Dynamic Laws of Returns under Uncertainty

Abstract

The study of the effect of resource constraints (limitations) on production has always been an important topic in the theory of production. Turgot [1967] introduced into economic thought a proposition which has come to be known as the Law of Diminishing Returns at the intensive margin. The original spirit of the law was concerned with the restraint on agricultural production imposed by the scarcity of land. From this viewpoint, the particular formulation of the law in terms of diminishing product increments is nonessential to its significance. In bare form, the issue is: whether a bound on the inputs of a proper subset of factors leads to bounded outputs, when the other inputs may be applied in unlimited amounts. This more basic formulation of the law is described by Menger [1936] as an intersecting assertion.

An abstract model of dynamic stochastic production correspondences and a model of production policies are outlined. They are used, together with the notion of essentiality of input factors and a new deduction for strong limitationality, to give formulations of dynamic laws of returns under uncertainty. The formulations given serve to indicate the relationship between technology, information and production policy in a stochastic model of production.