On the International Technology Transfer through Licensing

Hideo Noda (Yamagata University)

1 Introduction
Since the Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPs) came into force
in 1995, issues concerning intellectual property rights in international technology transfer have beenaddressed more actively. The objective of this paper is to show how intellectual property rights
protection in a developing country influences innovative performance, international technology
transfer and wage gap in a global economy, within the framework of an endogenous growth model ofopen economy.
Our model implies that reinforcement of intellectual property rights protection in a developing
country has positive effects on the rate of innovation in that developed country and the amount oftechnology transferred from that developed country to a developing country through licensing. As well,
the model suggests that, in general, although the impact of reinforcement of intellectual property rights
protection in a developing country on the wage difference between a developing and a developed
country is uncertain.

2 The Model
2.1 Consumers
Identical consumers live in one of two countries or regions, North and South, i ∈ {N , S } . For
simplicity, we assume that the households in the North receive wage by inelastically supplying labor tothe production sector or research and development (R&D) sector. On the other hand, the households in
the South receive wage by supplying labor to the production sector inelastically. Households in bothcountries are also able to earn asset income. In the following, we express total amount of labor of theNorth and the South as LN and LS , respectively.
The objective function of the households in each country is given by∞

U i = ∫ e − ρt ui (t )dt ,0

where symbol t denotes a time variable, ρ represents the rate of time preference, and ui (t )represents the instantaneous utility of household at time t in each country. We now assume that eachindustry j corresponding to the production line of different goods is distributed continuously within

the interval [0,1] ; the goods produced in each industry all have an imperfect substitution relationshipwith one another. Under such an assumption, ui (t ) is formulated specifically as1ui (t ) = ∫ log ∑ λm xmi (t , j )dj , (λ > 1)0m

where xmi (t , j ) represents the consumption of good of quality m produced by industry j in eachcountry. In addition, λm is a qualitative indicator of goods having quality of level m . Therefore, thispaper develops an argument based on such an innovation model in which the quality of goods
improves over time, although the type of good is fixed.
In this paper, we regard the Southern labor as numeraire, and normalize the wage rate in theSouth to one. On the other hand, we express the Northern wage rate at time t as w(t ) . Then, it isassumed that a relation 1 < w(t ) < λ holds.
We turn now to examine the optimization problem that households face. Let pm (t , j ) andEi (t ) be
the price of good of quality m produced by industry j and total expenditure of household in eachcountry. Solving this problem, we obtain

E& i (t )= ri (t ) − ρ .
Ei (t )
2.2 Producers
We assume that such R&D activities for a next-generation product are not carried out by leader of theindustry producing the most advanced good, but by followers, which are producing goods of lower
quality than the most advanced good. We treat labor as the only factor of production and assume that
one unit of labor is required for producing one unit of an arbitrary good. Consequently, the marginal
cost of all goods produced by the Northern firms equals the wage rate w(t ) ; the marginal cost of all
goods produced by tthe Southern firms equals one. As mentioned above, innovation derived fromR&D activities occurring only in the North. Then, a Southern firm (licensee) is able to produce themost advanced product by obtaining technical information about its product from a Northern firm
(licensor) through a license.
Let us first consider price competition among firms in a state of oligopoly in each industry. We now
assume that a firm in the North is able to use the technology for the most advanced good, while a firmin the South is able to produce goods of quality that is one rank lower. As a result of Bertrand
competition, the firm in the North producing the most advanced good will set limit price of such goodat λ , which drives the firm in the South to produce goods of a rank of lower quality out of the market.
Hence, the resulting prices become equal in all industries and the aggregate demand for each good willbe [E N (t ) LN + ES (t ) LS ]/ λ ≡ E (t ) / λ . Hence, if the profit of the firm in the North producing themost advanced goods is expressed as π N (t ) , the following relation holds.



π N (t ) = E (t ) 1 −w(t ) .
λ Next, we examine that a firm in the South is able to use the technology for the most advanced good
through a license and another firm in the South is able to produce good of quality that is one rank
lower. As a result of Bertrand competition, the Southern firm producing the most advanced good will
price the good at λ , which consequently drives the other firm in the South producing good of lower
quality out of the market. In this case, too, because the resulting prices do not depend on the industry
index j , the prices become equal in all industries. Therefore, the aggregate demand for these goods
will be expressed as E (t ) / λ . Hence, if the profit of the firm in the South producing the mostadvanced good is expressed as π L (t ) ,then we get1π L (t ) = E (t ) 1 − .
 λ

(1)

Let us discuss the relationship between R&D investment and new technology created by suchinvestment. In our model, R&D activities in each industry are accompanied by uncertainty and that theoccurrence of innovation is governed by a Poisson process. Specifically, we assume that a firm thatinvests resources I (t ) during a sufficiently short time interval of length ∆t will develop newtechnology at a probability I (t )∆t . Thus, I (t ) represents a Poisson arrival rate of an innovation,
which indicates the momentary probability of successful innovation. Accordingly, I (t ) is interpreted
as an indicator for measuring the rate of innovation. In addition, we assume that labor in a unit ofaI I (t ) per unit time must be invested for the rate of innovation at level I (t ) to occur.
A firm that has successfully developed technology for producing goods of the highest quality is ableto gain exclusive profits by selling such goods, unless any of the firms following behind succeeds indeveloping goods for the next generation. Here we will express the sum total of the discounted presentvalues of the profits as VI (t ) . On the other hand, it is found that the cost for R&D becomesaI I (t )∆t . Therefore, the expected net profit of the firm that has succeeded in innovation can bewritten as

VI (t ) I (t )∆t − w(t )aI I (t )∆t.
Let us assume free entry into the R&D business. We focus on equilibria with positive R&D, that is,innovation occurs in terms of I (t ) > 0 . Then, we obtain

VI (t ) = w(t )aI .

