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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 2 ()
Pages: 833-849

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:2:p:833-849

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Web page: http://www.elsevier.com/locate/inca/622869

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

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  1. Majumdar, Mukul & Mitra, Tapan, 1982. "Intertemporal allocation with a non-convex technology: The aggregative framework," Journal of Economic Theory, Elsevier, Elsevier, vol. 27(1), pages 101-136, June.
  2. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(2), pages 200-223, April.
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Cited by:
  1. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2014. "Intertemporal equilibrium with production: bubbles and efficiency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020888, HAL.
  2. 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, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 14043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Acemoglu, Daron, 2012. "Introduction to economic growth," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(2), pages 545-550.
  4. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2014. "Intertemporal equilibrium with production: bubbles and efficiency," Working Papers 2014-306, Department of Research, Ipag Business School.

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