Some Of The Theorems Of International Trade With Many Goods And Factors

The Heckscher–Ohlin model yields three important results beyond the Heckscher–Ohlin theorem itself: the Rybczynski, Stolper–Samuelson, and factor price equalization theorems. Recent years have witnessed many investigations of whether these results generalize to the case of n goods and n factors. This literature has succeeded both in clarifying our understanding of the neoclassical production model and in obtaining difficult and frequently elegant results. However, most of these results imply that the n by n generalizations of the simple and powerful 2 by 2 properties are true only subject to conditions on the relevant determinants that are at once stringent, complicated, and, frequently, economically arcane. A reader might not unnaturally conclude that the most significant implication is that the interesting 2 by 2 properties can not in practice be expected to hold in any essential way in the more general n by n environment and therefore reflect nothing more than the simplification to a world of two goods and two factors1[Note: This impression would be reinforced by the fact that the conditions for many of the n by n results to hold can be interpreted as requiring that the n × n case reduce in some sense to the 2 × 2 case. See in particular Kemp and Wegge (1969), Uekawa (1971), and Uekawa, Kemp and Wegge (1973).]. This I think would be a mistake. It is the primary intent of this note to argue that to a significant degree the powerful 2 by 2 results reflect essential properties of the neoclassical general equilibrium of production (as opposed to properties of a 2 by 2 model) and that therefore a central economic core of these results generalizes in a straightforward way to the n by n case. These generalizations depend on no complicated matrix properties and indeed follow immediately from the most elementary properties of the model…