Application of M-Convex Submodular Flow Problem to Mathematical Economics

Kazuo Murota, Akihisa Tamura

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2003 Oct
Externally publishedYes


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

ASJC Scopus subject areas

  • General Engineering
  • Applied Mathematics


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