A Theory of International Trade

When production theory is discussed in traditional economic custom, somehow, either intermediate goodsIntermediate goods or price determination are often not examined precisely. The prices are usually fixed, while scarcity of resources is exceptionally attached importance. The efficiency of production is consequently forced to be adapted to a given price system of goods. However, this kind of restrictive treatments of production came up against several difficulties when the theory of international trade is argued in terms of Ricardo and Heckscher-Ohlin, i.e., comparative cost theory. The object of international transactions may not be limited to such resources as regulations are often imposed. It is rather important to trade not only among the different intermediate goods but also even among the same kinds of intermediate goods empirically shown in Ikeda (2016). Thus the introduction of intermediate goods for production is indispensable to develop the theory of international trade. Even in the 21st century, however, economists were still frustrated to escape from a special two country-two commodity case. Fortunately, by remarking geometry, Shiozawa (2007, 2016), Shiozawa et al. (2017)Shiozawa, Y., has been successful to establish a price determinationPrice determination in a more general case of three country-three commodity. In Shiozawa (2016), he smartly employed a sub-tropical geometrySubtropical geometry to examine a general case of international trade, i.e., three country-three commodity case. Behind his idea, there is the idea of Minkowski space of productionMinkowski space of production, in particular, zonotopeZonotope. This approach will give a different view of production set, and possibly suggest a further generalization more than three of the number of country and commodity. First of all, this article gives a brief look of the new essence of Shiozawa’s theory, and then gives by some numerical simulation a new characterization of international tradeInternational trade in line with Shiozawa’s theory. Furthermore, this article examines the effect of the introduction of free international trade. The introduction of the optimization rule to international trade results in drastic changes in network structures. Finally, the link with the network analysis and econophysics will be argued.