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PATENTS, NORTH-SOUTH TRADE AND GLOBAL GROWTH
By
PIPAWIN LEESAMPHANDH
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2008
O 2008 Pipawin Leesamphandh
To my parents and my husband for their love and support
ACKNOWLEDGMENTS
First and foremost, I would like to thank my advisor, Elias Dinopoulos, for his help and
guidance. He has inspired and motivated me through his valuable ideas and suggestions. I am
grateful for his time, patience and knowledge in economics. I would like to thank my supervisory
committee, David Denslow, Steven Slutsky and James Seale for their comments, suggestions and
for reading my dissertation and attending committee meetings.
Additionally, I appreciate the help and support from my fellow graduate students, office
staff and professors in the Economics Department at the University of Florida. I thank them for
making my years in Florida a memorable experience in my life. I am thankful for financial
support from the Thai Government and for assistance provided by the staff of the Office of Civil
Service Commission. My personal gratitude goes to Dr. Kanit Sangsubhan, who encouraged me
to take this journey and believe in me.
Last but not least, I thank my mother (Dr. Wipawee Jampangern) for her endless love and
support, and my father (Nop Usawattanakul) who always believes in me. I thank my good
friends (Dr. Saijit Daosukho, Dr. Kornvica Pimukmanaskit and Noppun Wongkittikraiwan) for
their help and mental support. I would like to thank the Phadungcharoen family for their
kindness. Finally, I thank my beloved husband Theerapat Leesamphandh, for his love and
support, for making me feel like I am at home in Florida and for always making me laugh and
happy.
TABLE OF CONTENTS
page
ACKNOWLEDGMENT S .............. ...............4.....
LI ST OF FIGURE S .............. ...............7.....
AB S TRAC T ......_ ................. ............_........8
CHAPTER
1 INTRODUCTION ................. ...............10.......... ......
2 TECHNOLOGY TRANSFER, TRADE COSTS AND ECONOMIC GROWTH ................12
Introducti on ................. ...............12.................
M odel .................. ... ........ ...............14.......
Household Behavior ................. ...............14.......... ......
Production and Trade Costs.................. ...............17
Innovative Research and Development ................. ...............20................
Imitative Research and Development............... ..............2
Labor M markets .............. ...............26....
Steady-State Equilibrium ................. ...............28.................
S chumpeterian Growth ................. ...............3 1...._.__....
Comparative Steady-State Analysis .............. ...............33....
Conclusion ........._.. ..... ._ ._ ...............37....
Al gebraic Detail s .............. ...............37....
3 PATENT ENFORCEMENT POLICIES AND ENDOGENOUS GROWTH .......................44
Introducti on ........._.... ...... .._ ._ ...............44....
Closed-Economy Model .............. ...............46....
Household Sector. ........._............ ...._.._ .. ......_._ .............4
Domestic Production and Patent Enforcement Sector. .....__.___ ........_._ ..............48
Innovation Process............... ...............49
Domestic Labor Market ................. ...............52........... ....
Steady-State Equilibrium ................. ...............53.................
Long-Run Schumpeterian Growth............... ...............54.
Comparative Steady-State Analysis .............. ...............56....
Conclusion ................ ...............58......_ ._ .....
4 MULTNTINAINAL CORPORATIONS, PATENT ENFORCEMENT AND
ENDOGENOUS GROWTH .............. ...............60....
Introducti on ................. ...............60.................
M odel ................ .. .......... ... ...............61.......
Consumers and Workers............... ...............62
Production and Multinationalization ................. ....._.. ...............64......
Innovation............... ...............6
Labor M markets .............. ...............69....
Steady-State Equilibrium .......__................. ..........__..........7
Long-Run Schumpeterian Growth............... ...............73.
Comparative Steady-State Analysis .............. ...............74....
Conclusion ................ ...............78......_._ .....
Al gebraic Detail s .............. ...............79....
5 CONCLU SION................ ..............8
LIST OF REFERENCES ........._... ........... ...............88....
BIOGRAPHICAL SKETCH .............. ...............91....
LIST OF FIGURES
FiMr page
2-1 Pricing structure of the Northern quality leaders ................. ...............43..............
2-2 Pricing structure of the Southern quality leaders ................. ...............43..............
3-1 Closed-economy's steady-state equilibrium .............. ...............59....
4-1 Multinationalization process in a North-South model ................... .... ...........8
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PATENTS, NORTH-SOUTH TRADE AND GLOBAL GROWTH
By
Pipawin Leesamphandh
August 2008
Chair: Elias Dinopoulos
Major: Economics
We developed a North-South model with global patent protection in the presence of trade
costs. The model generated endogenous Schumpeterian growth and product-cycle trade. The first
model was used to analyze the effects of globalization through trade liberalization and a
geographic expansion in the size of the South. A reduction in trade costs worsens the North-
South income inequality by increasing the wage-gap between the two regions. Globalization has
an ambiguous effect on the steady-state rate of technology transfer and has no effect on either
innovation or the growth rate.
Next, we built a simple general-equilibrium model of scale-invariant long-run
Schumpeterian (R&D-based) growth, finite-length patents, and endogenous patent enforcement
policies. The latter were captured by a probability function which depends on the government
resources engaged in the enforcement of patents granted to firms that discover new higher-
quality products. An increase in the patent length raises the probability of patent enforcement;
this result is consistent with cross country evidence showing that patent enforcement and patent
duration are complements. In addition, the model predicted that economies with low productivity
of R&D researchers have weaker patent enforcement policies and lower long-run Schumpeterian
growth.
Lastly, we introduced an endogenous multi-nationalization process into a North-South
model of scale-invariant long-run Schumpeterian growth with a finite-length patent protection.
The latter is perfectly enforceable in the North but imperfectly enforceable in the South. The
model was used to examine the effects of intellectual property rights policy and globalization on
Foreign Direct Investment (FDI) and the world income distribution. The effectiveness of patent
enforcement does not effect the decision of a firm to become MNCs. However, an increase in
patent length reduces the flow of FDI and worsens the income distribution between regions. In
addition, globalization, measured as a geographic expansion in the size of the South, increases
the flow of FDI but worsens the North-South income distribution. Lastly, an improvement in
innovation technology leads to a decline in FDI and worsens the North-South wage gap.
CHAPTER 1
INTTRODUCTION
We developed three models to study various issues in international economic field such as
globalization, intellectual property rights (IPRs) protection and foreign direct investment. All
models are based on similar building blocks of quality-ladder framework, finite patent length,
and Bertrand price competition. Each model has quality leaders who invent the new state-of-the-
art product and enj oy global monopoly profit as they sell product to the world using limit
pricing. There are quality followers in each model with different patent protection policy. In
addition, all three models are based on the same innovation technology where we assumed an
increase in Research and Development (R&D) difficulty overtime in order to remove an
undesirable scale effect property from the model.
The first model is a North-South product-cycle trade model with global patents protection.
We introduced trade costs into the first model to examine the effect of globalization to global
innovation, imitation and wage-income distribution between regions as trade costs are an integral
part in the international trade flow. In the first model, quality followers in the North produce
generic products while quality leaders in the South target generic products in the North for their
imitative R&D.
The second model is a closed-economy model with imperfect patent enforcement policy.
We introduced a resource-using endogenously determined patents-enforcement mechanism to
examine the link between patent length, and various factors to resources used in the patent
enforcement sector. Intellectual property rights protection becomes a maj or sector that many
countries are required to allocate their scarce resources in order to meet the minimum standard
set by the agreement on Trade-Related Aspects of Intellectual Property Right (TRIPs). Quality
leaders receive a finite patent with some probability of patents protection. There is no imitative
R&D since the method of production of the newly invented product becomes general knowledge
without patents protection; therefore, quality followers can produce and sell products
competitively in the market.
The third model is a North-South product-cycle trade model with free trade. We introduced
endogenous multi-nationalization process to investigate the effect of patents protection,
globalization and innovation technology to the flow of foreign direct investment and wage-
income distribution between regions. Northern quality leaders received patent protection that is
perfectly enforceable only in the North but imperfectly enforceable in the South. There is no
imitative R&D in this model as Southern quality followers can produce and sell the products
when there is no patents protection and the method of production becomes general knowledge.
Therefore, only multi-national corporations face the risk of imitation after they transfer their
production based to the South.
CHAPTER 2
TECHNOLOGY TRANSFER, TRADE COSTS AND ECONOMIC GROWTH
Introduction
International trade has continually expanded and become a large share of the world income
in the past decade. This continuing trend indicates the acceleration of globalization in the world
economy. Globalization leads to a substantial reduction in trade costs which include: a sharp
drop in the price of communication due to the intense competition in telecommunication markets
and the emergence of the internet technology, an increase in cheaper and faster modes of
transportation, and a decline in barriers to trades in goods and services under the General
Agreement on Tariffs and Trade (GATT). The average tariff rate on manufactured goods in
developed countries has dropped sharply from 20 % to approximately 4 % in the past 50 years
(Hill 2002)
However, trade costs still remain as a significant portion of international trade flow.
Anderson and Wincoop (2004) estimated a 170 % ad-valorem tax equivalent of total trade costs
for developed countries. We developed a simple product-cycle trade model that incorporates
trade costs in order to analyze the effect of globalization to the world income distribution. Trade
costs can be considered as all costs incurred in getting a good to final consumers other than the
marginal cost of producing the good itself which include costs related to transportation, policy
barriers, information, contract enforcement, currency exchange risk, regulation and local
distribution. Anderson and Wincoop (2004) provided empirical studies of trade costs and
emphasized the importance of trade costs in international trade flows. In general, trade costs can
be classified into two main categories which are domestic and international trade costs. This
paper emphasizes only the international trade costs since the domestic trade costs are faced by
both domestic and foreign firms.
A class of North-South trade models has long been developed in conjunction with the
development of the new growth theory starting with the pioneer work of Krugman (1979). The
state-of-the-art dynamic North-South models featuring endogenous Schumpeterian (R&D-based)
growth have been extensively used to examine various aspects of interest in the international
trade and growth literatures. Dinopoulos et al. (2005) found that globalization, modeled as an
increase in the size of the South, worsens the wage-income distribution between the North and
the South, increases the rate of imitation and does not affect the long-run rate of innovation and
growth. While, an increase in the global patent length worsens the wage-income inequality
between the North and the South, increases the rate of product imitation and has an ambiguous
effect on the long-run Schumpeterian growth. Their main assumptions are zero transportation
cost and enforceable global patent protection.
Dinopoulos and Segerstrom (2005), also assuming free trade and Dixit-Stiglitz consumer
preferences, concluded that globalization taking the form of an expansion in the size of the
South, leads to less wage-income inequality between the Northern and the Southern workers,
increases the imitation rate and speeds up the technological change, while stronger intellectual
property protection has the opposite steady-state effect. Next, Dinopoulos and Segerstrom (1999)
introduced tariffs into the North-North trade model where workers have different skill levels.
They concluded that trade liberalization reduces the relative wage of unskilled workers, increases
R&D investment, boosts the rate of technology change and results in skill upgrading within each
industry.
Other studies relating patent protection, intellectual property rights and growth include
Sener (2006), also assuming free trade, found that stronger intellectual property rights protection
leads to a larger North-South wage gap and reduces the rate of innovation and imitation. In
addition, more integration of the South into the world economy, taking the form of an increase in
relative size of the Southern population, also leads to a larger North-South wage gap and reduces
the rate of innovation, but increases the rate of imitation.
The contribution of this model is that we examined the effects of globalization to the wage-
income inequality between the North and the South and the rate of international technology
transfer by taking into account the presence of trade costs and enforceable global patent
protection. In this model, globalization takes the form of not only an increase in the size of the
South, but also a reduction in international trade costs.
Model
We generalized the North-South model of trade and growth by Dinopoulos et al. (2005) by
introducing international trade costs. The model followed the quality-ladder framework
assuming a finite patent length and increasing R&D difficulty over time in order to remove the
undesirable scale effects property. The model generated endogenous long-run Schumpeterian
(R&D-based) growth which depends on patent length and the rate of population growth. This
study added to the existing North-South trade models by explicitly studying the long-run effects
of trade costs on the global wage-income inequality and the rate of international technology
transfer.
Household Behavior
The global economy consists of two regions: the innovating-North and the imitating-South.
Both regions are assumed to have common trade costs and identical consumers' preferences.
World population grows at an exogenous rate n > 0. There is a fixed measure of dynastic
households with infinitely lived members. Each household member is endowed with one unit of
labor which is supplied inelastically to the market. New household members are born
continually; therefore, the size of each household grows exponentially at the rate of n > 0. We
simplified the model by normalizing the initial size of each household to unity. The number of
household members at time t is then, e"t. Let L, (t) = L,e"' denote the level of the Northern
population and the supply of labor in the North at time t, where L, is the initial level of the
Northern population. Similarly, let Ls (t) = Lse"' denote the level of the Southern population and
the supply of labor in the South at time t where Ls is the initial level of the Southern population.
The world population at time t is given by L(t) = Le"' = L, (t) + Ls (t) = (L, + Ls )e"'
There is a continuum of industries indexed by B E [0,1] Each industry produces a final
consumption good with different quality level. The quality level of a product is indexed by j,
where j is restricted to integer values and represents the number of innovations in each industry.
Let Al'8,t denote the quality level of a product in industry B where Ai > 1 is the quality
increment generated by each innovation which, by assumption, is identical across industries.
Each household, modeled as a dynastic family, maximizes the following discounted
lifetime utility
U "In u(t)dt, (2-1)
where p > n is the constant subjective discount rate.
The instantaneous per-capita utility function at time t is defined by
Inu~)= n[ 'q(j 6 ) (2-2)
where q(j,0, t) denotes the quantity demanded per person of a product in industry B with
quality level A'" at time t. Equation 2-2 is the standard quality-augmented Cobb-Douglas utility
function across all industries. It also implies that consumers prefer higher quality products.
The consumer's problem is solved in three stages: First, each consumer considers the
within-industry static optimization problem.
max C A' q( j, 6, t) (2-3)
subj ect to C p7(j,0,~t, )q(j,0, t) = c(B, t) where p7(j,0,~t) is a consumer price of product j
in an industry B at time t and c(0, t) is per-capita expenditure. The solution to this within-
industry optimization problem is to buy the product with the lowest quality-adjusted price
p, (8,t)
.If two products have the same adjusted price, consumers always buy the higher-quality
product.
Second, consumers allocate their budgets across all industries by solving the following
across-industry static optimization problem.
max jAl;(o,t)q(,td (2-4)
subject to pl(0, t,)q(i(, t~d = c(t), where q(0, t) is per-capita quantity demanded for the
lowest quality-adjusted price product in industry 8 at time t, j(B, t) is the quality index of the
product with the lowest quality-adjusted price in industry 8 at time t, p(B, t, ) is the price of the
product and c(t) is per-capita consumption expenditure at time t. The solution to this static
problem yields a unit elastic demand function. Grossman and Helpman (1991) provided a detail
derivation of this unit elastic demand function.
c(t)
q(B, t) = (2-5)
p(8, t)
Lastly, consumers solve the dynamic optimization problem by substituting the demand
function from Equation 2-5 into the instantaneous per capital utility function (Equation 2-2) and
maximizing discounted life time utility (Equation 2-1).
maO e ""In ct) +In -I p0 t (2-6)
subject to an intertemporal budget constraint z(t) = w(t) + r(t):(t) c(t) nz(t) ,where z(t)
is the level of consumer assets at time t, w(t) is the wage rate at time t, and r(t) is the market
interest rate at time t. The solution to this optimal control problem yields the following well-
known differential equation
c(t)
= r(t) p. (2-7)
c(t)
At the steady-state equilibrium, per-capita consumption expenditure is constant. Therefore,
the market interest rate equals the constant subj ective discount rate.
Production and Trade Costs
Labor is the only factor of production and perfectly mobile within each region. Labor
markets are perfectly competitive in both regions. One unit of labor produces one unit of output
independently of its quality level or location in each industry. Therefore, each industry has a
constant marginal cost which is equal to the wage rate in each region. The model follows the
quality-ladder framework and assuming Bertrand price competition.
Only Northern producers engage in innovative R&D activities. A Northern firm that
discovers a new product becomes a Northern quality leader and receives a perfectly enforceable
global patent of Einite duration T > 0. A Northern quality leader enj oys a flow of temporary
monopoly profits by selling the product to the world. The-state-of the-art product turns generic
as its patent expires and is then produced under perfect competition. The method of production
becomes general knowledge only in the North. Southern firms, having a cost advantage from a
lower-wage rate, target generic products in the North for imitation. A Southern firm that
successfully copies a Northern product becomes a Southern quality leader and enj oys global
monopoly profits until the next higher-quality product is discovered and a Northemn quality
leader replaces a copied product through limit pricing.
In the steady-state equilibrium, only Southern quality leaders target generic products and
only Northern quality leaders produce new products. Let w, and ws denote the wage in the
North and the South respectively and r > 1 represents trade costs, where 1 is the ad-valorem
tax equivalent of trade cost. If w, > wst, then imitation occurs only in the South. Also, if
w,r < Alws, then innovation takes place only in the North. As a result, we assume that at the
steady-state equilibrium the following condition is satisfied
A Northern quality leader, producing the state-of-the-art quality product j in industry B ,
charges p, = Alw, to drive out Northemn quality followers who produce the j-1 product. If a
product j -1 has been successfully copied by a Southemn firm, a Northern quality leader initially
charges pyr = Alws to drive a Southemn quality leader out of the market. Assuming the existence
of substantial re-entry costs in the South, a Northemn quality leader can use a trigger price
strategy to charge pyR = Alw, after a Southern quality leader exits the market. This process is
illustrated in Figure 2-1.
The profit flow of the Northern quality leader is derived by calculating the profit from the
sale in each region using prices and costs previously described. Define c = (c,L, + csLs )/L as
the per-capita global consumption expenditure. We use the per-capita global consumption
expenditure to derive the global demand for each type of product. The profit flow of a Northemn
quality leader can be written as i, = (iw, w)q,L, +i "I wN:, qss hee, and qs
are per-capita quantities demanded by Northern and Southern consumers respectively.
Substituting a demand function, previously solved in the consumer problem (Equation 2-5) by
using the per-capita global consumption expenditure then, a Northern quality leader's profit flow
can be written as
=[ a- 1 LN (t)1 ( a- r Ls (t) 4i) 29
a L(t) Arz L(t)
The profit is generated from a general price marked-up from its cost. An increase in trade
costs reduces Northern firms' profits. Trade costs impose an additional constraint on the size of
each innovation. The next innovation needs to have a quality increment parameter greater than
trade costs in order for a Northern quality leader to be profitable in the South.
Ai > r. (2-10)
A Southern quality leader charges the limit price ps? = we to drive its Northern
competitors out of the market and charges ps = wur in the domestic market. Notice that a
Southern quality leader also sells a product at a higher price in home market in the presence of
trade costs. Figure 2-2 illustrates the pricing structure in the presence of trade costs. The profit
flow fr a Sh o ut e uaity l eadembr c n b e writ na ss L +( r -ws s s
Define re, = "- > 1 as a North-South wage gap. Substituting per-capita quantity demanded from
consumer maximization problem (Equation 2-5) using the per-capita global consumption
expenditure then, a Southern quality leader's profit flow can be rewritten as
Frs -- =, (+ cL(t) (2-11)
my L(t) myLt~
For a given level of the relative wage 0i an increase in trade costs may increase or
decrease a Southern quality leader' s profit, depending on the size of the population in both
regions. If Ls > miL,, then the profit of a southern quality leader increases in trade costs and vice
versa. The following condition guarantees positive profits associated with exports for a Southern
quality leader
0 ,> r. (2-12)
Innovative Research and Development
This model adopted basic assumptions on innovation and imitation technology from
Dinopoulos et al. (2005) where the main focus is on the balanced-growth equilibrium properties
of the model. This is done for both tractability and comparability. Define a as an innovative
R&D productivity parameter and let ev"' capture the R&D difficulty at long-run equilibrium
at a dt
where p > 0 is a parameter. A Northern firm i produces with certainty dAl = 4,units of the
state-of-the-art quality products when it hires 2 units of workers for innovative R&D activities
during a time interval dt. Also define dA = C1 dA, as the aggregate flow of new products and
LA, = C1 as the aggregate labor in innovative R&D activities. Then the economy wide rate of
aL~dt dA(t)
patents can be written as dA = ao(t nd A(t) = is the steady-state instantaneous flow of
evr dt
new products per industry. The long-run innovation rate can be written as
A(t) = yo()(2-13)
Define x(t)= (v, (t) A~t) as the steady-state evolution of x(t), where 0 < v, (t) < is the
measure of industries with active patents. The parameter P e (-1,1) captures the correlation
between the patent length and Schumpeterian growth. P takes a negative value when patents
enhance the innovation process by reducing R&D difficulty. On the other hand, P takes a
positive value when patents reduce the flow of knowledge spillovers and increase R&D
difficulty. Lastly, P = 0 when there is structural symmetry across industries.
In the steady-state equilibrium, the measure of industries protected by patents v, (t) is
bounded and must be constant over time. The flow of patents A(t) is also constant over time in
order to have a bounded per-capita long-run growth rate. The steady-state value of R&D
difficulty is given by
x(t) = (v ) A (2-14)
8A(t)
Differentiating Equation 2-13 with respect to labor yields, = ae V""', the
8LA
productivity of R&D workers which decreases over time. This implies that the innovative R&D
labor requirement increases over time in the steady-state equilibrium. Rewrite the long-run
innovations rate (Equatlion 2-13) as Ait).Y = a L(t)e-"' '. The term in square brackets is the
share of innovative R&D workers and will be constant in the steady-state equilibrium. Since
A(t) is constant over time, the term L(t)ev""') = Le("v"(t) will also be constant over time.
Substituting the steady-state value of R&D difficulty x(t) from Equation 2-14, the steady-state
rate of new products can be written as
A (2-15)
The steady-state rate of new products is directly related to population growth n, and
inversely related to the R&D difficulty parameter
quality leaders raised to the power which provides the endogenous link between patent
coverage and the rate of innovation A When p = 0, the steady-state rate of innovation is
exogenous.
Northern firms target generic products for engaging in innovative R&D activities. Let
yA (8, t) denote the market value of a patent at time t in industry B that can be written as
V (B,t)= Ir,(t fs)e-'"("ds. (2-16)
Assuming structural symmetry across all industries, consequently the value of a patent is
identical across industries. Substitute the Northern firm's profit function from Equation 2-9,
using the result from the consumer optimization problem (Equation 2-7) and integrating
Equation 2-16 yields the steady-state market value of a typical patent
V (t) = l- (An) -[ 1,() +-\ L (2-17)
AA()= j p -n L(t) r L(t)
At the steady-state equilibrium, the value of a typical patent is increasing in the patent
length T, the quality increment Ai, and the population growth rate n. The value of a patent is
inversely related to trade costs r and the subj ective discount rate p .
A Northern firm i that hires I, units of workers for innovative R&D activities during a
af ,dt
time interval dt produces the-state-of-the-art product with a market value of I dAl = F
The cost of innovation is (1 r, )w ,8,dt where r 2 > 0 is an ad-volarem subsidy to R&D
innovation. The discounted net profits can be rewritten as [a~ce"i' -(1- r 2)wv ],dt .We
assumed free entry into innovative R&D activities; as a result, the zero profit condition must
prevail in the R&D innovation sector. The following equation provides the condition that the
marginal product of labor in innovative R&D equals the subsidy-adjusted wage rate of labor.
VA -(t) (_ A N. (2-18)
Substitute the steady-state value of patent VA fTOm Equation 2-17 and the steady-state
value of R&D difficulty x(t) from Equation 2-14, we have
Ae i p -n L(t) r L(t)
From L, (t)e-w't) = Lge'tn-w~t) = L,, the innovative R&D condition can be obtained as
Ai p-n L r L
The innovative R&D condition shows a positive linear relationship between per-capita
global consumption expenditure and the Northern wage rate. As per-capita global consumption
expenditure increases, the innovation price increases. In order to restore the zero profit condition
for net discounted profit, the wage of Northern workers need to be increased.
Imitative Research and Development
Assume that the process of imitation is endogenous and depends on the amount of workers
used. Also, assume that products become more difficult to copy as the population increases.
Southern firms target generic products for imitative R&D activity. A Southern firm j hires ,
units of workers for imitative R&D during time interval dt and succeeds in copying
pl ,dt
dM, = units of generic products, where pu is an imitative productivity parameter. Define
SL(t)
L,, (t) = C, c as the aggregate labor devoted to R&D imitation. The economy wide rate of
imitation can be written as
ULM (t)
M~(t) = ^ (2-21)
L(t)
dM~
where Mi =~ dt ad dM~ = CI dMl The aggregate rate of imitation depends on the share
of labor devoted to imitative R&D. Let (8, t) denote the expected discounted profit of a
successful imitator j of a product in industry B at time t. A Southern firm j hires 8, units of
ptQ~dt
workers for imitative R&D during time interval dt and succeeds in copying dM, = umits
SL(t)
,(8, t)pQ, dt
of generic products with a market value of y,;(8, t)dM~, =. At the same time
L(t)
interval, the cost of imitative R&D equals the subsidy-adjusted wage (1 z,)ws Idt where z,
is an ad-valorem subsidy to imitative R&D. Also, we assumed that there is free entry into
imitative R&D activities which leads to the zero profit condition in the imitative R&D sector.
The following imitative R&D condition can be obtained where a firm hires labor until the value
of the marginal product of labor devoted to imitative R&D equals the subsidy-adjusted wage in
the South
'"= (1- ,)'9s. (2-22)
L(t)
To find expected discounted profit & ,, we use no arbitrage condition and a stock market
valuation of a Southern monopoly profit. Denote v, as a measure (and set) of industries with
Northern quality followers, vs as a measure of industries with a Southern quality leader and vP
as a measure of industries with a Northern quality leader. We assume that v,, + v,, + vs = 1 .
