The Phelps–Koopmans theorem and potential optimality

Debraj Ray

International Journal of Economic Theory, 2010, vol. 6, issue 1, 11-28

Abstract: The Phelps–Koopmans theorem states that if every limit point of a path of capital stocks exceeds the “golden rule,” then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false in a strong sense. Not only can there be efficient paths with capital stocks forever above and bounded away from a unique golden rule, such paths can also be optimal under the infinite discounted sum of a one‐period utility function. The paper makes clear, moreover, that this latter criterion is strictly more demanding than the efficiency of a path.

Date: 2010
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https://doi.org/10.1111/j.1742-7363.2009.00119.x

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