Equilibria for economies with production: constant-returns technologies and production planning constraints

  • Authors:

  • Kamal Jain;Kasturi Varadarajan

  • Affiliations:

  • One Microsoft Way, Redmond, WA;The University of Iowa, Iowa City IA

  • Venue:
  • SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
  • Year:
  • 2006

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Abstract

We consider the computation of equilibria in two economic models that generalize the exchange model by including production. In the constant returns model, each producer has a convex, constant-returns-to-scale, technology. In particular, this means that if the technology can output a certain quantity of a good using as input certain quantities of other goods, then scaling all these quantities by a common, non-negative, number also results in a technologically feasible plan. The technology also accomodates the no-free-lunch property, which says that it is not possible to produce something from nothing. At a given price, the producer picks a technologically feasible plan that maximizes her profit. Associated with each consumer is an initial endowment of goods and a utility function that describes her preferences between various bundles of goods. At a given price, the consumer sells her initial endowment, thus obtaining a certain income, and demands the bundle of goods maximizing her utility among all bundles that she can afford at the given price with her income.