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.
Citation:
V. I. Shmyrev, “A linear production-exchange model: Polyhedral complexes and a criterion for an equilibrium”, Sib. Zh. Ind. Mat., 14:2 (2011), 124–131; J. Appl. Industr. Math., 6:2 (2012), 240–247
\Bibitem{Shm11}
\by V.~I.~Shmyrev
\paper A linear production-exchange model: Polyhedral complexes and a~criterion for an equilibrium
\jour Sib. Zh. Ind. Mat.
\yr 2011
\vol 14
\issue 2
\pages 124--131
\mathnet{http://mi.mathnet.ru/sjim674}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2962162}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 2
\pages 240--247
\crossref{https://doi.org/10.1134/S1990478912020135}
Linking options:
https://www.mathnet.ru/eng/sjim674
https://www.mathnet.ru/eng/sjim/v14/i2/p124
This publication is cited in the following 4 articles:
V. I. Shmyrev, “Polyhedral complementarity on a simplex. Potentiality of regular mappings”, J. Appl. Industr. Math., 12:1 (2018), 167–176
V. I. Shmyrev, “An iterative approach for searching an equilibrium in piecewise linear exchange model”, Discrete Optimization and Operations Research, DOOR 2016, Lecture Notes in Computer Science, 9869, eds. Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski, P. Pardalos, Springer Int. Publishing Ag, 2016, 61–73
V. I. Shmyrev, “Algoritmy poliedralnoi komplementarnosti dlya otyskaniya ravnovesiya v lineinykh modelyakh konkurentnoi ekonomiki”, Diskretn. analiz i issled. oper., 21:2 (2014), 84–101
V. I. Shmyrev, “The method of meeting trajectories for a linear production-exchange model”, J. Appl. Industr. Math., 6:4 (2012), 490–500
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