Mathematical modeling in task of optimal managing by savings in the middle class

• Main Author: Derevyankina P.O.
• Format: Article
• Language: English
• Published: EDP Sciences 2020-01-01
• Series: E3S Web of Conferences
• Online Access: https://www.e3s-conferences.org/articles/e3sconf/pdf/2020/84/e3sconf_TPACEE2020_03002.pdf

Consumption and saving balance issues in the middle class, as the most economically active cluster of society, are the subject of extensive expert discussion and require systematic government regulation. The present paper deals with mathematical model of middle class differentiation by savings which dynamics is described by initial boundary value problem with a parabolic equation. This study aims to investigate a case of savings regulation by changing of non-savers share. The paper presents formulation this problem as an optimal boundary control problem for distributed system of savings. Based on the Lagrange principle, the necessary conditions for the solvability of the problem are derived in the form of an optimization system. The optimal control law establishing the relationship between the non-savers share and the structure of the middle class in terms of savings is obtained. The paper also considers an approach to the numerical implementation of the optimal control model in the Comsol Multiphysics simulation software. An example of model calculating for a region of Russia based on real data is given.