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Intra-industry Trade and International Technology Conlpetition
塩 澤 恵 理
Eri Shiozawa
Introd〔」ction
In traditional trade theory, one country buys goods from another and sells other
goods to another country according to the rules of comparative advantage. Here
the goods imported and exported are different products;thus, there is no room for
competition between the traded goods. This simple theory of comparative advantage
originally developed by David Ricardo,1ater refined by Hecksher and Ohlin with the
final touch by Paul Samuelson, envisions trade situations in a static context.
Therefore, the countries and commodities concerned are by no means competitive.
Instead, countries engaged in trade are cooperative and achieve the so called 貿gains
from trade”. As an example, Japan imports oil from Saudi Arabia in exchange for
Sony’s Walkman. Japan needs oil and Saudi Arabia needs electric appliances. By
Japan specializing in high-tech products while Saudi Arabia specializes in oil
production, both countries get what they need in large quantities.
Two countries will naturally cooperate, because that is the only way that gains
from trade will result. Here the essential point in traditional trade theory is that
both countries’comparative advantages do not change and that two countries are
willing to cooperate. This may be called trade with static and cooperative game.
However, in actual situations, history has proved that in the long-run, a country’s
comparative advantage can be and should be improved. This is known as更ぞ
?モ盾獅盾高奄メ@development”.
254 『明大商学論叢』第82巻第1号 (254)
Japan fifty years ago was a poor country specializing in low-tech toy
manufacturing while the U.S. fifty years ago. @was already engaged in the advanced
manufacturing industry. Japan sold toys in exchange for advanced machinery made
in the U,S.;since then, Japan achieved economic development and is now exporting
high-tech products to the U.S. in exchange for agricultural products. This is the
definite trend that we observe now. In this case, the comparative advantage
reverses itself in favor of Japan;but still goods traded between the U.S. and Japan
are different products. However, in the course of Japan’s economic development,
there is another trend which is disturbing to some economists and politicians. Japan
has developed to the stage that she can produce the same products which the U.S.
has been proud of;that is, Japan can compete with the U.S. in many fields
including automobile and other high-tech products such as semi-conductors.
America was the champion of auto manufacturing, but Japan may claim
superiority in the same auto industry thereby creating trade friction. This situation
has never been explained by static trade theory. It was only over a decade ago (1)
when Paul Krugman of the Massachusetts Institute of Technology saw this situation
as different from the traditional one. This is trade within the same industry known
as intra-industry trade: trade actually occurs in the same industry between
industrial countries that have relatively similar factor endowments or si’milar factor
intensity. However, what Krugman did not do is construct a model which creates
intra-industry trade as a natural consequence. Earlier papers attempted to do this (2)
by introducing the product cycle theory by Raymond Vernon and much earlier by (3}
Kaname Akamatsu. Akamatsu’s geese flying model in the 1930s already assumed
that the very concept of comparative advantage needed to be revised.
If one accepts that trade may be based not only on static comparative advantage,
but also on dynalnic comparative advantage of intra-industry trade, then one must
also accept possibilities of friction and competition among trading partners. This is
an entirely different situation from the case where trade will automatically benefit
the countries involved in trade.11n fact, trade may hurt the partner relationship. If
Japan exports too many cars to the U.S. while shutting out American cars from
Japan, America may accuse Japan of exercising unfair trade practices.
(1)E.Helpman and P. Krugman, Market Structure and勘吻gηTrade,(Cambridge,
Mass.:The MIT Press,1985).
(2)Raymond Vernon, tclnternational Investment and International Trade in the Product
Cycle,”Quarterlyノ磁甥α10f Economics,(1969, May),190-207.
(3)Kaname Akamatsu, Sekai Keizai Ron,(Tokyo:Kunimoto Shobo,1965),165-181.
