − n̄N )
aL
=
+
1−
n̄N
J13 = −22
∂VL,t
(1 − δ)λ(V̄L )(1 − δ)λ(V̄L )aN1 LS LN=−(1 − n̄N ) > 0,aN
V̄L aLJ21 =∂ ṅM,t
aLn̄M
=
− mγ,
∂nN,t
aN (1 − δ)λV̄L

J22 = −∂ ṅM,t= I¯ + mγ > 0,∂nM,t∂ ṅM,tn̄M=
J23 = −∂VL,tV̄L

J31 = −

J33 =

J44 =

"





LN
− I¯ > 0,aN∂ V̇L,t
aL
=
> 0,
∂nN,t
aN (1 − δ)λ∂ ṅN,tLN=+ mγ + ρ > 0,
∂nN,t
aN

∂ ṅN,taL=+ I¯ + ῑ + ρ > 0,∂nN,taN (1 − δ)λV̄L

and J41 , J42 , and J43 are not relevant to the following analysis. Note that it is not clear

33

whether J21 is positive or negative. Defining matrix J as:⎛⎞⎜ −J11
⎜
⎜
J≡⎜
⎜ J21
⎜
⎝

−J31

J12
−J22
0

−J13 ⎟⎟⎟−J23 ⎟⎟,⎟⎠

J33

we obtain the characteristic equation of the coefficient matrix on the right-hand side ofequation (37) as follows:(J44 − x)(−x3 + Tr J x2 − B J x + Det J ) = 0,(38)

Tr J = −J11 − J22 + J33 ,(39)

B J = J11J22 − J11 J33 − J12J21 − J13J31 − J22J33 ,(40)

Det J = J11 J22J33 + J12 J23J31 + J13 J22J31 − J12J21 J33.

(41)

where

Since J44 is positive, we must show that the polynomial:−x3 + Tr J x2 − B J x + Det J = 0(42)

has one root with a positive real part and two roots with negative real parts in order to provethat the steady state has a stable manifold of dimension two.
To show this, we exploit the following application of ‘Ruth’s theorem’ to a third-orderpolynomial as shown in Benhabib and Perli (1994).

34

Theorem (Benhabib and Perli, 1994) The number of roots of the polynomial in (42) withpositive real parts is equal to the number of variations of sign in the scheme:
−1

−BJ +

Tr J

Det J
Tr J

Det J.

(43)

A proof of the more general version of Ruth’s theorem is, for example, given by Gantmacher(1960, vol. 2, Ch. XV).
To make use of the theorem, and show that the scheme (43) has one variation of sign, we
next verify that Det J > 0. From the components of the Jacobian matrix, each term on theright-hand side of (41) is:

J11 J22J33



J12J23J31

n̄M LNaL
λ−1=
×− I¯ ×(1 − δ)λV̄L
aN (1 − δ)λV̄L aN
 LN
aL mγ(1 − n̄N )
¯
¯
=
−I ,
I + mγ + ρaN (1 − δ)2λV̄L (I¯ + mγ)aN

J13J22J31





 LN
aL (1 − n̄N )  ¯
1= Ī +++ mγ + ρ
I + mγ(1 − δ)λV̄L aN (1 − δ)λV̄LaN
aL (1 − n̄N )  ¯>
I + mγ I¯ + mγ + ρ ,aN (1 − δ)λV̄L!

