Two Theorems on Generalized Diminishing Returns and their Applications to Economic Analysis*

Under certain weak assumptions such as free disposal and non-satiety, it is shown that the concavity of utility and of technology implies that the maximum value of the set of all attainable programmes is a concave function of the initial capital stocks. For time-independent problems, this implies that along an optimal path, as a capital stock is accumulated, its shadow price falls. The usefulness of the theorems is demonstrated in a number of examples, including Kemp's cake-eating problem and Forster's pollution-control problem.