TY - JOUR

T1 - On the Phelps-Koopmans theorem

AU - Mitra, Tapan

AU - Ray, Debraj

N1 - Funding Information:
✩ We are grateful to an Associate Editor and three anonymous referees for helpful comments that provoked Proposition 1. Ray’s research was funded by National Science Foundation Grant no. 0617827. * Corresponding author. E-mail address: [email protected] (T. Mitra).

PY - 2012/3

Y1 - 2012/3

N2 - 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.

AB - 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.

KW - Capital overaccumulation

KW - Inefficiency

KW - Nonconvex production set

KW - Phelps-Koopmans theorem

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U2 - 10.1016/j.jet.2009.08.004

DO - 10.1016/j.jet.2009.08.004

M3 - Article

AN - SCOPUS:84858006345

SN - 0022-0531

VL - 147

SP - 833

EP - 849

JO - Journal of Economic Theory

JF - Journal of Economic Theory

IS - 2

ER -