Productivity differences, world-market shares and conflicting national interests in linear trade models: Comments

ELSEVIER

Japan and the World Economy 9 (1997) 151-158

[ ~ a p a n and the WORLD ECONOMY

Productivity differences, world-market shares and conflicting national interests in linear trade models: Comments G.E. Johnson*, EP. Stafford University of Michigan, Ann Arbor, Michigan 48109-1220, USA

I. Introduction

The paper by Ralph Gomory and William Baumol (G-B) is part of an emerging reassessment of how trade can effect an economy's well being. In this new view, technology plays a prominent role. Possibly one could even say that there now exists a set of models addressing the general issue of trade and technological competition (TTC). Empirically, the importance of TTC is highlighted by the argument that in the Post-war era international technology diffusion was more important than capital deepening in shaping manufacturing growth rates among the technologically advanced countries (Eaton and Kortum, 1995). Capital formation itself is seen as induced by technology flows, as investment is directed to take advantage of rising marginal product in countries where technology is advancing. In the G-B work, technology, represented as industry scale economies within each country's borders, is center stage. In work we have been doing, the transfer of technology across borders plays a prominent role (Johnson and Stafford, 1992, Johnson and Stafford, 1993). Other work has revitalized Vernon's product cycle model (Vernon, 1979), put it in a more dynamic setting (Brezis et al. (1993), Jones and Ohyama, 1993), and postulated endogenous technology enhancement (Grossman and Helpman, 1991). Perhaps not too far in the distant future these various elements will come together in a clearer vision and understanding of how technology plays out in international economics. Were David Ricardo to return to this planet he might be surprised by the results! In this paper, we summarize the main thrust of the Gomory-Baumol paper and related work (Gomory, 1994), compare it to some of our own work, and develop a formal model of technology transfer along the lines offered by Samuelson (Samuelson, 1972). All of this seems particularly relevant today as firms within rich countries, especially, those in Japan with its strong currency and high share of trade-based GDP, find themselves in a similar situation; their economic interest and even survival is in operating production outposts outside the home country, which retains 'headquarters' functions in Samuelson's terms. * Corresponding author. 0922-1425/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0922-1425(97)00005-4

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Suppose main design functions continue to be conducted out of rich countries, but a host of supplementary and production activities are increasingly carried out in lower wage countries. Eventually, the lower wage and technologically less sophisticated countries may emerge as economic peers. How does this diffusion process influence the level and distribution of well being in the different communities?

2.

Scale economies and conflicting interests of trading partners

The model of scale economies set out by Gomory and Baumol, 1995 postulates two countries in which consumers have what may be described as baseline, Cobb-Douglas preferences. In each country there is a single homogeneous labor input that can be allocated to any of a set of potential industries. Each industry has a declining average cost and a minimum level of activity before any output can be produced. This they termed as startup cost assumption. The resulting equilibrium is locally stable and with industries exclusively specialized to a given country. The number of such specialized equilibria is large, and when one country 'takes on' an industry a new locally stable equilibrium obtains. Much of the setup of their model is similar to the approach set out in the new international trade theory (NITT). All we need to do is think of the industries as producing differentiated products. Here the taking on of the production of a particular product by one country may or may not be in the interest of the other This can occur in the NITT as illustrated by Scherer's geometric model of spatial competition in size of airliner (Scherer, 1992). There another country enters size-differentiated production of aircraft. The initial producers could be worse off if the gains to their consumers from more product choice are more than offset by the losses to their producers. In the G-B approach there is only one input, so consumers and producers are one in the same. The stylized model of aircraft competition is also not solved out as a formal general equilibrium trade model, but the issue is the same. Can foreign entry into an industry or displacement of one's own production lead to a net loss, or are we to expect virtually automatic gains in aggregate well being to each country from realignment of production in a trade environment? Here the G-B approach is in sharp contrast to the familiar textbook, two-industry, Ricardo model (e.g. Baumol and Blinder, 1994). There, with stationary technology, two goods, and constant returns, only an initial mistake of insufficient or incorrect specialization can be remedied, and the real wage in both countries will rise as production is reassigned. In the G-B world, it is by no means automatic that a country's acquisition of one industry implies that some other is 'given up,' nor will each country necessarily gain. Unlike the case of constant or decreasing returns, acquisition of an industry can occur without the loss of some other industry. In this process the 'acquiring' country can gain partly at the expense of the other country and can 'have its cake and eat it too.' There seems to be a stronger role for something like absolute advantage. The most dramatic illustration of their approach is in the Fig. 3 (of 'Summary' or Fig. 1 in the Journal of Economic Theory, 1994), and can be used to develop their idea of the 'ideal trading partner.' Consider an initial situation where an advanced country (the United States or Japan), having production in the majority of industries, trades with a partner