(255) Intra-industry Trade and International Technology Competition 255
1n this paper we attempt to analyze a simple model of trade competition when
two countries engage in intra-industry trade utilizing the analysis of Ryuzo Sato’s (4)
work,ヒThe Technology Game and Dynamic Comparative Advantage:An Application
to U.S.-Japan Competition”. Two Oountries try to change their comparative
advantage in the same sector by investing in research and development(R&D)
activities. Japan’s industrial policy is known to have contributed to the postwar
success in catching up to the U.S. in auto and other high-tech industries.
Following Sato’s work, we analyze the model which incorporates a non-cooperatlve
dynamic game since trade has two faces;cooperative and bonfronting.
THE MODEL We will consider an abstract model in which intra-industry trade takes place for a
homogeneous commodity Y which two countries produce’to sell in the world
market. The two countries involved may be identified as Country A and Country
B. (Country A may be the U,S. and B, Japan.) Country A and Country B use
く喝 ≠撃高盾唐煤hidentical technology to produce commodity Y, say, automobiles. The world
market consists of an aggregation of all the markets in the world including
American, Japanese, European, Latin Amerian and Asian markets. Japanese cars
may be exported to these foreign markets, while American cars may be imported
by these markets. Therefore, trade will take place in automobile exports and
imports--intra-industry trade in automobile. For simplicity, we will first consider a
two-country mode1, which implies that Europe and other Asian countries do not
produce cars and/or do not engage in automobile trade.
Stage l
Technology is更璽almost”identical in that Country A is the innovator while Country B
is the follower. With appropriate investment, Country A develops and innovates the
technology necessary to produce commodity Y. Country A sells Y in the world
market, temporarily catching the position of monopolist and making abnormal short-
run profit. However, this situation does not last long, because entrepreneurs in
Country B see the opportunity to produce a similar product to Y. What
entrepren6urs in Country B do next is to import the technology from Country A by
paying a certain fraction of the development cost. In many cases, Country B must
pay patent fees to Country A. The amount of the total cost paid depends on the
(4)Ryuzo Sato,ヒ曜The Technology Game and Dynamic Comparative Advantage:An
ApPlication to U.S.-Japan Competition,”in lnternational Co〃zpetitivene∬, eds. M.
Spence and H. Hazard(NY:BaUinger Publishing,1988),373-98.
256 『明大商学論叢』第82巻第1号 (256)
situation where entrepreneurs in Country B find it difficult to produce cofnmodity Y
without access to the technology. It also depends on how easily the technology can
be imitated by Country B. Above all, it depends on how entrepreneurs in Country
Blook at future profit conditions.. More than a decade ago, two Japanese
electronics companies were caught by the U.S. legal authority for suspicion of
stealing a certain technology from their U.S. counterpart. In this case, the amount
they paid for acquiring the information was minimal although the social and legal
costs dealing with the scandal may have been enormous.
In Inore fair negotiation, Country A and Country B may share the cost of
developing the original technology by equal amounts. The recent agreement
between the U.S. and Japan on a certain aspect of space exploration falls into this
category.
Stage ll
The second stage of negotiations or the second stage of thiS game strategy is
concerned with the amount of technology information that Country A is willing to
give Country B in exchange for fees Country B pays to Couhtry A. As Country A
is a sole owner of that information of new technology, it tries to release the
minimum amount to Country B. For example, if General Motors(GM)happens to
develop a new technology on automobile manufacturing, it attempts to give away as
little information as possible to Tgyota even after Toyota pays a certain amount of
fees to GM. It is not illegal or immoral on the side of GM for doing this;it is
simply trying to minirnize cost, In fact this is the power of the monopolist in the
technology development.