During the time interval dt, a Southern firm which does not have patent protection faces a risk of
default from a creative-destruction process with instantaneous probability A~~t. The generic
vs + v,
product can be replaced by the discovery of a higher-quality product in the North. Then, a
Southern quality leader suffers a loss equal to (0O V,). If there is no discovery of the next
higher-quality product, a Southern firm receives a capital gain equal to dV, = V,dt Therefore,
the no arbitrage condition is
s~~~ dty + dt 1- t dt= r(t)dt. (2-23)
Vi, V, + MX vs + v, V) vs+v
The first term in the left-hand side represents a dividend from investing in the stock of an
imitative R&D firm. The second term denotes the capital gain when there is no discovery and the
last term denotes the capital loss if there is a discovery of a new higher-quality product. The
right-hand side is a riskless rate of return. Taking limits as dt approaches zero and solving for the
market value of a Southern quality leader yields
V, s (2-24)
vs + V, Y
Substitute a Southern profit (Equation 2-11) into Equation 2-24. In the steady-state
equilibrium, r(t) = p and "- = n; therefore, the Southern market value can be written as
m L ( t ) r 1 L ( t
+ cLtt
V, (t) = (2-25)
p+ -n
vs + V,
Substituting Equation 2-25 into the zero profit condition (Equation 2-22) yields the
imitative R&D condition
+ + 'y n], (2-26)
my wr L puc
where ry = A is the risk of default for a Southern quality leader.
Labor Markets
We assumed prefect labor mobility and full employment to prevail within each region. The
demand for labor in the North comes from three activities which include innovative R&D,
manufacturing of new products and manufacturing of generic products. First, one could derive
the demand for innovative-R&D labor by substituting the steady-state value of R&D difficulty
(Equation 2-14) into the long-run innovation rate (Equation 2-13). These substitutions yield the
Ae t~,g
following expression for innovative-R&D labor L (t) =
cN (t) cs (t)
Second, each Northern quality leader produces L, (t) + Ls (t) units of
p, (8, t) pR (8, t) r
new products. Substitute the price p, = Avw, and p',r = il9, yields the quantity produced as
c(t)
L(t) There are vP industries producing new products; therefore, the demand for labor in
c(t)
manufacturing new products equals vp L(t). Using the same methodology and noticing that
there are v, industries producing generic products in the North, the demand for labor in
c(t)L(t) L, (t) Ls (t)
manufacturing of generic products can be written as v, +N .~t zL The Northern
full-employment condition can be derived from setting the aggregate demand equal to the
aggregate supply
Ae''~": V,c(t)L(t) vNc(t)L(t) L, (t) Ls (t) (-7
a, Aw, w L(t) rL(t)
Substitute the steady-state rate of new product A = and divide Equation 2-27 by L(t).
results in the per-capita Northern full-employment condition which can be written as
L, nZ VC Vc v, LN Ls
+ (2-28)
L, amgGp' Aw, wy L r
Next, we considered the Southern labor market. The aggregate demand for labor comes
from two activities which are imitative R&D and manufacturing of generic products. Using
Equation 2-21, the demand for imitative R&D labor can be written as L,, (t) = Mt). Each
c(t)L(t)( L, (t) Ls (t)zLt i mnr m~l ll r
Southern quality leader produces + unt fgeei rout.Thr r
s, industries copying generic products in the South at each instant of time. The Southern full-
employment condition can be derived by setting the aggregate demand for labor equal to the
aggregate labor supply
M~L(t) c(t)L(t)( L, (t) Ls (t)
Ls (t) = + vs + .~) (2-29)
pu wy Lt L(t)
Dividing Equation 2-29 by L(t), the per-capita Southern full-employment condition is
Ls Mi vsc L, Lsz 2-0
L p w L r
Steady-State Equilibrium
We focused on the balanced growth equilibrium in which each variable grows at a constant
rate over time. Variables that are constant in the steady-state equilibrium are the market interest
rate r, per-capita global consumption expenditure c, all product prices, wage rates w, and ws,
the rate of innovation A the rate of imitation Mi, the measure of industries with a Northern
quality leader vP, the measure of industries with Northern firms producing generic products vy,
and the measure of industries with a Southern quality leader vs Variables that grow at the
constant rate of population growth rate include quantities produced, labor allocated to various
activities, the flow of Southern and Northern profits and the market value of quality leaders.
To solve for the steady-state equilibrium solution, let the wage of Southern labor be a
numeraire ws = 1 so that co, = w, > 1 captures the North-South wage gap. In the steady-state
equilibrium, the measure of industries with a Northern quality leader is related to the strictly
positive patent length as
v, = Akds= AT. (2-31)
Since patent protection is finite and the rate of patents is constant overtime, the measure of
industries with active patents protection is equal to the rate of innovation times the patent length
T > 0 Substituting the steady-state rate of new product (Equation 2-15), the steady-state
solution for the measure of industries with a Northern quality leader can be obtained as
v = (2-32)
We imposed the condition 9 > Tn to ensure that the measure of industries with patent
protection is less than unity. The fraction of industries with a Northern quality leader increases in
the rate of population growth and the patent length. Substituting Equation 2-32 to Equation 2-15,
we rewrite the steady-state solution for the rate of global innovation which equals the flow of
patents as
n fl+P)
A = T (2-33)
The long-run rate of global innovation is increasing in the rate of population growth and
decreasing in the R&D difficulty parameter An increase in the parameter p raises the level
of R&D difficulty and reduces the rate of innovation. The relationship between the long-run rate
of global innovation and the patent period depends on the parameter /7 .
Denote variables with a hat (^`) as the long-run equilibrium value of endogenous variables.
The explicit steady-state solution for all variables can be solved using the innovative R&D
condition (Equation 2-20) and the imitative R&D condition (Equation 2-26). The steady-state
value of global per-capita consumption expenditure can be written as
c^= A(-)1 )L +L (-)pynr L .(2-34)
"G(1-e /A -1)L + --1 rLs L +iLs
The steady-state value of the North-South wage gap can be written as
co = ( (1 n) en +1z+( z 1Lz+ (2-3 5)
(1- Z ) Ap~(p n) L + Lst L + Ls'
where ry = is the risk of default for a Southern quality leader. Substitute the steady-
1- v
state solution for the measure of industries with a Northern quality leader (Equation 2-32) and
the rate of global innovation or the flow of patents (Equation 2-33) ry can be written as
ryr= -1 .iT (2-36)
The long-run North-South wage gap is increasing in factors that enhance the process of
innovation including the productivity of innovative R&D labor a the subsidy to innovative
R&D z and the magnitude of innovations Ai On the other hand, the long-run North-South
wage gap is decreasing in parameters that encourage the transfer of technology from the North to
the South which includes the productivity of imitative R&D labor pu, and the subsidy to
imitative R&D rat. The detail calculation is provided in the Algebraic detail section. In addition,
we used computer simulation analysis to check for the wage equilibrium condition (Equation 2-
8) that we imposed earlier and found that there is a range of different value of parameters that
satisfied the upper and lower limit from Equation 2-8. For instance, if the subsidy to imitation or
innovation is equal or close to unity, the size of innovation Ai need to be greater
L r2 +Lsz
than Ai > However, this is just a sufficient condition but not a necessary condition
L + Lst
for the steady-state wage condition (Equation 2-8) to hold.
To solve for the steady-state value of the rate of imitation, adding the per-capita Northern
full-employment condition (Equation 2-28) and the per-capita Southern full-employment
conditions (Equation 2-30) then, substitute the steady-state solution for the measure of Northern
quality leaders (Equation 2-32)
n M c T Dr 1# iL L,
1 = + +- + 1--+-s (2-3 7)
Using the innovative R&D condition (Equation 2-20), the steady-state rate of imitation can
be written as
n IpL s Tn 1 ,r+L
1- T f a- x-~ \ [Lz+LIiLz+L
dM
=~ l p<"T ~ i L (2-38)
The steady-state value of the measure of industries with the Southern quality leaders can
also be solved using the Southern full-employment condition and the steady-state rate of
imitation.
Schumpeterian Growth
To derive the long-run Schumpeterian growth, we considered the long-run growth rate of
each consumer' s utility function. Let A(t) denote the economy-wide number of innovations at
time t, as well as the average number of innovations per industry since the measure of industries
is normalized to unity and all industries are structurally identical. At each instant in time, there
are v, industries with a Northern quality leader. The average number of innovations in each of
these industries is j(B, t) = A(t). Northern quality leader charge p, = Am~i in the North and
charge pyR = Am i. The remaining industries v, + vs are characterized by an average number of
innovations j(B, t) = A(t) Every Southern quality leader and every competitive firm in the North
producing a generic product charges a price equal to the Northern wage in the North psz = 0i
and charges a price equal to the wage times trade costs in the South. ps = wr~ Thus, the
instantaneous utility of a typical household member in the North at time t is
Inu~t)= In A +t) N A1t)N dO. (2-39)
Integrating Equation 2-39 yields the level of the instantaneous utility at time t for a typical
Northern consumer
Inu(t)= A(t)1niiv In[ c s1c" (2-40)
The instantaneous utility of a typical household member in the South at time t is
In~ut) In; AA]t) S A[t) S dO. (2-41)
Integrating Equation 2-41 yields the level of instantaneous utility at time t for a Southern
consumer
Inu(t)= A(t)1ni+v In c ') c (2-42)
In the steady-state equilibrium, all variables on the right-hand side of the Equations 2-40
and Equation 2-42 are constant over time, except for the number of innovations A(t) = At .
Differentiating the level of instantaneous utility with respect to time and using the steady-state
flow of patents (Equation 2-33) yields
ui n 0'+P)
g, A n =T IP'n 2 (2-43)
g~ u =,, pi
The model has a steady-state equilibrium that generates a process of Schumpeterian
creative destruction which results in product-cycle trade, long-run scale-invariant Schumpeterian
growth and a North-South wage gap. Growth is proportional to the rate of innovation A which
is equal to the steady-state flow of patents. More importantly, the rate of innovation depends on
patent protection which is governed by the parameter /7 E (-1,1) that captures the structure of
knowledge spillovers. In the case of symmetric knowledge spillovers (P = 0), long-run growth
is exogenous. If patents decrease knowledge spillovers P e (0,1), then an increase in patent
protection decreases long-run Schumpeterian growth. In contrast, if patents enhance knowledge
spillovers, an increase in patent protection increases long-run Schumpeterian growth. With the
imposition of trade cost, we still obtain the same properties of long-run Schumpeterian growth as
in the absence of trade cost. The long-run Schumpeterian growth is increasing in the rate of
population growth and the size of innovation but decreasing in the parameter of R&D difficulty
as in Dinopoulos et al. (2005).
Comparative Steady-State Analysis
We have solved the steady-state value for each variable of interest. In this section, we
studied the long-run effects of globalization and intellectual property rights. As in Dinopoulos et
al. (2005), globalization is viewed as a geographic once-for-all increase in the size of the South
measured by the level of the Southern population. The entering to World Trade Organization by
China at the end of 2001 is an important example of globalization in this aspect. This
globalization trend is also supported by a study from Wacziarg and Welch (2003). They found
that countries with an open trade policy have increased significantly from 15.6 % to 73 % of all
countries in the world during 1960 to 2000.
Additionally, we examined a second dimension of the globalization process by studying
the effect of a reduction in trade costs. The invention of containerization technology in the
shipping industry has standardized and sharply decreased transportation costs all over the world.
Moreover, email and internet communication reduces the cost of communication in most
business transactions. As globalization becomes prevalent, trade costs which include
transportation costs, tariffs, language barriers costs, marketing cost etc. have decreased
substantially. The following proposition summarizes the effects of various dimensions of
globalization in which this model provided:
Proposition 2-1. Globalization, viewed as a permanent decrease in trade cost (r 1)
(i) worsens the long-run wage-income distribution between the North and the South by raising
the relative wage of Northemn workers (m, ~) if and only if the population size of the South
is greater or equal to that of the North (Ls > L, )
(ii) has an ambiguous effect on the relative wage of Northern workers (0i ?) if the North
population is greater than those in the South (Ls < L, )
(iii) has an ambiguous effect on the rate of technology transfer from the North to the South
(M~ ?)
(iv) does not affect the long-run rates of innovation A(++) and Schumpeterian growth (g, ++)
Proof. See Algebraic Details
A long-run decrease in trade costs has different effects depending on the size of the
population in each region. Proposition 2-1 (i) tends to resemble the real world situation where
most of developing nations, such as China and India, have more population than developed
countries. The size of the population can capture not only the number of people but also the size
of the market in each region. The economic intuition behind this proposition is that as trade costs
decrease, Northern quality leaders receive more profit from selling the-state-of-the-art products
to the South and demand more labor which leads to an increase in the wage rate in the North. On
the other hand, Southern quality leaders receive more profit from selling generic products to the
North but become less profitable in the South due to a decrease in the price of generic products.
Given that there is more population in the South, the profit of Southemn quality leaders would
decrease. Therefore, a decrease in trade costs would lead to an increase in North-South wage
gap. However, when there is more population in the North, Northemn quality leaders and
Southern quality leaders both become more profitable; therefore, the effect on the North-South
wage gap is ambiguous. In addition, the effect of trade costs to the rate of imitation is also
ambiguous since a decrease in trade cost could result in either an increase or a decrease in the
profit of a Southern quality leader. In the latter case, Southern quality leaders have less incentive
to do more imitative R&D activities.
Proposition 2-2. Globalization, viewed as a permanent expansion in the size of the South
(i) has an ambiguous effect on the long run wage-income distribution between North and
South (co, ?)
(ii) has an ambiguous effect on the rate of technology transfer from North to South (M~?)
(iii) does not affect the long-run rates of innovation A(++) and Schumpeterian growth (g, ++)
Proof. See Equation 2-43 and Algebraic Details
As population in the South increases, demand for both generic and the-state-of-the-art
products increase. The effects on the demand for labor and the wage rate in each region depend
on all parameters in the model especially, the value of trade costs, the parameter of innovation
and the size of population in both regions. Therefore, an increase in the size of developing
countries has an ambiguous effect on the North-South wage gap and the rate of imitation. An
expansion in the size of the South does not necessarily worsen the world income distribution or
enhance the rate of imitation as has been found in previous studies.
Proposition 2-3. A permanent increase in the global patent protection generated by an
increase in the patent length (T 1)
(i) permanently raises the rate of technology transfer from North to South (Mi T) if the
following sufficient condition holds: Ly + Ls 1~
(ii) permanently increases the wage-income inequality between North and South (mi ?) if the
S 1+ 1 1 1+
follow~ing sufficient condition holds: > -1!)"
Proof. See Algebraic Details
The effect of an increase in patent length and the R&D subsidy remains robust to the
introduction of trade costs. The economic intuition of the Proposition 2-3 is that longer patent
protection shifts resource away from the innovative R&D sector and manufacturing to the
imitative R&D sector. This resource allocation results in a permanent increase in the rate of
global imitation M Moreover, longer patent protection increases the duration that Northern
quality leader enj oys the global monopoly profit and increases the risk of default for the
Southern quality leader which leads to an increase in wage-income inequality between North and
South.
Proposition 2-4. The effect of a change in the subsidy to innovative R&D and imitative
R&D can be summarized as follow
(i) A permanent increase in the innovative R&D subsidy (zA ~) WOrsens wage-income
inequality (m, ~) and raises the rate of imitation (hi ) .
(ii) A permanent increase in the imitative R&D subsidy (r, 1) decreases the North-South
wage gap (0i 1) and does not affect the rate of imitation (hi ++).
Proof. See Equation 2-35 and Equation 2-38
The long-run North-South wage gap is increasing in factors that enhance the process of
innovation and decreasing in parameters that encourage the transfer of technology from North to
South. The subsidy to imitative R&D activities does not affect the long-run values of the set of
industries which are protected by patent, vp and the risk of default of a Southern quality leader,
ry. Therefore, it has no effect on the long-run rate of imitation in this model.
Conclusion
In this chapter, we develop a North-South model with global patent protection, endogenous
growth and product-cycle trade in the presence of trade costs. The model was used to analyze the
effects of globalization measured by a reduction in trade costs (caused by trade liberalization or
technological advances in transportation and communication) and a geographic expansion of
developing countries. A reduction in trade costs worsens the wage-income distribution between
regions. Trade liberalization has an ambiguous effect on the steady state rate of imitation and has
no effect on either innovation or the growth rate. The effect of an increase in the Southern
population is inconclusive in the presence of trade costs.
Algebraic Details
We calculated the steady-state value of North-South wage gap by using innovative R&D
condition (Equation 2-20) and solving for per-capita global consumption expenditure
c = (2-44)
a~l -e P")., (i -zL 1)
Then we used imitative R&D condition (Equation 2-26) to solve for per-capita global
consumption expenditure
c = (2-45)
We equated the per-capita global consumption expenditure c from Equation 2-44 and 2-45
and solved for the steady-state value ofNorth-South wage gap
ci)= aLZ(1-r)(kp + V-n)1- e F"')3 )I(- 1)r+ (Al- )L~s Ly + Ls (2-46)
Ap(1O- zA (p n) L, + Lst L, + Ls'
Next, we performed comparative static for each variable in the model. First we
differentiated the steady-state value of North-South wage gap &i (Equation 2-46) with respect to
the productivity of labor in innovative R&D activity a
a; ~ (1 e (n ( -)z / L > 0. (2-47)
aa (1- z,) Ap~(p -n) L, +Ls'
Then, we differentiated the steady-state value of North-South wage gap & (Equation 2-46)
with respect to the subsidy to innovative R&D activities z,
a; O- L~ y )(1 e (p) / )~ / )~1> 0. (2-48)
az, (1- z,)2 Ap(p -n) L, +Ls'
Lastly, we differentiated the steady-state value of North-South wage gap & (Equation 2-
46) with respect to the magnitude of innovations Ai
c3j_(- ~ YZ( I- )( e"))> 0. (2-49)
Sa/ (1- ")A (p-n) +Ls'
We can see that the steady-state value of North-South wage gap &i is increasing in the
productivity of labor in innovative R&D activity a the subsidy to innovative R&D activities z,
and the magnitude of innovations Ai On the other hand, the steady-state value of North-South
wage gap & is decreasing in the productivity of labor in imitative R&D activities p, and the
subsidy to imitative R&D activities g, To show this we differentiate the steady-state value of
North-South wage gap & ,(Equation 2-46) with respect to the productivity of labor in imitative
R&D activities pu
a; ~(1 -ep) e < 0. (2-50)
dSp (1- z,) p A/(p n) L, + Ls'
Then, we differentiated the steady-state value of North-South wage gap & (Equation 2-46)
with respect to the subsidy to imitative R&D activities z,
(IeP' )ol(y n < 0. (2-51)
raz, 1 -7 Ap) 2(p -n) L, +Ls'
Next, we showed the calculation of the steady-state value of global per-capita consumption
expenditure E .We solved for the North-South wage gap 0i from innovative R&D condition
(Equation 2-20)
ac(; 1 I I (
0 = (2-52)
Using imitative R&D condition (Equation 2-26), to solve for the North-South wage gap 0i
L~+~t~ (-z, L~ r/- zz~C+ L + rLs (2-53)
We equated the North-South wage gap a ~from Equation 2-52 and 2-53 and solve for the
steady-state value of per-capita global consumption expenditure
c Z A~ (pn(- ) LxfLs (1 -z, )(p + y- n)z L .(-4
Proof of Proposition 2-1 (i) and (ii). By differentiate Equation 2-35 with respect to trade
costs, we have the following equation
c32r2 + Ls')
where k= 1q afp -n1- '>0
The sign of depends on the size of labor in both regions. If the initial population in the
South is greater than or equal to that in the North Ls > L,,, then -is negative. However, if the
initial population in the South is less than that in the North Ls < L ,, then can be both
negative or positive.
Proof of Proposition 2-1 (iii). By differentiate Equation 2-3 8 with respect to trade costs
dhM
r we can see that has an ambiguous sign
8 r a(1- e (")
i~( -1) :" +IL 1 Ls
1- -+-I -
(A -1)L s L, + 1, Ls~ 1"
Proof of Proposition 2-1 (iv). By differentiate Equation 2-33 and Equation 2-43 with
dA ag,
respect to trade costs r O and = 0, We see that both variables are not affected by
trade costs r .
(1-7, )a(p+y -n)1- e("j
Proof of Proposition 2-2 (i). Define z = > 0, the long-
(1-7 ) A(p -n)
run Northern relative wage rZ can be written as
&L = z(LN + Ls, sn s1Lz +(1 )~ Lz+L
L, + Lst L, + Ls*
Differentiate the long-run Northern relative wage a), with respect to the Southern
population
84, (/Z- 2 + /7z- /7 +7 Z)L ,+ (AZ-)2L,Ls (/ z)z u(1-2 )
8LsL~ +LsZ (L, + LsT)2
To determine the sign of _, the denominators of both terms are positive while, the
dLS
numerator in the square bracket has ambiguous sign.
(AZ + ATz + 22 27 Ar 2)L, + (AZ z)2L,Ls + (AZ z)rzs
? + +
The numerator of the second term is negative L,(1 22 ) <0. Given that : is positive, the
sign of is ambiguous
Proof of Proposition 2-2 (ii). We can see that the sign of _can not be determined by
dLS
differentiate Equation 2-3 8 with respect to the Southern population Ls
a(1- e'"T i")
csnM ~~n 1+ ,,
n ;1+
A A Lz rI + + n1
1~ ~ ~ : (Y A )L,+1L -s1-
(pe "2(
- e )2( -
Proof of Proposition 2-3 (i). Differentiating Equations 2-38 with respect to patent length
d2M 1
T, we can see that is positive if LV r+L ."
dT Lz r
1 1+2P -
-h -Y 'P T La +
dT 1+ P
A Lyr+Ls
a(1
1
2
"! Ly + Ls z
n (- )
Proof of Proposition 2-3 (iii). For simplicity of the calculation define
Kt =/ s)~ / zLL ~ and differntiate Equation 2-35 with respect to
patent length
1
K<
n)(p + 1 + -
T Tn
-1 +~ 1 +#-
1-~T Tnc"
ep'! "l e p l(p
-(p-n)T
is positive if
a(1- e P"') (A-)L +L
S 1 n
puT ''
Ly + Ls Tn I
- Lr p
S+ 1 1
n) \1+P T
n \1+ P T Tn
charges
charges p
Pv = Aw" to drive out
to drive out
North
Follower
Figure 2-1. Pricing structure of the Northern quality leaders
charges
North Followers
producet~o drives out
Figure 2-2. Pricing structure of the Southern quality leaders
CHAPTER 3
PATENT ENFORCEMENT POLICIES AND ENDOGENOUS GROWTH
Introduction
The protection of intellectual property rights (IPRs) is one of the most debating issues in
the international economic scene. Various arguments in favor and against stronger IPRs have
emerged as many believe that General Agreement on Trade-Related Aspects of Intellectual
Property Right (TRIPs) is a rent-transfer mechanism from developing countries to the more
powerful developed nations. As each country differs in its economic fundamentals, the
implementation of TRIPs poses an imbalance in social and economic development among rich
and poor countries. In addition, stronger enforcement could restrict diffusion of knowledge and
competition and resulted in a higher product price. On the other hand, strengthening enforcement
of IPRs, not only improves the business and investment climate, but also boosts incentives for
domestic innovation and technology transfer to developing countries. Moreover, the enforcement
of IPRs serves as a remedy to a market failure for the growing knowledge-based market and
reduces transaction cost that might arise from information asymmetries. Consumers have more
choices in product variety and quality. The diffusion of information and technology would lead
to an improvement in labor productivity and enhance economic growth.
Balancing these dynamic gains and costs that arise from strengthening IPRs is a
challenging task for policy makers. The signing of TRIPs required member nations of World
Trade Organization (WTO) to conform to a set of minimum standards in protecting and
enforcing IPRs in their countries. Each government needs to implement various policies i.e.
enforcement effectiveness, scope of protection, length of patent, trademark and copy right, etc.,
while allocates scare resources toward the patent enforcement sector i.e. training of enforcement
officer, lawyers, judges and setting up monitoring system, legal framework, etc. Extensive works
have been conducted to answer questions like who will gain and who will lose from the
strengthening IPRs protection? Is the harmonization of the standard and enforcement of IPRs a
necessary or sufficient condition for increasing global welfare and economic growth? Does IPRs
protection encourage innovation and R&D investment? What determine the incentive for patent
protection? In the second chapter, we developed a simple dynamic closed-economy model to
examine the effect of various factors on the resources used in patent enforcement activities which
is represented by the probability of patent enforcement.
Various studies have examined the effects of patent protection on the income distribution,
innovation, imitation and economic growth. Helpman (1993) developed a general-equilibrium
model of an innovative North and an imitative South. He concluded that an increase in IPRs
protection harms the South because of the change in the term of trade and a reallocation of
resource toward Northern products while the North might not necessary gain many benefits due
to an increase in product price. Glass and Saggi (2002), built a product-cycle model of
endogenous innovation, imitation and foreign direct investment (FDI), and found similar
negative results, namely that stronger IPRs in the South reduces innovation, imitation, and FDI.
Park (2002), using OEDC data on 21 countries, showed that patent protection and enforcement
stimulates private R&D. Also, Dinopoulos and Kottaridi (2006) used a North-South model with
exogenous patent enforcement and found that a move towards harmonization by the South
accelerates the long-run rates of innovation and growth, improves the global wage-income
distribution, but has an ambiguous effect on the rate of international technology transfer. In the
presence of harmonized patent policies, stricter global patent enforcement increases long-run
global growth, accelerates the rate of international technology transfer and has no impact on the
global income distribution.
The relationship between IPRs protection and economic development is indeed
complicated. Ginarte and Park (1997) constructed the index of patent rights and found that more
developed countries tend to provide stronger protection of intellectual property. He concluded
that the level of Research and Development (R&D) activities, market environment and
international integration are significant factors in determining the protection level. Grossman and
Lai (2004), using a North-South framework and exogenous patent enforcement, concluded that a
country with a larger market for innovative R&D, higher human capital endowments and greater
capacity to conduct R&D offers stronger IPRs protection while patent protection is weaker if a
country is close to international trade. This paper added to the literature on intellectual property
protection by introducing a resource-using endogenously determined patent- enforcement
mechanism and therefore provides a novel link between patent length and the degree of patent
enforcement.
Closed-Economy Model
In this chapter, we developed a closed-economy model with an exogenous rate of
population growth. The model is based on the quality-ladder framework where the quality
leaders invent new products and receive a finite-length patent with some probability of patent
enforcement. This paper contributed to the existing literature on growth and intellectual property
protection by introducing resource-using and thus endogenous patent enforcement and by
studying the relationship between patent enforcement and the long run rates of innovation and
economic growth.
