On the Phelps–Koopmans theorem

Tapan Mitra and Debraj Ray

Journal of Economic Theory, 2012, vol. 147, issue 2, 833-849

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.

Keywords: Capital overaccumulation; Inefficiency; Phelps–Koopmans theorem; Nonconvex production set (search for similar items in EconPapers)
JEL-codes: C61 O41 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (19)

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Working Paper: On the Phelps-Koopmans Theorem (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:147:y:2012:i:2:p:833-849

DOI: 10.1016/j.jet.2009.08.004

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