(1 − n̄N )aL(λ − 1)n̄M
=
+
1−
n̄N
2
2
(1 − δ)λ(V̄L )(1 − δ)λ(V̄L )aN
aLmγ(1 − n̄N )  ¯
,
>
I
+
mγ
+
ρ
aN (1 − δ)2λV̄L

−J12J21 J33

"







× I¯ + mγ ×aLaN (1 − δ)λλ−1aL n̄MLN= −− mγ+ mγ + ρ(1 − δ)λV̄L aN (1 − δ)λV̄L
aN



 LN
aLmγ(1 − n̄N )> −+ mγ + ρ .
I¯ + mγ + ρaN (1 − δ)2λV̄L (I¯ + mγ)
aN

35

Therefore, we have the following inequality:

Det J >)*

aL (1 − n̄N )(I¯ + mγ + ρ)
¯ + mγ 2 − mγρ .
(1
−
δ)
I
aN (1 − δ)2λV̄L (I¯ + mγ)(44)Equation (44) together with the assumption that mγ > ρ/(1 − δ) implies Det J > 0. Thus,
we can conclude that the scheme (43) varies its sign an uneven number (one or three) times.
To show that the number of variations is always one, we consider three cases according to
the sign of Tr J : Tr J < 0, Tr J = 0, and Tr J > 0.
(i) The case of Tr J < 0
If Tr J < 0, then the scheme (43) must have only one variation of the sign regardless ofthe signs of −B J + Det J/Tr J . Hence, in this case, the characteristic equation (38) has
always two positive solutions and two solutions with negative real parts, so that the steadystate is saddle-point stable and the equilibrium path is locally determinate.
(ii) The case of Tr J = 0
If Tr J = 0, then the sum of the three solutions of equation (42) is equal to zero. Because
the product of the three solutions, which is equal to DetJ , is strictly positive, it can occur
only if equation (42) has one positive solution and two solutions with negative real parts.
Thus, in the case of Tr J = 0, the characteristic equation (38) has two positive solutions andtwo solutions with negative real parts.
(iii) The case of Tr J > 0
Now suppose that Tr J > 0. In this case, we must verify that −B J + Det J/Tr J > 0
to show that scheme (43) has one variation of signs. Since the sign of −B J + Det J/Tr J
coincides with that of −B J Tr J + Det J , we prove below that −B J Tr J + Det J is positive.
Using equations (39) – (41), we can rewrite −B J Tr J + Det J as follows:−B J Tr J + Det J = Tr J [J11J33 + J13J31 + J22J33] + J11J22 (J11 + J22)
+J31 (J12J23 + J13 J22) − J12J21 (J11 + J22) .

36

(45)

Recall that the sign of J21 is ambiguous, while the signs of J11, J12, J13, J21, J22, J23, J31,
and J33 are all positive. Equation (45) directly shows that −B J Tr J + Det J is positive if
J21 is negative or zero, so that scheme (43) varies its sign only once in that case.
On the other hand, −B J Tr J + Det J is still positive, even if J21 > 0. To verify it, weagain rewrite −B J Tr J + Det J into:−B J Tr J + Det J = Tr J [J11J33 + J12 J21 + J22J33 ] + J11 [J22 (J11 + J22 ) − J13J31]+J33 (J13J31 − J12J21) + J12 J23J31.

(46)

The second term on the right-hand side of equation (46) is positive because:
J22 (J11 + J22) − J13 J31











aL (1 − n̄N )= I¯ + mγ I¯ ++ I¯ + mγ
aN (1 − δ)λV̄L




1
LS
aL LN (1 − n̄N )¯++,
I + mγ −(1 − δ)λV̄LaN(aN )2 (1 − δ)λV̄L

where (I¯ + mγ) − (LS /aN ) > 0 under condition (19). In addition, the third term on theright-hand side of equation (46) is also positive since:!

"aL(1 − n̄N )aLmγ(λ − 1)
J13J31 − J12 J21 =
1−
n̄N +
> 0.
2
2
2
aN (1 − δ) λ (V̄L )aN(1 − δ)λV̄L
As a result, equation (46) implies that −B J Tr J + Det J is positive even if J21 > 0, so that
scheme (43) turns its signs only once in this case also. Therefore, in the case of Tr J > 0,
two solutions of the characteristic equation (38) are positive real numbers and the other twosolutions are complex numbers with negative real parts.
Thus, the proof to confirm saddle-point stability and local determinacy of the steady state
has been completed.

