Hicks and Hollander on Ricardo: A Mathematical Note

Abstract

The model of Ricardo's economy that John Hicks and Samuel Hollander [1977] explored in this Journal laid to rest notion that Ricardian models can be adequately constructed with wage assumed to be at subsistence. The model in that paper dealt, for most part, with an economy possessed of circulating capital only.1 It examined behavior of wage and labor force as economy approaches stationary state. In course of their investigation, Hicks and Hollander encountered possibility that wage and labor force might not approach stationary state levels in a smooth way, but might instead oscillate: wage passing sometimes below subsistence, sometimes above it; labor force increasing and decreasing. Such behavior, which Ricardo mentioned only briefly,2 they named the exception [Hicks and Hollander, 1977, p. 358]. When such a possibility arises, it is natural enough to investigate conditions that give rise to it. Hicks and Hollander did so and concluded that approach to stationary state equilibrium will be smooth, provided only that the elasticity of marginal product curve must be greater than 1 [Hicks and Hollander, 1977, p. 356]. This note reexamines model formally,3 on basis of Pasinetti's 1960 article. It shows that Hicks-Hollander condition for nonoscillatory behavior is sufficient, but not necessary.