(2)

The Northern firm that has successfully developed the most advanced goods not only profits fromthe sale of the goods, but also becomes able to receive fees, i.e., royalties, by licensing technicalknowledge as an intellectual property to the firm in the South. For simplicity, we assume that theamount of the royalty is the value obtained by multiplying the sum total of the discounted presentvalues of the profits from the sale of the goods gained using the firm in the South receiving thetechnology transferred by a constant percentage δ ∈ (0,1) , that is, δVL (t ) . We regard δ as aparameter. We also assume that technology transfer through licensing is governed by a Poisson process
and that technology transfer is successful at the probability of ι∆t . That is, ι represents a Poisson
arrival rate, which indicates the momentary probability of successful technology transfer throughlicensing. Therefore, a firm that succeeds in the development of new technology will gain an expected
revenue of δVL (t )ι∆t by licensing the technical information as an intellectual property. Here, we
assume that the firm in the North uses labor of aLι∆t for instructing technical data provided to theSouthern firm, training of manufacturing know-how, and other purposes. Accordingly, parameter aL
can be considered as an indicator that reflects the average absorptive capacity of the firms in the South.
We should also take note that the firm in the North, which provides the license, incurs an opportunity
cost of VI (t )ι∆t . As a result, if the Northern firm that succeeds in developing the most advanced
goods is to license, the firm receives the following expected net profit:δVL (t )ι∆t − w(t )aLι∆t − VI (t )ι∆t.
Therefore, in the equilibrium in which technology transfer through licensing occurs in terms of ι > 0 ,we obtainδVL (t ) = w(t )aL + VI (t ).

(3)

2.3 Market Equilibrium
Here we will ascertain the conditions that hold in an equilibrium of asset and labor markets in eachcountry. From the equilibrium condition of asset market in the North, we get

π N (t ) V&I (t ) ιδVL (t )VI (t )+VI (t )+VI (t )− [I (t ) + ι ] = rN (t ).

As is well known, because the South lacks a legal infrastructure for intellectual property rights

and their control, the licensee faces the risk of potential imitation within the South. We assume that
imitation occurs according to the Poisson process with an arrival rate, κ , which denotes themomentary probability of imitation's occurrence. Consequently, in the equilibrium of the asset market
in the South, the following condition holds:

π L (t ) V&L (t )VL (t )+VL (t )− [I (t ) + κ ] = rS (t ).

(4)

In our model, we consider the situation that asset markets are integrated internationally. Thus, arelation rN (t ) = rS (t ) ≡ r (t ) will hold.
If the number of variety of goods produced in the North and the South is expressed as nN (t )nS (t ) respectively, then labor nN (t ) E (t ) / λ for the production of goods,I (t )aI nN (t ) + I (t )aI nS (t ) for R&D, and ιaL nN (t ) for technology transfer will be demanded in theandlabor market in the North. Therefore, the following equation holds as the equilibrium condition of thelabor market in the North:E (t )λnN (t ) + I (t )aI (t )nN (t ) + I (t )aI (t )nS (t ) + ιaL nN (t ) = LN

On the other hand, the equilibrium condition of the labor market in the South is given byE (t )λnS (t ) = LS .

(5)

3 Steady-State Comparative Statics
We focus on a steady state, that is, a situation in which all variables grow at constant rates.
Consequently, after some manipulation, we obtain the following equations.

(1 − nS )LS + IaI + aL InS = LN ,nSnL  1 
(aI + aL )( ρ + I + κ ) = δ 1 −  aI ( ρ + I ) − aL I S + S .
1 − nS nS  λ 

(6)

(7)

Based on the preliminary discussion so far, we will now examine the comparative statics. Here, theparameter of imitation risk κ is regarded as a proxy for the level of protection of intellectualproperty rights in the South, and a decrease in the imitation risk will be interpreted as reinforcement ofprotection of intellectual property rights. Using eqs. (6) and (7), when the level of protection of
intellectual property rights in the South is reinforced, we find that the rate of innovation will increase
and so will international technology transfer.
We will now inquire into how the wage gap between the two countries changes when the level ofprotection of intellectual property rights in the South is reinforced. Let us recall now that the wage ratein the South has been normalized to one. Hence, the wage rate w in the North can be construed as
the relative wage between the North and the South. From eqs. (1), (2), (3), (4), (5) and (6), we obtainL 
LN + LS − S λL  1 nS 
w = δ S 1 −  (aI + aS ) ρ + κ +nS  λ  aI + aL nS ≡ w(nS (κ ), κ ).

−1

Therefore, we getdw ∂w dw ∂w=+.
dκ ∂nS dκ ∂κ
In this regard, however, the sign of dw / dκ is inconclusive.
4 Concluding Remarks
This paper has developed an argument on the effects that reinforcement of protection of intellectual
property rights in a developing country would have on innovation and international technology
transfer and how the wage gap in labor income between a developing and developed countries wouldchange, within the context of a quality-ladder model.
Main results can be summarized as follows. First, reinforcement of intellectual property rights
protection in a developing country positively influences the rate of innovation in a developed country
and the amount of technology transferred from a developed country to a developing country throughlicensing. Secondly, although the impact of reinforcement of intellectual property rights protection in adeveloping country on the wage difference between two countries is uncertain, such a difference issuggested to become smaller when R&D investment by a developed country is active and theabsorptive capacity of the developing country is at a high level.