### Abstract

This paper considers an economic model in which producers and consumers trade various indivisible commodities through a perfectly divisible commodity, money. On the basis of the recent developments in discrete mathematics (combinatorial optimization), 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, where M-convexity is closely related to the gross substitutes condition.

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

Pages (from-to) | 257-277 |

Number of pages | 21 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 20 |

Issue number | 3 |

Publication status | Published - 2003 Oct |

Externally published | Yes |

### Fingerprint

### Keywords

- Combinatorial optimization
- Competitive equilibria
- Indivisibilities
- M-convex/concave functions
- Mathematical economics

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Japan Journal of Industrial and Applied Mathematics*,

*20*(3), 257-277.

**Application of M-Convex Submodular Flow Problem to Mathematical Economics.** / Murota, Kazuo; Tamura, Akihisa.

Research output: Contribution to journal › Article

*Japan Journal of Industrial and Applied Mathematics*, vol. 20, no. 3, pp. 257-277.

}

TY - JOUR

T1 - Application of M-Convex Submodular Flow Problem to Mathematical Economics

AU - Murota, Kazuo

AU - Tamura, Akihisa

PY - 2003/10

Y1 - 2003/10

N2 - This paper considers an economic model in which producers and consumers trade various indivisible commodities through a perfectly divisible commodity, money. On the basis of the recent developments in discrete mathematics (combinatorial optimization), 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, where M-convexity is closely related to the gross substitutes condition.

AB - This paper considers an economic model in which producers and consumers trade various indivisible commodities through a perfectly divisible commodity, money. On the basis of the recent developments in discrete mathematics (combinatorial optimization), 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, where M-convexity is closely related to the gross substitutes condition.

KW - Combinatorial optimization

KW - Competitive equilibria

KW - Indivisibilities

KW - M-convex/concave functions

KW - Mathematical economics

UR - http://www.scopus.com/inward/record.url?scp=0347532861&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347532861&partnerID=8YFLogxK

M3 - Article

VL - 20

SP - 257

EP - 277

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 3

ER -