Three-factor mathematical model of enterprise development at the account of internal and external investments

The published article proposes new models of the dynamics of enterprise development, the restoration of production capacities of which is due to internal and external investments. The constructed mathematical models are systems of differential equations for three production factors, which were used as the amount of fixed capital, the volume of labor involved in the production and the volume of materials used in the production. Dynamic production functions made up of the solutions of these systems are able to describe various options for the development of output by enterprises. Cases of monotonous progressive production output by enterprises, temporary suspension of enterprises during their technical re-equipment, and temporary curtailment of production are considered. The interaction of proportional, progressive and digressive depreciation deductions with internal and external investments is studied, and equations for calculating the marginal volumes of production factors of enterprises are obtained.