INTEGRO-DIFFERENTIAL MODELING OF GROSS PRODUCT

The aim of the work is to obtain the analytical dependence of the gross domestic product on changes in the main factors of production: labor resources, physical capital and natural resources. The integro-differential equation of the gross product change was obtained based on the apparatus of vector analysis. Cases of the equation describing the stable growth of the gross product are considered. The equation obtained in this case is a generalization of Lagrange’s theorem on finite increments. Investment, commissioning of equipment, development of natural resources, and creation of human capital — these are phenomena that do not happen instantly, but take a length of time. Therefore, the derivation of the integro-differential equation was based on the concept of dynamic divergence and its properties. Dynamic divergence allows one to take into account the lag processes that arise in the development of the economy. A finite-difference model of an integro-differential equation is presented. For the forecast value of the gross product, the values of the gross product and factors of production of the two previous years are used. Numerical modeling of changes in gross domestic product and gross value added in the period from 2001 to 2018 was carried out. The results obtained provide a very good model in the period of stable economic growth, but in the crisis and post-crisis period it is possible only to capture the general dynamics of development. This phenomenon is due to the fact that the time step was taken for one year, and according to the theory of difference schemes, a good result should be expected only on monthly data. The econometric analogue of the equation can be one of the tools for forecasting the gross product in the short term.

gross domestic product, main factors of production, gross value added, mathematical modeling, marginal labor productivity, marginal capital productivity, GDP growth, econometric model, dynamic divergence.

Kuznetsov S. B., Kuligin E. V. Integro-differential modeling of gross product. Business. Education. Law, 2021, no. 2, pp. 127—134. DOI: 10.25683/VOLBI.2021.55.228.