Uniqueness of competitive equilibrium with solvency constraints under gross-substitution

Gaetano Bloise, Alessandro Citanna

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)287-295
Number of pages9
JournalJournal of Mathematical Economics
Volume61
DOIs
StatePublished - Dec 1 2015

Fingerprint

Competitive Equilibrium
Gross
Distribution functions
Substitution
Mathematical operators
Orbits
Substitution reactions
Uniqueness
Risk Sharing
Wealth Distribution
Exchange Economy
Accumulation point
Monotone Operator
Infinite Horizon
Welfare
Financial Markets
Coincidence
Shock
State Space
Distribution Function

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.

In: Journal of Mathematical Economics, Vol. 61, 01.12.2015, p. 287-295.

Research output: Contribution to journalArticle

@article{419f9b0fd7dc4bdda69643e61352da3a,
title = "Uniqueness of competitive equilibrium with solvency constraints under gross-substitution",
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.",
keywords = "Competitive equilibrium, Gross substitution, Monotone operator, Solvency constraints",
author = "Gaetano Bloise and Alessandro Citanna",
year = "2015",
month = "12",
day = "1",
doi = "10.1016/j.jmateco.2015.09.008",
language = "English (US)",
volume = "61",
pages = "287--295",
journal = "Journal of Mathematical Economics",
issn = "0304-4068",
publisher = "Elsevier",

}

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 -