The next aspect of this dynamic game is related to the fact that Country B’s
technology is almost identical to that of Country A. That portion of information
that Country B acquires from Country A is identica1, but the remaining portion
must be created by B’s own efforts;that is to say, the basic information of
automobile production is the same in both countries. Country A has its own unique
way of using that information while Country B also has its own method of utilizing
that information. This distinction is often referred to as uniqueness of applied
technology。
For example, although the basic information on automobile manufacturing is the
same in the two countries, the actual method and strategy of production may be
(257) Intra-industry Trade and International Technology Competition 257
very different. The so called American management practice vs. Japanese system
in producing cars may be very different. Toyota may use the so called t’Kanban (5}
Hoshiki”(or just-in-time method)while GM may use the traditional optimal (6)
inventory method. The question is how to quantify these qualitative differences in
rnanagement systems. In a purely theoretical model, it is advisable to use some
quantitative index to express differences in the managelnent systems. Here we
would simply differenciate the two approaches by the effectivess of management;
that is, the cost differences or the productivity differences. It does not matter
whether the Japanese management practice uses the so called t{cho-rei”(or morning
greeting ceremony)or the three o’clock exercise or karaoke party after five.. The
point is whether Toyota’s overall productivity is higher, equal to or lower than that
of GM. Therefore, we will ignore all the qualitative aspects but compare. Dsimply
the productivity differences.
Let us summarize below what we have assumed:
1. Country A is the innovator of the technology to produce commodity Y.
II. Country B imports that technology in order to produce a product identical to
commodity Y.
III. Country B pays a certain amount of fees to Country A for acquiring the
information to produce commodity Y.
IV. Each country has its own management strategy dealing with the applied aspect
of technology management. The difference may be quantitatively measured by cost
effectiveness or productivity difference.
STRA丁EGY
We now consider how two countries adopt different strategies to coordinate all
aspects of production, exportation and profit maximization. First, two countries
must agree on what type of strategy to adopt. Here it is assumed that the
technology game is a Cournot-Nash differential game . There are two well known ⑦
strategies:open loop and closed loop feedback strategies. An economic
interpretation of the open loop strategy is very easy;that is, once two parties make
adecision, they will never change the time path so that they follow the fixed routes
(5)Michael Cusumano, The/4加η6sθAutomobile Industry(Cambridge, MA:The Council
on East Asian Studies at Harvard University,1985),265.
(6) Ibid.,270, 281.
(7) T.Basar and G.J. Olsder, Dynamic Noncool)erative Game Theo ry.(London:The
Academic Press,1992.2nd edition,1995).
258. @ 『明大商学論叢』第82巻第1号 (258)
to the end. Therefore, open 一 loop strategies are functions of calendar time alone.
In the budget process as an illustration, this strategy is known as an inflexible
system. Once a decision is made, there is no room for adjustment and there is no
room for change of path regardless of whether economic environrnents have
changed.
The closed loop feedback strategy is a more f.lexible one because changes in
economic environment force the players to adopt different paths. In other words,
the strategy they adopt is determined by the state of the environment。 In technical
terminology, environment is the state variable;thus, the closed loop feedback
system requires strategy(or the control variable)to depend on the state variables at
each moment. This strategy is certainly much more flexible and in the budget
process it is known as a flexible budget. If the players can condition their
strategies on other variables in addition to calendar time, they may not want to use
open-loop strategies in order to react to exogenous moves by nature and/or mixed
strategies by rivals, etc,;thus, players can respond to their rivals’actions at each
period.
We now discuss the objective function of this dynamic game. The sole purpose of
each country’s entrepreneurs is the maximization of Iong-run profit. Therefore, the
criterion that we use to judge the outcome of the game should be profit itself.
But, since the objective of the firm is the functional rather than the function, it is
almost impossible to compare two functionals in a dynamic game. In this case, the
integral of each year’s profit i.e. the long-run profit from period t zero to infinity
is hard to evaluate. Therefore, it is much easier to use the market share rather
than profit itself for comparison. The market share is nothing but output itself.
