Stochastic models of the dynamics of the maximum and optimal profit of a manufacturing enterprise introducing technological innovations

Abstract

The published article presents new stochastic models that describe the dynamics of profit formation in manufacturing enterprises using innovative technologies. The dependence of the enterprise's profit not only on the level of production (transformation) costs, but also on the level of non-production (transactional) costs resulting from the search and processing of economic information, financing of negotiation procedures, conclusion of contracts with partners, protection of property rights and payment for opportunistic behavior has been studied. employees and management of the company. It has been established that in order to find the optimal values of profit, it is necessary to maximize not only the profit function, but also the target transactional utility function that redistributes the profit of the enterprise, both in the interests of management and for the implementation of socially oriented programs. It is shown that the presence of transaction costs makes it unattainable for an enterprise to obtain the maximum possible value of profit, instead of which it is necessary to limit itself to its lower optimal value. For indicators of innovative transformations in the production of an enterprise that affect the increase in output and reduce costs, stochastic differential equations are established, random solutions of which describe the stochastic diffusion process of introducing technological innovations. Algorithms for the numerical solution of the stochastic differential equations of the model are constructed using the EulerMaruyama method, according to which each of their implementations is a stochastic trajectory of random functions of indicators of the dynamics of the development of manufacturing enterprises. For the mathematical expectations of the considered random functions, the corresponding differential equations are obtained. Numerical analysis of the developed model showed that taking into account the external random perturbing factor in the stochastic model leads to significant deviations from the deterministic model of the profit formation dynamics of manufacturing enterprises.