### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 833-849 |

Number of pages | 17 |

Journal | Journal of Economic Theory |

Volume | 147 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2012 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Journal of Economic Theory*,

*147*(2), 833-849. https://doi.org/10.1016/j.jet.2009.08.004

**On the Phelps-Koopmans theorem.** / Mitra, Tapan; Ray, Debraj.

Research output: Contribution to journal › Article

*Journal of Economic Theory*, vol. 147, no. 2, pp. 833-849. https://doi.org/10.1016/j.jet.2009.08.004

}

TY - JOUR

T1 - On the Phelps-Koopmans theorem

AU - Mitra, Tapan

AU - Ray, Debraj

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

UR - http://www.scopus.com/inward/record.url?scp=84858006345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858006345&partnerID=8YFLogxK

U2 - 10.1016/j.jet.2009.08.004

DO - 10.1016/j.jet.2009.08.004

M3 - Article

VL - 147

SP - 833

EP - 849

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

IS - 2

ER -