Household Sector
The demand side of the economy is generated by dynastic households with infinitely lived
members. Each household member is endowed with one unit of labor which is supplied
inelastically to the market. The size of each household grows exponentially at the rate of n > 0,
where new household members are born continually. We normalized the initial size of each
household to unity for simplification; therefore, the number of household members at time t is
e"t. Let L(t) = Le"' denote the level of population and the supply of labor at time t, where L is
the initial level of population.
There is a continuum of industries indexed by B E [0,1]. Each industry produces a final
consumption good of different quality levels which are indexed by j, where j represents the
number of innovations in each industry. Let Al'8.t denote the quality increment generated by
each innovation in industry 8, where Ai > 1 captures the size of each innovation.
Each household maximizes the following discounted lifetime utility
U e P" "" nu(t)dt, (3-1)
where p > n is the constant subjective discount rate.
The instantaneous per-capita utility function at time t is defined by
In o) In4*qj0,)6 (3-2)
where q(j,0, t) denotes the quantity demanded per person of a product in industry B with
quality level A'" at time t. Equation 3-2 also implies that, all else equal, consumers prefer higher
quality products to lower quality ones. Consumers choose their consumption to maximize their
discounted lifetime utility. The consumer maximization problem can be decomposed into the
following steps: first, consumers choose to consume the product with the lowest quality-adjusted
p, (8,t)~
pnice in each industry. Then, consumers allocate their budgets across all industries by
solving the across-industry static optimization problem. The result is the following unit elastic
c(t)
demand function q(B, t) = ,where c(t)is each consumer's consumption expenditure
p (B, t)~
function at time t. Lastly, consumers solve the dynamic optimization problem as to maximize
their discounted life time utility subj ect to their intertemporal budget constraint;
maO e I c, ) +In -I p0 t (3-3)
subj ect to z(t) = w(t) + r(t):(t) c(t) nz(t) where z(t) is the level of consumer assets at
time t, w(t) is the wage rate at time t, and r(t) is the market interest rate at time t. Solving the
dynamic optimization problem yield the following differential equation
c(t)
= r(t) p (3 -4)
c(t)
The market interest rate equals the constant subj ective discount rate since per-capita
consumption expenditure is constant at the steady-state equilibrium.
Domestic Production and Patent Enforcement Sector
Labor is the only factor of production and is perfectly mobile within a country. We
assumed that the labor market is perfectly competitive and one unit of labor produces one unit of
output independently of its quality level. Therefore, each industry has a constant marginal cost
equals to the wage rate. The model followed the quality-ladder growth framework by assuming
Bertrand price competition.
A firm that discovers the-state-of-the-art product becomes a quality leader and receives a
finite patent length T > 0, with the probability of patent enforcement represent by OZE (0,1) .
oL,
Define 0Z = E, Where LE is the amount of labor employed in patent enforcement activities
and a > 0 is a parameter that captures and productivity of enforcement activities. Variable L,
represents resources used in patent enforcement activities such as training of the enforcement
officers, lawyers, judges and examiners etc., disciplining infringement, establishing legal
framework and related court procedures, seizure and destruction of counterfeit goods, setting up
responsible agency, office and institutions. We can also interpret 0Z as an effectiveness of patent
enforcement. In addition, we imposed that cr <-~ to guarantee that the probability of patent
LE
enforcement is not greater than one.
After a patent expires, products become generic and sell competitively. A quality leader
charges p, = Alw to drive out producers of generic products through limit pricing. However, if a
patent is not enforced, with a probability of 1 02, the method of production becomes general
knowledge and quality followers imitate a product and sell competitively at p, = w There is no
imitative R&D in this model since the quality followers can produce a product whenever the
production method becomes general knowledge. Quality followers receive zero economic profit.
The profit flow of the quality leader can be described by the following equation
Al-1
yir(t) = sz(t)( )cL(t) (3-5)
The profit flow is increasing in the probability or effectiveness of patent enforcement and
the quality incremental which is generated by each innovation.
Innovation Process
The basic assumption of the innovation technology is adopted from Dinopoulos et al.
(2005). Let ev"mt capture the R&D difficulty at the long run equilibrium where a is a parameter
for innovative R&D productivity and
0 is a parameter for R&D difficulty. A quality leader
hires 8, units of workers for innovative R&D activities during time interval dt and produces
at ~dt
dA, = 7,, units of new products. Define dA = C2 dAI as the aggregate flow of new products
and LA = C1C as the aggregate labor in the innovative R&D activities. We can write the
aL~dt
economy wide rate of patents as dA = e""() The long-run innovation rate can be written as
aLA(t dA(t)
A(t) = e" ,where A(t) = dt is the steady-state instantaneous flow of new products per
industry.
Define x-(t) = (v, (t) A~t) as the steady-state evolution ofx(t), where 0 < v, (t) <1 is the
measure of industries with active patents. The parameter P e (-1, 1) captures the correlation
between the patent length and Schumpeterian growth. In the steady-state equilibrium, the
measure of industries protected by patents v, (t) and the flow of patents A(t) are bounded and
must be constant over time in order to have a bounded per-capita long-run growth rate. The
steady-state value of R&D difficulty is given by x(t) = (vp)B A~ We can re-write the long-run
innovation,, rat asA~t =- a, (L(t)e-,(c). The term in square brackets is the share of
innovative R&D workers which is constant in the steady-state equilibrium.
L(t)e-w'") = Le(hV-w(t)) is also constant over time since A(t) is constant over time. Therefore, the
steady-state rate of new products can be written as
k=n
Apl =. (3-6)
The steady-state rate of new products is increasing in population growth rate n but
decreasing in the R&D difficulty parameter
the measure of industries with active patents v, depends on the value of parameter /7 .
Let V, (8, t) denote the market value of a patent at time t in industry B that can be written
V, (0, t) = 79 (t + s)e "'"ds.(37
The value of a patent is identical across industries as we assume str-uctural symmetry.
Substituting the profit function of a quality leader from Equation 3-5 and integrating Equation 3-
7 yields the steady-state market value of a patent
Vi-i (t =Ot) cnt (3-8)
At the steady-state equilibrium, the value of a typical patent is increasing in the patent
length T, the quality increment Ai, the population growth rate n and the probability of patent
enforcement DZ. The value of a patent is inversely related to the subj ective discount rate p For
l-e-(p-n)T
simplicity, define gr(T) = to capture the effect of patent length and the effective
p-n
discount rate on the value of the patent.
In order to derive an equilibrium condition, we first considered the innovative R&D sector.
af ,dt
The market value of any innovative R&D activities can be written as V dAI = V il The
cost of innovation is (1 z, )we,dt where z, > 0 is an ad-volarem subsidy to R&D innovation.
The discounted net profits in the R&D sector can be written as [V,ae-"' (1- r )w r,dt We
assumed free entry into innovative R&D activities which leads to a zero profit condition in this
sector. The following equation provides the condition that the marginal product of labor in
innovative R&D equals the subsidy-adjusted wage rate of labor.
ViaeVLt = (1- 2)w (3 -9)
To find the closed economy innovative R&D condition, we substitute the steady-state value
of a patent from Equation 3-8
DacL p(r() =(1- r )w (3-10)
The innovative R&D condition shows a negative relationship between per-capita
consumption expenditure and the probability of patent enforcement. The intuition behind this
condition could be that as the effectiveness of patent enforcement increases, counterfeit good is
substantially reduced while, the price of product increases. Consumer has to reduce their
consumption.
Domestic Labor Market
The demand for labor comes from four activities which include innovative R&D L ,
patent enforcement LE,, and manufacturing of the-state-of-the-art product and generic products.
The demand for innovative R&D labor can be derived from substituting the steady-state value of
R&D difficulty into the long-run innovative rate which yields the demand for innovative R&D
Aeil' ) c(t)
labor as L, (t) = Each quality leader produces L(t) units of new products. The
c(t)
demand for labor in manufacturing new product equals vp L(t) The demand for labor in
producing generic products is vc ,t L(t), where v, is a measure of industries producing
generics product. This assumptions implies that v, + v, = 1 Setting aggregate demand equal to
aggregate supply for labor, we derive the full- employment condition as
Ae "i~i") c(t) c(t)
L(t) = -+v, L(t) + (1 v, ) L(t) +LE(t) (3-11)
Substituting the steady-state rate of innovation A = an iiigevr emb
L(t) gives us the per-capita fudl-employment condition
n c(t) c(t) c(t) LE t
1= + + v, +~ (3-12)
ap~L (vp)B P A~ w w L(t)
Steady-State Equilibrium
In the steady-state equilibrium, the measure of industries with an active patent depends not
only on patent length but also the probability of patent enforcement.
v, = JAds = A T (3-13)
Substituting the steady-state rate of new products, the steady-state solution for the measure
of industries with active patents can be written as
Pv =iT 1 (3-14)
We imposed the parameter restriction nT < p to ensure that the measure of industries with
patents protection is less than unity. This restriction holds for large values of parameter p .
According to Equation 3-14, the measure of industries with a quality leader increases with the
population growth rate n, patent length T and the probability or strength of patent
enforcement 0Z It is inversely related to the R&D difficulty parameter p .
We now rewrite the steady-state solution for the rate of innovation or the flow of patent as
A = (RT)(l+p) (3-15)
The long-run innovation rate is increasing in the rate of population growth n but decreasing
in R&D difficulty parameter 9 patent length T, and enforcement probability 0Z This result
based on the assumption that /7 > 0, where patents reduce the flow of spillovers knowledge and
create more difficulty to innovative R&D activities.
To solve for the steady-state equilibrium solution, we normalized the wage rate equal to
unity. Substituting the steady-state solution of the measure of industries with patents from
Equation 3-14 and using the definition of the probability of patent enforcement, we can rewrite
the per-capita full-employment condition as
nZ )'+ (Tn)i p n TOZ ''P 1-i A
1= +c+-. (3-16)
Performing computer simulations by using value of parameters similarly to Dinopoulos
and Segerstrom (1999) and Sener (2006), we find that there is a negative relationship between
per-capita consumption and the probability of patent enforcement. This relationship is based on
the per-capita full-employment condition (Equation 3-16). We can plot the innovative- R&D
condition (Equation 3-10) and the per-capita full-employment condition (Equation 3-16) in order
to solve for both the per-capital consumption expenditure and the probability of patent
enforcement as in Figure 3-1. The equilibrium now depends on all parameters in the model
including those which are related to policy changes.
Long-Run Schumpeterian Growth
To derive the long-run Schumpeterian growth, we consider the long-run growth rate of
each consumer' s utility function. At each instant in time, there are v, industries with a quality
leader. The average number of innovations in each of these industries is j(B, t) = A(t),
where A(t) denotes the economy-wide number of innovations at time t. The quantity produced by
c(t) c(t)
each quality leader equals L(t) while each quality follower produces L(t). Thus, the
instantaneous utility of a typical household member at time t is
Ino u; l(t) =l]81 In 14, cd +I 1,, c dO (3-17)
Integrating Equation 3-17 yields the level of the instantaneous utility at time t for a typical
consumer
c c
Inu~)= ~)1 +v In ]i + I (") (3-18)
At the steady-state equilibrium, all variables on the right-hand side are constant over time,
except for the number of innovations A(t) = At Differentiating the level of the instantaneous
utility with respect to time and substituting the steady-state flow of patents yields
g, Az =ln2ij Z( A! (T)M ln (3-19)
The long-run Schumpeterian growth now depends on all parameters in the model. Growth
is proportional to the rate of innovation A More importantly, the rate of innovation depends on
both patent length and the probability of patent enforcement which are governed by the
parameter fE (--1, 1) Parameter p captures the structure of knowledge spillovers. For example;
if patents decrease knowledge spillovers, that is if fE (0,1); then an increase in patent length
decreases long-run Schumpeterian growth. In addition, long-run Schumpeterian growth is
increasing in the rate of population growth and the size of innovation but decreasing in the
parameter of R&D difficulty. These results are similar to Dinopoulos et al. (2005).
Comparative Steady-State Analysis
Using computer-simulation analysis, we performed various comparative static exercises to
examine the effects of several parameters. The following proposition summarizes the main
results
Proposition 3-1. An increase in patent length increases the probability of patent
enforcement.
This result provides an important link between the patent length and patent enforcement
which has not been done in the previous literature. Most of previous literatures modeled the
probability of patent enforcement as an exogenous parameter or as a set of a policy choice from a
government. Using the definition of patent enforcement, we can see that an increase in patent
length will lead to an increase in per-capita resources devoted to patent enforcement activities.
An increase in patent length shifts up the full-employment curve while shifts down the
innovative R&D curve in Figure 3-1 and increases the probability of enforcement.
Proposition 3-2. An economy experiencing larger innovations, measured by parameter Ai,
or offering higher innovative-R&D subsidies T,, engages in stricter patent enforcement.
An increase in both the quality incremental parameter A and the subsidy to R&D sector T,
shift up the full-employment curve and shift down the innovative R&D curve in Figure 3-1. This
leads to an increase in the probability of patent enforcement. This result also conforms to the
patent rights index constructed by Ginart and Park (1997, 2002). Means of indexes of patent
right are higher among developed countries than those of developing countries. This result is
consistent with the results obtained by Grossman and Lai (2004).
Proposition 3-3. A country with the larger market size or population has a stricter patent
enforcement policy.
Using Figure 3-1, an increase in population shifts up the full-employment condition and
shifts down the innovative R&D curve which leads to a higher value of the probability of patent
enforcement. This result is also consistent with Grossman and Lai (2004) who found that a
higher relative endowment of human capital leads to an increase in the relative incentive to
protect IPRs; moreover, a larger market for innovative product enhances a government' s
incentive to grant stronger patent rights. The intuition behind this proposition is that as a country
becomes larger, a government might be able to allocate more resources toward patent
enforcement sector.
Proposition 3-4. An increase in the innovative R&D difficulty parameter
decrease in patent enforcement.
An increase in the innovative R&D difficulty shifts down the full-employment condition
curve, while the innovative R&D condition remains unchanged. This results in a decrease in the
strength or the probability of patent enforcement. The intuition is that as products become harder
to discover and produce, resources are devoted more to innovative R&D sector. A reduction in
the resources used in the enforcement sector directly affects the effectiveness of patent
enforcement.
Proposition 3-5. An increase in the strength of patent enforcement
(i) accelerates economic growth if patent increases knowledge diffusion in the economy
PE (- 1, 0)
(ii) decelerates economic growth if patent decrease knowledge diffusion in the economy
PE (0,1)
The effect of an increase in patent protection to economic growth depends entirely on the
characteristic of patent process. As some views that stronger IPRs might restrict the access to
new information and technology while others argues that the knowledge from patent application
encourages further innovation of new products and an increase in average quality of product in
the market.
Conclusion
In this chapter, we developed a simple closed-economy model using the quality ladder
framework. The model generated endogenous Schumpeterian growth and also provides an
endogenous link between the patent length and the probability of patent enforcement. The novel
result is that as the patent length increases, the probability of patent enforcement also increases.
Our finding is consistent with the previous literature in that a country with more advanced
technology or with a larger market tends to have higher probability of patent enforcement. On
the other hand, we found that the higher the difficulty in innovative R&D activity, the less the
probability or strength of patent enforcement will be. Various dimensions in this model can be
developed to answer additional question related to IPRs. It might be interesting to differentiate
wage and skill level of labor in different sectors and also to explore more on the government
budget constraint to finance the expense in the patent enforcement sector
Full-employment condition
Innovative R&D condition
Figure 3-1. Closed-economy's steady-state equilibrium
CHAPTER 4
MULTINATIONAL CORPORATIONS, PATENT ENFORCEMENT AND ENDOGENOUS
GROWTH
Introduction
A wide range of studies have examined the effects of stronger intellectual property rights
(IPRs) protection in developing countries as all WTO (World Trade Organization) members are
required to strengthen IPRs protection since the Uruguay round of multilateral trade negotiations
in 1994. Helpman (1993) concluded that a stronger IPRs protection hurts the South but benefits
the North, and increases the fraction of products that are produced by multinational corporations
(MNCs). These results are based on assumptions of a low imitation rate, factor price equalization
and a similar risk of product imitation in all type of firms. Lai (1998), assuming infinite life
patents and a higher risk of product imitation for MNCs, examined different methods of
production transfer and the effects of the strengthening of IPRs protection. He emphasized an
important of foreign direct investment (FDI) by showing that if FDI is the main channel of
production transfer, stronger IPRs protection increases the rate of product innovation, production
transfer and improves income distribution between regions. In his model, the rate of
multinationalization is based on optimization of Northern firms.
FDI has been the largest international capital inflow to developing countries in the past
decade. The tremendous increase in FDI, from $22 billion to $325 billion during 1990 to 2006
(World Bank 2007), provides additional financial resource to developing countries for achieving
higher level of economic growth and improving their living standards. Benefits and drawbacks
from FDI vary and depend on various factors including the type of investment, the level of
technology, and the pattern of knowledge diffusion as well as policies and institutions framework
in the recipient countries.
Many studies have used a North-South product cycle trade model to examine the effects of
stronger patent enforcement to FDI. Glass and Saggi (2002) found that stronger Southern IPRs
protection reduces both FDI and innovation. The main assumption behind their result is that
stronger IPRs protection in the South does not alter the expected profit stream of MNCs relative
to that of Northern firms. Branstetter et al. (2007) assumed positive knowledge spillovers and a
reduction in the costs of innovation and imitation overtime. They concluded that IPRs reform in
the South increases FDI and the rate of innovation, decreases imitation rate and improves the
income distribution between regions. These works have examined the effect of stronger IPRs
protection through the change in the cost of imitation and provided indirect link between IPRs
protection and FDI
The purpose of this paper is to analyze the effects of a change in IPRs protection policy,
globalization, and innovation technology on FDI and income distribution between the North and
the South. Our model adopted the same assumption of different risks of product imitation among
firms as in Lai (1998) and Branstetter et al. (2007). The expected discounted profit of MNCs is
directly affected by the change in the probability of patent enforcement in the South. In addition,
we assumed negative knowledge spillovers from FDI and an increase in R&D difficulty overtime
in order to remove the undesirable scale effect property. This paper contributed to the existing
literature by providing a link between FDI and patent enforcement policy and explicitly studying
the effects of a geographic expansion in the size of the South and an improvement in innovation
process on FDI and income distribution between regions.
Model
In the third chapter, we developed a two regions model of North-South trade and
Schumpeterian (R&D-based) growth with free trade. The model followed the quality-ladder
framework where Northern quality leaders invent new products and receive finite patents that are
perfectly enforceable in the North but imperfectly enforceable in the South. Northern quality
leaders have a choice to decide whether to become Multinational Corporation (MNC) in order to
take advantage of lower labor cost by moving their production to the South or to remain in the
North with lower probability of product imitation.
Consumers and Workers
Each region consists of a fixed measure of dynastic households with infinitely lived
members. Each household member is endowed with one unit of labor which is supplied
inelastically to the market. The size of each household grows exponentially at the exogenous rate
of n > 0, where new household members are born continually. We normalized the initial size of
each household to unity for simplification; therefore, the number of household members at time t
equals e"t. Let L, (t) = L,e"' denote the level of Northern population and the supply of labor in
the North at time t, where L, is the initial level of Northern population (households). Similarly,
let Ls (t) = Lse"' denote the level of Southern population and the supply of labor in the South at
time t where Ls is the initial level of Southern population. The world population at time t is
given by L(t) = Le"' = L, (t)+ Ls (t) = (L, + Ls )e"'
The global economy consists of a continuum of industries indexed by B E [0,1]. Each
industry produces a final consumption good of different quality levels which are indexed by j,
where j represents the number of innovations in each industry. Let Aer).t denote the quality
increment generated by each innovation in industry 8, where parameter Ai > 1 captures the size
of each innovation which, by assumption, is identical across industries. Each household
maximizes the following discounted lifetime utility
U "Inu(t)dt, (4-1)
where p > n is the constant subjective discount rate.
The instantaneous per-capita utility function at time t is defined by
Inut)=I [ A ( j, 8, t) 6 (4-2)
where q(j,0, t) denotes the quantity demanded per person of a product in industry B with
quality level A'" at time t. Consumers prefer higher-quality products to lower-quality ones and
choose their consumption to maximize their discounted lifetime utility in three steps. First,
p, (8,t)
consumers choose to consume the product with the lowest quality-adjusted price in
each industry.
Then, consumers allocate their budgets across all industries by solving the across-industry
static optimization problem. The result is the following unit elastic demand function
c(t)
q(B, t) = ,(4-3)
p (B, t)~
where c(t) is each consumer' s consumption expenditure function at time t. Lastly,
consumers solve the dynamic optimization problem in order to maximize their discounted life
time utility
ma~x e "In c(t) + I~n A1'".' -In p(8, t)EI 6t (4-4)
subject to their intertemporal budget constraint z(t) = w(t) + r(t):(t) c(t) nz(t) where
z(t), w(t) and r(t) is the level of consumer assets, the wage rate and the market interest rate at
time t, respectively. Solving the intertemporal problem yields the following differential equation
c(t)
= r(t) p. (4-5)
c(t)
The market interest rate r equals the constant subjective discount rate p as per-capita
consumption expenditure c is constant in the steady-state equilibrium.
Production and Multinationalization
Labor is the only factor of production and perfectly mobile within a country. Labor
markets are perfectly competitive. One unit of labor produces one unit of output for all quality
levels of products. This assumption simplifies the model as each industry has a constant marginal
cost equal to a wage rate. The model is based on quality ladder framework and Bertrand price
competition.
A Northern frm becomes a Northern quality leader when it discovers the new state-of-the-
art product and receives a Einite patent length T > 0 which is perfectly enforceable only in the
North and imperfectly enforceable in the South. The effectiveness of patent enforcement in the
South depends on several factors including the strength of law, regulation, quality of institutions,
resources devoted to enforcement activities, etc. These factors can be captured by the probability
of enforcement which is represented by OZE (0,1) A Northemn quality leader has the following
choice: if a Northern quality leader remains in the North, it faces a lower probability of product
imitation. For simplicity, we assumed that the probability of imitation of a Northern-based firm
is zero. Therefore, a Northemn frm faces the risk of imitation only after it becomes a
multinational company. A Northern quality leader can achieve a higher level of profit by moving
its production to the South in order to take advantage of a lower Southern wage; however, once a
firm becomes a MNC, it faces a higher risk of imitation equal to 1- Z. Define r as the
probability that a firm will become a MNC. The multi-nationalization process is depicted in
Figure 4-1.
A Northern-based firm, producing the-state-of-the-art quality product j in industry B ,
charges p, = Alw, and uses a trigger price strategy to drive out of the market Northern quality
followers and Southern imitators. After the patent expires, products become generic and sell
competitively in the market. The profit flow of the Northern quality leader is
ni~ (t) = (ilw, w, )(q,L, + qsLs) where q, and qs are per-capita quantities demanded by
Northern and Southern consumers respectively. Substituting the demand function from Equation
4-3 and the Northern quality leader' s profit flow can be written as
i -1
uz,(t) = ( )(cN L,'(t)+ cs Is(t)). (4-6)
MNCs face a higher risk of imitation than a Northern-based firm. If the patent is not
enforced in the South with a probability 1- 02, a method of production becomes general
knowledge in the South. There is no imitative R&D in this model since a production method
become general knowledge in the South when there is no patents protection with the probability
of 1- DZ. Southern quality followers produce the product and sell competitively in the South at
price ps = ws. On the other hand, with a probability of patent enforcement 02, MNCs use a
trigger price strategy to drive out Northern and Southern quality followers by setting the price
equal Pa = il Assuming no Eixed cost for MNCs in the South except for production cost,
the expected profit flow of MNCs can be derived similarly as that of a Northern quality leader
where rac (t) = (ilw, ws)qL, + O2(iw, ws)qsLs Define 0i = "- > 1 as a North-South
wage gap. Substituting the unit demand function from consumer maximization problem
(Equation 4-3) the MNCs' profit flow can be written as
we~ (t) = (1 )(cNLN (t) + OZcsLs (t)) (4-7)
The profit flow of MNCs increases in the probability of patent enforcement in the South
2, the size of each innovation ii, and the wage gap between the two regions ro .
Innovation
This model adopted basic assumptions on the innovation technology from Dinopoulos et
al. (2005) where innovation process depends on the amount of labor devoted to research and
development (R&D) activity, the productivity and the difficulty of R&D. Let a be an innovative
R&D productivity parameter and let ev"'t' capture the R&D difficulty, where
0 is a
parameter. A Northern quality leader, who hires 2 units of workers for innovative R&D
at ~dt
activities during a time interval dt, produces dA, = e" a, units of the-state-of-the-art products.
Define dA = C2dAI as the aggregate flow of new products and LA, = CIC as the aggregate
labor in innovative R&D. Then, the economy wide rate of new products can be written
aL~dt dA(t)
as dA = Define A(t) = as the steady-state instantaneous flow of new products then,
ever) dt
the long-run innovation rate can be written as
A(t) = y( (4-8)
Define xi(t) = v, (t)A(t) as the steady-state evolution of R&D difficulty x(t) where
0 < vp (t) <1 is the measure of industries with active patents. We assumed that patents have
negative knowledge spillovers to innovation process. Patents reduce the flow of knowledge
spillovers. A discovery of new product becomes more difficult as more patents is being issued or
protected. The steady-state value of R&D difficulty is given by x(t) = v p~. In the steady-state
equilibrium, the flow of patents A(t) and the measure of industries with active patents v, is
constant over time for a bounded per-capita long-run growth rate. The long-run innovation rate
can be ewritte as At =, a (t)t)e-",, "' '. The term in square brackets is the share of
innovative R&D workers which is constant in the steady-state equilibrium. Moreover,
L(t)e-""(" = Le""-"""t) is constant overtime. Therefore, the steady-state rate of new product can
be written as
A = n (4-9)
The innovation rate is increasing in the population growth rate n but decreasing in the
R&D difficulty parameter p and the measure of industries with active patents v, .
To derive the equilibrium condition in the innovative R&D sector, let (8, t) denote the
market value of a patent of a Northemn-based firm at time t in industry B which can be written as
S, (, t)= 4i, (t + s)e "t'"d~s (4-10)
The value of a patent is identical across industries as we assume structural symmetry.
