MARGINAL UTILITY FOR ECONOMICAL PROCESSES WITH MEMORY
Tarasova Valentina Vasil'evna, Tarasov Vasily Evgen'evich
Lomonosov Moscow State University
Abstract. The article examines the conception of marginal utility and the methods to describe economical processes considering the dependence of the subject’s current state not only on infinitesimally close previous states (i.e. integer order derivatives) but also on all the previous states on a finite interval. The paper justifies the necessity to consider economical subjects’ memory in the models of consumer economical behaviour. To generalize the conception of marginal utility, which allows describing the behaviour of economical subjects with memory the authors use non-integer order derivatives.
Key words and phrases: экономический субъект, предельная полезность, экономическое поведение, эредитарность, эффект памяти, economical subject, marginal utility, economical behaviour, hereditarity, effect of memory
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References:
Letnikov A. V. Ob istoricheskom razvitii teorii differentsirovaniya s proizvol'nym ukazatelem [Elektronnyi resurs] // Matematicheskii sbornik. 1868. T. 3. № 2. S. 85-112. URL: http://mi.mathnet.ru/msb8048 (data obrashcheniya: 01.07.2016).
Menger K. Izbrannye raboty [Elektronnyi resurs]. M.: Izdatel'skii dom "Territoriya budushchego", 2005. 496 s. URL: http://www.prognosis.ru/lib/Menger%20RRR.pdf (data obrashcheniya: 01.07.2016).
Samko S. G., Kilbas A. A., Marychev O. I. Integraly i proizvodnye drobnogo poryadka i nekotorye prilozheniya. Minsk: Nauka i tekhnika, 1987. 688 s.
Tarasova V. V., Tarasov V. E. O primenimosti tochechnoi elastichnosti sprosa po tsene dlya birzhevykh torgov po dollaru SShA // Nauchnaya perspektiva. 2016. № 6. S. 6-11.
Tarasova V. V., Tarasov V. E. Tsenovaya elastichnost' sprosa s pamyat'yu // Ekonomika, cotsiologiya i pravo. 2016. № 4-1. S. 98-106.
Tarasova V. V., Tarasov V. E. Ekonomicheskie indikatory: neodnoznachnost' i effekty pamyati // Ekonomika. Upravlenie. Pravo. 2016. № 3 (66).
Tarasova V. V., Tarasov V. E. Elastichnost' vnebirzhevogo kassovogo oborota valyutnogo rynka RF // Aktual'nye problemy gumanitarnykh i estestvennykh nauk. 2016. № 7-1. S. 207-215.
Uchaikin V. V. Metod drobnykh proizvodnykh. Ul'yanovsk: Artishok, 2008. 512 s.
Debnath L. A Brief Historical Introduction to Fractional Calculus // International Journal of Mathematical Education in Science and Technology. 2004. Vol. 35. № 4. P. 487-501.
Kilbas A. A., Srivastava H. M., Trujillo J. J. Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier, 2006. 540 p.
Laskin N. Fractional Market Dynamics // Physica A. 2000. Vol. 287. № 3. P. 482-492.
Mainardi F., Raberto M., Gorenflo R., Scalas E. Fractional Calculus and Continuous-Time Finance II: The Waiting-Time Distribution // Physica A. 2000. Vol. 287. № 3-4. P. 468-481.
Scalas E., Gorenflo R., Mainardi F. Fractional Calculus and Continuous-Time Finance // Physica A. 2000. Vol. 284. № 1-4. P. 376-384.
Skovranek T., Podlubny I., Petras I. Modeling of the National Economies in State-Space: A Fractional Calculus Approach // Economic Modelling. 2012. Vol. 29. № 4. P. 1322-1327.
Tarasov V. E. Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. N. Y.: Springer, 2011. 505 p.
Tarasov V. E. Leibniz Rule and Fractional Derivatives of Power Functions // Journal of Computational and Nonlinear Dynamics. 2016. Vol. 11. № 3. Article ID 031014. 4 p.
Tarasov V. E. No Violation of the Leibniz Rule. No Fractional Derivative // Communications in Nonlinear Science and Numerical Simulation. 2013. Vol. 18. № 11. P. 2945-2948.
Tarasov V. E. On Chain Rule for Fractional Derivatives // Communications in Nonlinear Science and Numerical Simulation. 2016. Vol. 30. № 1-3. P. 1-4.
Tarasova V. V., Tarasov V. E. Elasticity for Economic Processes with Memory: Fractional Differential Calculus Approach // Fractional Differential Calculus. 2016. Vol. 6. № 2. P. 219-232.
Tenreiro Machado J. A., Galhano A. M. S. F., Trujillo J. J. On Development of Fractional Calculus during the Last Fifty Years // Scientometrics. 2014. Vol. 98. № 1. P. 577-582.
Tenreiro Machado J. A., Mata M. E. A Fractional Perspective to the Bond Graph Modelling of World Economies // Nonlinear Dynamics. 2015. Vol. 80. № 4. P. 1839-1852.