Factor Price Equalization and the Stolper-Samuelson Theorem

It is important at the outset to remove an ambiguity in the statement just made. It is one thing to say that, given any initial equilibrium position, there exists a one-to-one association between commodities and factors such that a change in any commodity price will lead to a more than proportionate change (in the same direction) in the corresponding factor price. It is quite another thing to state that it is possible to find a one-to-one association between goods and factors in advance such that, starting from any equilibrium, a change in any commodity price will lead to a more than proportionate change in the price of the already specified factor. The first may be called the local version of the Stolper-Samuelson theorem, and the second the global version. Another distinction must be made. In the case of two factors and two commodities (the only case treated rigorously by Stolper and Samuelson), it turns out that if, as a result of an increase in the price of a good, one of the factor prices rises more than proportionately, then the other factor price must actually fall. In generalizing the theory to more than two commodities and two factors, it no longer holds that a more than proportionate increase in one factor price entails a fall in all the remaining factor prices. The case in which this does occur will be referred to as the strong form of the StolperSamuelson theorem, whereas the more general case will be called the weak form. We shall explore the various ways in which the theory first set forth by Stolper and Samuelson may be extended to n goods and factors. The main conclusions can be summarized as follows (the wording is necessarily vague, inasmuch as it constitutes a translation of mathematical conditions): (1) The Stolper-Samuelson theorem (strong, as well as weak form) is true locally (almost everywhere) for n 2, and globally whenever reversal of factor intensity is ruled out, as is, by now, quite well known. However, it is no longer true for n > 2, even under conditions which guarantee full factor price equalization. (2) Under certain special conditions, the weak form of