Abstract
International competition among firms and units of a multinational enterprise is a game with wage rates as handicaps. This simple truth is commonly known among managers of firms competing in the international arena. Although it is instinctively trivial and evident, this image of international competition is quite different from the traditional comparative advantage argument. Supporting the new view requires a new theory. Sections 2, 3, 4, 5, and 6 are an introduction to the new theory of international values. The second part of the chapter (Sects. 7, 8, and 9) offers some preliminary remarks on how to use it. The third part (Sects. 10, 11, and 12) is a demonstration of how the new theory can be used to analyze international competition among firms. The last part (Sects. 13 and 14) illustrates how the new theory can be applied to a more realistic situation and provides some remarks regarding the wider scope of application of the new theory.
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Notes
- 1.
A greater problem of the HOS model is that it assumes the same technology for all countries. This excludes firm-level competition, as its main aspect is competition in technology for better products and production techniques.
- 2.
Another important and much more radical exception is Pasinetti (1993 Chap. 9). This paper focuses on wage rate differences at the very basis of international economic relations. Its exposition is complementary to the new theory of international values, since it offers a good illustration of why wage rate differences are crucial in the examination of international trade.
- 3.
- 4.
Chipman considered Ricardo’s explanation a “non sequitur” (Chipman 1965, p. 479).
- 5.
Jones (1961) claims that he explored the case in which intermediate goods are freely traded, but his theory was restricted to RII in my classification (Shiozawa 2017a Sect. 2). Jones and Kierzkowski (1990, 2001) and Jones (2000) are about a theory of fragmentation but not a general theory of input trade.
- 6.
In later works, Graham makes a clear distinction between Ricardo’s classical theory of international trade and the theory developed by John Stuart Mill and his successors (Graham 1932, p. 616).
- 7.
It does matter in the arguments of gains from trade. See Chipman’s mistake, mentioned above.
- 8.
- 9.
The term “complete specialization” is in fact ambiguous. It may signify two different situations: [A] Each product is produced only within a country. [B] There are no products that are produced in more than two countries. In this chapter we use the term complete specialization only in the meaning [A].
- 10.
There are other possibilities, such as the case of two countries producing all three goods simultaneously. This case should be excluded from the general situation, because it is possible only when the input coefficients satisfy special constraints.
- 11.
We exclude the case where (3-5) contains equality, as it is not the generative case.
- 12.
- 13.
Codimension of a face is the dimension of the space minus the dimension of the face. It can also be defined as the dimension of the normal cone to the face.
- 14.
- 15.
There are about 200 countries in the world, but the number of commodities easily exceeds 10 million.
- 16.
This situation inevitably led Mill to consider international trade as a problem of “pure” exchange economy (Shiozawa 2017b).
- 17.
In opposition to neoclassical economics, which considers capital a factor of production, we do not regard capital goods as the same factors of production as labor, because capital goods are products from production activities, whereas labor power is not produced inside the capitalist production system. At least, capital goods are not primary factors. It may be better to say that there are as many primary factors as the number of countries.
- 18.
This is the new result which does not appear in Shiozawa (2017a).
- 19.
- 20.
In Pasinetti’s terminology, pure labor (production) economy (Pasinetti 1993)
- 21.
For character string expressions such as A13B23, see the explanation at the end of Sect. 4.
- 22.
This theorem can be easily extended to the RI and RII cases in Shiozawa (2017a).
- 23.
In Sect. 6 we define the same concept using more explicit inequalities. The concept of admissible value assumes a set of production techniques, and, if the set changes, the same value may become non-admissible. Shiozawa (2017a Definition 3–7) provides a different definition. Concerning the equivalence of the two definitions, see the argument put forward later in this section.
- 24.
This fact is vaguely stated in McKenzie (1953 p 172–3).
- 25.
We distinguish between y ≤ z and y≦z. The former means y≦z and y ≠ z.
- 26.
This condition is necessary because, in a degenerated case, F may not be a facet of codimension 1. The meaning of “general position” will be explained in Sect. 6.
- 27.
See, for example, Berge (1971 p 108).
- 28.
The formula is true for RI and RII, because they have the same structure (Shiozawa 2017a Sect. 2). Little is known about the RS economy case.
- 29.
Thus, the new theory of international values provides the theory that Pasinetti (1993 Chap. 9) thought necessary.
- 30.
- 31.
This does not exclude production by using global supply chains, because it is treated as using chains of trades and productions. In the RS economy, input goods are freely traded among countries.
- 32.
Regarding the case with positive transportation costs, see Shiozawa (2017a Sect. 9).
- 33.
“Profit rate” is normally defined as the ratio between gross profit and the total value of fixed capital. Thus, it is a function of demand or production volume and is not determined by unit cost and product price.
- 34.