We will use output, Y as the criterion of win and loss of the game. For instance,
if Country A’s output Y is greater than Country B’s Y, we say that Country A won
the game;or that Country B lost the game. When output produced by each country
is exactly the same, we say that the game is tied. We have to warn here that we
are going to exclude two corner solutions. The first one is the case where Country
Amonopolizes the output;that is, Country B’s output is zero. The second corner
solution case is where Country B monopolizes the market;that is, Country A’s
output is zero. We must exclude these cases because game will not take place under
these extreme points. In passing, we may say that if Country A’s market share is
(259) Intra-industry Trade and International Technology Competition 259
90%rather than 60%, Country A is winning big and vice versa.
lNTERTEMPORAL PATH OR STEADY STATE
Let us assume that two countries have agreed to play the game under either open
or closed loop conditions. Given the initial conditions, two players start
implementing their control variables in investment and research to improve
productivity and output in order to maximize the market share. What happens
nextP That depends on the inter-temporal paths. Two players usually follow the so
called turnpike path in order to reach the equilibrium point or the steady state. It
is known that there exists the steady state where two parties no longer want to
move away from it. Technically, we must assume nice concavity conditions on each
Hamiltonian function. It is usually very difficult or almost impossible to describe
the inter-temporal path mathematically under this type of differential game.
Therefore, we may be happy to study only the characteristics of the steady state (8}
path.
RESULTS
Without becoming technically involved, we may analyze the economic implication
of this game.
Case I.
The simplest case is equal payment of development cost;that is, Country A and
Country B share the equal amount of development cost of theltechnology. In
addition, Country A gives 100%technology information or full information.
Furthermore, Country A’s productivity is exactly the same as that of Country B’s.
Under these conditions, the game result is predictable. That is to say, Country A’s
market share is exactly.identical to that of Country B’s(50%vs.50%)。Here,
exports and imports exactly balance out. There is no unfairness and there will be
no trade friction. The trade system and game will continue forever. This result
apPlies not only to the open but also to the closed strategy.
Case II.
Now assume that even though Country B pays development fees of exactly one half
to Country A, Country A has the power to exercise information control over the
technology on Country B. For example, Country A gives away only 80%of
technology information to Country B. What can Country B do to play the game~
The only solution for Country B is to make an extra effort to raise its productivity.
(8)Sato solves the technology game under specific assumptions in his mathematical
appendix,393.
260 『明大商学論叢』第82巻第1号 (260)
If Country B is successful, then they can match Country A in the final outcome.
In other words, provided that Country B can substitute higher productivity for the
lack of information, Country B can cQmpete with Country A in the world market.
If productivity of Country B compensates for the lack of information, there is a
possibility that Country B’s market share niay even exceed that of Country A.
Case III.
If Country A further reduces the defusion of technology information to Country B,
it is increasingly difficult for Country B to compensate this loss by productivity
increase;this is due to the law of diminishing returns. There is an obvious
advantage for Country A because it monopolizes technology information. Is this
fair? Country B has paid one half of the development cost, but has received less
than full information. Country B. @has had an expectation of receiving full
information when the payment was made. Therefore, this is the case of
expectation unfulfilled. This situation always happens when game is played in two
stages, and nothing can be done. The overall result shows that when technology
competition takes place, it is not only the productivity difference that makes the
market share larger, but also the degree of substitution between the diffusion of
technology information and productivity of manufacturing.
Toyota had to work harder and develop a method of”Kanban Hoshiki”, because
Toyota was originally the follower in the auto industry. GM and other American’
auto makers had the advantage of full utilization of the technology. The only thing
Toyota and other Japanese car makers could do was to depend on an alternative
method of raising productivity. This model clearly shows this type of structural
characteristics faced by late comers in the market.
COMPARISON OF DIFFERENT STRATEGIES
We have indicated that under the open loop strategy, optimal paths are Iess
flexible than the case under the closed loop strategy. In other words, the steady
state position under the open loop strategy may be quite far from the steady state
under the closed loop. There is no reason to believe that the two steady state
positions coincide. In fact in many cases, the closed loop steady state gives more
realistic value simply because the inter-temporal path can be adjusted to a more
realistic environment or state variable.