Substituting the profit function of a Northern-based firm from Equation 3-6 and integrating
Equation 4-10 yields the steady-state market value of a patent for a Northemn-based firm
A-1 1-e~,,r,,,- "p
illi t ( L,(t sn t (4-11)
At the steady-state equilibrium, the value of a Northemn-based firm's patent is increasing in
the patent length T, the quality increment Ai, and the population growth rate n. The value of a
patent is inversely related to the subj ective discount rate p For notation purpose, we define
ry(T) = 1-e to capture the effect of the patent length and the effective discount rate on the
p-n
value of the patent.
Similarly, we can derive Vwc (8, t) as the market value of MNCs' patent at time t in
industry B by substituting the profit function of a MNC from Equation 4-7 in Equation 4-10 and
integrating it yields the steady-state market value of a patent for a MNC
Ve~rrcit)=I 1 c,1L,(t)+ cspst) (4-12)
At the steady-state equilibrium, the value of a MNC's patent is increasing in the duration
of patent T, the quality increment ii, the population growth rate n and the probability of patent
enforcement D2. The value of a patent is inversely related to the subj ective discount rate p .
Next, we derive the zero profit condition in the innovative R&D sector. The market values
at a dt
of the innovative R&D activities can be written as V~dA, = VA yo(t) Define
VA = (1 r V, + qrar~rc as the expected market value of a patent for a Northern quality leader,
where r represents the probability that a firm becomes a MNC. The cost of innovation equal to
(1- TA N i~dt, where TA > 0 is an ad-volarem subsidy to R&D innovation. The discounted net
profits in the R&D sector can be written as ((1- 17)V + q~cvrec"a (1- rA NM, ]dt The
zero profit condition in this sector is a result of the assumption of free entry into innovative R&D
SThere are 2 ways to model international property rights enforcement and imitation. This paper models probability
of patent enforcement with an instantaneous of time where the probability ranges from 0-1. This method works well
with a finite time of patent as we assume in this paper. Another method models probability of imitation with an
exponential distribution where the probability can range from0O 00 This method is preferred if the patent duration
is infinite. See Lai (1998) for detail of the second methodology.
activities. The following equation provides the condition that the marginal product of labor in
innovative R&D equals the subsidy-adjusted wage rate of labor
[(1- q)V, + 1?1, c je (") = (1- TA N ,. (4-13)
From L, (t)e-w't) = Lge'tn-w~t) = L, and the same is hold for Ls, we substitute the steady-
state values of a patent for a Northern-based and a MNC from Equation 4-11 and Equation 4-12
into Equation 4-13 to establish the Innovative R&D condition
agr (T) r,i~ix i1\
(1 )(,, s-)A )+q cNL c~)=(-T (4-14)
Labor Markets
We assumed perfect labor mobility and full employment to prevail within each region. The
demand for labor in the North comes from two activities which include innovative R&D and
manufacturing of new products. The demand for innovative R&D labor can be derived from
substituting the steady-state value of R&D difficulty into the long-run innovative rate which
kt(cp-lv,)
yields the demand for innovative R&D labor as LA (t) = Northern quality leaders
cN (t) cs (t) c(t)
produce L, (t) + Ls (t) -L(t) units of new products, where
p, (8, t) p, (8, t) AIw,
c = (c,L, + csLs )/L is the per-capita global consumption expenditure. Setting aggregate
demand equal to aggregate supply of labor yields the Northern full- employment condition
Ae"'" c(t)L~(t)
L, (t) = -+ (4-15)
Substituting the steady-state rate of innovation A = n- and dividing every term by L(t)
v <
gives us the per-capita Northern full-employment condition
-"- + -(4-16)
L avp~L Alw,
Next, consider the Southern labor market where the aggregate demand for labor comes
from two activities which include manufacturing of MNCs' products and manufacturing of
c(t)
generic products. Each MNC produces L(t) units of new products. There are v, industries
in the South producing MNCs' product; therefore, the demand for labor for manufacturing of
MNCs' product equalsv,L~t (t) Each Southern quality follower produces L(t) c~)units of
AIw, ws
generic products. There are v, industries produce generic products in the South at each instant of
time, where v, + v, = 1 The demand for labor for manufacturing generic products is vL(t) ct
The Southern full-employment condition can be derived by setting the aggregate demand for
labor equal to the aggregate labor supply
Ls (t) = v,L(t) c~)+ vL(t) c~)(4-17)
AIw, ws
Divide the above equation by L(t) and substitute ve = 1 vp yields the per-capita .ainrl i~ n
full-employment condition,
L, v,c (1 vP )
s_-+ (4-18)
L Alw, ws
Steady-State Equilibrium
At the Steady-state equilibrium, a Northern quality leader should be indifferent between
producing in the South as a MNC and producing in the North. Therefore, the value of Northern-
based firm' s patent and those of the MNCs should be equal, where V, = VMce We can use
Equation 4-11 and Equation 4-12 to derive the M~ulti-nationalization equilibrium as
il-li-(p-n)T~ ,cL, +~cL l-(p-n)pT 1(-
]'L, + csLs 1-- (cL, + Oc=s. 4-9
Simplifying Equation 4-19, we can solve for the value of the North-South wage gap which
prevail in the Multi-nationalization equilibrium that can be written as
m = _(4-20)
A -(A 1)(c,L, + csLs
c,L, + OcsLs
The Multi-nationalization equilibrium condition establishes the link between the relative
wage and the probability of patent enforcement where an increase in the probability of patent
enforcement leads to an improvement in the relative wage between North and South. In addition,
the value of the North-South wage gap from Equation (4-20) is greater than unity. This result
contrasts to the wage equalization equilibrium in Helpman (1993). To solve for the explicit
steady-state solution of the North-South wage gap, let the wage of Southern labor be a numeraire
where ws = 1, so that ai = w, > 1 captures the North-South wage gap. The innovative R&D
condition can be rewritten as
ar (1- ) ccL, + csLs A -1)+ --- (c,\/LN + OZcsLs) = 1- T) (4-21)
Substituting the value of the North-South wage gap from Equation 4-20 into Equation 4-
21, we can solve the North-South wage gap in term of the per-capita global consumption
expenditure as
aW(T)(;1 -1)cL
m = (4-22)
To solve for the steady-state value of the global per-capita consumption expenditure, first;
we rewrite the per-capita Northern full-employment condition from Equation 4-16 and the per-
capita Southern full-employment condition from Equation 4-18 in term of the measure of
industries with active patents v,, assuming the wage in the Southern as a numeraire. Then, we
equate both full-employment conditions as
n Lc Ls 20
-~ = -1,\e L .X (4-23)
Substitute the North-South wage gap from Equation 4-20 into Equation 4-23 and let 8
denote the steady-state value of the per capital global consumption expenditure which can be
solved as
Ls L,(1-A
c = (4-24)
L,
Next, we solve for the steady-state value of the North-South wage gap by substitute the
steady-state value of the per-capita global consumption expenditure from Equation 4-24 into
Equation 4-22 and let r$ denote the steady-state value of the North-South wage gap, we have
(1- TA
LsL, -r()i-1 Ls
(1 TA Aj L
Lastly, to find the steady-state value of the measure of industries with active patents, we
solve the per-capita Northern full-employment condition (Equation 4-16) and the per-capita
Southern full-employment condition (Equation 4-18) in term of the North-South wage gap, then
we equate both full-employment condition and substitute the steady-state value of the per-capita
global consumption expenditure from Equation 4-24. Let i;, denote the steady-state value of the
measure of industries with active patents that can be solved as
L,, r (T(l-(1 r ) a3 n
LL, L +
L,
v -.(4-26)
aW(T>(;1- ) a~n
Ls IL, LsI
(T(;1- r )n
Long-Run Schumpeterian Growth
We use the long-run growth rate of each consumer' s utility function to derive the long-run
Schumpeterian growth. At each instant in time, there are v, industries with active patents and v,
industries with inactive patents. The average number of innovations in each of these industries
equals j(B, t) = A(t). The quantity produced by each quality leader in the North or by each MNC
c(t)
in the South equals L(t). each quality follower in the South produces c(t)L(t). Quality
followers in the South produce generic product in the competitive market and charge price equal
to the unit cost of production. We can derive the instantaneous utility of a typical household
member in the North at time t as
In ut) =In A" dO+ InA'"c 8 .(4-2)
Integrating Equation 4-27 yields the level of the instantaneous utility at time t for a typical
Northern consumer
Inu(t)= A(t)1nii v In c, c~loncy (4-28)
The instantaneous utility of a typical household member in the South at time t is
Inut)= InA dB+In A"cs8 (429
Integrating Equation 4-29 yields the level of instantaneous utility at time t for a Southern
consumer
In u~) = At)1n + v n In cs (4-3 0)
In the steady-state equilibrium, all variables on the right-hand side of the Equation 4-28
and Equation 4-30 are constant over time, except for the number of innovations A(t) = At .
Differentiating the level of instantaneous utility with respect to time and using the steady-state
flow of patents from Equation 4-9 yields
g, Aln A In Ai. (4-31)
The long-run growth rate is proportion to the rate of innovation which also depends on the
measure of MNCs. As we assumed an increase in R&D difficulty overtime with an increase in
the measure of industries with active patents, the measure of MNCs inversely relates to the
growth rate due to its effect to the innovation process. The long-run Schumpeterian growth now
depends on all parameters in the model as the measure of MNCs is determined within the model.
The long-run Schumpeterian growth is increasing in the rate of population growth and the size of
innovation but decreasing in the parameter of R&D difficulty.
Comparative Steady-State Analysis
We have solved the steady-state value for the North-South wage gap, the per-capita global
consumption expenditure and the measure of industries with active patents or the measure of
MNCs. Next, we performed various comparative steady-state analyses using both algebraic
calculation and computer simulation to examine the effects of several parameters to the steady-
state value of the North-South wage gap and the measure of MNCs. The following propositions
summarize the main results
Proposition 4-1. An increase in the strength of patent enforcement policy in the South
modeled as an increase in the probability of patent enforcement policy (Of ~) does not affect the
long-run level of Foreign Direct Investment and the long-run wage-income distribution between
North and South.
Proof See Equation 4-25 and 4-26.
It is interesting that the probability of patent enforcement or the effectiveness of patent
enforcement policy dose not matter to the decision of a firm to become MNCs at the steady-state
equilibrium. One explanation is the steady-state value of the relative wage that equalizes the
profit flow of the Northern-based firms and MNCs at the steady-state equilibrium. By
construction of the model, the steady-state value of relative wage between North and South
always adjusts it valued to equalize the profit flow between Northern-based firms at the steady-
state equilibrium
Proposition 4-2. A stronger intellectual property rights protection modeled as an increase
in patent length (T 1)
(i) reduces the flow of Foreign Direct Investment to the South as the measure of Multinational
Corporations in the South decline (v:, 1)
(ii) worsens the long-run wage-income distribution between the North and the South by raising
the relative wage of Northern workers (co, 1)
Proof. See Equations 4-25 and 4-26.
We provided a direct link between a patent length and a flow of FDI. These results are
consistent with Glass and Saggi (2002) and Glass and Wu (2007) where they found that stronger
IPRs protection reduces the flow of FDI but contrast with Lai (1998) and Branstetter et al.
(2007). A longer duration of a patent length enables quality leaders to enjoy longer period of
monopoly profit. This might reduce an incentive for a Northemn based firm to move their
production based to the South region since they faces higher risk of imitation and a reduction in
profit when they become MNCs. As more industries remain in the North with an increase in
patent length, the relative wage of Northern workers will increase as more demand of labor
prevail in the region. This result is consistent with Dinopoulos et al. (2005) who found that an
increase in global patent length worsens the wage-income inequality between the North and the
South.
Proposition 4-3. Globalization, viewed as a permanent increase in the size of the Southern
population (L 1)
(i) increases the flow of Foreign Direct Investment to the South as the measure of industries
with active patents in the South increase (v, 1)
(ii) worsens the long-run wage-income distribution between the North and the South by raising
the relative wage of Northemn workers (co, 1)
Proof. See Equations 4-25, 4-26 and Algebraic Details
One view of globalization is a geographic expansion in the size of the South measured by
the level of Southern population. An example of this view is the entering of China to WTO at the
end of 2001 and the trend of an increase in the openness to trade in developing countries around
the world (Wacziarg and Welch 2003). Our finding contributed to the existing literature by
adding the direct link between globalization and FDI. An increase in the size of the Southemn
market attracts more flows of FDI to the region as the demand for product increases. However,
an increase in the level of population in the South deteriorates the income distribution between
regions as more supply of labor emerges in the market and drives down the relative wage of
Southern workers. Interestingly, the model predicts a complete opposite effect for a permanent
increase in the level of the Northern population (L ?) An expansion in the size of the Northern
market holds back the flow of FDI to the South as the number of MNCs in the South
declines(v, 1) and improves the North-South wage gap as the relative wage of Northern worker
declines. The intuitive explanation is that an expansion in the size of the Northern market might
out weight the cost saving advantage of a lower-Southern wage as the supply of labor in the
North increases.
Proposition 4-4. An improvement in innovation research and development modeled as an
increase in the size of innovation (il 1), the innovative R&D productivity parameter (a 1), and
a subsidy to innovation (zA~
(i) decreases the flow of Foreign Direct Investment to the South as the measure of Multinational
Corporations in the South decline (vp 1)
(ii) worsens the long-run wage-income distribution between the North and the South by raising
the relative wage of Northern workers (co, 1)
Proof. See Equations 4-25 and 4-26.
While, most papers studied the effect of FDI to innovation rate, we used computer
simulation to analyze the effect of an improvement in the innovation process to a firms' decision
to become a MNC. An increase in the size of innovation enables Northern quality leaders to
charge a higher price and achieve a higher level of profit without moving their production to the
South. In addition, the larger innovation size in the North increases the relative wage of Northern
workers as more industries keep their production of the- state- of-the-art product in the North
which in turn increases the North-South wage gap. Other factors that encourage innovation
process such as a subsidy to innovation and an improvement in the innovative R&D productivity
also increase the North-South wage gap and decrease the flow of FDI to the South region.
Proposition 4-4. An increase in the population growth rate (n 1) increases the measure of
Multinational Corporations in the South (vp 1) and the North-South wage gap (c~ 1) while, an
increase in R&D difficulty (cp 1) has the opposite steady-state effect.
Proof. See Equations 4-25 and 4-26.
An increase in the population growth rate leads to an increase in FDI since the market sizes
in both regions expand. This induces the Northern quality leader to move their production based
to the South in order to enj oy higher level of profit. On the other hand, an increase in the level of
R&D difficulty reduces the flow of MNCs as technology transfer between regions might be more
difficult to complete. Moreover, more resources are devoted to innovative R&D sector as the
level of difficulty increase. These results are based on an assumption of negative spillovers of
patents to innovation process.
Conclusion
This paper has introduced an endogenous process of multi-nationalization into a North-
South model with a finite patent protection which is perfectly enforceable in the North but
imperfectly enforceable in the South. The main focus of the paper is to examine the steady-state
effects of patent protection policy, globalization measured as a geographic expansion of
developing countries and changes in innovation technology on the decision of becoming MNCs
and income distribution. We found that stronger IPRs protection in the South modeled as an
increase in patent length decreases the flow of FDI and also worsens the wage- income
distribution between regions. On the other hand, an increase in the size of the Southern
population accelerates FDI but also worsens the North-South wage gap due to an increase in the
supply of labor in the South. Then, we explored the effect of changes in innovation process and
concluded that an improvement in innovation technology leads to a decline in FDI to the South
and also worsens the income distribution between regions.
Further study could be extended in various areas regard patent enforcement and FDI. Trade
cost and technology transfer cost could be introduced into the present model. The structure of
knowledge spillovers from FDI to innovation is also an interesting area to explore. Lastly, a
growing trend known as South-North FDI as occurring between India and United Kingdom
(World Bank 2007) suggests that the innovation could happen not only in the North but also in
the South. A study of the effects from this phenomenon on income distribution and global
innovation is an interesting area of research.
Algebraic Details
To show that the value of the North-South wage gap in Equation 4-20 is greater than 1, let
assume
2 A 1(c,,+css)<1. (4-32)
c,L, + OcsLs
Rearranging Equation 4-32, we have
A<+A1(c,,+ss). (4-33)
c,L, + OcsLs
c,L, + csL
Equation 4-33 is true since a s> 1 from the assumption that the probability of
c,L, + OcsLs
patent enforcement is OZE (0,1) Therefore, Equation 4-32 is also true.
Next, we show the derivation of the North-South wage gap equation from Equation 4-20.
Simplifying the Multi-nationalization equilibrium condition (Equation 4-19) as
;1-1 1
,L,+ s~)=1 (-,+Oss.(-4
Rearranging Equation 4-34, we have
ii-1 c,L, + csLs
= 1 (4-35)
Ai1 c,L, + OcsLs =1 i0,
Adding both side of Equation 4-3 5 with --and rearranging Equation 4-3 5, we have
1 i -1 c,L, + csLs
ii = 1-i (cL,+~cL (4-36)
Multiplying both side of Equation 4-36 with As~i and rearranging Equation 4-36, we have
the North-South wage gap condition as in Equation 4-20.
m = (4-37)
i(~(,, ZcLc,L, + csLs
The derivation of the North-South wage gap in term of the per-capita global consumption
expenditure (Equation 4-22) can be shown by substituting the relative wage from Equation 4-20
to the left- hand side of the Innovative R&D condition (Equation 4-21).
(1- I7)(c,L, +cLsLs X; -1)+ 17 ; _1 (-8
i ic,, Zc,L,cL +csLs,
x C\ 'L. + 1cs Is)
Simplifying Equation 4-38 and rewriting it as
(1-~~cL 9) c,,+ccsA-) qA- scL Oss (4-39)
aryT[,,, +cLx ,~ c,L, + OcsLs: L +~cL
Simplifying Equation 4-39 and using the definition of the per-capita global consumption
expenditure. Then, we equate Equation 4-39 to the right-hand side of the innovative R&D
condition (Equation 4-21) as
aW(T)(A1 -1)cL
= (1- 4)m .(4-40)
Finally, we can solve the North-South wage gap in term of the per-capita global
consumption expenditure as in Equation 4-22 as
aW(T)(A1 -1)cL
m = (4-41)
To solve for the steady-state solution of the per-capita global consumption expenditure, we
rewrite the per-capita Northern full-employment condition (Equation 4-16) in term of the
measure of industries with active patents. From Equation 4-16, we have
nZ L C
-" -(4-42)
Rearranging Equation 4-42, we have
Sn \L, c
v = -(4-43)
Then, we rewrite the per-capita Southern full-employment condition (Equation 4-18) in
term of the measure of industries with active patents. First, we rewrite Equation 4-18 as
s (4-44)
Simplifying Equation 4-44, we have
E L (-m)A
s (4-45)
Rearranging Equation 4-45, we have
v s 1~li (4-46)
Next, we equate Equation 4-43 with Equation 4-46 to solve for the steady-state value of
the per-capita global consumption expenditure as
L
Lc
(4-47)
Simplifying Equation 4-47, we have
L,Ls
Lsc L,c
L AmZ-c L Am~i
(4-48)
Substituting the North-South wage gap from Equation 4-22 into Equation 4-48 as
(4-49)
L,Ls
L2c
Llary(T)(il-1)cL
L, c1r
L ilay(T)(il-1)cL
Multiplying L to both side of Equation 4-49 as
L,Ls
Lc
-L, +
aW(T)(;1 -1)cL a (T)(;1 -1)
(1- rA)n n
pa2W(T)(;1 -1)cL
(4-50)
Rearranging Equation 4-50 as
L,Ls
Lc
Ls(1-r A,)
aW(T)(;1-1)cL pa2 yT)i- lcL
L
SaW(T)(1- 1)
(4-51)
Rearranging Equation 4-51 as
[aW(T)(1- 1) ap n
1I L,Ls
cl L
Ls(1-r A,)
aW(T)(1- 1)L pa2 y(T)(l- 1)L
(4-52)
Using Equation 4-52, we can solve for the steady-state value of the per-capita global
consumption expenditure as in Equation 4-24 as
!no! 1-Am
L c
1 -
L Am
i ~n -1 i,
Ls L, (
L ary(T)(Al -1)L (a p3
c = (4-53)
(1 r ) n
L,
Next, we show the derivation of the steady-state value of the measure of industries with
active patents. First, we solve the per-capita Northern full-employment condition from Equation
4-16 in term of the North South wage gap as
i i l = - ( 4 5 4 )
Second, we solve the per capital Southern full-employment condition from Equation 4-18
in term of the North-South wage gap as
m i = L -( 1 ) ( 4 5 5 )
Then, we equate Equation 4-54 and Equate 4-55 as
s -(1- v )c = vp -"---~ (4-56)
Simplifying Equation 4-56 and moving the measure of industries with active patents to the
same side as
L, n L
s c+- -"v -cv, (4-57)
L apL L
Rearrange Equation 4-57 and solve for the measure of industries with active patents as
v I- I -1c(-8
S\ ~LnI\L
We imposed the condition L, > Ls + -- to ensure that the measure of industries with
active patents is less than unity. Substituting the steady-state value of the per-capita global
consumption expenditure from Equation 4-24 into Equation 4-58, we can solve for the steady-
state value of the measure of the industries with active patent as in Equation 4-26 as
LsL, (-r) n
Ls L ,ary(T)(l- 1)L ap n
L L
v = (4-59)
LsL,(1 ) n
L, L ary(T)(Al -1)L ( ap3
L,
Proof of Proposition 4-3 (i). By differentiate Equation 4-26 with respect to the size of the
Southern population
aWT(;1- r ) (;1- r )
d~LLsLL, Ls + L,-
av (1rn 1rn
dL L,- L,-(1- 1 WT>;- 1
x s- L, + -a3
LL -ar(1 (- r ) n
LsL Ls
L,
Proof of Proposition 4-3(ii). By differentiate Equation 4-25 with respect to the size of the
Southern population
am a(T)(;1-1) Z
aL,
L-
"aW(T)(;1-1)
a(T)(;1 -1) r
North
South
Innovation
MNC rate Production of MNCs
and (r)
Production MNCs products
of become generic
new products with probability
Figure 4-1. Multi-nationalization process in a North-South model
CHAPTER 5
CONCLUSION
We developed a closed-economy product-cycle model and the North-South product-cycle
trade models with different setting in patents protection. We found that globalization has an
adverse effect to the wage-income distribution between regions by increasing the North-South
wage gap. Moreover, with the introduction of foreign direct investment and free trade to the
model, patent protection reduces the flow of foreign direct investment to the South and also
worsens the wage-income distribution between regions. We also found the same steady-state
effects from an improvement in innovation technology to the flow of FDI and the North-South
wage gap. Lastly, we investigated various effects to the resources used in the patent enforcement
sector and found that an increase in patent length induces an increase in the resources used in
patent enforcement sector and increases the probability of patent enforcement in the country. We
concluded that economies with low productivity of R&D have weaker patent enforcement
policies and lower long-run Schumpeterian growth.
Various aspects of the models can be extended for further study. Skilled and unskilled
labors can be introduced to analyze effects to income distribution within a country. An
introduction of trade cost to the North-South model with FDI is also interesting to examine.
Further study regard welfare implication can be investigated. However, welfare analysis is
complicated due to different components that depend on various factors. It is beyond the scope of
the current model to examine the change in the discounted consumer utility overtime. See
Dinopoulos and Segerstrom (2007) for a study of the steady-state welfare analysis where they
examine the change in the steady-state utility paths before and after policies change.
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802
BIOGRAPHICAL SKETCH
Pipawin Leesamphandh was bomn in Bangkok, Thailand. She attended Bodin Decha (Sing
Singhasaenee) school from 1990-1994. She graduated from Thammasat University and received
a Bachelor of Arts in economics in 1998. After she received a Master of Arts in Intemnational
Economics and Finance from Chulalongkorn University in 1999, she began to work as a
financial analyst in the financial planning department at Kasikorn Bank. In 2001, she became a
research assistant at the Fiscal Policy Research Institute. Pipawin received a scholarship from the
Thai Govemnment to study economics and began her graduate studies at the University of
Florida, Gainesville, USA in August 2003. She specialized in international trade and economic
theory. After she graduated from the University of Florida in August 2008, she went back to
Thailand and works for the Thai government.
PAGE 1
1 PATENTS, NORTH-SOUTH TRADE AND GLOBAL GROWTH By PIPAWIN LEESAMPHANDH A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008
PAGE 2
2 2008 Pipawin Leesamphandh
PAGE 3
3 To my parents and my husband for their love and support
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4 ACKNOWLEDGMENTS First and foremost, I would like to thank my advisor, Elias Dinopoulos, for his help and guidance. He has inspired and motivated me th rough his valuable ideas and suggestions. I am grateful for his time, patience and knowledge in economics. I would like to thank my supervisory committee, David Denslow, Steven Slutsky and Ja mes Seale for their comments, suggestions and for reading my dissertation a nd attending committee meetings. Additionally, I appreciate the help and support from my fellow graduate students, office staff and professors in the Economics Department at the University of Flor ida. I thank them for making my years in Florida a memorable experien ce in my life. I am thankful for financial support from the Thai Government and for assist ance provided by the staff of the Office of Civil Service Commission. My personal gratitude goes to Dr. Kanit Sangsubhan, who encouraged me to take this journey and believe in me. Last but not least, I thank my mother (Dr. Wipawee Jamp angern) for her endless love and support, and my father (Nop Usawattanakul) w ho always believes in me. I thank my good friends (Dr. Saijit Daosukho, Dr. Kornvica Pimukmanaskit and Noppun Wongkittikraiwan) for their help and mental support. I would like to thank the Ph adungcharoen family for their kindness. Finally, I thank my beloved husband Theerapat Leesamphandh, for his love and support, for making me feel like I am at home in Florida and for always making me laugh and happy.
