Market equilibria for homothetic, quasi-concave utilities and economies of scale in production

  • Authors:
  • Kamal Jain;Vijay V. Vazirani;Yinyu Ye

  • Affiliations:
  • One Microsoft Way, Redmond, WA;Georgia Institute of Technology, Atlanta, GA;Management, Science and Engineering, Stanford, CA

  • Venue:
  • SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2005

Quantified Score

Hi-index 0.01

Visualization

Abstract

Eisenberg and Gale (1959) gave a convex program for computing market equilibrium for Fisher's model for linear utility functions, and Eisenberg (1961) generalized this to concave homogeneous functions of degree one. We further generalize to:1. Homothetic, quasi-concave utilities. This also helps extend Eisenberg's result to concave homogeneous functions of arbitrary degree.2. We introduce the notion of a trading cone which enables us to compute market equilibrium in the presence of economies of scale in production provided differential pricing is allowed. Applications to network pricing are provided.