Aparadox may also exist under the closed loop strategy. For example, even if
(261) Intra-industry Trade.and International Technology Competition 261
Country A restricts the diffusion of technology informaton to Country B, say a
20%restriction, Country B may not lose the competition;or in an extrerne case,
Country B’s market share may improve--aparadox. If this is the case, Country A
might accuse Country B of unfair practice because this situatibn does not coincide
with common sense. The more Country A restricts information, the more share
Country B gets out of from this game.
There may be possible explanations for this type of paradox. First, Country A
has two control variables to deal with, one in developing the original(basic)
technology and the other.in managing actual(applied)technology competition. On
the other hand, Country B ha呂only one control variable of managing actual
technology to worry about. Therefore, the closed loop strategy puts an extra
burden on Country A. In Sato’s model, he points out that an asymmetry exists in
the Hamiltonian functions as shown in his mathematical appendix。 Second, there is
asunken cost in developing the original technology by Country A. Country A must
have invested a larger proportion of resources even before they started the current
technology development. To develop automoりile technology, many researchers must
have invested their time and money before they finally succeeded in the actual
manufacturing;but the question is who pays for this type of past investment.
Country B is not expected to pay for the past investment cost, only the current
cost.
An extreme case may be the importation of technology from the U.S. by an
agrarian country, say a country in Africa. The U.S. has invested a large sum of
money for the last 200 years in general technology developrnent while a country in
Africa by comparison basically has not invested in manufacturing technology. If
suddenly an African country wants to import the technology to produce the
homogeneous product Y, it should pay the U.S. more than one half of the current
investment cost. However in actuality, this is usually not required. In the closed
loop strategy, this difference may create the existence of a paradox.
CONCLUDING REMARKS
We have seen how intra-industry trade in a certain industry(automobile
manufacturing)may be a factor that creates trade friction between nations(Japan
and the U.S.);this is the result of international competitiveness in the same
industry which is a departure from the orthodox way of explaining trade as a
(263) Intra-industry Trade and International Technology Competition 263
example, even if Country A restricts the diffusion of technology information(say by
20%)to Country B, Country B may not lose theとompetition, but might on the
contrary achieve improvement in overall rnarket share. This is a theoretical
possibility and to Country A, it will seem that Country B is practicing unfair
competition. There may be two reasons for this paradox:First, with the closed
loop strategy, an extra burden is put on Country A since there are two control
variables to worry about;that is, Country A must worry about developing the
original technology and then managing actual technology competition. Whereas,
Country B has to deal with only one control variable of managing actual
technology. Second, for Country A, there is a sunken cost in developing the
original technology. We cah assume that Country A/must have greatly invested in ノコ
resources even before starting the development of t1免technology. Country B is not
expected to pay for the past investment cost, only the current cost. Therefore,
this analysis raises two policy issues. One having to do with international
cooperation, the other with the development of innovative technology in Country B.
Innovative technologies are usually considered to be public goods; thus, the question
is how can control be managed..This becomes a possible disputing point among
countrles.
There may be a number of applications of the model to empirical data. Sato
applies the model in order to study the relationship between the market share and
productivity of the Japanese auto industry in the U.S. market. Sato shows how
some of the more general conclusions of the model can be tested. It is widely
believed that Japan gained a competitive advantage in the world automobile market
during the 1970s by introducing efficient process innovation;and he illustrates the
relevancy of the model by comparing the actual trend of Japan’s share in the
automobile market with the productivity trend of Japanese applied technology. Sato
points out that Japan achieved comparative equality with that of the U,S. by 1979
and gained comparative advantage by nearly 30%in 1981;therefore, a clear
association between the increase of Japan’s share and the rise of its relative
efficiency could be seen.