37

References[1] Antràs, P., 2005, Incomplete Contracts and the Product Cycle. American Economic
Review 95, 1054–1073.
[2] Benhabib, J., Perli, R., 1994, Uniqueness and Indeterminacy: On the Dynamics ofEndogenous Growth. Journal of Economic Theory 63, 113–142.
[3] Coe, D., Helpman, E., Hoffmaister, A., 1997, North-South R&D Spillovers. The Economic Journal 107, 134–149.
[4] Enos, J. L., Park, W. H., 1988, The Adoption and Diffusion of Imported Technology:
The Case of Korea. Croom Helm, New York.
[5] Gantmacher, F. R., 1960, The Theory of Matrices. Chelsea Publishing Company, New
York.
[6] Glass, A. J., Saggi, K., 2002a, Licensing versus Direct Investment: Implications for
Economic Growth. Journal of International Economics 56, 131–153.
[7] Glass, A. J., Saggi, K., 2002b, Intellectual Property Rights and Foreign Direct Investment. Journal of International Economics 56, 387–410.
[8] Grinols, E., Lin, H. C., 2006, Global Patent Protection: Channels of North and South
Welfare Gain. Journal of Economic Dynamics and Control 30, 205–227.
[9] Grossman, G. M., Helpman, E., 1991, Innovation and Growth in the Global Economy.
The MIT Press, Cambridge, MA.
[10] Helpman, E., 1993, Innovation, Imitation, and Intellectual Property Rights. Econometrica 61, 1247–1280.
[11] Kwan, Y. K., Lai, E. L.-C., 2003, Intellectual Property Rights Protection and Endogenous Economic Growth. Journal of Economic Dynamics and Control 27, 853–873.
[12] Lai, E. L.-C., 1998, International Intellectual Property Rights Protection and the Rateof Product Innovation. Journal of Development Economics 55, 133–153.
[13] Ozawa, T., 1980, Government Control over Technology Acquisition and Firms’ Entry
into New Sectors: The Experience of Japan’s Synthetic-Fibre Industry. Cambridge
Journal of Economics 4, 133–146.
[14] Park, W. G., Lippoldt, D., 2005, International Licensing and the Strengthening of Intellectual Property Rights in Developing Countries during the 1990s. OECD Economic
Studies 40, 7–48.
[15] Peck, M., 1976, Technology, in H. Patrick and H. Rosovsky, eds., Asia’s New Giant:
How the Japanese Economy Works. Brookings Institution Press, Washington.

38[16] Smith, P. J., 2001, How Do Foreign Patent Rights Affect U.S. Exports, Affiliate Sales,and Licenses? Journal of International Economics 55, 411–439.
[17] Tanaka, H., Iwaisako, T., Futagami, K., 2007, Dynamic Analysis of Innovation and International Transfer of Technology Through Licensing. Journal of International Economics, forthcoming.
[18] Yang, G., Maskus, K. E., 2001a, Intellectual Property Rights and Licensing: An
Econometric Investigation. Weltwirtschaftliches Archiv 137, 58–79.
[19] Yang, G., Maskus, K. E., 2001b, Intellectual Property Rights, Licensing, and Innovation in an Endogenous Product-cycle Model. Journal of International Economics 53,
169–187.

39

innovation: ItnM,tinnovation: ItnL,timitated industriesnM,tlicensed industriesnL,tinnovation:
It nN,tindustries in the North
nN,t

0

1

imitation: mγnL,tlicense agreement: ιt nN,tFigure 1: The structure of industries

40

nN
1

SL
SL’

(1−δ)(λ−1)LN(aL/κ)(mγ+ρ)ES

1 − (a(1−δ)(λ−1)LL /κ)(mγ+ρ)λ

E’
NL’
NL

LN
aN

O

Figure 2: Determination of the steady state

41

I

nN
1

SL’
SL

E’

E
NL
NL’

LN
aN

O

Figure 3: The effects of the rise of δ

42I