### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 14-25 |

Number of pages | 12 |

Volume | 2223 LNCS |

DOIs | |

Publication status | Published - 2001 |

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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 2223 LNCS, 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

**Application of M-Convex submodular flow problem to mathematical economics.** / Murota, Kazuo; Tamura, Akihisa.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 2223 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2223 LNCS, pp. 14-25, 12th International Symposium on Algorithms and Computation, ISAAC 2001, Christchurch, New Zealand, 01/12/19. https://doi.org/10.1007/3-540-45678-3_2

}

TY - GEN

T1 - Application of M-Convex submodular flow problem to mathematical economics

AU - Murota, Kazuo

AU - Tamura, Akihisa

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038768365&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038768365&partnerID=8YFLogxK

U2 - 10.1007/3-540-45678-3_2

DO - 10.1007/3-540-45678-3_2

M3 - Conference contribution

AN - SCOPUS:0038768365

SN - 3540429859

SN - 9783540429852

VL - 2223 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 14

EP - 25

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -