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DETERMINATION OF THE OPTIMAL PRODUCTION VOLUMES AND SALES PRICES IN THE LINEAR MODEL OF MULTIPRODUCT MONOPOLY
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DETERMINATION OF THE OPTIMAL PRODUCTION VOLUMES AND SALES PRICES IN THE LINEAR MODEL OF MULTIPRODUCT MONOPOLY
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Aleksandr Perevozchikov  Ilya Lesik
Edition
Volume 52 Issue 1
Pages
132-140
Abstract
An algorithm of determining the volume of production and sales prices, maximizing firm profit in a multiproduct manufacturing and general resource limits is proposed. This article is based on the ideas of (Mishenko and Artyomenko, 2012). The main peculiarity of the model dis-cussed in the article is the assumption that in addition to the production volumes it enables to set the product selling price. As in the Mishchenko-Artyomenko model, the case planning for one period is analyzed. It is proved that the decision of the primary problem of optimizing Pareto non-dominant process and output volumes can be reduced to the problem of quadratic program-ming. It allows to find an alternative function of annual income for monopolies for the dynamic model of investment described in (Perevozchikov, Lesik, 2014). A model of monopoly from (Vasin, Morozov, 2005) for multiproduct market is analyzed in the article. A function of supply and Walras equilibrium is proposed for the purpose. Proved the theorem of existence and uniqueness of balanced and monopolistic prices, Pareto non-dominated. Obtained geometrical balanced and monopolistic prices providing the difference between monopolistic and balanced prices.
Keywords
multiproduct monopoly model, production volume, sales prices, general limitations on resources, the optimal strategy
Date of publication
01.01.2016
Number of purchasers
1
Views
983
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Vasin A.A. (2005). Nekooperativnye igry v prirode i obschestve. M.: MAKS Press.


Vasin A.A., Morozov V.V. (2005). Teoriya igr i modeli matematicheskoj ehkonomiki. M.: MAKS Press.          


Vilenskij P.L., Lifshits V.N., Smolyak S.A. (2004). Otsenka ehffektivnosti investitsionnykh proektov. Teoriya i praktika. M.: Delo.     


Karmanov V.G. (1980). Matematicheskoe programmirovanie. M.: Nauka.         


Makarov V.L., Rubinov F.M. (1973). Matematicheskaya teoriya ehkonomicheskoj dinamiki i ravnovesiya. M.: Nauka. 


Mischenko A.V., Artemenko O.A. (2012). Modeli upravleniya proizvodstvenno-finansovoj deyatel'nost'yu predpriyatiya v usloviyakh privlecheniya zaemnogo kapitala // Finansovaya analitika: problemy i resheniya. № 42 (132). S. 2-13.                    


Perevozchikov A.G., Lesik I.A. (2014a). Prostejshaya model' investitsij v osnovnye sredstva predpriyatiya // Audit i finansovyj analiz. № 2. S. 233-440.                


Perevozchikov A.G., Lesik I.A. (2014b). Model'nyj primer investitsij v osnovnye sredstva kompanii // Audit i finansovyj analiz. № 3. S. 267-276.             


Perevozchikov A.G., Lesik I.A. (2014 v). Obschaya model' investitsij v osnovnye sredstva predpriyatiya // Audit i finansovyj analiz. № 4. S. 206-209. 


Perevozchikov A.G., Lesik I.A. (2014g). Nestatsionarnaya model' investitsij v osnovnye sredstva predpriyatiya. V sb.: “Prikladnaya matematika i informatika: Trudy fakul'teta VMK MGU imeni M.V.Lomonosova”. Pod red. V.I. Dmitrieva. M.: MAKS Press. № 46. S. 76-88.       


Polyak B.T. (1983). Vvedenie v optimizatsiyu. M.: Nauka. Fedorov V.V. (1979). Chislennye metody maksimina. M.: Nauka.

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