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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF FIGURES................................................................................................................ .........7 ABSTRACT....................................................................................................................... ..............8 CHAPTER 1 INTRODUCTION................................................................................................................. .10 2 TECHNOLOGY TRANSFER, TRADE COSTS AND ECONOMIC GROWTH................12 Introduction................................................................................................................... ..........12 Model.......................................................................................................................... ............14 Household Behavior........................................................................................................14 Production and Trade Costs.............................................................................................17 Innovative Research and Development...........................................................................20 Imitative Research and Development..............................................................................23 Labor Markets.................................................................................................................2 6 Steady-State Equilibrium....................................................................................................... .28 Schumpeterian Growth........................................................................................................... 31 Comparative Steady-State Analysis.......................................................................................33 Conclusion..................................................................................................................... .........37 Algebraic Details.............................................................................................................. ......37 3 PATENT ENFORCEMENT POLICIES AND ENDOGENOUS GROWTH.......................44 Introduction................................................................................................................... ..........44 Closed-Economy Model.........................................................................................................46 Household Sector.............................................................................................................46 Domestic Production and Patent Enforcement Sector.....................................................48 Innovation Process...........................................................................................................49 Domestic Labor Market...................................................................................................52 Steady-State Equilibrium....................................................................................................... .53 Long-Run Schumpeterian Growth..........................................................................................54 Comparative Steady-State Analysis.......................................................................................56 Conclusion..................................................................................................................... .........58 4 MULTINATIONAL CORPORATIONS, PATENT ENFORCEMENT AND ENDOGENOUS GROWTH..................................................................................................60 Introduction................................................................................................................... ..........60 Model.......................................................................................................................... ............61 Consumers and Workers..................................................................................................62
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6 Production and Multinationalization...............................................................................64 Innovation..................................................................................................................... ...66 Labor Markets.................................................................................................................6 9 Steady-State Equilibrium....................................................................................................... .70 Long-Run Schumpeterian Growth..........................................................................................73 Comparative Steady-State Analysis.......................................................................................74 Conclusion..................................................................................................................... .........78 Algebraic Details.............................................................................................................. ......79 5 CONCLUSION................................................................................................................... ....87 LIST OF REFERENCES............................................................................................................. ..88 BIOGRAPHICAL SKETCH.........................................................................................................91
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7 LIST OF FIGURES Figure page 2-1 Pricing structure of the Northern quality leaders...............................................................43 2-2 Pricing structure of the Southern quality leaders...............................................................43 3-1 Closed economys steady-state equilibrium......................................................................59 4-1 Multinationalization process in a North-South model.......................................................86
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8 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PATENTS, NORTH-SOUTH TRADE AND GLOBAL GROWTH By Pipawin Leesamphandh August 2008 Chair: Elias Dinopoulos Major: Economics We developed a North-South model with global patent protection in the presence of trade costs. The model generated endogenous Schumpeteri an growth and product-cycle trade. The first model was used to analyze the effects of gl obalization through trade liberalization and a geographic expansion in the si ze of the South. A reduction in trade costs worsens the NorthSouth income inequality by increasing the wage -gap between the two regions. Globalization has an ambiguous effect on the steady-state rate of technology transfer and has no effect on either innovation or the growth rate. Next, we built a simple general-equilibrium model of scale-invariant long-run Schumpeterian (R&D-based) growth, finite-lengt h patents, and endogenous patent enforcement policies. The latter were captu red by a probability function which depends on the government resources engaged in the enforcement of pate nts granted to firms that discover new higherquality products. An increase in the patent lengt h raises the probability of patent enforcement; this result is consistent with cross country evid ence showing that patent enforcement and patent duration are complements. In addition, the model predicted that economies with low productivity of R&D researchers have weaker patent enfor cement policies and lower long-run Schumpeterian growth.
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9 Lastly, we introduced an endogenous multi-na tionalization process into a North-South model of scale-invariant long-r un Schumpeterian growth with a finite-length patent protection. The latter is perfectly enforceable in the Nort h but imperfectly enforceable in the South. The model was used to examine the effects of inte llectual property rights po licy and globalization on Foreign Direct Investment (FDI) and the world in come distribution. The effectiveness of patent enforcement does not effect the decision of a firm to become MNCs. However, an increase in patent length reduces the flow of FDI and worsens the income distribution between regions. In addition, globalization, measured as a geographic expansion in the size of the South, increases the flow of FDI but worsens the North-South in come distribution. Lastl y, an improvement in innovation technology leads to a decline in FD I and worsens the North-South wage gap.
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10 CHAPTER 1 INTRODUCTION We developed three models to study various i ssues in international economic field such as globalization, intellectual property rights (IPRs) protection and fo reign direct investment. All models are based on similar building blocks of quality-ladder framework, finite patent length, and Bertrand price competition. Ea ch model has quality leaders w ho invent the new state-of-theart product and enjoy global monopoly profit as they sell product to the world using limit pricing. There are quality followers in each mode l with different patent protection policy. In addition, all three models are based on the sa me innovation technology where we assumed an increase in Research and Development (R&D) difficulty overtime in order to remove an undesirable scale effect pr operty from the model. The first model is a North-South product-cycl e trade model with global patents protection. We introduced trade costs into th e first model to examine the e ffect of globalization to global innovation, imitation and wage-income distribution between regions as trade costs are an integral part in the international trade flow. In the fi rst model, quality followe rs in the North produce generic products while quality leaders in the Sout h target generic products in the North for their imitative R&D. The second model is a closed-economy model with imperfect patent enforcement policy. We introduced a resource-using endogenously de termined patents-enforcement mechanism to examine the link between patent length, and vari ous factors to resources used in the patent enforcement sector. Intellectual property right s protection becomes a major sector that many countries are required to allocate their scarce resources in order to meet the minimum standard set by the agreement on Trade-Related Aspects of Intellectual Property Right (TRIPs). Quality leaders receive a finite patent with some proba bility of patents protection. There is no imitative
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11 R&D since the method of production of the newl y invented product becomes general knowledge without patents protect ion; therefore, quality follow ers can produce and sell products competitively in the market. The third model is a North-South product-cycle trade model with free trade. We introduced endogenous multi-nationalization process to inves tigate the effect of patents protection, globalization and innovation techno logy to the flow of foreign direct investment and wageincome distribution between regions. Northern qual ity leaders received patent protection that is perfectly enforceable only in the North but impe rfectly enforceable in the South. There is no imitative R&D in this model as Southern qual ity followers can produce and sell the products when there is no patents protection and the method of production becomes general knowledge. Therefore, only multi-national corporations face th e risk of imitation after they transfer their production based to the South.
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12 CHAPTER 2 TECHNOLOGY TRANSFER, TRADE COSTS AND ECONOMIC GROWTH Introduction International trade has continua lly expanded and become a large share of the world income in the past decade. This continuing trend indicat es the acceleration of gl obalization in the world economy. Globalization leads to a substantial redu ction in trade costs which include: a sharp drop in the price of communicati on due to the intense competiti on in telecommunication markets and the emergence of the intern et technology, an increase in cheaper and faster modes of transportation, and a decline in barriers to trades in goods a nd services under the General Agreement on Tariffs and Trade (GATT). The av erage tariff rate on manufactured goods in developed countries has dropped sh arply from 20 % to approximately 4 % in the past 50 years (Hill 2002) However, trade costs still remain as a si gnificant portion of inte rnational trade flow. Anderson and Wincoop (2004) estimated a 170 % ad-val orem tax equivalent of total trade costs for developed countries. We developed a simple product-cycle trade mode l that incorporates trade costs in order to analyze the effect of globalization to th e world income distribution. Trade costs can be considered as all costs incurred in getting a good to final consumers other than the marginal cost of producing the good itself which in clude costs related to transportation, policy barriers, information, contract enforcement, currency exchange ris k, regulation and local distribution. Anderson and Winc oop (2004) provided empirical st udies of trade costs and emphasized the importance of trade costs in interna tional trade flows. In general, trade costs can be classified into two main categories which ar e domestic and international trade costs. This paper emphasizes only the international trade co sts since the domestic trade costs are faced by both domestic and foreign firms.
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13 A class of North-South trade models has l ong been developed in conjunction with the development of the new growth theory starting with the pioneer work of Krugman (1979). The state-of-the-art dynamic NorthSouth models featuring endoge nous Schumpeterian (R&D-based) growth have been extensively us ed to examine various aspects of interest in the international trade and growth literatures. Di nopoulos et al. (2005) found that globalization, modeled as an increase in the size of the South, worsens the wage-income distribution between the North and the South, increases the rate of imitation and does not affect the long-run rate of innovation and growth. While, an increase in the global pa tent length worsens the wage-income inequality between the North and the Sout h, increases the rate of produc t imitation and has an ambiguous effect on the long-run Schumpet erian growth. Their main assu mptions are zero transportation cost and enforceable global patent protection. Dinopoulos and Segerstrom (2005), also assumi ng free trade and DixitStiglitz consumer preferences, concluded that gl obalization taking the form of an expansion in the size of the South, leads to less wage-income inequality betw een the Northern and the Southern workers, increases the imitation rate and speeds up the technological cha nge, while stronge r intellectual property protection has the opposit e steady-state effect. Next, Di nopoulos and Segerstrom (1999) introduced tariffs into the North-North trade mo del where workers have different skill levels. They concluded that trade liberalization reduces th e relative wage of unskilled workers, increases R&D investment, boosts the rate of technology cha nge and results in skill upgrading within each industry. Other studies relating patent protection, intellectual propert y rights and growth include Sener (2006), also assuming free trade, found that str onger intellectual propert y rights protection leads to a larger North-South wage gap and reduces the rate of innovation and imitation. In
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14 addition, more integration of the South into the world economy, taking the form of an increase in relative size of the Southern populat ion, also leads to a larger No rth-South wage gap and reduces the rate of innovation, but incr eases the rate of imitation. The contribution of this model is that we exam ined the effects of gl obalization to the wageincome inequality between the North and the So uth and the rate of in ternational technology transfer by taking into account the presence of trade costs and enforceable global patent protection. In this model, globalization takes the form of not only an increase in the size of the South, but also a reduction in international trade costs. Model We generalized the North-South model of tr ade and growth by Dinopoul os et al. (2005) by introducing international trade costs. The model followed the quality-ladder framework assuming a finite patent length and increasing R& D difficulty over time in order to remove the undesirable scale effects property. The model generated endogenous long-run Schumpeterian (R&D-based) growth which depe nds on patent length and the ra te of population growth. This study added to the existing NorthSouth trade models by explicitly studying the long-run effects of trade costs on the global wage-income ine quality and the rate of international technology transfer. Household Behavior The global economy consists of two regions: the innovating-North and the imitating-South. Both regions are assumed to have common trad e costs and identical consumers preferences. World population grows at an exogenous rate n > 0. There is a fixe d measure of dynastic households with infinitely lived members. Each household member is endowed with one unit of labor which is supplied inelastically to the market. New household members are born continually; therefore, the size of each household grows exponen tially at the rate of n > 0. We
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15 simplified the model by normalizing the initial si ze of each household to unity. The number of household members at time t is then, nte. Let nt N Ne L t L ) ( denote the level of the Northern population and the supply of labor in the North at time t, where NL is the initial level of the Northern population. Similarly, let nt S Se L t L ) ( denote the level of th e Southern population and the supply of labor in the South at time t where SL is the initial level of the Southern population. The world population at time t is given by nt S N S N nte L L t L t L e L t L ) ( ) ( ) ( ) ( There is a continuum of industries indexed by 1 0 Each industry produces a final consumption good with different quality level. Th e quality level of a pr oduct is indexed by j, where j is restricted to intege r values and represents the numbe r of innovations in each industry. Let ) (t j denote the quality level of a product in industry where 1 is the quality increment generated by each innovation which, by assumption, is identical across industries. Each household, modeled as a dynastic fa mily, maximizes the following discounted lifetime utility 0 ) () ( ln dt t u e Ut n, (2-1) where n is the constant su bjective discount rate. The instantaneous per-capita utility function at time t is defined by 1 0) ( ln ) ( ln d t j q t uj j, (2-2) where ) (t j q denotes the quantity demanded per person of a product in industry with quality level j at time t. Equation 2-2 is the standa rd quality-augmented Cobb-Douglas utility function across all industries. It also implies that consumers prefer higher quality products.
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16 The consumers problem is solved in three stages: First, each consumer considers the within-industry static optimization problem. j j qt j q ) ( max) ( (2-3) subject to jt c t j q t j p ) ( ) ( ) ( where ) ( t j p is a consumer price of product j in an industry at time t and ) ( t c is per-capita expenditure. The solution to this withinindustry optimization problem is to buy the produ ct with the lowest quality-adjusted price j jt p ) ( If two products have the same adjusted price, consumers always buy the higher-quality product. Second, consumers allocate their budgets ac ross all industries by so lving the following across-industry static optimization problem. d t qt j q 1 0 ) ( ) () ( max (2-4) subject to 1 0) ( ) ( ) ( t c d t q t p where ) (t q is per-capita quantity demanded for the lowest quality-adjusted price product in industry at time t, ) (t j is the quality index of the product with the lowest qualit y-adjusted price in industry at time t, ) (t p is the price of the product and ) (t c is per-capita consumption expenditure at time t. The solution to this static problem yields a unit elastic demand function. Grossman and Helpman (1991) provided a detail derivation of this unit el astic demand function. ) ( ) ( ) (t p t c t q (2-5)
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17 Lastly, consumers solve the dynamic optimi zation problem by substituting the demand function from Equation 2-5 into the instantaneous per capita util ity function (Equation 2-2) and maximizing discounted life time utility (Equation 2-1). dt d t p t c et j t n t c 0 1 0 ) ( ) ( ) () ( ln ln ) ( ln max (2-6) subject to an intertem poral budget constraint ) ( ) ( ) ( ) ( ) ( ) ( t nz t c t z t r t w t z ,where z(t) is the level of consumer assets at time t, w(t) is the wage rate at time t, and r(t) is the market interest rate at time t. The solution to this optimal control problem yields the following wellknown differential equation ) ( ) ( ) ( t r t c t c. (2-7) At the steady-state equilibrium, per-capita cons umption expenditure is constant. Therefore, the market interest rate equals the constant subjective discount rate. Production and Trade Costs Labor is the only factor of production and pe rfectly mobile within each region. Labor markets are perfectly competitive in both regions One unit of labor produces one unit of output independently of its quality level or location in each industry. Therefore, each industry has a constant marginal cost which is equal to the wa ge rate in each region. The model follows the quality-ladder framework and assumi ng Bertrand price competition. Only Northern producers engage in innovativ e R&D activities. A Northern firm that discovers a new product becomes a Northern qualit y leader and receives a perfectly enforceable global patent of finite duration T > 0. A Northe rn quality leader enjoys a flow of temporary monopoly profits by selling the prod uct to the world. The-state-of the-art product turns generic as its patent expires and is then produced under perfect competition. The method of production
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18 becomes general knowledge only in the North. Sout hern firms, having a cost advantage from a lower-wage rate, target generic products in th e North for imitation. A Southern firm that successfully copies a Northern product becomes a Southern quality leader and enjoys global monopoly profits until the next hi gher-quality product is discove red and a Northern quality leader replaces a copied product through limit pricing. In the steady-state equilibrium, only Southern quality leaders target generic products and only Northern quality leader s produce new products. Let Nw and Sw denote the wage in the North and the South respectively and 1 represents trade costs, where 1 is the ad-valorem tax equivalent of trade cost. If S Nw w, then imitation occurs only in the South. Also, if S Nw w then innovation takes place only in the Nort h. As a result, we assume that at the steady-state equilibrium the fo llowing condition is satisfied S N Sw w w (2-8) A Northern quality leader, producing the st ate-of-the-art quality product j in industry charges N Nw p to drive out Northern quality follo wers who produce the j-1 product. If a product j-1 has been successfully copied by a Southern firm, a Nort hern quality leader initially charges S Nw p to drive a Southern quality leader ou t of the market. Assuming the existence of substantial re-entry costs in the South, a Northern quality leader can use a trigger price strategy to charge N Nw p after a Southern quality leader exits the market. This process is illustrated in Figure 2-1. The profit flow of the Northern quality leader is derived by calculating the profit from the sale in each region using prices and costs previously described. Define L L c L c cS S N N/ ) ( as the per-capita global consumption expenditure We use the per-capita global consumption
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19 expenditure to derive the global demand for each t ype of product. The prof it flow of a Northern quality leader can be written as S S N N N N N N NL q w w L q w w ) ( whereNq and Sq are per-capita quantities dema nded by Northern and Southern consumers respectively. Substituting a demand function, previously solved in the consumer problem (Equation 2-5) by using the per-capita global consumption expenditure then, a Northern qualit y leaders profit flow can be written as ) ( ) ( ) ( ) ( ) ( 1 t cL t L t L t L t LS N N (2-9) The profit is generated from a ge neral price marked-up from its cost. An increase in trade costs reduces Northern firms profits. Trade costs impose an additional constraint on the size of each innovation. The next innovation needs to have a quality increment parameter greater than trade costs in order for a Northern qualit y leader to be prof itable in the South. (2-10) A Southern quality leader charges the limit price N Sw p* to drive its Northern competitors out of the market and charges N Sw p in the domestic market. Notice that a Southern quality leader also se lls a product at a higher price in home market in the presence of trade costs. Figure 2-2 illustrates the pricing structure in the pres ence of trade costs. The profit flow for a Southern quality leader can be written as S S S N N N S N SL q w w L q w w ) ( Define 1 S Nw w as a North-South wage gap. Substituting per-capita quantity demanded from consumer maximization problem (Equation 2-5) using the per-capita global consumption expenditure then, a Southern quality lead ers profit flow can be rewritten as
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20 ) ( 1 ) ( ) ( t cL Lt Ls t L t LN S (2-11) For a given level of the relative wage an increase in trade costs may increase or decrease a Southern quality l eaders profit, depending on the size of the population in both regions. If N SL L then the profit of a southern quality leader increases in trade costs and vice versa. The following condition guarantees positive pr ofits associated with exports for a Southern quality leader (2-12) Innovative Research and Development This model adopted basic assumptions on innovation and imitation technology from Dinopoulos et al. (2005) where the main focus is on the balanced -growth equilibrium properties of the model. This is done for both tractability and comparability. Define as an innovative R&D productivity parameter and let ) (t xecapture the R&D difficulty at long-run equilibrium where0 is a parameter. A Northern firm i produces with certainty ) (t x i ie dt dA units of the state-of-the-art quality products when it hires i units of workers for innovative R&D activities during a time interval dt. Also define i idA dA as the aggregate flow of new products and i i AL as the aggregate labor in innovative R&D activities. Then the economy wide rate of patents can be written as ) ( t x Ae dt L dA and dt t dA t A ) ( ) ( is the steady-state in stantaneous flow of new products per industry. The long-r un innovation rate can be written as ) () ( ) (t x Ae t L t A. (2-13)
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21 Define ) ( ) ( ( ) ( t A t v t xp as the steady-state evolution of ) ( t x where 1 ) ( 0 t vp is the measure of industries with active patents. The parameter ) 1 1 ( captures the correlation between the patent length and Schumpeterian growth. takes a negative value when patents enhance the innovation process by reduci ng R&D difficulty. On the other hand, takes a positive value when patents reduce the flow of knowledge spillovers and increase R&D difficulty. Lastly, 0 when there is structural symmetry across industries. In the steady-state equilibrium, the meas ure of industries protected by patents ) ( t vp is bounded and must be constant over time. The flow of patents ) ( t A is also constant over time in order to have a bounded per-capita long-run gr owth rate. The steady-state value of R&D difficulty is given by t A v t xp) ( ) ( (2-14) Differentiating Equation 2-13 with respect to labor yields, ) () (t x Ae L t A the productivity of R&D workers whic h decreases over time. This im plies that the innovative R&D labor requirement increases over time in the steady-state equilibrium. Rewrite the long-run innovation rate (Equation 2-13) as ) () ( ) ( ) ( ) (t x Ae t L t L t L t A The term in square brackets is the share of innovative R&D workers and will be cons tant in the steady-state equilibrium. Since ) ( t A is constant over time, the term )) ( ( ) () (t x tn t xe L e t L will also be constant over time. Substituting the steady-state value of R&D difficulty x(t) from Equation 2-14, the steady-state rate of new products can be written as pv n A (2-15)
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22 The steady-state rate of new products is directly related to population growth n, and inversely related to the R&D difficulty parameter and the measure of industries with Northern quality leaders raised to the power which provides the endogenous link between patent coverage and the rate of innovation A When 0 the steady-state rate of innovation is exogenous. Northern firms target generic products fo r engaging in innovative R&D activities. Let ) ( t VA denote the market value of a patent at time t in industry that can be written as T s t r N Ads e s t t V0 ) () ( ) ( (2-16) Assuming structural symmetry across all industrie s, consequently the value of a patent is identical across industries. Subs titute the Northern firms profit function from Equation 2-9, using the result from the consumer optimiza tion problem (Equation 2-7) and integrating Equation 2-16 yields the steady-state market valu e of a typical patent ) ( ) ( ) ( ) ( ) 1 ( 1 ) ( ) () (t L t L t L t L n e t cL t VS N T n A (2-17) At the steady-state equilibrium, the value of a typical patent is increasing in the patent length T, the quality increment and the population growth rate n. The value of a patent is inversely related to trade costs and the subjective discount rate A Northern firm i that hires i units of workers for innova tive R&D activities during a time interval dt produces the-state-of-the -art product with a market value of ) (t x i A i Ae dt V dA V The cost of innovation is dt wi N A ) 1 ( where 0A is an ad-volarem subsidy to R&D innovation. The discounted net pr ofits can be rewritten as dt w e Vi N A t x A) 1 () ( We
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23 assumed free entry into innovativ e R&D activities; as a result, the zero profit condition must prevail in the R&D innovation sector. The follo wing equation provides the condition that the marginal product of labor in innovative R&D equa ls the subsidy-adjusted wage rate of labor. N A t x Aw e V ) 1 () ( (2-18) Substitute the steady-state value of patent AV from Equation 2-17 and the steady-state value of R&D difficulty ) ( t x from Equation 2-14, we have ) (t xe ) ( ) ( ) ( ) ( ) 1 ( 1 ) () (t L t L t L t L n e t cLS N T n =N Aw ) 1 ( (2-19) From N t x tn N t x NL e L e t L )) ( ( ) () ( the innovative R&D condition can be obtained as L L L L n e L cS N T n ) 1 ( 1) (=N Aw ) 1 ( (2-20) The innovative R&D condition shows a positiv e linear relationship between per-capita global consumption expenditure and the Northern wage rate. As per-capita global consumption expenditure increases, the innovati on price increases. In order to restore the zero profit condition for net discounted profit, the wage of Northern workers need to be increased. Imitative Research and Development Assume that the process of imitation is endogenous and depe nds on the amount of workers used. Also, assume that products become more difficult to copy as the population increases. Southern firms target generic products for im itative R&D activity. A Southern firm j hires j units of workers for imitative R&D during time interval dt and succeeds in copying ) ( t L dt dMj j units of generic products, where is an imitative productivity parameter. Define
