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The Phelps–Koopmans theorem and potential optimality

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  • Debraj Ray

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.

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  • Debraj Ray, 2010. "The Phelps–Koopmans theorem and potential optimality," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 11-28, March.
    • Handle: RePEc:bla:ijethy:v:6:y:2010:i:1:p:11-28
    DOI: 10.1111/j.1742-7363.2009.00119.x
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    1. Mitra, Tapan & Ray, Debraj, 2012. "On the Phelps–Koopmans theorem," Journal of Economic Theory, Elsevier, vol. 147(2), pages 833-849.
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    Cited by:

    1. Dai, Darong, 2011. "Wealth Martingale and Neighborhood Turnpike Property in Dynamically Complete Market with Heterogeneous Investors," MPRA Paper 46416, University Library of Munich, Germany.
    2. Darong Dai, 2013. "Wealth Martingale and Neighborhood Turnpike Property In Dynamically Complete Market With Heterogeneous Investors," Economic Research Guardian, Weissberg Publishing, vol. 3(2), pages 86-110, December.

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