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Mathematics 2019, 7(2), 178; https://doi.org/10.3390/math7020178

Dynamic Keynesian Model of Economic Growth with Memory and Lag

1
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
2
Faculty of Economics, Lomonosov Moscow State University, 119991 Moscow, Russia
3
Yandex, Ulitsa Lva Tolstogo 16, 119021 Moscow, Russia
*
Author to whom correspondence should be addressed.
Received: 24 January 2019 / Revised: 6 February 2019 / Accepted: 7 February 2019 / Published: 15 February 2019
(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)
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Abstract

A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral and integro-differential operators with the confluent hypergeometric Kummer function in the kernel. These operators allow us to propose an economic accelerator, in which the memory and lag are taken into account. The fractional differential equation, which describes the dynamics of national income in this generalized model, is suggested. The solution of this fractional differential equation is obtained in the form of series of the confluent hypergeometric Kummer functions. The asymptotic behavior of national income, which is described by this solution, is considered. View Full-Text
Keywords: fractional differential equations; fractional derivative; Abel-type integral; time delay; distributed lag; gamma distribution; macroeconomics; Keynesian model fractional differential equations; fractional derivative; Abel-type integral; time delay; distributed lag; gamma distribution; macroeconomics; Keynesian model
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Tarasov, V.E.; Tarasova, V.V. Dynamic Keynesian Model of Economic Growth with Memory and Lag. Mathematics 2019, 7, 178.

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