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24 j j Mt L ) ( as the aggregate labor devoted to R&D imitation. The economy wide rate of imitation can be written as ) ( ) ( ) ( t L t L t MM (2-21) where dt dM M and j jdM dM. The aggregate rate of imitation depends on the share of labor devoted to imitative R&D. Let ) ( t VM denote the expected discounted profit of a successful imitator j of a product in industry at time t. A Southern firm j hires j units of workers for imitative R&D during time in terval dt and succeeds in copying ) ( t L dt dMj j units of generic products with a market value of ) ( ) ( ) ( t L dt t V dM t Vj M j M At the same time interval, the cost of imitative R&D equals the subsidy-adjusted wage dt wi S M) 1 ( where M is an ad-valorem subsidy to imitative R&D. Al so, we assumed that there is free entry into imitative R&D activities which leads to the zer o profit condition in the imitative R&D sector. The following imitative R&D condition can be obtain ed where a firm hires labor until the value of the marginal product of labor devoted to imitative R&D equals the subsidy-adju sted wage in the South S M Mw t L V ) 1 ( ) ( (2-22) To find expected discounted profit MV, we use no arbitrage condition and a stock market valuation of a Southern monopoly profit. Denote Nv as a measure (and set) of industries with Northern quality followers, Sv as a measure of industries with a Southern quality leader and Pv as a measure of industries with a Northe rn quality leader. We assume that 1 S N Pv v v
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25 During the time interval dt, a Sout hern firm which does not have pa tent protection faces a risk of default from a creative-destruction pr ocess with instanta neous probability N Sv v dt t A ) (. The generic product can be replaced by the discovery of a hi gher-quality product in the North. Then, a Southern quality leader suffers a loss equal to (MV 0). If there is no discovery of the next higher-quality product, a Southern firm receives a capital gain equal to dt V dVM M Therefore, the no arbitrage condition is dt t r dt v v A V V dt v v A dt V V dt VN S M M N S M M M S) ( 0 1 (2-23) The first term in the left-hand side represents a dividend from investi ng in the stock of an imitative R&D firm. The second term denotes the cap ital gain when there is no discovery and the last term denotes the capital loss if there is a discovery of a new higher-quality product. The right-hand side is a riskless rate of return. Taking limits as dt approaches zero and solving for the market value of a Southern quality leader yields M M N S S MV V v v A r V (2-24) Substitute a Southern profit (Equation 2-11) into Equation 2-24. In the steady-state equilibrium, ) (t r and n V VM M ; therefore, the Southern market value can be written as n v v A t cL t L t L t L t L t VN S S N M ) ( ) ( ) ( 1 ) ( ) ( ) (. (2-25)
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26 Substituting Equation 2-25 into the zero pr ofit condition (Equation 2-22) yields the imitative R&D condition n c w L L L LS M S N ) 1 ( 1, (2-26) where N Sv v A is the risk of default for a Southern quality leader. Labor Markets We assumed prefect labor mobility and full empl oyment to prevail within each region. The demand for labor in the North comes from th ree activities which in clude innovative R&D, manufacturing of new products a nd manufacturing of generic produc ts. First, one could derive the demand for innovative-R&D labor by substitu ting the steady-state va lue of R&D difficulty (Equation 2-14) into the long-run innovation rate (Equation 2-13). These substitutions yield the following expression for innovative-R&D labor ) () (pv A t Ae A t L Second, each Northern quality leader produces ) ( ) ( ) ( ) ( ) ( ) (*t L t p t c t L t p t cS N S N N N units of new products. Substitute the price N Nw p and N Nw p yields the quantity produced as ) ( ) ( t L w t cN. There are Pv industries producing new products; th erefore, the demand for labor in manufacturing new products equals ) ( ) ( t L w t c vN p. Using the same method ology and noticing that there are Nv industries producing gene ric products in the North, the demand for labor in manufacturing of generic pr oducts can be written as ) ( ) ( ) ( ) ( ) ( ) ( t L t L t L t L w t L t c vS N N N. The Northern
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27 full-employment condition can be derived from setting the aggregate demand equal to the aggregate supply ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) () (t L t L t L t L w t L t c v w t L t c v e A t LS N N N N p v A t Np (2-27) Substitute the steady-state rate of new product pv n A and divide Equation 2-27 by L(t). results in the per-capita Northern full-emp loyment condition which can be written as L L L L w c v w c v L v n L LS N N N N p p N (2-28) Next, we considered the Southern labor ma rket. The aggregate demand for labor comes from two activities which are imitative R&D and manufacturing of generic products. Using Equation 2-21, the demand for imitative R&D labor can be written as ) ( ) ( t L M t LM Each Southern quality leader produces ) ( ) ( ) ( ) ( ) ( ) ( t L t L t L t L w t L t cS N N units of generic products. There are Sv industries copying generic product s in the South at each instan t of time. The Southern fullemployment condition can be de rived by setting the aggregate demand for labor equal to the aggregate labor supply ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( t L t L t L t L w t L t c v t L M t LS N N S S (2-29) Dividing Equation 2-29 by L(t), the per-capita Southern fu ll-employment condition is L L L L w c v M L LS N N S S (2-30)
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28 Steady-State Equilibrium We focused on the balanced growth equilibrium in which each variable grows at a constant rate over time. Variables that are constant in th e steady-state equilibrium are the market interest rate r, per-capita global consumption expenditure c, all product prices, wage rates Nw and Sw the rate of innovation A, the rate of imitation M the measure of industries with a Northern quality leader Pv, the measure of industries with Nort hern firms producing generic products Nv and the measure of industries w ith a Southern quality leader Sv Variables that grow at the constant rate of population growth rate include quantities produ ced, labor allocated to various activities, the flow of Southern and Northern profits and the market value of quality leaders. To solve for the steady-state equilibrium solu tion, let the wage of Southern labor be a numeraire 1 Sw so that 1 Nw captures the North-South wage gap. In the steady-state equilibrium, the measure of industries with a Nort hern quality leader is related to the strictly positive patent length as T A ds A vT p 0. (2-31) Since patent protection is finite and the rate of patents is c onstant overtime, the measure of industries with active patents protection is equal to the rate of innovation times the patent length 0 T. Substituting the steady-state rate of ne w product (Equation 2-15), the steady-state solution for the measure of industries with a Northern quality leader can be obtained as 1 1Tn vp. (2-32) We imposed the condition Tn to ensure that the measure of industries with patent protection is less than un ity. The fraction of industries with a No rthern quality lead er increases in
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29 the rate of population growth a nd the patent length. Substituti ng Equation 2-32 to Equation 2-15, we rewrite the steady-state solution for the rate of global innovation whic h equals the flow of patents as ) 1 ( ) 1 ( 1 T n A (2-33) The long-run rate of global innovation is incr easing in the rate of population growth and decreasing in the R&D difficulty parameter An increase in the parameter raises the level of R&D difficulty and reduces the rate of innova tion. The relationship between the long-run rate of global innovation and the patent period depends on the parameter Denote variables with a hat ) (^ as the long-run equilibrium value of endogenous variables. The explicit steady-state soluti on for all variables can be so lved using the innovative R&D condition (Equation 2-20) and the imitative R&D condition (Equation 2-26). The steady-state value of global per-capita consumption expenditure can be written as ) ( ) 1 ( ) ( 1 1 1 ) 1 )( ( S N M S N S N S N T n AL L L n L L L L L L e n c .(2-34) The steady-state value of the North-South wage gap can be written as S N S N S N S N T n A ML L L L L L L L e n n L 1 1 ) ( ) ( 1 1 ) (, (2-35) where pv A 1 is the risk of default for a Southern quality leader. Substitute the steadystate solution for the measure of industries with a Northern quality l eader (Equation 2-32) and the rate of global innovation or th e flow of patents (Equation 2-33) can be written as
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30 1 1 11 1 Tn T. (2-36) The long-run North-South wage gap is increasin g in factors that enhance the process of innovation including the productivi ty of innovative R&D labor the subsidy to innovative R&D A and the magnitude of innovations On the other hand, th e long-run North-South wage gap is decreasing in parame ters that encourage the transfer of technology from the North to the South which includes the productivity of imitative R&D labor and the subsidy to imitative R&D M The detail calculation is provided in th e Algebraic detail sec tion. In addition, we used computer simulation analysis to check for the wage equilibr ium condition (Equation 28) that we imposed earlier and f ound that there is a range of diffe rent value of parameters that satisfied the upper and lower limit from Equation 2-8. For instance, if the subsidy to imitation or innovation is equal or close to unity, the size of innovation need to be greater than S N S NL L L L 2. However, this is just a sufficient condition but not a necessary condition for the steady-state wage condition (Equation 2-8) to hold. To solve for the steady-state value of the rate of imitation, adding the per-capita Northern full-employment condition (Equation 2-28) and the per-capita Southern full-employment conditions (Equation 2-30) then, substitute the stea dy-state solution for the measure of Northern quality leaders (Equation 2-32) L L L L Tn Tn w c M L Tn nS N N1 1 1 1 11 1 (2-37)
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31 Using the innovative R&D condition (Equation 220), the steady-state ra te of imitation can be written as S N T n A S N S NL L e n L L L Tn L L L L T n dt M d 1 ) 1 ( ) 1 ( ) 1 )( ( 1 1 ) ( 1 1 1 1 1 1 (2-38) The steady-state value of the measure of indus tries with the Southern quality leaders can also be solved using the Southern full-employment condi tion and the steady-state rate of imitation. Schumpeterian Growth To derive the long-run Schumpeterian growth, we considered the long -run growth rate of each consumers utility function. Let) ( t A denote the economy-wide number of innovations at time t, as well as the average number of innovatio ns per industry since the measure of industries is normalized to unity and all industries are struct urally identical. At each instant in time, there are pv industries with a Northern qu ality leader. The average number of innovations in each of these industries is ) ( ) ( t A t j Northern quality leader charge Np in the North and charge *Np The remaining industries S Nv v are characterized by an average number of innovations) ( ) ( t A t j Every Southern quality leader and every competitive firm in the North producing a generic product char ges a price equal to the Northern wage in the North *Sp and charges a price equal to the wage times trade costs in the South. Sp Thus, the instantaneous utility of a typical household member in the North at time t is
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32 pS Nvv v N t A N t Ad c d c t u ) ( ) (ln ln ) ( ln. (2-39) Integrating Equation 2-39 yields the level of the instantaneous utility at time t for a typical Northern consumer N S N N pc v v c v t A t u ln ) ( ln ln ) ( ) ( ln. (2-40) The instantaneous utility of a typical household member in the South at time t is pS Nvv v S t A S t Ad c d c t u ) ( ) (ln ln ) ( ln. (2-41) Integrating Equation 2-41 yields the level of instantaneous utility at time t for a Southern consumer S S N S pc v v c v t A t u ln ) ( ln ln ) ( ) ( ln. (2-42) In the steady-state equilibrium, all variables on the right-hand side of the Equations 2-40 and Equation 2-42 are consta nt over time, except for the number of innovations t A t A ) (. Differentiating the level of instantaneous utility with respect to time and using the steady-state flow of patents (Equation 2-33) yields ln ln) 1 ( ) 1 ( 1 T n A u u gU (2-43) The model has a steady-state equilibrium th at generates a process of Schumpeterian creative destruction which result s in product-cycle trad e, long-run scale-inva riant Schumpeterian growth and a North-South wage gap. Growth is proportional to the rate of innovation A which is equal to the steady-state flow of patents. More importantly, the rate of innovation depends on patent protection which is governed by the parameter ) 1 1 ( that captures the structure of
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33 knowledge spillovers. In the case of symmetric knowledge spillovers ) 0 ( long-run growth is exogenous. If patents d ecrease knowledge spillovers) 1 0 ( then an increase in patent protection decreases long-run Schu mpeterian growth. In contrast if patents enhance knowledge spillovers, an increase in patent protection in creases long-run Schumpet erian growth. With the imposition of trade cost, we still obtain the same properties of long-run Schumpeterian growth as in the absence of trade cost. The long-run Schumpeterian growth is increasing in the rate of population growth and the size of innovation but decreasing in th e parameter of R&D difficulty as in Dinopoulos et al. (2005). Comparative Steady-State Analysis We have solved the steady-state value for each variable of interest. In this section, we studied the long-run effects of globalization and intellectual prope rty rights. As in Dinopoulos et al. (2005), globalization is viewed as a geographic once-for-all incr ease in the size of the South measured by the level of the Southern population. The entering to World Trade Organization by China at the end of 2001 is an important exam ple of globalization in this aspect. This globalization trend is also supported by a st udy from Wacziarg and We lch (2003). They found that countries with an open trad e policy have increased significan tly from 15.6 % to 73 % of all countries in the world during 1960 to 2000. Additionally, we examined a second dimens ion of the globalization process by studying the effect of a reduction in trade costs. The invention of containeri zation technology in the shipping industry has standardized and sharply d ecreased transportation co sts all over the world. Moreover, email and internet communication re duces the cost of communication in most business transactions. As globalization beco mes prevalent, trade costs which include transportation costs, tariffs, language barriers costs, marketing cost etc. have decreased
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34 substantially. The following proposition summarizes the effects of various dimensions of globalization in which this model provided: Proposition 2-1. Globalization, viewed as a permanent decrease in trade cost () (i) worsens the long-run wage-income distribution between the North and the South by raising the relative wage of Northern workers ) ( if and only if the population size of the South is greater or equal to that of the North ) (N SL L (ii) has an ambiguous effect on the relative wage of Northern workers ?) ( if the North population is greater than those in the South ) (N SL L (iii) has an ambiguous effect on the rate of tec hnology transfer from the North to the South ?) ( M (iv) does not affect the long-run rates of innovation ) ( A and Schumpeterian growth ) ( Ug Proof. See Algebraic Details A long-run decrease in trade costs has di fferent effects depending on the size of the population in each region. Proposition 2-1 (i) tends to resemble the real world situation where most of developing nations, such as China a nd India, have more population than developed countries. The size of the populatio n can capture not only the number of people but also the size of the market in each region. The economic intuiti on behind this proposition is that as trade costs decrease, Northern quality leaders receive more profit from selling the-state-of-the-art products to the South and demand more labor which leads to an increase in the wage rate in the North. On the other hand, Southern quality leaders receive more profit from selling generic products to the North but become less profitable in the South due to a decrease in the price of generic products. Given that there is more population in the South, the profit of Southern quality leaders would decrease. Therefore, a decrease in trade costs wo uld lead to an increase in NorthSouth wage gap. However, when there is more population in the North, Northern quality leaders and Southern quality leaders both beco me more profitable; therefore, the effect on the North-South
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35 wage gap is ambiguous. In addition, the effect of trade costs to the rate of imitation is also ambiguous since a decrease in trade cost could re sult in either an increas e or a decrease in the profit of a Southern quality leader In the latter case, Southern quality leaders have less incentive to do more imitative R&D activities. Proposition 2-2. Globalization, viewed as a permanen t expansion in the size of the South ) ( SL (i) has an ambiguous effect on the long run wa ge-income distribution between North and South ?) ( (ii) has an ambiguous effect on the rate of t echnology transfer from North to South?) ( M (iii) does not affect the long-run rates of innovation ) ( A and Schumpeterian growth ) ( Ug Proof. See Equation 2-43 and Algebraic Details As population in the South increases, demand for both generic and th e-state-of-the-art products increase. The effects on the demand for la bor and the wage rate in each region depend on all parameters in the model especially, the value of trade costs, the parameter of innovation and the size of population in both regions. Theref ore, an increase in the size of developing countries has an ambiguous effect on the North-S outh wage gap and the rate of imitation. An expansion in the size of the South does not necess arily worsen the world income distribution or enhance the rate of imitation as ha s been found in previous studies. Proposition 2-3. A permanent increase in the global patent protection generated by an increase in the patent length ) ( T (i) permanently raises the rate of tec hnology transfer from North to South ) ( M if the following sufficient condition holds: 1 L L LS N.
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36 (ii) permanently increases the wage-income inequality between North and South ) ( if the following sufficient condition holds: 1 1 1 11 1 1 1 Tn T n Proof. See Algebraic Details The effect of an increase in patent lengt h and the R&D subsidy remains robust to the introduction of trade costs. The economic intuiti on of the Proposition 2-3 is that longer patent protection shifts resource away from the i nnovative R&D sector and manufacturing to the imitative R&D sector. This resource allocation re sults in a permanent increase in the rate of global imitation M Moreover, longer patent protection increases the duration that Northern quality leader enjoys the global monopoly profit and increases the risk of default for the Southern quality leader which leads to an incr ease in wage-income inequality between North and South. Proposition 2-4. The effect of a change in the subsidy to innovative R&D and imitative R&D can be summarized as follow (i) A permanent increase in th e innovative R&D subsidy ) ( Aworsens wage-income inequality) ( and raises the rate of imitation) ( M (ii) A permanent increase in the imitative R&D subsidy) ( M decreases the North-South wage gap ) ( and does not affect the rate of imitation ) ( M Proof. See Equation 2-35 and Equation 2-38 The long-run North-South wage gap is increasin g in factors that enhance the process of innovation and decreasing in parameters that enco urage the transfer of technology from North to South. The subsidy to imitative R&D activities does not affect the long-run values of the set of industries which are protected by patent, pv and the risk of default of a Southern quality leader, Therefore, it has no effect on the long -run rate of imitation in this model.
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37 Conclusion In this chapter, we develop a North-South m odel with global patent protection, endogenous growth and product-cycle trade in the presence of trade costs. The model was used to analyze the effects of globalization measured by a reduction in trade costs (cau sed by trade liberalization or technological advances in tr ansportation and communication) and a geographic expansion of developing countries. A reduction in trade costs worsens the wa ge-income distribution between regions. Trade liberalization has an ambiguous eff ect on the steady state rate of imitation and has no effect on either innovation or the growth rate. The effect of an increase in the Southern population is inconclusive in the presence of trade costs. Algebraic Details We calculated the steady-state value of No rth-South wage gap by using innovative R&D condition (Equation 2-20) and solving for pe r-capita global consumption expenditure L L L L e n L w cS N T n A N 1 1 ) )( 1 () (. (2-44) Then we used imitative R&D condition (Equati on 2-26) to solve for per-capita global consumption expenditure L L L L n w cS N S M 1 1 1 (2-45) We equated the per-capita global consumpti on expenditure c from Equation 2-44 and 2-45 and solved for the steady-state va lue of North-South wage gap S N S N S N S N A T n ML L L L L L L L n e n L 1 ) ( 1 1 ) ( 1 ) (. (2-46)
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38 Next, we performed comparative static for each variable in the model. First we differentiated the steady-state va lue of North-South wage gap (Equation 2-46) with respect to the productivity of labor in innovative R&D activity 0 1 1 ) ( ) ( 1 1 ) ( S N S N T n A ML L L L e n n L. (2-47) Then, we differentiated the steady-st ate value of North-South wage gap (Equation 2-46) with respect to the subsidy to innovative R&D activities A 0 1 1 ) ( ) ( 1 1 ) ( 2 S N S N T n A M AL L L L e n n L. (2-48) Lastly, we differentiated the steady-st ate value of North-South wage gap (Equation 246) with respect to the magnitude of innovations 0 1 ) ( ) ( 1 1 ) ( 2 2 S N T n A ML L e n n L. (2-49) We can see that the steady-state value of North-South wage gap is increasing in the productivity of labor in innovative R&D activity the subsidy to i nnovative R&D activitiesA and the magnitude of innovations On the other hand, the stead y-state value of North-South wage gap is decreasing in the productivity of labor in imitative R&D activities and the subsidy to imitative R&D activities M To show this we differentia te the steady-state value of North-South wage gap (Equation 2-46) with respect to the productivity of labor in imitative R&D activities 0 1 1 ) ( ) ( 1 1 ) ( 2 S N S N T n A ML L L L e n n L. (2-50)
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39 Then, we differentiated the steady-st ate value of North-South wage gap (Equation 2-46) with respect to the subsidy to imitative R&D activities M 0 1 ) ( ) ( 1 1 ) ( S N S N A T n ML L L L n n L e. (2-51) Next, we showed the calculation of the steadystate value of global per-capita consumption expenditure c .We solved for the North-South wage gap from innovative R&D condition (Equation 2-20) ) 1 )( ( 1 1 1A S N T nn L L e c (2-52) Using imitative R&D condition (Equation 2-26) to solve for the North-South wage gap S N M S NL L c n L L L ) 1 ( 1 1. (2-53) We equated the North-South wage gap from Equation 2-52 and 2-53 and solve for the steady-state value of per-capita global consumption expenditure ) ( ) 1 ( ) ( 1 1 1 ) 1 )( ( S N M S N S N S N T n AL L L n L L L L L L e n c .(2-54) Proof of Proposition 2-1 (i) and (ii). By differentiate Equation 2-35 with respect to trade costs, we have the following equation 2 2 2 2) )( 1 ( S N S N N S NL L L L k L k L L k where 0 1 ) ( ) ( 1 1) ( T n A Me n n L k
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40 The sign of depends on the size of labor in both re gions. If the initial population in the South is greater than or e qual to that in the North N SL L then is negative. However, if the initial population in the South is less than that in the North N SL L then can be both negative or positive. Proof of Proposition 2-1 (iii). By differentiate Equation 2-38 with respect to trade costs we can see that Mhas an ambiguous sign 1 1 1 1 2 2 2 1 1 ) (1 1 1 ) 1 ( 1 ) 1 ( 1 1 1 ( ) 1 )( ( Tn Tn L L L L L L L L L L Tn e n MS N S N S S N S T n A Proof of Proposition 2-1 (iv). By differentiate Equation 2-33 and Equation 2-43 with respect to trade costs 0 A and 0 Ug, We see that both variables are not affected by trade costs Proof of Proposition 2-2 (i). Define 0 ) ( 1 ) ( 1 1) ( n e n zT n A M the longrun Northern relative wage can be written as
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41 S N S N S N S N S NL L L L L L L L L L z 1 ) ( Differentiate the long-run Northern relative wage with respect to the Southern population 2 2 2 2 2 2 2) ( ) 1 ( ) ( 2 ) ( ) 2 ( S N N S N S S N N SL L L L L L L L L z L To determine the sign of SL the denominators of both terms are positive while, the numerator in the square br acket has ambiguous sign. 2 2 2 2) ( 2 ) ( ) 2 (S S N NL L L L ? + + The numerator of the second term is negative ) 1 (2NL<0. Given that z is positive, the sign of SL is ambiguous Proof of Proposition 2-2 (ii). We can see that the sign of SL M can not be determined by differentiate Equation 2-38 with respect to the Southern population SL 1 1 1 1 2 2 1 1 ) ( 1 2 1 1 11 1 1 ) 1 ( 1 1 ) 1 ( 1 ( 1 ) 1 ( ) 1 )( ( Tn n L L L L L L L L L L L n e n L T n L MS N S N S N S N T n A S
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42 Proof of Proposition 2-3 (i). Differentiating Equations 2-38 with respect to patent length T, we can see that T M is positive if 1 L L LS N. 1 1 ) 1 ( ) 1 ( ) 1 ( ) ( 1 ) 1 ( ) 1 ( ) 1 )( ( 1 1 1 11 1 2 ) ( 2 ) ( ) ( 1 1 1 1 1 2 1 1 1L L L Tn L L L L L e n e L L e n L L L n T L T n T MS N S N S N T n A T n S N T n A S N Proof of Proposition 2-3 (iii). For simplicity of the calculation define S N S N A ML L L L n L K 1 ) ( 1 1 and differentiate Equation 2-35 with respect to patent length 1 21 1 1 1 1 1 1 1 ) 1 1 )( ( 1 1 1 2 1 1 1 1 1 2 ) ( 1 1 1 ) ( 1 ) (T n Tn T Tn T e n Tn T n e e K TT n T n T n T is positive if 1 1 1 11 1 1 1 Tn T n
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43 Figure 2-1. Pricing structure of the Northern quality leaders Figure 2-2. Pricing st ructure of the Southe rn quality leaders South Leader sells domestically N Sw p charges N Sw p to drives out North Followers produce generic product North Leader charges N Nw p to drive out North Follower South Leader imitates j1 product charges N Nw p to drive out
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44 CHAPTER 3 PATENT ENFORCEMENT POLICIES AND ENDOGENOUS GROWTH Introduction The protection of intellectual property rights (IPRs) is one of the most debating issues in the international economic scene. Various argume nts in favor and against stronger IPRs have emerged as many believe that General Agreem ent on Trade-Related Aspects of Intellectual Property Right (TRIPs) is a rent-transfer mech anism from developing co untries to the more powerful developed nations. As each country differs in its economic fundamentals, the implementation of TRIPs poses an imbalance in social and economic development among rich and poor countries. In addition, stronger enforc ement could restrict diffusion of knowledge and competition and resulted in a higher product price. On the other hand, strengthening enforcement of IPRs, not only improves the business and invest ment climate, but also boosts incentives for domestic innovation and technology transfer to developing countri es. Moreover, the enforcement of IPRs serves as a remedy to a market failure for the growing knowledge-based market and reduces transaction cost that might arise from information asymmetries. Consumers have more choices in product variety and quality. The diffusion of inform ation and technology would lead to an improvement in labor productivity and enhance economic growth. Balancing these dynamic gains and costs that arise from strengthening IPRs is a challenging task for policy makers. The signing of TRIPs required member nations of World Trade Organization (WTO) to conform to a se t of minimum standards in protecting and enforcing IPRs in their countries. Each governme nt needs to implement various policies i.e. enforcement effectiveness, scope of protection, length of patent, trademark and copy right, etc., while allocates scare resources toward the patent enforcement sector i.e. training of enforcement officer, lawyers, judges and setti ng up monitoring system, legal fr amework, etc. Extensive works
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45 have been conducted to answer questions like who will gain and who will lose from the strengthening IPRs protection? Is the harmonization of the standa rd and enforcement of IPRs a necessary or sufficient condition for increasing global welfare and economic growth? Does IPRs protection encourage innovation an d R&D investment? What determine the incentive for patent protection? In the second chapter, we deve loped a simple dynamic closed-economy model to examine the effect of various factors on the resour ces used in patent enforcement activities which is represented by the probability of patent enforcement. Various studies have examined the effects of patent protection on the income distribution, innovation, imitation and economic growth. Help man (1993) developed a general-equilibrium model of an innovative North and an imitative S outh. He concluded that an increase in IPRs protection harms the South because of the change in the term of trad e and a reallocation of resource toward Northern products while the No rth might not necessary gain many benefits due to an increase in product pri ce. Glass and Saggi (2002), bui lt a product-cycle model of endogenous innovation, imitation an d foreign direct investment (FDI), and found similar negative results, namely that stronger IPRs in th e South reduces innovation, imitation, and FDI. Park (2002), using OEDC data on 21 countries, showed that pate nt protection and enforcement stimulates private R&D. Also, Dinopoulos and Kottaridi (2006) us ed a North-South model with exogenous patent enforcement and found that a move towards harmonization by the South accelerates the long-run rates of innovation a nd growth, improves the global wage-income distribution, but has an ambiguous effect on the rate of inte rnational technology transfer. In the presence of harmonized patent policies, strict er global patent enfor cement increases long-run global growth, accelerates the rate of international technology tran sfer and has no impact on the global income distribution.
