Variable Returns to Scale and Factor Price Equalization

In their classical expositions of the Factor Price Equalization (FPE) Theorem, Heckscher (1919), Lerner (1952), Samuelson (1948, 1949) and McKenzie (1955) provided sufficient conditions for the equality of equilibrium factor rewards in two or more countries. Those conditions invariably included the specification of perfectly competitive markets supported by convex production sets and freedom of entry. The focus on convexity continues in modern textbook presentations of the theory, suggesting a widespread belief that FPE is ‘less likely’ in a context of non-convexities. In contrast, we shall argue that if the non-convexities flow from external economies associated with changes in world-wide industry outputs then the existing theory of FPE is already sufficiently general to accommodate the non-convexities. In particular, it will be shown that, leaving aside singular cases in which the input vectors of industries are linearly dependent, the set of international factor assignments compatible with FPE is of full rank if and only if there are at least as many tradeable commodities as primary factors.