Mathematical modeling of economic society structure in the case study of the Perm region statistical data

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

For citation

Pervadchuk V.P., Vladimirova D.B., Derevyankina P.O. Mathematical modeling of economic society structure in the case study of the Perm region statistical data. Perm University Herald. Economy, 2018, vol. 13, no. 3, pp. 390–401. DOI 10.17072/1994-9960-2018-3-390-401

References

1. Chernavskii D.S., Pirogov G.G. et. al. Dinamika ekonomicheskoi struktury obshchestva [Dynamics of society economic structure]. Izvestiya vuzov. Prikladnaya nelineinaya dinamika [News of Universities. Applied Nonlinear Dynamics], 1996, vol. 4, no. 3, pp. 67–75. (In Russian).
2. Igonina L.L. Investitsionnaya znachimost' sberezhenii naseleniya v Rossiiskoi ekonomike [Significance of population’s savings as investment for Russian economy]. Daidzhest-Finansy [Digest Finance], 2017, vol. 22, iss. 1 (241), pp. 4–18. (In Russian).
3. Chernavskii D.S., Popkov Yu.S., Rakhimov A.Kh. Matematicheskie modeli tipologii semeinykh nakoplenii [Mathematical modelling of household savings classification]. Ekonomika i matematicheskie metody [Economics and Mathematical Methods], 1994, vol. 30, no. 2, pp. 98–106. (In Russian).
4. Chernavskii D.S., Starkov N.I., Shcherbakov A.V. O problemakh fizicheskoi ekonomiki [On some problems of physical economics]. Uspekhi fizicheskikh nauk [Success of Physical Sciences], 2002, no. 9 (172). (In Russian). doi: 10.3367/UFNr.0172.200209c.1045.
5. Ivanov Yu.N., Khomenko T.A. Problemy i metody statistiki sberezheniya naseleniya v sootvetstvii s kontseptsiyami SNS [Problems and methods of statistics of population’s savings according to the system of national accounts statisctics]. Ekonomicheskii zhurnal VSHE [Higher School of Economics Economics Journal], 1998, no. 4, pp. 508–515. (In Russian).
6. Ruggles R. Accounting for saving and capital formation in the United States, 1947–1991. Journal of Economic Perspectives, 1993, vol. 7, no. 2, pp. 3–17. doi: 10.1257/jep.7.2.3.
7. Späth J., Schmid K.D. The Distribution of household savings in Germany. IMK Studies, 2016, no. 50. 36 p.
8. Kitamura Y., Takayama N., Arita F. Household savings and wealth distribution in Japan. In Book: Life cycle savings and public policy: A cross-national study of six countries. Ed. A. Börsch-Supan. San Diego, Academic Press, 2003. 34 p.
9. Jäntti M., Sierminska E., Van Kerm P. Modelling the joint distribution of income and wealth. IZA Discussion Papers, 2015, no. 9190. 31 p.
10. Rimashevskaya N.M., Diskin I.E. Sberezheniya naseleniya kak istochnik investitsii [Personal saving as a source of investments]. Ekonomicheskie nauki sovremennoi Rossii [Economic Sciences of Contemporary Russia], 1998, no. 2. (In Russian) Available at: http://www.cemi.rssi.ru/ecr/1998/ 2/content2.htm (accessed 19.04.2018).
11. Matovnikov M.Yu. Sberegatel'naya aktivnost' naseleniya Rossii [Savings activity of Russian population]. Den'gi i kredit [Money and Credit], 2015, no. 9, pp. 34–39. (In Russian).
12. Chernavskii D.S., Shcherbakov A.V. Sotsial'no-ekonomicheskii byulleten'. 2016 [Social and economic bulletin. 2016]. Tsentr sotsial'no-ekonomicheskogo prognozirovaniya im. D.I. Mendeleeva. Moscow, Grifon Publ., 2016. 72 p. (In Russian).
13. Chernavskii D.S., Suslakov B.A., Chernavskaya O.D. et.al. O sotsial'no-ekonomicheskoi strukture obshchestva [About social and economic structure of society]. Zakonodatel'stvo i ekonomika [Legistlation and Economy], 1995, no. 7-8, pp. 8–14. (In Russian).
14. Gyul'mamedova G. Sravnitel'nyi analiz modelei denezhnykh i material'nykh nakoplenii [Comparative Analysis of the models of money and materials accumulation]. Aktual'nye problemy ekonomiki [Acute Issues of Economy], 2012, vol. 138, no. 12, pp. 322–327. (In Russian).
15. Orudzhev E.G., Gyul'mamedova G.A. O smeshannykh zadachakh na konechnom prostranstve nakoplenii [About mixed tasks at the final space of savings]. Aktual'nye problemy ekonomiki [Acute Issues of Economy], 2011, no. 11, pp. 431–441. (In Russian).
16. Krysova E.V., Shatrov A.V. Metody stokhasticheskoi dinamiki v matematicheskom modelirovanii sotsial'no-ekonomicheskikh protsessov [Stochastic dynamics methods in mathematical modelling of social and economic processes]. Matematicheskii vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona [Mathematical Bulletin of Pedagogical Universities and Other Universities of Volga-Vyatka Region], 2006, no. 8, pp. 301–315. (In Russian).
17. Mandel' L., Vol'f E. Opticheskaya kogerentnost' i kvantovaya optika. Per. s angl. [Optical coherence and quantum optics. Trans. from Engl.]. Moscow, Fizmatlit Publ., 2000. 896 p. (In Russian).
18. Tikhonov V.I., Mironov M.A. Markovskie protsessy [Markov chain]. Moscow, Sovetskoe radio Publ., 1977. 488 p. (In Russian).
19. Kurzenev V.A., Lychagina E.B. Stokhasticheskoe modelirovanie dinamiki ekonomicheskoi sistemy [Stochastic modelling of dynamics of economic system]. Upravlencheskoe konsul'tirovanie [Management Consulting], 2013, no. 5 (53), pp. 78–83. (In Russian).
20. Oksendal' B. Stokhasticheskie differentsial'nye uravneniya. Vvedenie v teoriyu i prilozheniya. Per. s angl. [Stochastic differential equations. Introduction to the theory and application]. Moscow, Mir, AST Publ., 2003. 408 p. (In Russian).
21. Chen Mu-Fa. Stochastic models of economic optimization. Recent Developments in Stochastic Analysis and Related Topics, 2004. doi: 10.1142/9789812702241_0007.
22. Mantegna R.N., Stanley H.E. An introduction to econophysics, correlation and complexity in finance. Cambridge University Press, 2000. 162 p. doi: 10.1063/1.1341926.
23. Kendrick D.A. Stochastic control for economic models. The University of Texas. 2002. Available at: https://liberalarts.utexas.edu/files/495395 (accessed 19.04.2018).
24. Vladimirova D.B., Derevyankina P.O. Optimal'noe upravlenie raspredelennymi sistemami v zadachakh sotsial'no-ekonomicheskogo analiza [Optimal management of distribution systems in the tasks of social and economic analysis]. Global'nyi nauchnyi potentsial [Global Scientific Potential], 2016, no. 3 (60), pp. 40–43. (In Russian).
25. Fursikov A.V. Optimal'noe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya [Optimal management of distribution systems. Theory and application]. Novosibirsk, Nauchnaya kniga Publ., 1999. 350 s. (In Russian).

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