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46 The relationship between IPRs protecti on and economic development is indeed complicated. Ginarte and Park (199 7) constructed the index of pa tent rights and found that more developed countries tend to pr ovide stronger protecti on of intellectual property. He concluded that the level of Research and Development (R&D) activities, market environment and international integration are significant factors in determining the protectio n level. Grossman and Lai (2004), using a North-South fr amework and exogenous patent en forcement, concluded that a country with a larger market for innovative R&D, higher human capital endowments and greater capacity to conduct R&D offers st ronger IPRs protection while pate nt protection is weaker if a country is close to inte rnational trade. This paper added to the literature on in tellectual property protection by introducing a resource-using e ndogenously determined patentenforcement mechanism and therefore provides a novel link between patent length and the degree of patent enforcement. Closed-Economy Model In this chapter, we developed a closed -economy model with an exogenous rate of population growth. The model is based on the quality-ladder framewor k where the quality leaders invent new products and receive a finite-length patent with some probability of patent enforcement. This paper contributed to the exis ting literature on growth and intellectual property protection by introducing resource-using a nd thus endogenous patent enforcement and by studying the relationship between patent enforcement and the long run rates of innovation and economic growth. Household Sector The demand side of the economy is generated by dynastic households w ith infinitely lived members. Each household member is endowed with one unit of labor which is supplied inelastically to the market. The size of each hous ehold grows exponentially at the rate of n > 0,
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47 where new household members are born continua lly. We normalized the initial size of each household to unity for simplification; therefore, the number of household members at time t is nte. Let nte L t L ) ( denote the level of population and th e supply of labor at time t, where L is the initial leve l of population. There is a continuum of industries indexed by 1 0 Each industry produces a final consumption good of different quality levels wh ich are indexed by j, where j represents the number of innovations in each industry. Let ) ( t j denote the quality increment generated by each innovation in industry where1 captures the size of each innovation. Each household maximizes the follo wing discounted lifetime utility 0 ) () ( lndt t u e Ut n, (3-1) where n is the constant su bjective discount rate. The instantaneous per-capita utility function at time t is defined by 1 0) ( ln ) ( ln d t j q t uj j, (3-2) where ) ( t j q denotes the quantity demanded per person of a product in industry with quality level j at time t. Equation 3-2 also implies that all else equal, consumers prefer higher quality products to lower qual ity ones. Consumers choose their consumption to maximize their discounted lifetime utility. The consumer maximization problem can be decomposed into the following steps: first, consumers choose to cons ume the product with the lowest quality-adjusted price j jt p ) ( in each industry. Then, consumers alloca te their budgets across all industries by solving the across-industry static optimization problem. The resu lt is the following unit elastic
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48 demand function ) ( ) ( ) (t p t c t q where () ctis each consumers consumption expenditure function at time t. Lastly, consumers solve th e dynamic optimization pr oblem as to maximize their discounted life time utility subject to their intertemporal budget constraint; dt d t p t c et j t n t c 0 1 0 ) ( ) ( ) () ( ln ln ) ( ln max (3-3) subject to ) ( ) ( ) ( ) ( ) ( ) (t nz t c t z t r t w t z where z(t) is the level of consumer assets at time t, w(t) is the wage rate at time t, and r(t) is the market interest rate at time t. Solving the dynamic optimization problem yield the following differential equation ) ( ) ( ) (t r t c t c (3-4) The market interest rate equals the constant subjective discount rate since per-capita consumption expenditure is constant at the steady-state equilibrium. Domestic Production and Patent Enforcement Sector Labor is the only factor of production and is perfectly mobile within a country. We assumed that the labor market is perfectly comp etitive and one unit of la bor produces one unit of output independently of its quality level. Therefore, each industry has a constant marginal cost equals to the wage rate. The model followed the quality-ladder growth framework by assuming Bertrand price competition. A firm that discovers the-state-of-the-art product becomes a quality leader and receives a finite patent length T > 0, with the probabi lity of patent enforcement represent by ) 1 0 ( Define L LE where EL is the amount of labor employed in patent enforcement activities and 0 is a parameter that captures and productivi ty of enforcement activities. Variable EL
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49 represents resources used in patent enforcement activities such as training of the enforcement officers, lawyers, judges and examiners etc., disciplining infringement, establishing legal framework and related court procedures, seizur e and destruction of counterfeit goods, setting up responsible agency, office and inst itutions. We can also interpret as an effectiveness of patent enforcement. In addition, we imposed that EL L to guarantee that the probability of patent enforcement is not greater than one. After a patent expires, products become gene ric and sell competitively. A quality leader charges w pj to drive out producers of generic produc ts through limit pricing. However, if a patent is not enforced, with a probability of 1, the method of production becomes general knowledge and quality followers imitate a product and sell competitively at w pj. There is no imitative R&D in this model since the quality followers can produce a product whenever the production method becomes general knowledge. Quality followers receive zero economic profit. The profit flow of the quality leader can be described by the following equation ) ( ) 1 )( ( ) (t cL t t (3-5) The profit flow is increasing in the probability or effectiveness of patent enforcement and the quality incremental which is generated by each innovation. Innovation Process The basic assumption of the innovation technol ogy is adopted from Dinopoulos et al. (2005). Let ) ( t xe capture the R&D difficulty at the long run equilibrium where is a parameter for innovative R&D productivity and 0 is a parameter for R&D difficulty. A quality leader hires i units of workers for innova tive R&D activities during time interval dt and produces
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50 ) ( t x i ie dt dA units of new products. Define i idA dA as the aggregate flow of new products and i i AL as the aggregate labor in the innova tive R&D activities. We can write the economy wide rate of patents as ) ( t x Ae dt L dA. The long-run innovation ra te can be written as ) () ( ) (t x Ae t L t A, where dt t dA t A) ( ) ( is the steady-state instanta neous flow of new products per industry. Define ) ( ) ( ( ) (t A t v t xp as the steady-state evolution of) (t x, where 1 ) ( 0 t vp is the measure of industries with active patents. The parameter (1,1) captures the correlation between the patent length and Schumpeterian gr owth. In the steady-state equilibrium, the measure of industries protected by patents ) (t vp and the flow of patents ) (t A are bounded and must be constant over time in order to have a bounded per-capita l ong-run growth rate. The steady-state value of R& D difficulty is given by t A v t xp) ( ) (. We can re-write the long-run innovation rate as ) () ( ) ( ) ( ) (t x Ae t L t L t L t A The term in square brackets is the share of innovative R&D workers whic h is constant in the st eady-state equilibrium. )) ( ( ) () (t x tn t xe L e t L is also constant over time since ) (t A is constant over time. Therefore, the steady-state rate of new pr oducts can be written as pv n A (3-6)
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51 The steady-state rate of ne w products is increasing in population growth rate n but decreasing in the R&D difficulty parameter The relationship between the innovation rate and the measure of industries with active patents pv depends on the value of parameter Let ) (t VA denote the market value of a patent at time t in industry that can be written as T s t r N Ads e s t t V0 ) () ( ) ( (3-7) The value of a patent is identical across i ndustries as we assume structural symmetry. Substituting the profit function of a quality leader from Equation 3-5 and integrating Equation 37 yields the steady-state ma rket value of a patent n e t cL t t VT n A ) (1 ) ( 1 ) ( ) (. (3-8) At the steady-state equilibrium, the value of a typical patent is increasing in the patent length T, the quality increment the population growth rate n and the probability of patent enforcement. The value of a patent is inversely related to the subjective discount rate For simplicity, define n e TT n ) (1 ) ( to capture the effect of pa tent length and the effective discount rate on the value of the patent. In order to derive an equilibrium condition, we first considered the innovative R&D sector. The market value of any innovative R&D activities can be written as ) (t x i A i Ae dt V dA V The cost of innovation is dt wi A) 1 ( where 0A is an ad-volarem subsidy to R&D innovation. The discounted net profits in the R&D sector can be written as dt w e Vi A t x A) 1 () ( We
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52 assumed free entry into innovativ e R&D activities which leads to a zero profit condition in this sector. The following equation provides the cond ition that the marginal product of labor in innovative R&D equals the subsidyadjusted wage rate of labor. w e VA t x A) 1 () ( (3-9) To find the closed economy innovative R&D condition, we substitute the steady-state value of a patent from Equation 3-8 w T L cA) 1 ( ) ( 1 (3-10) The innovative R&D condition shows a nega tive relationship between per-capita consumption expenditure and the probability of patent enforcement. The intuition behind this condition could be that as the effectiveness of patent enforcement increases, counterfeit good is substantially reduced while, the price of product increases Consumer has to reduce their consumption. Domestic Labor Market The demand for labor comes from four activities which include innovative R&D AL, patent enforcement EL, and manufacturing of the-state-of-t he-art product and generic products. The demand for innovative R&D labor can be deri ved from substituting the steady-state value of R&D difficulty into the long-r un innovative rate which yields the demand for innovative R&D labor as ) () (pv A t Ae A t L Each quality leader produces ) ( ) (t L w t cunits of new products. The demand for labor in manufacturing new product equals ) ( ) (t L w t c vp. The demand for labor in producing generic products is ) ( ) (t L w t c vC, where Cv is a measure of industries producing
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53 generics product. This assumptions implies that 1 C pv v. Setting aggregate demand equal to aggregate supply for labor, we derive the fullemployment condition as ) ( ) ( ) ( ) 1 ( ) ( ) ( ) () (t L t L w t c v t L w t c v e A t LE p p v A tp (3-11) Substituting the steady-state rate of innovation pv n A and dividing every term by L(t) gives us the per-capita full-employment condition ) ( ) ( ) ( ) ( ) ( ) ( 1t L t L w t c v w t c w t c v v L nE p p p (3-12) Steady-State Equilibrium In the steady-state equilibrium, the measure of industries with an active patent depends not only on patent length but also the pr obability of patent enforcement. T A ds A vT p 0 (3-13) Substituting the steady-state rate of new products the steady-state solution for the measure of industries with active pa tents can be written as 1 1nT vp. (3-14) We imposed the parameter restriction nT to ensure that the measure of industries with patents protection is less than unity. This restriction holds for large values of parameter According to Equation 3-14, the measure of indust ries with a quality lead er increases with the population growth rate n, patent length T and the probability or strength of patent enforcement. It is inversely related to the R&D difficulty parameter We now rewrite the steady-state solution for the ra te of innovation or the flow of patent as
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54 ) 1 ( ) 1 ( 1 T n A. (3-15) The long-run innovation rate is increasing in the rate of popul ation growth n but decreasing in R&D difficulty parameter patent length T, and enforcement probability. This result based on the assumption that 0 where patents reduce the flow of spillovers knowledge and create more difficulty to innovative R&D activities. To solve for the steady-state equilibrium solu tion, we normalized the wage rate equal to unity. Substituting the steady-state solution of the measure of industries with patents from Equation 3-14 and using the definition of the probabi lity of patent enforcement, we can rewrite the per-capita full-employment condition as c c nT L T n1 11 11 1 1. (3-16) Performing computer simulations by using va lue of parameters similarly to Dinopoulos and Segerstrom (1999) and Sener (2006), we find that there is a negati ve relationship between per-capita consumption and the prob ability of patent enforcement. This relationship is based on the per-capita full-employment condition (Equa tion 3-16). We can plot the innovativeR&D condition (Equation 3-10) and the per-capita full -employment condition (Equation 3-16) in order to solve for both the per-capit al consumption expenditure and the probability of patent enforcement as in Figure 3-1. The equilibrium now depends on all parameters in the model including those which are re lated to policy changes. Long-Run Schumpeterian Growth To derive the long-run Schumpeterian growth, we consider the long-run growth rate of each consumers utility function. At each instant in time, there are pv industries with a quality
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55 leader. The average number of innovations in each of these industries is ) ( ) (t A t j where) (t Adenotes the economy-wide number of innovations at time t. The quantity produced by each quality leader equals ) ( ) (t L w t c while each quality follower produces ) ( ) (t L w t c. Thus, the instantaneous utility of a typical household member at time t is pcvv t A t Ad w c d w c t u ) ( ) (ln ln ) ( ln. (3-17) Integrating Equation 3-17 yields the level of the instantaneous utility at time t for a typical consumer w c v w c v t A t uc pln ) ( ln ln ) ( ) ( ln (3-18) At the steady-state equilibrium, all variables on the right-hand side are constant over time, except for the number of innovationst A t A) (. Differentiating the level of the instantaneous utility with respect to time and substituti ng the steady-state flow of patents yields ln ln) 1 ( ) 1 ( 1 T n A u u gU (3-19) The long-run Schumpeterian growth now depends on all parameters in the model. Growth is proportional to th e rate of innovationA. More importantly, the rate of innovation depends on both patent length and the probability of pa tent enforcement which are governed by the parameter(1,1) Parameter captures the structure of knowledge spillovers. For example; if patents decrease knowledge spillovers, that is if) 1 0 ( ; then an increase in patent length decreases long-run Schumpeteria n growth. In addition, long-r un Schumpeterian growth is increasing in the rate of population growth a nd the size of innovation but decreasing in the parameter of R&D difficulty. These results are similar to Di nopoulos et al. (2005).
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56Comparative Steady-State Analysis Using computer-simulation analysis, we perfor med various comparative static exercises to examine the effects of several parameters. The following proposition summarizes the main results Proposition 3-1. An increase in patent length increases the probability of patent enforcement. This result provides an important link between the patent length and patent enforcement which has not been done in the previous literatur e. Most of previous literatures modeled the probability of patent enforcement as an exogenous parameter or as a set of a policy choice from a government. Using the definition of patent enforcem ent, we can see that an increase in patent length will lead to an increase in per-capita resources devoted to patent enforcement activities. An increase in patent length shifts up the full-employment curve while shifts down the innovative R&D curve in Figure 3-1 and incr eases the probability of enforcement. Proposition 3-2. An economy experiencing larger innovations, measured by parameter or offering higher innovative-R&D subsidies aT, engages in stricter patent enforcement. An increase in both the quality incremental parameter and the subsidy to R&D sector aT shift up the full-employment curve and shift down the innovative R& D curve in Figure 3-1. This leads to an increase in the probability of patent enforcement. This result also conforms to the patent rights index constructe d by Ginart and Park (1997, 2002). Means of indexes of patent right are higher among developed countries than those of devel oping countries. This result is consistent with the results obtai ned by Grossman and Lai (2004). Proposition 3-3. A country with the larger market size or population has a stricter patent enforcement policy.
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57 Using Figure 3-1, an increase in population shifts up the full-employment condition and shifts down the innovative R&D curve which leads to a higher value of the probability of patent enforcement. This result is also consistent with Grossman and Lai (2004) who found that a higher relative endowment of human capital leads to an increase in th e relative incentive to protect IPRs; moreover, a larger market fo r innovative product enhances a governments incentive to grant stronger patent rights. The intuition behind this proposition is that as a country becomes larger, a government might be able to allocate more resources toward patent enforcement sector. Proposition 3-4. An increase in the innovative R&D difficulty parameter leads to a decrease in patent enforcement. An increase in the innovative R&D difficulty shifts down the full-employment condition curve, while the innovative R&D condition remains unchanged. This results in a decrease in the strength or the probability of pa tent enforcement. The intuition is that as products become harder to discover and produce, resources are devoted more to innovative R&D sector. A reduction in the resources used in the enforcement sector directly affects the e ffectiveness of patent enforcement. Proposition 3-5. An increase in the strength of patent enforcement (i) accelerates economic growth if patent increases knowledge diffusion in the economy ) 0 1 ( (ii) decelerates economic growth if patent decrease knowledge diffusion in the economy ) 1 0 ( The effect of an increase in patent protecti on to economic growth depends entirely on the characteristic of patent process. As some views that stronger IP Rs might restrict the access to new information and technology while others argues that the knowledge from patent application
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58 encourages further innovation of new products an d an increase in averag e quality of product in the market. Conclusion In this chapter, we developed a simple cl osed-economy model us ing the quality ladder framework. The model generated endogenous Sc humpeterian growth a nd also provides an endogenous link between the patent length and the probability of patent enforcement. The novel result is that as the patent length increases, the probability of patent enforcement also increases. Our finding is consistent with the previous lite rature in that a count ry with more advanced technology or with a larger market tends to have higher probability of patent enforcement. On the other hand, we found that the higher the di fficulty in innovative R&D activity, the less the probability or strength of patent enforcement will be. Various dimensions in this model can be developed to answer additional question related to IPRs. It might be interesting to differentiate wage and skill level of labor in different sect ors and also to explore more on the government budget constraint to finance the expens e in the patent enforcement sector
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59 Figure 3-1. Closed-economys steady-state equilibrium 0 c 1 Full-employment condition Innovative R&D condition
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60 CHAPTER 4 MULTINATIONAL CORPORATIONS, PATENT ENFORCEMENT AND ENDOGENOUS GROWTH Introduction A wide range of studies have examined the e ffects of stronger intelle ctual property rights (IPRs) protection in developing co untries as all WTO (World Trade Organization) members are required to strengthen IPRs protection since th e Uruguay round of multilat eral trade negotiations in 1994. Helpman (1993) concluded that a stronger IPRs protecti on hurts the Sout h but benefits the North, and increases the fraction of products that are produced by mul tinational corporations (MNCs). These results are based on assumptions of a low imitation rate, factor price equalization and a similar risk of product imitation in all t ype of firms. Lai (1998), assuming infinite life patents and a higher risk of product imitation for MNCs, examined different methods of production transfer and the effects of the strengt hening of IPRs protection. He emphasized an important of foreign direct investment (FDI) by showing that if FDI is the main channel of production transfer, stronger IPRs protection incr eases the rate of pr oduct innovation, production transfer and improves income distribution be tween regions. In his model, the rate of multinationalization is based on optimization of Northern firms. FDI has been the largest intern ational capital inflow to deve loping countries in the past decade. The tremendous increase in FDI, fr om $22 billion to $325 billion during 1990 to 2006 (World Bank 2007), provides additional financial resource to developing countries for achieving higher level of economic growth and improving th eir living standards. Be nefits and drawbacks from FDI vary and depend on various factors in cluding the type of inve stment, the level of technology, and the pattern of knowledge diffusion as well as policies and institutions framework in the recipient countries.
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61 Many studies have used a Nort h-South product cycle trade model to examine the effects of stronger patent enforcement to FDI. Glass and Saggi (2002) found that st ronger Southern IPRs protection reduces both FDI and innovation. The main assumption behind their result is that stronger IPRs protection in the S outh does not alter the expected profit stream of MNCs relative to that of Northern firms. Br anstetter et al. (2007) assumed positive knowledge spillovers and a reduction in the costs of innovation and imitation ove rtime. They concluded that IPRs reform in the South increases FDI and the rate of innovation, decreases imitation rate and improves the income distribution between regions. These works have examined the effect of stronger IPRs protection through the change in the cost of imitation and provide d indirect link between IPRs protection and FDI The purpose of this paper is to analyze the e ffects of a change in IPRs protection policy, globalization, and innovation t echnology on FDI and income dist ribution between the North and the South. Our model adopted the same assump tion of different risks of product imitation among firms as in Lai (1998) and Branstetter et al. ( 2007). The expected discounted profit of MNCs is directly affected by the change in the probability of patent enforcement in the South. In addition, we assumed negative knowledge spillovers from FDI and an increase in R&D difficulty overtime in order to remove the undesirable scale effect property. This paper cont ributed to the existing literature by providing a link betw een FDI and patent enforcemen t policy and explicitly studying the effects of a geographic expansion in the si ze of the South and an improvement in innovation process on FDI and income distribution between regions. Model In the third chapter, we developed a tw o regions model of No rth-South trade and Schumpeterian (R&D-based) growth with free trade. The model followed the quality-ladder framework where Northern quality leaders invent new products and receive fi nite patents that are
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62 perfectly enforceable in the Nort h but imperfectly enforceable in the South. Northern quality leaders have a choice to decide whether to beco me Multinational Corporation (MNC) in order to take advantage of lower labor cost by moving thei r production to the South or to remain in the North with lower probabili ty of product imitation. Consumers and Workers Each region consists of a fixed measure of dynastic households with infinitely lived members. Each household member is endowed with one unit of labor which is supplied inelastically to the market. The size of each hous ehold grows exponentially at the exogenous rate of 0 n, where new household members are born conti nually. We normalized the initial size of each household to unity for simplification; theref ore, the number of household members at time t equals nte. Let nt N Ne L t L ) ( denote the level of Northern popul ation and the supply of labor in the North at time t, where NL is the initial level of Northern population (households). Similarly, let nt S Se L t L ) ( denote the level of Southern population and the supply of labor in the South at time t where SL is the initial le vel of Southern population. Th e world population at time t is given by nt S N S N nte L L t L t L e L t L) ( ) ( ) ( ) ( The global economy consists of a continuum of industries indexed by 1 0 Each industry produces a final consumption good of diffe rent quality levels which are indexed by j, where j represents the number of innovations in each industry. Let ) ( t j denote the quality increment generated by each innovation in industry where parameter 1 captures the size of each innovation which, by assumption, is identical across industries. Each household maximizes the following discounted lifetime utility 0 ) () ( lndt t u e Ut n, (4-1)
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63 where n is the constant su bjective discount rate. The instantaneous per-capita utility function at time t is defined by 1 0) ( ln ) ( ln d t j q t uj j, (4-2) where ) ( t j q denotes the quantity demanded per person of a product in industry with quality level j at time t. Consumers prefer higher-quality pr oducts to lowerquality ones and choose their consumption to maximize their discount ed lifetime utility in three steps. First, consumers choose to consume the product w ith the lowest quality-adjusted price j jt p ) ( in each industry. Then, consumers allocate their budgets across al l industries by solving the across-industry static optimization problem. The result is the following unit elastic demand function ) ( ) ( ) (t p t c t q (4-3) where ()ct is each consumers consumption expe nditure function at time t. Lastly, consumers solve the dynamic optimization problem in order to maximize their discounted life time utility dt d t p t c et j t n t c 0 1 0 ) ( ) ( ) () ( ln ln ) ( ln max (4-4) subject to their intertemporal budget constraint ) ( ) ( ) ( ) ( ) ( ) (t nz t c t z t r t w t z where z(t), w(t) and r(t) is the level of consumer assets the wage rate and the market interest rate at time t, respectively. Solving the intertemporal problem yields the following differential equation ) ( ) ( ) (t r t c t c. (4-5)
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64 The market interest rate r equals the constant subjective discount rate as per-capita consumption expenditure c is constant in the steady-state equilibrium. Production and Multinationalization Labor is the only factor of production and perfectly mobile within a country. Labor markets are perfectly competitive. One unit of labor produces one unit of output for all quality levels of products. This assumption simplifies the model as each industry has a constant marginal cost equal to a wage rate. The model is base d on quality ladder framew ork and Bertrand price competition. A Northern firm becomes a Northern quality l eader when it discovers the new state-of-theart product and receives a finite patent length T > 0 which is pe rfectly enforceable only in the North and imperfectly enforceable in the South. The effectiveness of patent enforcement in the South depends on several factors including the strengt h of law, regulation, quality of institutions, resources devoted to enforcement activities, etc. These factors can be captured by the probability of enforcement which is represented by ) 1 0 ( A Northern quality leader has the following choice: if a Northern quality leader remains in the North, it faces a lo wer probability of product imitation. For simplicity, we assumed that the probability of imitation of a Northern-based firm is zero. Therefore, a Northern firm faces the risk of imitation only after it becomes a multinational company. A Northern quality leader can achieve a higher level of profit by moving its production to the South in or der to take advantage of a lowe r Southern wage; however, once a firm becomes a MNC, it faces a high er risk of imitation equal to 1. Define as the probability that a firm will become a MNC. The multi-nationalization process is depicted in Figure 4-1.
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65 A Northern-based firm, produc ing the-state-of-t he-art quality product j in industry charges N Nw p and uses a trigger price strategy to dr ive out of the market Northern quality followers and Southern imitators. After the pate nt expires, products become generic and sell competitively in the market. The profit flow of the Northern quality leader is ) )( ( ) (S S N N N N NL q L q w w t where Nq and Sq are per-capita quant ities demanded by Northern and Southern consumers respectively. Substituting the demand function from Equation 4-3 and the Northern quality leader s profit flow can be written as ) ( ) ( ) 1 ( ) (t L c t L c tS S N N N (4-6) MNCs face a higher risk of imitation than a No rthern-based firm. If the patent is not enforced in the South with a probability 1, a method of production becomes general knowledge in the South. There is no imitative R&D in this model since a production method become general knowledge in the South when there is no patents protection with the probability of 1. Southern quality followers produce the pr oduct and sell competitively in the South at price S Sw p On the other hand, with a prob ability of patent enforcement MNCs use a trigger price strategy to drive out Northern and Southern quality followers by setting the price equalN MNCw P Assuming no fixed cost for MNCs in the South except for production cost, the expected profit flow of MNCs can be derived similarly as that of a Northern quality leader where S S S N N N S N MNCL q w w L q w w t) ( ) ( ) ( Define 1 S Nw w as a North-South wage gap. Substituting the unit demand function from consumer maximization problem (Equation 4-3) the MNCs profit flow can be written as )) ( ) ( )( 1 1 ( ) (t L c t L c tS S N N MNC (4-7)
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66 The profit flow of MNCs increases in the proba bility of patent enforcement in the South the size of each innovation and the wage gap between the two regions Innovation This model adopted basic assumptions on the innovation technology from Dinopoulos et al. (2005) where innovation pro cess depends on the amount of la bor devoted to research and development (R&D) activity, the productivity and the difficulty of R&D. Let be an innovative R&D productivity parameter and let ) ( t xe capture the R&D difficulty, where 0 is a parameter. A Northern qua lity leader, who hires i units of workers for innovative R&D activities during a time interval dt, produces ) (t x i ie dt dA units of the-state-of-the-art products. Define i idA dA as the aggregate flow of new products and i i AL as the aggregate labor in innovative R&D. Then, the economy wi de rate of new products can be written as ) (t x Ae dt L dA. Define dt t dA t A) ( ) ( as the steady-state instantaneous flow of new products then, the long-run innovation rate can be written as ) () ( ) (t x Ae t L t A. (4-8) Define ) ( ) ( ) (t A t v t xp as the steady-state evolution of R&D difficulty) (t x, where 1 ) ( 0 t vp is the measure of industries with active patents. We assumed that patents have negative knowledge spillovers to innovation process. Patents reduce the flow of knowledge spillovers. A discovery of new product becomes more difficult as more patents is being issued or protected. The steady-state valu e of R&D difficulty is given by t A v t xp) (. In the steady-state equilibrium, the flow of patents ) (t A and the measure of industries with active patents pv is
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67 constant over time for a bounded per-capita long-r un growth rate. The long-run innovation rate can be rewritten as ) () ( ) ( ) ( ) (t x Ae t L t L t L t A The term in square brackets is the share of innovative R&D workers which is constant in the steady-st ate equilibrium. Moreover, )) ( ( ) () (t x tn t xe L e t L is constant overtime. Therefore, th e steady-state rate of new product can be written as pv n A (4-9) The innovation rate is increasi ng in the population growth ra te n but decreasing in the R&D difficulty parameter and the measure of industries with active patentspv. To derive the equilibrium condition in the innovative R&D sector, let ) (t VN denote the market value of a patent of a Northe rn-based firm at time t in industry which can be written as T s t r N Nds e s t t V0 ) () ( ) ( (4-10) The value of a patent is identical across i ndustries as we assume structural symmetry. Substituting the profit function of a Northern-bas ed firm from Equation 3-6 and integrating Equation 4-10 yields the steady-st ate market value of a patent for a Northern-based firm n e t L c t L c t VT n S S N N N ) (1 ) ( ) ( 1 ) (. (4-11) At the steady-state equilibrium, the value of a Northern-based firms patent is increasing in the patent length T, the quality increment and the population growth rate n. The value of a patent is inversely related to the subjective discount rate For notation purpose, we define
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68 n e TT n ) (1 ) ( to capture the effect of the patent leng th and the effective discount rate on the value of the patent. Similarly, we can derive ) (t VMNC as the market value of MNCs patent at time t in industry by substituting the profit fu nction of a MNC from Equati on 4-7 in Equation 4-10 and integrating it yields th e steady-state market value of a patent for a MNC1 n e t L c t L c t VT n S S N N MNC ) (1 ) ( ) ( 1 1 ) (. (4-12) At the steady-state equilibrium, the value of a MNCs patent is increasing in the duration of patent T, the quality increment the population growth rate n a nd the probability of patent enforcement The value of a patent is inversely related to the subjective discount rate Next, we derive the zero profit condition in the innovative R&D sector. The market values of the innovative R&D activ ities can be written as ) (t x i A i Ae dt V dA V Define MNC N AV V V ) 1 ( as the expected market value of a patent for a Northern quality leader, where represents the probability th at a firm becomes a MNC. Th e cost of innovation equal to dt wi N A) 1 ( where 0A is an ad-volarem subsidy to R&D innovation. The discounted net profits in the R&D sector can be written as dt w e V Vi N A t x MNC N) 1 ( ) ) 1 (() ( The zero profit condition in this sector is a result of the assumption of free entry into innovative R&D 1 There are 2 ways to model international property rights enforcement and imitation. This paper models probability of patent enforcement with an instantaneous of time wh ere the probability ranges from 0-1. This method works well with a finite time of patent as we assume in this pape r. Another method models prob ability of imitation with an exponential distribution where the probability can range from 0. This method is preferred if the patent duration is infinite. See Lai (1998) for detail of the second methodology.