FURTHER EXTENSIONS
The above is certainly not the full application of the differential game. In fact,
we know no method of such an application as the model involves the differential
262 『明大商学論叢』第82巻第1号 (262)
consequence of comparative advantage among different industries as analyzed by
Ricardo and his successors. Whether it is a result of economic development in
which a country’s comparative advantage improves through research and
development, or simply the result of product cycles, in the case of intra-industry
tradei trade may hurt the country(ies)involved. This is clearly different from
static traditional theory in which there is cooperation and/or gains from trade.
Therefore, in the analysis of this dynamic intra-industry trade theory, win or loss
(measured by market share)of the{{trading game”becomes a crucial point.
We have described a game-theoretic model of international technology competition
following Sato’s original model. Country A(the U.S.)which is a technologically
mature country pursuing in both basic research and development and applied
technology, competes in the world market with Country B(Japan),which
specializes in applied technology. The model assumes that the technologically mature
country has a dynamic comparative advantage to the extent that it can control the
diffusion of information related to the basic technology. Meanwhile, the
technologically less mature country has a comparative advantage in applied
technology provided that the flow of basic information is sufficient.
The outcomes of the game(Cournot-Nash dynamic game)depend on the types of
strategies that the two countries employ. In both the open and closed loop
strategy, as long there is equal payment of development cost of the technology
between the two countries;and Country A gives 100%technology information(full
information);and the productivity of the two countries is exactly the same, the two
countries’share will be 50%and 50%. Exports and imports、will exactly balance
out;there is no unfairness and no trade friction.
If they adopt the open loop strategy and Country B receives less than full
information of the basic technology from Country A, then the Inarket share will
depend on the productivity difference;that is, how can Country B substitute higher
productivity for the lack of information resulting from export control of the
technology by Country A. In addition to the productivity difference, the degree of
substitution between the diffusion of technology information and productivity of
manufacturing influence the market share.
Under the closed loop strategy, in which the values may be more feasible since
adjustment to a more realistic environment is possible, a paradox may exist. For
264 『明大商学論叢』第82巻第1号 (264)
and functional equations. It should be clearly noted that the original Sato model
deals with an asymmetric differential game model which generally has no clear cut
analytical solutions. Most books on differential garnes do not deal with asymmetric
games at all;hence, the more complete solutions, particularly under the closed Ioop
strategy, may exist which may be very different from what the original Sato model
presented. To verify the validity of the original Sato model, we may have to
employ simulation analysis. It seems that the solutions developed in the original
Sato model for the closed loop strategy may not really be the standard feedback
solutions as claimed. This presents a further challenge for research. In addition,
we may extend this model to analyze three countries at a different stage of
development in technological efficiency;or an application of this model to other
industries such as home electronics may also be interesting for future studies.
MATHEMATICAL APPENDIXCountry A’s problem:
鮒捌P(Y)距卸一(・一・)α聴肋 Y・・ UA s. t, UA・=・iPA(TA)
Country B’s problem:
M諮び・t[P(Y)距我一・s(・T・,・u・)]・dt
Y. s. t.TB=・a/v(γTA),
where P(Y)=the world(inverse)demand function
Y=YA十YB=Country A’s Y十Country B’s Y
TA=technical progress factor of Country A
TB=technical progress factor of Country B
S =cost of developing TA
θ=cost sharing parameter of Country B
Oくθ<1
γ=the diffusion parameter of TA for Country B by Country A.
Consider an extreme case’thatθ =0, i.e.,free rider=Country B;then Country B’s
profit function will always be larger than that of Country A’s provided that
(265). Intra-industry Trade and International Technology Competition 265
TB=ψ(γTA),special case of this being TB=γTA,γ=1
Another special case is θ=1;i.e.,Country B pays everything to Country A. In
this case, Country A’s profit tends to always be larger than that of Country B.
When O〈θ<1, then we have various possibilities ranging from YA芝 Y, depending
upon the types of strategies. Cases described in the model are by no means all
possible solutions but are the siMplest cases. We have assumed in actual
deterr【iination that the demand function is linear and the cost function is quadratic
which gives a quadratic dynamic game model.
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