Non-linear macroeconomic models of growth with memory

Tarasov, V.E.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Web of Science, Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 30 декабря 2020 г.

Автор: Tarasov V.E.
Журнал: Mathematics
Том: 8
Номер: 11
Год издания: 2020
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Первая страница: 1
Последняя страница: 22
Номер статьи: 2078
DOI: 10.3390/math8112078
Аннотация: In this article, two well-known standard models with continuous time, which areproposed by two Nobel laureates in economics, Robert M. Solow and Robert E. Lucas, aregeneralized. The continuous time standard models of economic growth do not account for memory effects. Mathematically, this is due to the fact that these models describe equations with derivatives of integer orders. These derivatives are determined by the properties of the function in an infinitely small neighborhood of the considered time. In this article, we proposed two non-linear models of economic growth with memory, for which equations are derived and solutions of these equations are obtained. In the differential equations of these models, instead of the derivative of integer order, fractional derivatives of non-integer order are used, which allow describing long memory with power-law fading. Exact solutions for these non-linear fractional differential equations are obtained. The purpose of this article is to study the influence of memory effects on the rate of economic growth using the proposed simple models with memory as examples. As the methods of this study, exact solutions of fractional differential equations of the proposed models are used. We prove that the effects of memory can significantly (several times) change the growth rate, when other parameters of the model are unchanged.
Добавил в систему: Тарасов Василий Евгеньевич

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