Application of M-Convex Submodular Flow Problem to Mathematical Economics
This paper shows an application of the M-convexs ubmodular flow problem to an economic model in which producers and consumers trade various indivisible commodities through a perfectly divisible commodity, money. 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. The algorithm consists of two phases: the first phase computes productions and consumptions in an equilibrium by solving an M-convexs ubmodular flow problem and the second finds an equilibrium price vector by solving a shortest path problem.
KeywordsCompetitive Equilibrium Short Path Problem Convex Polyhedron Price Vector Initial Endowment
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