Open AccessMathematical model of the dynamics of business development
Author(s) -
A. A. Sklyar
Publication year - 2020
Publication title -
teoretičeskaâ i prikladnaâ èkonomika
Language(s) - English
Resource type - Journals
ISSN - 2409-8647
DOI - 10.25136/2409-8647.2020.1.29404
Subject(s) - superposition principle , investment (military) , differential equation , aperiodic graph , differential (mechanical device) , econometrics , stochastic differential equation , system dynamics , production (economics) , economics , moment (physics) , business cycle , process (computing) , return on investment , computer science , mathematics , physics , mathematical analysis , microeconomics , macroeconomics , classical mechanics , combinatorics , artificial intelligence , politics , political science , law , thermodynamics , operating system
The subject of this research is the model of business development that describes the dependence of ongoing volume of production from previous investments and intensity of wear of production capacities. The investment process is characterized by a delay between the moment of investment, actual return and its continuation, gradual decrease in the level of return, and discreetness of investments. In the process of modeling, discrete investment were replaced by an integral, which leads to integral-differential equation, and in terms of facile assumption to the linear standard differential equation of second order or their system, solved by the disharmonious fluctuations on the background of an aperiodic trend. As the method of analysis of correspondence of the model data with the actual dynamics of business development, the research utilizes computational solution of the emerging differential equations. Comparison of the model data with the known statistics reveals their adequacy to the current economic processes. Statistical data contains noise component, which consists of various economic and political factors and principally limits the precision of forecasting. Differences in the length of fluctuation periods by industries impedes analysis of the economic behavior as a whole. At the same time, forecast of crisis phenomena that emerge in superposition of the phases of industry fluctuations can be executed with sufficient level of precision.