On the Phelps-Koopmans theorem

Tapan Mitra, Debraj Ray

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)833-849
    Number of pages17
    JournalJournal of Economic Theory
    Issue number2
    StatePublished - Mar 2012


    • Capital overaccumulation
    • Inefficiency
    • Nonconvex production set
    • Phelps-Koopmans theorem

    ASJC Scopus subject areas

    • Economics and Econometrics


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