Terutomo Ozawa's demonstration of the relationship between the commodity trade triangle, the factor trade triangle, and the equilibrium factor endowment ratio rays in two that initially trade with one another because of differences in tastes, is both logically correct and geometrically interesting. But while I admire his elegant proof, I must disagree with his assertion that ''we are not in a position to tell the exact locations of [the factor endowment ratio] rays unless we first know the exact amounts of labor and capital to be moved between the two countries (p. 668). This assertion not only runs counter to the general mathematical fact that the solution of a general equilibrium system requires that all unknowns be simultaneously determined, but as a specific proposition is demonstrably false as well. It is proved below that given the initial equilibrium commodity trade triangles, the equilibrium factor endowment ratio rays in the two can be determined without explicitly considering the exact amounts of labor and capital to be moved between the two countries. In Figure 1 (a simplified version of my earlier Figure 2), the initial common production vector is OP with OZf the consumption vector in the foreign country and OZd the consumption vector in the home country. The respective equilibrium triangles thus are CfFP and CdDP, and the equilibrium commodity price ratio given by the slope of Cf PCd. By the Stolper-Samuelson relation the factor price ratio is known once the commodity price ratio is known; and given factor prices, the optimal factor-intensity ratios OR, and OR, also are known. In Figure 2, point E represents the common factor endowment y

Since Paul Samuelson's factor-price equalization theorem that commodity trade could serve as a perfect substitute for factor mobility, the mirror image problem of the conditions under which factor mobility could perfectly substitute for commodity trade has attracted the attention of such trade theorists as Robert Mundell, Ernest Nadel, and most recently Frank Flatters. The latter, in analyzing the case where factor-owners move with their exported productive factors, does not consider the question of the uniqueness of the equilibrium obtained. This is the subject of the present paper. It will be demonstrated that in the case where factor prices differ between countries in closed economy equilibrium, and where such difference is due to different factor endowment ratios in the two countries, f actor-price equalization is consistent with an infinite number of combinations of factor flows, the determination among which on a priori grounds is impossible. There will, however, be a single determinate mirror image solution in the case where trade is due to differences in tastes between the two countries.