Application of M-Convex Submodular Flow Problem to Mathematical Economics

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.