Geodesic
Equilibrium prices in an economic equilibrium model
Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 3-22.

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In this paper, we study the existence of equilibrium price vector in a concurrent equilibrium model taking into account the transaction costs associated with the sale of products. In this model, the demand function is obtained as the solution to the problem of maximizing the utility function under budget constraints, and the supply function is obtained as the solution to the problem of profit maximization given transaction losses on the technology set. We establish sufficient conditions for the existence of quilibrium price vector. These conditions are consequences of general theorems on the existence of coincidence points in the theory of $\alpha$-covering mappings.
Keywords: economic equilibrium, transaction costs, coincidence points. 
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A. V. Arutyunov; N. G. Pavlova; A. A. Shananin. Equilibrium prices in an economic equilibrium model. Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 3-22. http://geodesic.mathdoc.fr/item/MM_2016_28_3_a0/

[1] A. Smith, An Inquiry into the Nature and Cause of the Wealth of Nations, 2 vols., London, 1776

[2] L. Walras, Elements d`Economie Politique Pure, Lausanne, 1874

[3] K. J. Arrow, G. Debreu, “Existence of an equilibrium for a competitive economy”, Econometrica, 22:3 (1954) | DOI | MR

[4] C. D. Aliprantis, D. J. Brown, O. Burkinshaw, Existence and optimality of competitive equilibria, Springer-Verlag, Berlin, 1990 | MR

[5] W. Hildenbrand, H. Sonnenschein (ed.), Handbook of mathematical economics, North-Holland, 1991 | MR | Zbl

[6] I. G. Pospelov, “Model povedeniia proizvoditelei v usloviiakh rynka i lgotnogo kreditovaniia”, Matematicheskoe modelirovanie, 7:10 (1995), 59–83 | MR | Zbl

[7] S. M. Guriev, I. G. Pospelov, “Model obshchego ravnovesiia ekonomiki perekhodnogo perioda”, Matematicheskoe modelirovanie, 6:2 (1994), 3–21

[8] A. A. Petrov, A. A. Shananin, I. G. Pospelov, Ot Gosplana k neeffektivnomu rynku: matematicheskii analiz evolyutsii rossiiskikh ekonomicheskikh struktur, The Edwin Mellen Press, 1999

[9] A. V. Rudeva, A. A. Shananin, “Variational inequalities for economic equilibrium in the model with the deficit of the working capital”, Moscow University Computational Mathematics and Cybernetics, 31:4 (2007), 170–178 | DOI | MR | Zbl

[10] A. A. Shananin, “Ispolzovanie variatsionnykh neravenstv dlia dokazatelstva sushchestvovaniia konkurentnogo ravnovesiia”, Matematicheskoe modelirovanie, 13:5 (2001), 29–36 | MR

[11] A. A. Shananin, “Dvoistvennost dlia zadach obobshchennogo programmirovaniia i variatsionnye printsipy v modeliakh ekonomicheskogo ravnovesiia”, Doklady RAN, 366:4 (1999), 462–464 | MR | Zbl

[12] A. V. Arutynov, “An iterative method for finding coincidence points of two mappings”, Computational Mathematics and Mathematical Physics, 52:11 (2012), 1483–1486 | DOI | MR | Zbl

[13] A. Arutyunov, E. Avakov, B. Gel'man, A. Dmitruk, V. Obukhovskii, “Locally covering maps in metric spaces and coincidence points”, J. Fixed Points Theory and Applications, 5:1 (2009), 5–16 | MR

[14] A. V. Arutynov, “Coincidence points of two maps”, Functional Analysis and its Applications, 48:1 (2014), 72–75 | DOI | DOI | MR | Zbl

[15] A. V. Arutynov, “Covering mappings in metric spaces and fixed points”, Doklady Mathematics, 76:2 (2007), 665–668 | DOI | MR | MR | Zbl

[16] A. V. Arutynov, “Stability of coincidence points and properties of covering mappings”, Mathematical Notes, 86:2 (2009), 153–158 | DOI | DOI | MR | Zbl