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
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U2 - 10.1007/BF03167422
DO - 10.1007/BF03167422
M3 - Article
AN - SCOPUS:0347532861
SN - 0916-7005
VL - 20
SP - 257
EP - 277
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
IS - 3
ER -