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A linear production-exchange model: Polyhedral complexes and a criterion for an equilibrium

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Abstract

Under study is an economic model of exchange whose participants include consumers as well as companies producing commodities. The production capabilities of the companies are constrained by the expenses of a certain single resource. We scrutinize the version of the model with fixed budgets of the participants, show that some equilibrium exists, and describe an original approach of polyhedral complementarity which enables us to obtain a criterion for an equilibrium state. Thus, we can propose a finite algorithm for finding an equilibrium.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    V. I. Shmyrev

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  1. V. I. Shmyrev
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Correspondence to V. I. Shmyrev.

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Original Russian Text © V.I. Shmyrev, 2011, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2011, Vol. XIV, No. 2, pp. 124–131.

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Shmyrev, V.I. A linear production-exchange model: Polyhedral complexes and a criterion for an equilibrium. J. Appl. Ind. Math. 6, 240–247 (2012). https://doi.org/10.1134/S1990478912020135

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  • DOI: https://doi.org/10.1134/S1990478912020135

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