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(Mexico or China) that has only a few industries, possibly those in resource based sectors such as mining and agriculture. While this can be very desirable for the advanced country, the partner may have a low standard of living. Now, suppose that the rich country gives up some of its industries to its trading partner. Over some range (a 'modest sucking sound' to rephrfise Ross Perot's contribution to trade theory), both countries will gain. Beyond some point, however, the gain to the trading partner will be accompanied by a loss to the 'rich' country. The ideal trading partner has become less than ideal, even though aggregate world GDP may have risen. This is an interesting result since it shows that the transfer of technology and industries across countries can have good or bad effects for the individual countries depending on particular circumstances. In short, considerable scope exists for there to be conflict as well as congruence between the interests of trading partners. Economic life is not simple! In the related work we have done much of this, same message appears. As we have set up the models, there are not scale economies but simply the diffusion of technology across borders. Our simplest Ricardian setup is with three goods. Country 1, initially, is the sole producer of Goods A and B, and the partner is the sole producer of Good C. The entrepreneurs in Country 2 improve their productivity in Good B, but over some range this improvement is just latent. At some point, however, they become good enough in B production that they begin producing some for their own use (as in the well-known discussion of import biased technical change (Hicks, 1953)). This corresponds to the G-B case with non-specialized equilibria in which both countries are active in a given industry. As we have phrased it, when both countries are active in the B industry, the country that is the source of productivity improvement in this industry realizes more than 100 percent of the world income gains arising from the improved productivity. That is, as one country improves, the absolute level of well being of its trading partner will decline. As G-D phrase it, "when a country is a joint producer in the same industry as another and then improves its productivity, it will increase its utility and decrease that of its trading partner." This appears to have applied to Great Britain as the other industrialized countries recovered after World War II (Johnson and Stafford, 1995). In the case of the 'niche' industries, A and C, productivity improvements by each country produce gains for the other as well. In our setup the ideal trading partner is one that improves in his/her own specialty and not industries in which you are active. We have not developed a case with more than three traded goods, but it could be that with, say, five goods (depending on consumption share parameters, relative country sizes, and specific functional form) it is, as in the G-B setup, in the leader's interest to give up an entire industry to its trading partner. What we do know is that the main result, a potential conflict in the economic well being of trading partners as the relative productivities change by industry and by country, appears to be robust. It does not depend on the traditional Ricardian assumptions of a linear production technology or a single input of production.

3.

A headquarters model

One of the most important application of TTC models is to the phenomenon of shifting of production activities from technologically advanced, high wage countries to low wage

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economies. This is, especially, relevant to recent developments in the Japanese economy. Here, we offer a formalization of the questions raised by Samuelson (1972). What are the effects of diffusion of rich country capital and management knowhow to the employment of foreign labor in the production process? Consider a very simple model of the world economy in which there are two countries, Country A much more advanced than Country B. There are two goods in the world economy: a 'finished' good, Y, which is initially produced entirely in Country A, and an intermediate good or 'raw material', X, which is produced in B. For simplicity of exposition we assume Cobb-Douglas technology for both goods. The production function for Good Yis r = u? 112x 3t¢

(1)

where U1 and $1 are the inputs of unskilled and skilled labor in that industry, X is the input of the intermediate good (imported from Country B), and KI is the stock of capital in Industry 1. The production function for Good X is ///31 ~,~2/,,-1-~1-~2 X = v 2 "2 "x2

(2)

where U2, $2, and K2 are the inputs of unskilled labor, skilled labor, and capital in that industry. Initially all production of Yis in Country A and all production of X is in Country B. Consequently, the volume of trade between the two countries is, a3 Y = PxX, where Px is the price of X relative to that of Y. Now, assume that technology and communications change such that finns producing Yin Country A can establish plants in Country B to produce a portion of their output. The needed managers (who are skilled workers) of these offshore plants are transferred from Country A, but the operatives in the new plants are recruited from the supply of unskilled labor in Country B. We posit that there is a knowhow deficit and the unskilled workers used to produce Yin Country B are 0(< l) times as productive as unskilled workers employed in Country A.1 This implies that the total flow of unskilled labor to the finished good industry is Ul = Ua + OUo

