Abstract
Monetary savings of the population are the subject of research of many specialists, since their detailed study in total with other various economic variables allows for a qualitative analysis of the current social and financial situation and make predictions. The definition of such an economic characteristic of society as the distribution of the population by money savings in practice is a very non-trivial task because of the lack of reliable information on the accumulation of citizens. Often, rather than a distributed value, a constant indicator is used – the average level of household savings. In the case when the savings are distributed according to the normal law in society (as in the developed countries), the replacement of the distributed quantity by a constant is possible to simplify the tasks. It is shown that Perm krai has bimodal structure of society savings, what essentially differs from the normal distribution law and therefore from the mathematical point of view it is unacceptable to replace one with a constant value, but it is necessary to take it into account as a distributed one. This ensures the relevance of this study, whose goal is to identify and analyze the numerical characteristics of the economic structure of Perm krai. The main idea of the work is to apply the mathematical model of the accumulation spectrum of the society of D.S. Chernavskii for Perm krai, the numerical calculation of the model and the economic analysis of the obtained characteristics. Similar numerical calculations of the distribution of the population of Perm krai on savings based on official statistics have not been conducted previously. Methods of economic analysis, mathematical and computer modeling, methods of theories of ordinary differential equations, partial differential equations and stochastic differential equations, probability theory and mathematical statistics are applied. A numerical study of the mathematical model of Perm krai economic society structure was carried out, the most probable stationary levels of population savings in Perm krai were calculated, which approximately amounted to 10 and 63 subsistence minimums for 2016 year. Families seem to accumulate in the vicinity of these savings values, like elementary particles under Brownian motion (this is not a coincidence, since both processes are described by the stochastic differential Fokker-Planck equation in partial derivatives of the parabolic type). Stationary savings levels numerically characterize the consumption standards and the standard of living of a society and are formed on the basis of the value of the consumer basket. In future, it is planned to conduct research on the optimal control of the economic structure of society. Keywords the economic society structure, population distribution density by savings, stationary levels of savings, spectrum of the savings, savings in the Perm Region, economic groups of the population, social stratification, Fokker – Planck equation, money balance equation, mathematical model of D.S. Chernavskii.
Highlights
Дарья Борисовна Владимирова ORCID ID: 0000-0001-8691-9883, Researcher ID: I-4484-2018 Пермский национальный исследовательский политехнический университет 614990, Россия, г
экономической структурой общества (ЭСО) Пермского края, как и любого региона России, в условиях рыночной экономики формировалась с 1990-х гг., поэтому для 2016 г. примем ее стационарной
В целом полученное распределение по накоплениям вполне соответствует распределению по доходам, публикуемом ежегодно в официальных источниках, согласно которому 20% населения с максимальными доходами распределяют между собой 47,1% всех доходов общества Пермского края, и более наглядно демонстрирует факт расслоения общества на «богатых» и «бедных»
Summary
Дарья Борисовна Владимирова ORCID ID: 0000-0001-8691-9883, Researcher ID: I-4484-2018 Пермский национальный исследовательский политехнический университет 614990, Россия, г. Определение такой экономической характеристики общества, как распределение населения по денежным накоплениям, на практике является весьма нетривиальной задачей из-за дефицита достоверной информации по накоплениям граждан. В работе показано, что для Пермского края структура накоплений общества бимодальна, т. Проведено численное исследование математической модели экономической структуры общества Пермского края, рассчитаны наиболее вероятные стационарные уровни накоплений населения Пермского края, которые приблизительно составили 10 и 63 прожиточных минимумов на 2016 г. Для математического описания того факта, что в реальности семья, помимо гарантированных, может иметь случайные доходы и расходы (выигрыш в лотерею, расходы в связи с болезнью), добавим выражение g t в правую часть уравнения накоплений (1), означающее общее количество денег, которое семья к моменту времени t накопит из случайных источников. Коэффициент g , отражающий величину случайных потерь или приобретений, задавался в интервале от 3 до 5,8
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