Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Danilov, G. Koshevoy, and K. Murota, Discrete convexity and equilibria in economies with indivisible goods and money, Math. Social Sci. 41 (2001) 251–273.
S. Fujishige and K. Murota, Notes on L-/M-convexfu nctions and the separation theorems, Math. Programming 88 (2000) 129–146.
S. Iwata and M. Shigeno, Conjugate scaling algorithm for Fenchel-type duality in discrete convexo ptimization, SIAM J. Optim., to appear.
K. Murota, Convexity and Steinitz’s exchange property, Adv. Math. 124 (1996) 272–311.
K. Murota, Discrete convexan alysis, Math. Programming 83 (1998) 313–371.
K. Murota, Submodular flow problem with a nonseparable cost function, Combinatorica 19 (1999) 87–109.
K. Murota, Discrete Convex Analysis(in Japanese) (Kyoritsu-Shuppan, Tokyo) to appear.
K. Murota and A. Shioura, M-convexfu nction on generalized polymatroid, Math. Oper. Res. 24 (1999) 95–105.
K. Murota and A. Shioura, Extension of M-convexity and L-convexity to polyhedral convexf unctions, Adv. in Appl. Math. 25 (2000) 352–427.
K. Murota and A. Shioura, Relationship of M-/L-convexfu nctions with discrete convexfu nctions by Miller and by Favati-Tardella, Discrete Appl. Math. to appear.
K. Murota and A. Tamura, New characterizations of M-convexfu nctions and their applications to economic equilibrium models with indivisibilities, Discrete Appl.Math., to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Murota, K., Tamura, A. (2001). Application of M-Convex Submodular Flow Problem to Mathematical Economics. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_2
Download citation
DOI: https://doi.org/10.1007/3-540-45678-3_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42985-2
Online ISBN: 978-3-540-45678-0
eBook Packages: Springer Book Archive