The Rybczynski Theorem under Decreasing Returns to Scale

Abstract

One of the most celebrated theorems of international trade is the Rybczynski theorem. This theorem was originally developed by Rybczynski (1955) within the context of a two-good, two-factor model. The theorem states that when the supply of a factor grows, output of the good which uses the growing factor intensively will increase at constant commodity prices, while the output of the other good will fall. The Rybczynski theorem was originally derived for the case of production functions which were assumed to be linearly homogeneous so that no advantages or disadvantages of scale existed in either industry. The case of variable returns to scale has, however, been treated by Jones (1968), Kemp (1969, pp. 154-67) and Panagariya (1980), who have used various methods to derive necessary and sufficient conditions for the theorem to carry over to this case as well. But these contributions are problematical because the conditions derived are such that simple economic interpretation of the results may be difficult. The difficulties are mainly due to the high level of generality of the exposition, where both increasing and decreasing returns to scale-defined in a wide sense-are included.' In this paper, we are concerned with deriving simple necessary and sufficient conditions under which the Rybczynski theorem carries over to a more restricted case: that of decreasing returns to scale in one or both industries, defined as a degree of homogeneity less than one in the sectoral production function.