### Abstract

This paper shows an application of the M-convexs ubmodular flow problem to an economic model in which producers and consumers trade various indivisible commodities through a perfectly divisible commodity, money. We give an efficient algorithm to decide whether a competitive equilibrium exists or not, when cost functions of the producers are M« convex and utility functions of the consumers are M« concave and quasilinear in money. The algorithm consists of two phases: the first phase computes productions and consumptions in an equilibrium by solving an M-convexs ubmodular flow problem and the second finds an equilibrium price vector by solving a shortest path problem.

Original language | English |
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Title of host publication | Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings |

Pages | 14-25 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2001 Dec 1 |

Externally published | Yes |

Event | 12th International Symposium on Algorithms and Computation, ISAAC 2001 - Christchurch, New Zealand Duration: 2001 Dec 19 → 2001 Dec 21 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2223 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Symposium on Algorithms and Computation, ISAAC 2001 |
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Country | New Zealand |

City | Christchurch |

Period | 01/12/19 → 01/12/21 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings*(pp. 14-25). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2223 LNCS). https://doi.org/10.1007/3-540-45678-3_2