(3)

where UA is the aggregate supply of skilled labor in Country A and Uo is the number of unskilled workers hired to produce Y in Country B. The flow of unskilled labor to the intermediate goods industry is now (4)

U2 = UB -- Uo

where UB is the fixed supply of unskilled labor in Country B. If they are permitted to do so by the government of Country A, the producers of Ywill set Uo such that OY/OUo is equal to its cost, the real wage rate for unskilled labor in Country B, PaOX/OU2. This means that Y OOq'-i'UUl~ PA~I

X

U'~2

(5)

~The value of 0 would reflect the costs of communication and transportation between Countries A and B as well as the quality of the Us's, the infrastructure of Country B, etc.

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This is an equality if 'outpost production' is a profitable undertaking. At the same time, the demand for the intermediate good satisfies Y

(6)

0:3 ~ = PA

Combining Eqs. (3-6), the solution value of the number of Un's used to produce Good Yis

u0 =

Ctl OUB - ol2/3Ua

requires that 0 > 0, = (a33/a1) and U2 are

gl

(7)

0(c~1 + ~23)

(UA/Un). Assuming an interior solution, the values of U1 (8)

0~1 (UA Ac OUB) -

~1 + c~33

and

u 2 = c~23(Wa + OU.) 0(Oll -t- O~3~)

(9)

Uo and U1 rise and U2 falls in response to an increase in 0. It is now possible to discern what happens to the level and distribution of world income as 0 increases - as the rich country production management knowhow is transferred abroad. The proportionate change in the output of the finished good in response to a proportionate change in 0 is

Celd(lnUl) + o~3~d(lnU2) = (OqS - - ct3/3(1 -- s))d(lnO) OUB/(UA + OUB) is the proportion of the world supply of unskilled

(10)

(

(ll,

d(lnY) =

where s = labor in terms of its productivity in industry Yaccounted for by Country B. The coefficient on d(ln0) in Eq. (10) is positive so long as 0 > 0.. The income levels of four of the six factors of production are proportional to Yand rise with 0. Skilled labor in Country A receives a2Y, and the owners of Kl receive (1 - cq - a2 -- a3)Y. Skilled labor in Country B and the owners of K2 receive, respectively, 32PxX and ( 1 - f l l - / ~ 2 ) P x X, but, since PxX = ct3Y, these incomes are also proportional to Y The earnings of unskilled workers in Country B receive /31013Y q- 0~1Ybgo/Ul, which rises at a faster rate with 0 than does g Finally, the income of unskilled workers in Country A is Y•A = C~1(Y/U1)UA. The proportionate change of Eq. (8) with respect to ln0 equals - s, which implies that OYvA/O0 < 0. Thus, an increase in the use of rich country knowhow abroad increases the income of skilled workers and capitalists in both countries and in unskilled workers in Country B, but it decreases the income of unskilled workers in Country A. It remains to be seen whether the total income of Country A - the combined earnings of unskilled and skilled labor and the earnings of the owners of the capital stock of the finished goods industry - rises or falls as a result of an increase in 0. The total income of Country A is

YA=

OUo'~

1 -- ct3 -- cq ~ - t ) Y =

((1--ctl--a3)OUn+(1--a3(1--3))UA)y UA~ O-UB

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As 0 rises above 0. and the practice of outsourcing becomes more prevalent, Y grows but the value of YA/Y falls from its initial value of 1 - c~3, so the sign of OYA/O0 is not obvious. The elasticity of YA with respect to/9 is

O(lnra) _ 0(In0)

(1 -- cq)OUB -- (s(1 -- o~1) + c~3/~1(1 -- S)) (l -- at -- c~3) + (1 -- ~3(1 --/~I))UA (12)