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69 activities. The following equati on provides the condition that the marginal product of labor in innovative R&D equals the subsidyadjusted wage rate of labor N A t x MNC Nw e V V) 1 ( ) 1 () ( (4-13) From N t x tn N t x NL e L e t L )) ( ( ) () ( and the same is hold for SL, we substitute the steadystate values of a patent for a Northern-based and a MNC from Equation 4-11 and Equation 4-12 into Equation 4-13 to establish the Innovative R&D condition N A S S N N S S N Nw L c L c L c L c T) 1 ( 1 1 1 ) ( (4-14) Labor Markets We assumed perfect labor mobility and full em ployment to prevail within each region. The demand for labor in the North comes from tw o activities which include innovative R&D and manufacturing of new products The demand for innovative R&D labor can be derived from substituting the steady-state value of R&D diffi culty into the long-run innovative rate which yields the demand for innovative R&D labor as ) () (pv A t Ae A t L. Northern quality leaders produce ) ( ) ( ) ( ) ( ) ( ) (t L t p t c t L t p t cS N S N N N = ) ( ) (t L w t cN units of new products, where L L c L c cS S N N/ ) ( is the per-capita global consump tion expenditure. Setting aggregate demand equal to aggregate supply of labor yields the Northern fullemployment condition N v A t Nw t L t c e A t Lp ) ( ) ( ) () ( (4-15) Substituting the steady-state rate of innovation pv n A and dividing every term by L(t) gives us the per-capita Northern full-employment condition
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70 N p Nw c L v n L L (4-16) Next, consider the Southern labor market where the aggregate demand for labor comes from two activities which include manufacturin g of MNCs products and manufacturing of generic products. Each MNC produces Nw t c t L) ( ) ( units of new products. There are pv industries in the South producing MNCs pr oduct; therefore, the demand for labor for manufacturing of MNCs product equals N pw t c t L v) ( ) ( Each Southern quality follower produces Sw t c t L) ( ) ( units of generic products. There are cv industries produce generic products in the South at each instant of time, where 1 c pv v. The demand for labor for manufacturing generic products is S cw t c t L v) ( ) (. The Southern full-employment condition can be derived by setting the aggregate demand for labor equal to the aggregate labor supply S c N p Sw t c t L v w t c t L v t L) ( ) ( ) ( ) ( ) ( (4-17) Divide the above equation by L(t) and substitute p cv v 1 yields the per-capita Southern full-employment condition, S P N p Sw c v w c v L L) 1 ( (4-18) Steady-State Equilibrium At the Steady-state equilibrium, a Northern qu ality leader should be indifferent between producing in the South as a MNC and producing in the North. Ther efore, the value of Northern-
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71 based firms patent and those of the MNCs should be equal, where MNC NV V We can use Equation 4-11 and Equati on 4-12 to derive the Multi-nationalization equilibrium as n e L c L c n e L c L cT n S S N N T n S S N N ) ( ) (1 1 1 1 1. (4-19) Simplifying Equation 4-19, we can solve for th e value of the North-South wage gap which prevail in the Multi-nationalization e quilibrium that can be written as ) ( 1 1S S N N S S N NL c L c L c L c (4-20) The Multi-nationalization equilibrium condition establishes the link between the relative wage and the probability of patent enforcement where an increase in the probability of patent enforcement leads to an improveme nt in the relative wage between North and South. In addition, the value of the North-South wage gap from Equa tion (4-20) is greater than unity. This result contrasts to the wage equalization equilibrium in Helpman (1993). To solve for the explicit steady-state solution of the NorthSouth wage gap, let the wage of Southern labor be a numeraire where1Sw, so that 1 Nw captures the North-South wage gap. The innovative R&D condition can be rewritten as ) 1 ( 1 1 1 ) (A S S N N S S N NL c L c L c L c T (4-21) Substituting the value of the North-South wage gap from Equation 4-20 into Equation 421, we can solve the North-South wage gap in term of the per-capita global consumption expenditure as ) 1 ( ) 1 )( (AL c T (4-22)
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72 To solve for the steady-state value of the gl obal per-capita consumpti on expenditure, first; we rewrite the per-capita Northern full-employ ment condition from Equation 4-16 and the percapita Southern full-employment condition from Equation 4-18 in term of the measure of industries with active patents pv, assuming the wage in the Southern as a numeraire. Then, we equate both full-employment conditions as 1 11c L L c L L L nS N. (4-23) Substitute the North-South wage gap from Equation 4-20 into Equation 4-23 and let c denote the steady-state value of the per capita global consumption expe nditure which can be solved as n T L n L L T L L L cA N S A N S ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( (4-24) Next, we solve for the steady-state value of the North-South wage gap by substitute the steady-state value of the per-c apita global consumption expenditure from Equation 4-24 into Equation 4-22 and let denote the steady-state value of th e North-South wage gap, we have n T L n L T L L TA N S A N S A) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 ( ) 1 )( ( . (4-25) Lastly, to find the steady-state value of the measure of industr ies with active patents, we solve the per-capita Northern full-employment condition (Equation 4-16) and the per-capita Southern full-employment condition (Equation 4-18) in term of the North-South wage gap, then we equate both full-employment condition and substitute the steady-state value of the per-capita
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73 global consumption expenditure from Equation 4-24. Let pv denote the steady-state value of the measure of industries with active patents that can be solved as n T L n L T L L L n n T L n L T L L L vA N S A N S N A N S A N S S p) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( . (4-26) Long-Run Schumpeterian Growth We use the long-run growth rate of each cons umers utility function to derive the long-run Schumpeterian growth. At each instant in time, there are pv industries with active patents and cv industries with inactive pa tents. The average number of innova tions in each of these industries equals ) ( ) (t A t j The quantity produced by each quality leader in the North or by each MNC in the South equals ) ( ) (t L t c. each quality follower in the South produces ) ( ) (t L t c. Quality followers in the South produce generic product in the competitive market and charge price equal to the unit cost of production. We can derive the instantaneous utility of a typical household member in the North at time t as pcvv N t A N t Ad c d c t u ) ( ) (ln ln ) ( ln. (4-27) Integrating Equation 4-27 yields the level of the instantaneous utility at time t for a typical Northern consumer N c N pc v c v t A t uln ln ln ) ( ) ( ln (4-28)
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74 The instantaneous utility of a typical household member in the South at time t is pcvv S t A S t Ad c d c t u ) ( ) (ln ln ) ( ln. (4-29) Integrating Equation 4-29 yields the level of instantaneous utility at time t for a Southern consumer S c S pc v c v t A t uln ln ln ) ( ) ( ln (4-30) In the steady-state equilibrium, all variable s on the right-hand side of the Equation 4-28 and Equation 4-30 are consta nt over time, except for the number of innovationst A t A) (. Differentiating the level of instantaneous utility with respect to time and using the steady-state flow of patents from Equation 4-9 yields ln ln p Uv n A u u g (4-31) The long-run growth rate is proportion to the rate of innovation which also depends on the measure of MNCs. As we assu med an increase in R&D difficulty overtime with an increase in the measure of industries with active patents, the measure of MNCs i nversely relates to the growth rate due to its effect to the innovation process. The lo ng-run Schumpeterian growth now depends on all parameters in the model as the measure of MNCs is determined within the model. The long-run Schumpeterian growth is increasing in the rate of population growth and the size of innovation but decreasing in the parameter of R&D difficulty. Comparative Steady-State Analysis We have solved the steady-state value for th e North-South wage gap, the per-capita global consumption expenditure and the measure of indu stries with active patents or the measure of MNCs. Next, we performed various comparativ e steady-state analyses using both algebraic
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75 calculation and computer simulation to examine th e effects of several parameters to the steadystate value of the North-South wage gap and the measure of MNCs. The following propositions summarize the main results Proposition 4-1. An increase in the strength of patent enforcement policy in the South modeled as an increase in the probability of patent enforcement policy ) ( does not affect the long-run level of Foreign Direct Investment and the long-run wa ge-income distribution between North and South. Proof See Equation 4-25 and 4-26. It is interesting that the probability of patent enforcement or the effectiveness of patent enforcement policy dose not matter to the decision of a firm to become MNCs at the steady-state equilibrium. One explanation is the steady-state value of the relative wage that equalizes the profit flow of the Northern-based firms and MNCs at the steady-state equilibrium. By construction of the model, the steady-state valu e of relative wage between North and South always adjusts it valued to equalize the profit flow between Northern-based firms at the steadystate equilibrium Proposition 4-2. A stronger intellectual property rights protection modeled as an increase in patent length ) ( T (i) reduces the flow of Foreign Direct Investment to the South as the measure of Multinational Corporations in the South decline ) ( pv (ii) worsens the long-run wage-income distribution between the North and the South by raising the relative wage of Northern workers ) ( Proof. See Equations 4-25 and 4-26. We provided a direct link betw een a patent length and a flow of FDI. These results are consistent with Glass and Saggi (2002) and Glass and Wu (2007) where they found that stronger
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76 IPRs protection reduces the flow of FDI but c ontrast with Lai (1998) and Branstetter et al. (2007). A longer duration of a patent length enab les quality leaders to enjoy longer period of monopoly profit. This might reduce an incentive for a Northern based firm to move their production based to the South region since they f aces higher risk of imitation and a reduction in profit when they become MNCs. As more industr ies remain in the North with an increase in patent length, the relative wage of Northern workers will increase as more demand of labor prevail in the region. This resu lt is consistent with Dinopoulos et al. (2005) who found that an increase in global patent length worsens the wa ge-income inequality between the North and the South. Proposition 4-3. Globalization, viewed as a permanent in crease in the size of the Southern population ) (SL (i) increases the flow of Foreign Direct Investment to the Sout h as the measure of industries with active patents in the South increase ) ( pv (ii) worsens the long-run wage-income distribution between the North and the South by raising the relative wage of Northern workers ) ( Proof. See Equations 4-25, 4-26 and Algebraic Details One view of globalization is a geographic expa nsion in the size of the South measured by the level of Southern population. An example of this view is the entering of China to WTO at the end of 2001 and the trend of an increase in th e openness to trade in developing countries around the world (Wacziarg and Welch 2003). Our finding contributed to the existing literature by adding the direct link between gl obalization and FDI. An increase in the size of the Southern market attracts more flows of FDI to the re gion as the demand for product increases. However, an increase in the level of population in the Sout h deteriorates the inco me distribution between regions as more supply of labor emerges in th e market and drives down the relative wage of
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77 Southern workers. Interestingly, the model predicts a complete opposite effect for a permanent increase in the level of the Northern population ) (NL. An expansion in the size of the Northern market holds back the flow of FDI to the South as the number of MNCs in the South declines) ( pvand improves the North-South wage gap as the relative wage of Northern worker declines. The intuitive explanation is that an expa nsion in the size of the Northern market might out weight the cost saving advant age of a lower-Southern wage as the supply of labor in the North increases. Proposition 4-4. An improvement in innovation research and development modeled as an increase in the size of innovation ) (, the innovative R&D pr oductivity parameter ) (, and a subsidy to innovation ) (A (i) decreases the flow of Foreign Di rect Investment to the South as the measure of Multinational Corporations in the South decline ) ( pv (ii) worsens the long-run wage-income distribution between the North and the South by raising the relative wage of Northern workers ) ( Proof. See Equations 4-25 and 4-26. While, most papers studied the effect of FDI to innovation rate, we used computer simulation to analyze the effect of an improvement in the innovation process to a firms decision to become a MNC. An increase in the size of innovation enables Northe rn quality leaders to charge a higher price and achieve a higher level of profit without moving their production to the South. In addition, the larger i nnovation size in the North increases the relative wage of Northern workers as more industries keep their production of thestateof-the-art product in the North which in turn increases the North-South wage gap. Other factors that encourage innovation process such as a subsidy to innovation and an improvement in the innovative R&D productivity also increase the North-South wage gap and d ecrease the flow of FDI to the South region.
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78Proposition 4-4. An increase in the popul ation growth rate ) ( n increases the measure of Multinational Corporations in the South ) ( pvand the North-South wage gap ) ( while, an increase in R&D difficulty ) (has the opposite steady-state effect. Proof. See Equations 4-25 and 4-26. An increase in the population grow th rate leads to an increase in FDI since the market sizes in both regions expand. This induc es the Northern quality leader to move their production based to the South in order to enjoy hi gher level of profit. On the other hand, an increase in the level of R&D difficulty reduces the flow of MNCs as te chnology transfer between regions might be more difficult to complete. Moreover, more resources are devoted to innovative R&D sector as the level of difficulty increase. These results are ba sed on an assumption of negative spillovers of patents to innovation process. Conclusion This paper has introduced an endogenous pro cess of multi-nationaliz ation into a NorthSouth model with a finite patent protection wh ich is perfectly enfor ceable in the North but imperfectly enforceable in the South. The main fo cus of the paper is to examine the steady-state effects of patent protection policy, globaliza tion measured as a geographic expansion of developing countries and change s in innovation technology on the decision of becoming MNCs and income distribution. We f ound that stronger IPRs protection in the South modeled as an increase in patent length decreases the flow of FDI and also worsens the wageincome distribution between regions. On the other hand, an increase in the size of the Southern population accelerates FDI but also worsens the No rth-South wage gap due to an increase in the supply of labor in the South. Then, we explored the effect of changes in innovation process and
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79 concluded that an improvement in innovation technology leads to a decline in FDI to the South and also worsens the income distribution between regions. Further study could be extended in various area s regard patent enforcement and FDI. Trade cost and technology transfer cost could be introduced into th e present model. The structure of knowledge spillovers from FDI to innovation is also an interesting area to explore. Lastly, a growing trend known as South-North FDI as occurring between Indi a and United Kingdom (World Bank 2007) suggests that the innovation could happen not only in the North but also in the South. A study of the effects from this phenomenon on income distribution and global innovation is an interesting area of research. Algebraic Details To show that the value of the North-South wage gap in Equation 4-20 is greater than 1, let assume 1 ) ( 1 S S N N S S N NL c L c L c L c (4-32) Rearranging Equation 4-32, we have ) ( 1 1S S N N S S N NL c L c L c L c (4-33) Equation 4-33 is true since 1 S S N N S S N NL c L c L c L c from the assumption that the probability of patent enforcement is) 1 0 ( Therefore, Equation 4-32 is also true. Next, we show the derivation of the NorthSouth wage gap equati on from Equation 4-20. Simplifying the Multi-nationalization e quilibrium condition (Equation 4-19) as S S N N S S N NL c L c L c L c 1 1 1 (4-34)
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80 Rearranging Equation 4-34, we have 1 1 1 S S N N S S N NL c L c L c L c. (4-35) Adding both side of Equation 4-35 with 1 and rearranging Equation 4-35, we have S S N N S S N NL c L c L c L c 1 1 1 (4-36) Multiplying both side of Equation 4-36 with and rearranging Equation 4-36, we have the North-South wage gap condition as in Equation 4-20. S S N N S S N NL c L c L c L c 1 1 (4-37) The derivation of the North-South wage gap in term of the per-capita global consumption expenditure (Equation 4-22) can be shown by s ubstituting the relative wage from Equation 4-20 to the lefthand side of the I nnovative R&D condition (Equation 4-21). S S N N S S N N S S N N S S N NL c L c L c L c L c L c L c L c T1 1 1 1 1 ) ( (4-38) Simplifying Equation 4-38 and rewriting it as S S N N S S N N S S N N S S N NL c L c L c L c L c L c L c L c T 1 1 1 ) ( (4-39)
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81 Simplifying Equation 4-39 and using the defini tion of the per-capit a global consumption expenditure. Then, we equate Equation 4-39 to the right-hand side of the innovative R&D condition (Equation 4-21) as ) 1 ( ) 1 )( (AL c T (4-40) Finally, we can solve the North-South wage gap in term of the per-capita global consumption expenditure as in Equation 4-22 as ) 1 ( ) 1 )( (AL c T (4-41) To solve for the steady-state solution of th e per-capita global consumption expenditure, we rewrite the per-capita Northern full-employm ent condition (Equation 4-16) in term of the measure of industries with active pate nts. From Equation 4-16, we have c L L L v nN p (4-42) Rearranging Equation 4-42, we have 1 c L L L n vN p. (4-43) Then, we rewrite the per-capita Southern full-employment condition (Equation 4-18) in term of the measure of industries with active pa tents. First, we rewr ite Equation 4-18 as ) 1 (p p Sv v c L L (4-44) Simplifying Equation 4-44, we have ) 1 (p Sv c L L (4-45) Rearranging Equation 4-45, we have
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82 1 1 c L L vS p. (4-46) Next, we equate Equation 443 with Equation 4-46 to solve for the steady-state value of the per-capita global cons umption expenditure as c L L c L L L nN S1 1. (4-47) Simplifying Equation 4-47, we have c L L c L c L c L L L L nN S S N 21 1 (4-48) Substituting the North-South wage gap from Equation 4-22 into Equation 4-48 as L c T c L L L c T L L c L L L L c T L nA N A S S N A) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( 1 ) 1 )( ( ) 1 ( 12 (4-49) Multiplying L to both side of Equation 4-49 as ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 (2 T L L c T L c L L L n L c T nA N A S S N A. (4-50) Rearranging Equation 4-50 as L c T n L c T L c L L L n T LA A S S N A N) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 (2 (4-51) Rearranging Equation 4-51 as L T n L T L L L L c n T LA A S S N A N) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( 1 ) 1 )( ( ) 1 (2 (4-52) Using Equation 4-52, we can solve for the steady-state value of the per-capita global consumption expenditure as in Equation 4-24 as
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83 n T L n L L T L L L cA N S A N S ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( (4-53) Next, we show the derivation of the steady-st ate value of the measure of industries with active patents. First, we solve the per-capita Northern full-employment condition from Equation 4-16 in term of the North South wage gap as 1 L v n L L cp N (4-54) Second, we solve the per capita Southern full-employment condition from Equation 4-18 in term of the North-South wage gap as 1) 1 ( c v L L c vp S p (4-55) Then, we equate Equation 4-54 and Equate 4-55 as L v n L L v c v L Lp N p p S ) 1 (. (4-56) Simplifying Equation 4-56 and moving the measure of industries with active patents to the same side as p p N Scv v L L L n c L L (4-57) Rearrange Equation 4-57 and solve for the m easure of industries with active patents as 1 c L L L n c L L vN S p (4-58)
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84 We imposed the condition n L LS N to ensure that the measure of industries with active patents is less than unity. Substituting th e steady-state value of the per-capita global consumption expenditure from Equation 4-24 into Equation 4-58, we can solve for the steadystate value of the measure of the industries with active patent as in Equation 4-26 as n T L n L L T L L L L L L n n T L n L L T L L L L L vA N S A N S N A N S A N S S p) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( . (4-59) Proof of Proposition 4-3 (i). By differentiate Equation 4-26 with respect to the size of the Southern population 0 ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 (2 n T L n L T L L L n L L n T L T L n T L n L T L L L L vA N S A N S N N S A N A N A N S A N S N S p Proof of Proposition 4-3(ii). By differentiate Equation 4-25 w ith respect to the size of the Southern population
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85 0 ) 1 )( ( ) 1 ( ) 1 )( ( ) 1 ( ) 1 ( ) 1 )( ( n T L T L T LA N A N A S
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86 Figure 4-1. Multi-nationalization process in a North-South model North South Innovation and Production of new products Production of MNCs MNCs products become generic with probability 1 MNC rate ( )
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87 CHAPTER 5 CONCLUSION We developed a closed-economy product-cycl e model and the Nort h-South product-cycle trade models with different setting in patents protection. We found that globalization has an adverse effect to the wage-income distributi on between regions by increasing the North-South wage gap. Moreover, with the introduction of fo reign direct investment and free trade to the model, patent protection reduces the flow of foreign direct inve stment to the South and also worsens the wage-income distri bution between regions. We also found the same steady-state effects from an improvement in innovation techno logy to the flow of FD I and the North-South wage gap. Lastly, we investigated various effects to the resources used in the patent enforcement sector and found that an increase in patent length induces an incr ease in the resources used in patent enforcement sector and increases the probab ility of patent enforcement in the country. We concluded that economies with low productivity of R&D have weaker patent enforcement policies and lower long-run Schumpeterian growth. Various aspects of the models can be exte nded for further study. Skilled and unskilled labors can be introduced to analyze effects to income distribution within a country. An introduction of trade cost to the North-South mo del with FDI is also interesting to examine. Further study regard welfare implication can be investigated. However, welfare analysis is complicated due to different components that depe nd on various factors. It is beyond the scope of the current model to examine the change in the discounted consumer utility overtime. See Dinopoulos and Segerstrom (2007) for a study of th e steady-state welfare analysis where they examine the change in the st eady-state utility paths before and after policies change.
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88 LIST OF REFERENCES Anderson, J.E., Wincoop, E., 2004. Trade costs. Journal of Economic Literature. 42(3), 691-751. Bhagwati, J.N., 2004. In Defense of Globalization. Oxford University Press, New York. Branstetter, L., Fisman, R., Foley, F.C., Saggi, K., 2007. Intellectual property rights, imitation, and foreign direct investment: Theory and evidence. NBER Working Paper 13033. Dinopoulos, E., 1996. Schumpeterian Growth Theo ry: An Overview. In: Helmstadter, E., Perlman, M. (Eds), Behavioral Norms, T echnological Progress and Economic Dynamics: Studies in Schumpeterian Economics. Univ ersity of Michigan Press, Ann Arbor, Michigan. Dinopoulos, E., Gungoraydinoglu, A., Syropoulos, C., 2005. Patent Protection and Global Schumpeterian Growth. In: Dinopoulos, E., Krishn a, P., Panagariya, A., Wong, K. (Eds), Trade, Globalization and Poverty, Routledge, New York. forthcoming. Dinopoulos, E., Kottaridi, C., The growth effect s of national patent policies. Review of International Economics. forthcoming. Dinopoulos, E., Segerstrom, P.S., 1999. A Schum peterian model of protection and relative wages. American Economic Review. 89(3), 450-472. Dinopoulos, E., Segerstrom, P.S., 2005, May 16. A theory of North-South trade and globalization. Retrieved September 7, 2005, from http://bear.cba.ufl.edu/dinopoulos/PDF/NorthSouthTrade.pdf. Dinopoulos, E., Segerstrom, P.S., 2007, August 6. Intellectual property rights, multinational firms and economic growth, Retrieved December 3, 2007, from http://bear.cba.ufl.edu/dinopoulos /PDF/MultinationalFirms.pdf. Fan, C.S., Cheung, K.Y., 2004. Trade and wage inequality: The Hong Kong case. Pacific Economic Review. 9(2), 131-142. Fink, C., Maskus, K.E., 2004. Intellectual Prop erty and Development: Lessons from Recent Economic Research. World Bank and Oxfo rd University Press, New York. Ginarte, J.C., Park, W.G., 1997. Determinants of patent rights: A crossnational study. Research Policy. 26(3), 283-301. Glass, A.J., Saggi, K., 2002. Intellectual property ri ghts and foreign direct investment. Journal of International Economics. 56(2), 387-410. Glass, A.J., Wu, X., 2007. Intellectual propert y rights and quality improvement. Journal of Development Economics. 82(2), 393-415.
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89 Grossman, G.M., Helpman, E., 1991. Quality la dders in the theory of growth. Review of Economic Studies. 58(1), 43-61. Grossman, G.M., Lai, E.L.-C., 2004. International protection of intellectua l property. American Economic Review. 94(5), 1635-1653. Helpman, E., 1993. Innovation, imitation and inte llectual property right s. Econometrica. 61(6), 1247-1280. Hill, C.W.L., 2002. International Business: Competing in the Global Market Place McGraw-Hill College, Columbus, Ohio. Howitt, P., 1999. Steady endogenous growth with population and R&D input s growing. Journal of Political Economy. 107(4), 715-730. Krugman, P.R., 1979. A model of innovation, technology transfer and the world distribution of income. Journal of Political Economy. 87(2), 253-266. Lai, E.L.-C., 1998. International intellectual prop erty rights protection an d the rate of product innovation. Journal of Developm ent Economics. 55(1), 133-153. Lee, J.Y., Mansfield, E., 1996. Intellectual property protection and U.S. foreign direct investment. Review of Economics and Statistics. 78(2), 181-186. Maskus, K.E., 2000. Intellectual Property Rights in the Global Economy. Institute of International Economics, Washington, DC. Park, W., 2001, December. R&D spillovers and intellectual property rights. Retrieved October 27, 2006, from http://www.american.edu/academic.depts/cas /econ/faculty/park/RD %20Spillovers%20IP Rs.pdf. Romer, P.M., 1990. Endogenous technology change Journal of Political Economy. 98(5), 71102. Segerstrom, P.S., 1998. Endogenous growth without scale effects. American Economic Review. 88(5), 1290-1310. Sener, M.F., 2005 August. Intellectual property rights and rent protection in a North-South product cycle model. Retrieved January 29, 2006 from http://www1.union.edu/senerm/Research/Sen er_IPRs_Rent_Protection_PAPER_July_06. pdf. Wacziarg, R., Welch, K. H., 2003. Trade liber alization and growth: New evidence. NBER Working Paper 10152. World Bank, 2007. Global Development Finance 2007: The Globalization of Corporate Finance in Developing Countries. Wo rld Bank, Washington, DC.
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90 Wu, Y., 2005. The effects of State R&D tax cr edit in stimulating private R&D expenditure: A cross-state empirical analysis. Journal of Policy Analysis and Management. 24(4), 785802
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91 BIOGRAPHICAL SKETCH Pipawin Leesamphandh was born in Bangkok, Tha iland. She attended Bodin Decha (Sing Singhasaenee) school from 1990-1994. She graduated from Thammasat University and received a Bachelor of Arts in economics in 1998. After she received a Master of Arts in International Economics and Finance from Chulalongkorn Univer sity in 1999, she began to work as a financial analyst in the financial planning depa rtment at Kasikorn Bank. In 2001, she became a research assistant at the Fiscal Policy Research Institute. Pipawin received a scholarship from the Thai Government to study economics and began he r graduate studies at the University of Florida, Gainesville, USA in August 2003. She sp ecialized in internati onal trade and economic theory. After she graduated from the University of Florida in August 2008, she went back to Thailand and works for the Thai government.