Abstract
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.
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