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On the Phelps–Koopmans theorem

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  • Mitra, Tapan
  • Ray, Debraj

Abstract

We examine whether the Phelps–Koopmans theorem is valid in models with nonconvex production technologies. We argue that a nonstationary path that converges to a capital stock above the smallest golden rule may indeed be efficient. This finding has the important implication that “capital overaccumulation” need not always imply inefficiency. Under mild regularity and smoothness assumptions, we provide an almost-complete characterization of situations in which every path with limit in excess of the smallest golden rule must be inefficient, so that a version of the Phelps–Koopmans theorem can be recovered. Finally, we establish that a nonconvergent path with limiting capital stocks above (and bounded away from) the smallest golden rule can be efficient, even if the model admits a unique golden rule. Thus the Phelps–Koopmans theorem in its general form fails to be valid, and we argue that this failure is robust across nonconvex models of growth.

Suggested Citation

  • Mitra, Tapan & Ray, Debraj, 2012. "On the Phelps–Koopmans theorem," Journal of Economic Theory, Elsevier, vol. 147(2), pages 833-849.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:2:p:833-849
    DOI: 10.1016/j.jet.2009.08.004
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    References listed on IDEAS

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    1. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April.
    2. Majumdar, Mukul & Mitra, Tapan, 1982. "Intertemporal allocation with a non-convex technology: The aggregative framework," Journal of Economic Theory, Elsevier, vol. 27(1), pages 101-136, June.
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    Cited by:

    1. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2014. "Intertemporal equilibrium with production: bubbles and efficiency," Documents de travail du Centre d'Economie de la Sorbonne 14043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Bosi, Stefano & Le Van, Cuong & Pham, Ngoc-Sang, 2017. "Asset bubbles and efficiency in a generalized two-sector model," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 37-48.
    3. Cuong Le Van & Ngoc-Sang Pham, 2016. "Intertemporal equilibrium with financial asset and physical capital," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 155-199, June.
    4. Acemoglu, Daron, 2012. "Introduction to economic growth," Journal of Economic Theory, Elsevier, vol. 147(2), pages 545-550.
    5. 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.
    6. Darong Dai, 2014. "On the Turnpike Property of the Modified Golden Rule," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(1), pages 26-32, August.
    7. repec:hal:journl:halshs-01316876 is not listed on IDEAS

    More about this item

    Keywords

    Capital overaccumulation; Inefficiency; Phelps–Koopmans theorem; Nonconvex production set;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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