Mathematical modeling of the human capital dynamic

Abstract

In the conditions of the development of modern economy, human capital is one of the main factors of economic growth. The formation of human capital begins with the birth of a person and continues throughout life, so the value of human capital is inseparable from its carriers, which in turn makes it difficult to account for this factor. This has led to the fact that currently there are no generally accepted methods of calculating the value of human capital. There are only a few approaches to the measurement of human capital: the cost approach (by income or investment) and the index approach, of which the most well-known approach developed under the auspices of the UN. This paper presents the assigned task in conjunction with the task of demographic dynamics solved in the time-age plane, which allows to more fully take into account the temporary changes in the demographic structure on the dynamics of human capital. The task of demographic dynamics is posed within the framework of the Mac-Kendrick-von Foerster model on the basis of the equation of age structure dynamics. The form of distribution functions for births, deaths and migration of the population is determined on the basis of the available statistical information. The numerical solution of the problem is given. The analysis and forecast of demographic indicators are presented. The economic and mathematical model of human capital dynamics is formulated on the basis of the demographic dynamics problem. The problem of modeling the human capital dynamics considers three components of capital: educational, health and cultural (spiritual). Description of the evolution of human capital components uses an equation of the transfer equation type. Investments in human capital components are determined on the basis of budget expenditures and private expenditures, taking into account the characteristic time life cycle of demographic elements. A one-dimensional kinetic equation is used to predict the dynamics of the total human capital. The method of calculating the dynamics of this factor is given as a time function. The calculated data on the human capital dynamics are presented for the Russian Federation. As studies have shown, the value of human capital increased rapidly until 2008, in the future there was a period of stabilization, but after 2014 there is a negative dynamics of this value.

Application of mathematical methods to solving problems of digitization of population movement

“…Thus, we will model quantitative demographic flows using the equation of demographic dynamics (Ketova, 2013), which contains dynamic functions of population distribution by age, functions of mortality, fertility and migration interaction. We will evaluate the qualitative characteristics of demographic flows using methods of correlation and regression analysis and constructing their mathematical models [18][19][20].…”

Influence of Structural Age Shifts of Population on Sectoral Structure of Employment

“…The scholars argue that there is a bidirectional link: one runs from human capital development to economic growth and overall human development, when human capital helps increase national income and social development; the other runs from economic growth to human capital development, as the resources from national income, are allocated to activities contributing to human capital development. The problem of modelling human capital dynamics considers three components of capital: educational, health, and cultural (spiritual) (Ketova et al, 2019).…”

Sustainable development of new technologies for clustering human capital (cenological approach)

“…The curve shown in Figure 1 is called the hyperbolic H-distribution and reflects the basic cenological law on the obligatory nature of this form for such systems. Some research groups [12] have implemented the research in the field of interdisciplinary modeling of the structure of human capital using data obtained by the Big Data analytics method. Distributions of a hyperbolic type are known in sociology and psychology.…”