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Equilibrium in a Production Economy

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Abstract

Consider a closed production-consumption economy with multiple agents and multiple resources. The resources are used to produce the consumption good. The agents derive utility from holding resources as well as consuming the good produced. They aim to maximize their utility while the manager of the production facility aims to maximize profits. With the aid of a representative agent (who has a multivariable utility function) it is shown that an Arrow-Debreu equilibrium exists. In so doing we establish technical results that will be used to solve the stochastic dynamic problem (a case with infinite dimensional commodity space so the General Equilibrium Theory does not apply) elsewhere.

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza, Facoltà di Economia, Università di Roma “La Sapienza”, via del Castro Laurenziano 9, 00161, Roma, Italy

    Maria B. Chiarolla

  2. Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Ulrich G. Haussmann

Authors
  1. Maria B. Chiarolla
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  2. Ulrich G. Haussmann
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Corresponding author

Correspondence to Ulrich G. Haussmann.

Additional information

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant 88051, and by the Program for Cultural and Scientific Cooperation between Università di Roma “La Sapienza” and the University of British Columbia.

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Chiarolla, M.B., Haussmann, U.G. Equilibrium in a Production Economy. Appl Math Optim 63, 435–461 (2011). https://doi.org/10.1007/s00245-010-9128-3

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