### Abstract

Original language | English |
---|---|

Pages (from-to) | 43-58 |

Journal | Journal of Mathematical Economics |

Volume | 45 |

Issue number | 1-2 |

Publication status | Published - 2009 |

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### Cite this

*Journal of Mathematical Economics*,

*45*(1-2), 43-58.

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*Journal of Mathematical Economics*, vol. 45, no. 1-2, pp. 43-58.

**Constrained suboptimality when prices are non-competitive.** / Herings, P.J.J.; Konovalov, A.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Constrained suboptimality when prices are non-competitive

AU - Herings, P.J.J.

AU - Konovalov, A.

N1 - Appeared earlier as CentER DP 2000-114

PY - 2009

Y1 - 2009

N2 - The paper addresses the following question: how efficient is the market system in allocating resources if trade takes place at prices that are not competitive? Even though there are many partial answers to this question, an answer that stands comparison to the rigor by which the first and second welfare theorems are derived is lacking. We first prove a “Folk Theorem” on the generic suboptimality of equilibria at non-competitive prices. The more interesting problem is whether equilibria are constrained optimal, i.e. efficient relative to all allocations that are consistent with prices at which trade takes place. We discuss an optimality notion due to Bénassy, and argue that this notion admits no general conclusions. We then turn to the notion of p-optimality and give a necessary condition, called the separating property, for constrained optimality: each constrained household should be constrained in each constrained market. If the number of commodities is less than or equal to two, the case usually treated in the textbook, then this necessary condition is also sufficient. In that case equilibria are constrained optimal. When there are three or more commodities, two or more constrained households, and two or more constrained markets, this necessary condition is typically not sufficient and equilibria are generically constrained suboptimal.

AB - The paper addresses the following question: how efficient is the market system in allocating resources if trade takes place at prices that are not competitive? Even though there are many partial answers to this question, an answer that stands comparison to the rigor by which the first and second welfare theorems are derived is lacking. We first prove a “Folk Theorem” on the generic suboptimality of equilibria at non-competitive prices. The more interesting problem is whether equilibria are constrained optimal, i.e. efficient relative to all allocations that are consistent with prices at which trade takes place. We discuss an optimality notion due to Bénassy, and argue that this notion admits no general conclusions. We then turn to the notion of p-optimality and give a necessary condition, called the separating property, for constrained optimality: each constrained household should be constrained in each constrained market. If the number of commodities is less than or equal to two, the case usually treated in the textbook, then this necessary condition is also sufficient. In that case equilibria are constrained optimal. When there are three or more commodities, two or more constrained households, and two or more constrained markets, this necessary condition is typically not sufficient and equilibria are generically constrained suboptimal.

M3 - Article

VL - 45

SP - 43

EP - 58

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 1-2

ER -