The set of M + N−1 vectors a(h) in R N forms a densely open set in R N(M + N−1), but we have to prove that the set of linearly independent T forms a densely open set in the set of M + N−1 vectors that satisfy (a), (b), and (c) by means of the topology induced by R N(M + N−1).
- 35.
Shiozawa wishes to thank Taichi Tabuchi and is grateful for the discussions in the Workshop on the Theory of International Values. Without Tabuchi’s criticism, he would have never attempted this theory reorientation.
- 36.
Although we essentially have the same idea, path dependence emerges in our case not through a multiplicity of institutions, but through the existence of mutually exclusive international values (i.e., pairs of wage rates and prices).
- 37.
- 38.
The case of agricultural products is excluded from our examination, because it requires a very different argument. Another important but implicit condition is that exchange rates are fixed.
- 39.
For the sake of simplicity, we do not refer to the capacity that a set of fixed capital determines, but we implicitly suppose that each firm has a set of equipment, machinery, buildings, facilities, and vehicles of proper proportion and suitably arranged. Within this framework, production is a proportional input-output relation which is possible within a capacity that is determined by capital equipment. If we take into account the depreciation of fixed costs, we are in fact considering an increasing-returns-to-scale situation. The approach based on the proportional cost assumption is retained if we suppose that the headquarters of the firm charge, as a part of input costs, a rate of capital usage which is proportional to the quantity of production. See Fujimoto (2012b).
- 40.
The assumption is always that the wage rate is expressed by an international currency.
- 41.
Shiozawa wishes to thank Hideo Sato for providing details on Graham’s usage of terms (mail of February 15, 2017). See also Sato 2017 Sect. 3.
- 42.
Graham avowed that he owed this naming to his former student C. R. Whittlesey (Graham 1932, p. 581, n.3).
- 43.
Dosi et al. (1990 p 200) distinguish between two groups of commodities: Ricardian commodities and innovative commodities. In our terminology, commodities in the first group are link commodities and those in the second group are monopolistic commodities.
- 44.
This is also one of three points that Faccarello (2017) identifies as Ricardo’s basic view of international trade.
- 45.
Remember that a in Sect. 2 stands for the labor input coefficient. We follow the same convention in this section.
- 46.
- 47.
The Marxian theory of international values tried to shed light on how the wage rate of each nation is determined. However, it failed because it relied too much on interpreting Marx’s texts. A rare exception is Kinoshita (2003). In the 1960s, Kinoshita asserted that the value added that a worker of a nation produces at a given unit of time is proportional to the productivity of the nation (p 52). Although he could not give an exact formulation, what he claimed was essentially correct.
- 48.
Officially, the reform and opening-up started in 1978 but it remained limited until 1992.
- 49.
Ronald Jones (Jones 1961 p 167) assumed that material input coefficients are the same for all countries (i.e., trade economy of type RII) when examining the trade of “intermediate products” (in his expression of 1961) or more simply “input trade” (in his later expression). “As a partial justification of this assumption,” Jones cited the fact that “the prices of intermediate (and final) commodities are the same in all countries with free trade and zero transport” (p. 167 note). This is an odd justification because, even when the prices of input products are the same, input coefficients may differ for various reasons: experience, skill of workers or engineers, product design, etc.
- 50.
Expression (11-1) really means that {log[ w J(t) u J(t) / w C(t) u C(t) ]}' > 0 for a time vaiable t. If this is always greater than constant δ, it is easy to see by integrating on the interval [0, T] that log [w J(T) u J(T) ] − log [w J(T) u J(T)] > δT + {log(w J(0) w J(0) − log (w J(0) u J(t)} > 0 for sufficiently large T.
- 51.
Here we assume a situation of pure labor input economy. When the material costs are the same in both countries, the argument applies with no modifications, but it needs to be modified appropriately if the material costs are different. See the pertinent part of Sect. 10.
- 52.
Compare these with the four conditions in Sect. 7. Conditions (1) and (3) are here replaced by a single condition (3). It is understood that T is in a general position. The world final demand d is not rquired to be on the production possibility frontier.
- 53.
This is not exactly the same as Linder’s hypothesis.
- 54.
The Dixit-Stiglitz utility function is given by U(x1, …, xn) = (x 1 σ + … + x n σ)1/σ with σ < 1. Each individual displaying a strong preference has a similar utility function but with σ > 1. See chapter “Product Variety for Effective Demand Creation” of this book, Sect. 2.1.1.
- 55.
See footnote 33.
- 56.
Product price is only one of the determinants of product demand. Many other factors, like weather, trade cycle, fads, and various events, contribute to changes in demand flows.
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Shiozawa, Y., Fujimoto, T. (2018). The Nature of International Competition Among Firms. In: Fujimoto, T., Ikuine, F. (eds) Industrial Competitiveness and Design Evolution. Evolutionary Economics and Social Complexity Science, vol 12. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55145-4_2
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