### Abstract

Under a gross substitution assumption, we prove existence and uniqueness of competitive equilibrium for an infinite-horizon exchange economy with limited commitment and complete financial markets. Risk-sharing is limited as only a part of the private endowment can be used as collateral to secure debt. The unique equilibrium is Markovian with respect to a minimal state space consisting of exogenous shocks and Negishi's welfare weights. We represent equilibrium dynamics via a monotone operator acting on entire wealth distribution functions. We construct a fixed point of this operator generating a lower and an upper orbit and proving coincidence of accumulation points.

Original language | English (US) |
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Pages (from-to) | 287-295 |

Number of pages | 9 |

Journal | Journal of Mathematical Economics |

Volume | 61 |

DOIs | |

State | Published - Dec 1 2015 |

### Fingerprint

### Keywords

- Competitive equilibrium
- Gross substitution
- Monotone operator
- Solvency constraints

### ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics

### Cite this

**Uniqueness of competitive equilibrium with solvency constraints under gross-substitution.** / Bloise, Gaetano; Citanna, Alessandro.

Research output: Contribution to journal › Article

*Journal of Mathematical Economics*, vol. 61, pp. 287-295. https://doi.org/10.1016/j.jmateco.2015.09.008

}

TY - JOUR

T1 - Uniqueness of competitive equilibrium with solvency constraints under gross-substitution

AU - Bloise, Gaetano

AU - Citanna, Alessandro

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Under a gross substitution assumption, we prove existence and uniqueness of competitive equilibrium for an infinite-horizon exchange economy with limited commitment and complete financial markets. Risk-sharing is limited as only a part of the private endowment can be used as collateral to secure debt. The unique equilibrium is Markovian with respect to a minimal state space consisting of exogenous shocks and Negishi's welfare weights. We represent equilibrium dynamics via a monotone operator acting on entire wealth distribution functions. We construct a fixed point of this operator generating a lower and an upper orbit and proving coincidence of accumulation points.

AB - Under a gross substitution assumption, we prove existence and uniqueness of competitive equilibrium for an infinite-horizon exchange economy with limited commitment and complete financial markets. Risk-sharing is limited as only a part of the private endowment can be used as collateral to secure debt. The unique equilibrium is Markovian with respect to a minimal state space consisting of exogenous shocks and Negishi's welfare weights. We represent equilibrium dynamics via a monotone operator acting on entire wealth distribution functions. We construct a fixed point of this operator generating a lower and an upper orbit and proving coincidence of accumulation points.

KW - Competitive equilibrium

KW - Gross substitution

KW - Monotone operator

KW - Solvency constraints

UR - http://www.scopus.com/inward/record.url?scp=84948733522&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948733522&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2015.09.008

DO - 10.1016/j.jmateco.2015.09.008

M3 - Article

AN - SCOPUS:84948733522

VL - 61

SP - 287

EP - 295

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -