The published article proposes new models of the dynamic development of enterprises that restore their production through internal and external investments. Equations of balance are established for such enterprises, which describe changes in output and factors of production. The developed economic and mathematical models are presented in the form of systems of differential equations for an arbitrary number of production factors. In these models, proportional, progressive and digressive depreciation charges are considered. Their interaction with internal and external investments is investigated. Equations are obtained that describe the equilibrium state of enterprises and the corresponding limit values of production factors are calculated. Constructed in the form of systems of differential equations, economic and mathematical models allow you to describe the various modes of operation of enterprises. Such regimes include stable production output by enterprises, temporary suspension of enterprises for the period of its technical re-equipment, and temporary partial winding up of production. As an example, a two-factor enterprise model is considered in detail. The regularities of the influence of depreciation, internal and external investments on the dynamics of the enterprise are established. Equilibrium equations are obtained and the marginal volumes of production factors of the enterprise – fixed capital and labor – are calculated.

About the authors

Alexander L. Saraev

Samara National Research University

Author for correspondence.
ORCID iD: 0000-0002-9223-6330

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

Russian Federation

Leonid A. Saraev

Samara National Research University

ORCID iD: 0000-0003-3625-5921

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

Russian Federation


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