Application of M-Convex Submodular Flow Problem to Mathematical Economics

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 languageEnglish
Pages (from-to)257-277
Number of pages21
JournalJapan Journal of Industrial and Applied Mathematics
Volume20
Issue number3
Publication statusPublished - 2003 Oct
Externally publishedYes

Fingerprint

Combinatorial optimization
Cost functions
Economics
Competitive Equilibrium
Indivisible
Economic Model
Combinatorial Optimization
Discrete mathematics
Divisible
Substitute
Utility Function
Gross
Convex function
Cost Function
Convexity
Efficient Algorithms
Money

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Japan Journal of Industrial and Applied Mathematics, Vol. 20, No. 3, 10.2003, p. 257-277.

Research output: Contribution to journalArticle

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