Evaluating Eq. (12) at 0 -- 0. (at which s = c~3/3/(CZl + c~3fl)), OYA/O0 < 0. AS OUB/UA goes to one (so that s ~ 1), Eq. (12) goes to c~t > 0. Thus, the effect of headquarters regime on the total income of Country A is initially negative (the fall in the income of the Ua's outweigh the gains of the SA'S and the owners of KI). Eventually, however, the income of unskilled labor becomes such a small fraction of the income of YA that further declines in their earnings are outweighed by the rise in the incomes of skilled labor and the owners of capital. There are several modifications and extensions of this model that are of considerable interest, but, due to space constraints, only a few of the more interesting ones will be mentioned. First, it was assumed that outpost production only affected unskilled labor; all skilled labor used in the Y plants in Country B was imported from Country A. This may be realistic in the early stages of outsourcing, but there are obvious advantages to the firms producing Y to train managers from Country B. Product development and central administration may be retained in Country A, but it is likely that outpost production may directly affect the SA'S as well. Second, the model above has only one final good and an intermediate good, so the UA'S have no alternative than to continue working in the production of Yonce production abroad has begun. A more complete model would include other goods besides Yand X, including a nontradeable service good in each country. In this case, some of the UA'S would upon the introduction of outpost production, then transfer to other industries - working in, for example, service industries rather than as operative in the Yindustry. The effects on YA and its distribution are obviously much more complicated than in the simple model above although the qualitative effects on the distribution of YA are similar. One interesting effect is that the displaced production workers in the advanced country can flow into the service sector, raising the well being of the skilled workers there as they can then purchase these non-traded goods more cheaply. Third, the simple model above is based on the assumption that there are only two countries and that only Country A has a monopoly on the technology associated with Good E It would be more realistic to specify that there is another country (or group of countries) that also produce Yand that has (have) the opportunity to shift part of its (their) production of Y to Country B. 2 In this case, if the government of Country A chooses not to allow outpost production by the firms over which it has control but the other country does allow such a shift, the negative effects on YA may be worse than they would otherwise have been.

2Again more realistically, the other country may have the option of outsourcingto a country that is similar to but different from B. For example, Japanese producers may use Malaysia and Thailand for outsourcingpurposes while the U.S. uses Mexico.

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That is, outpost production by one rich country creates strong incentives for the rest to follow. Fourth, the simple model is essentially static, but there are many possible modifications that involve dynamics and endogenous technological change. Specifically, investments by producers of Yin productivity-enhancing research will be greatly affected by expectations concerning where production will take place in the future. If a firm in A anticipates changing the location of a function when the present plant has depreciated, it will obviously allocate much of its research activities to the situation of the new plant in B rather than modifying the technology of the present plant.

4.

Conclusion

The operation of trade in conjunction with productivity shifts arising from scale economies or simple diffusion of technology, should cause us to rethink seriously the role of trade in a world where technology takes on greater importance than traditional capital deepening. The work by Gomory and Baumol makes this point in dramatic fashion. Work that we have done along related lines and illustrated with our formalization of a headquarters model, suggests that the issue is of broad applicability in a wide range of formal models. The scale economies or technological position achieved by one country may be partly the result of public as well as private investments. In this case it is hardly a matter of indifference where the technology ends up. On the other hand, consider the case of generic productivity enhancing technology developed in one country. If it lands in the non-traded sector or in the speciality niche industry of a trading partner, the source country is likely to be, respectively, no worse off or better off. Finally, as is the case of the G-B model where the less favored country acquires only 'a few' industries and as illustrated in our model in Section 2 and elsewhere, there need not be convergence costs and these may be only transitional.

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Jonathan, George E. and Frank E Stafford, Models of international competition and real wages, manuscript, Department of Economics, University of Michigan, Ann Arbor, Michigan, July 1992. Johnson, George E. and Frank P. Stafford, 1993, International competition and real wages, American Economic Review Papers and Proceedings, 127-130. Johnson, George E. and Frank P. Stafford, The hicks hypothesis, globalization and the distribution of real wages, paper presented at the Econometric Society Meetings, January 6-8, 1995, Washington, D.C. Jones, Ronald and Michihiro Ohyama, Technology choice, overtaking and comparative advantage, Conference on New Directions in Trade Theory, University of Michigan, Ann Arbor, October 1993. Samuelson, Paul A., International trade for a rich country, Stockholm: Federation of Swedish Industries, August, 1972, Reproduced as Chapter 250 in the Collected Scientific Papers of Paul A. Samuelson, Vol. 4, Cambridge Massachusetts: The M.I.T. Press, 1977. Scherer, Frederic M., International High Technology Competition (Harvard University Press, Cambridge, Massachusetts, 1992). Vernon, Raymond, 1979, The product cycle hypothesis in a new international environment, Oxford Bulletin of Economics and Statistics, 41,255-267.