Equations of nonlinear dynamics of development of industrial enterprises, taking into account the amount of its maximum profit

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Abstract

In the published article, new modifications of economic and mathematical models of the dynamic development of enterprises are proposed, the production of which is being restored due to the introduction of their own investments. The developed models are presented in the form of systems of differential equations for an arbitrary number of production factors. Stationary solutions of these systems of equations correspond to the equilibrium states of the operation of enterprises and represent the limiting values of the factors of production. Two versions of systems of differential balance equations for enterprises, describing the growth of factors of production and output, have been established. In the first case, the growth of resources and output is limited by the limiting values of the factors of production. In the second case, the growth of resources and output is limited by the pre-calculated values of the factors of production that correspond to the value of the maximum profit of the enterprise. It is shown that the growth of production factors of the enterprise should not exceed the values corresponding to the value of the maximum profit. Otherwise, the company starts to operate at a loss. In the presented models, proportional, progressive and digressive depreciation deductions are considered. The constructed models make it possible to describe various modes of operation of enterprises. Such regimes include a stable output of products by enterprises, a temporary suspension of the work of enterprises during its technical re-equipment, and a temporary partial curtailment of production.

About the authors

Alexander L. Saraev

Samara National Research University

Author for correspondence.
Email: alex.saraev@gmail.com
ORCID iD: 0000-0002-9223-6330

Candidate of Economic Sciences, associate professor of the Department of Mathematics and Business Informatics

Russian Federation, 34, Moskovskoye shosse, Samara

Leonid A. Saraev

Samara National Research University

Email: saraev_leo@mail.ru
ORCID iD: 0000-0003-3625-5921

Doctor of Physical and Mathematical Sciences, professor, head of the Department of Mathematics and Business Informatics

Russian Federation, 34, Moskovskoye shosse, Samara

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