Non-Linear Macroeconomic Models of Growth with Memory
In this article, two well-known standard models with continuous time, which are proposed by two Nobel laureates in economics, Robert M. Solow and Robert E. Lucas, are generalized. The continuous time standard models of economic growth do not account for memory effects. Mathematically, this is due to...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/2078 |
| _version_ | 1827701765131206656 |
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| author | Vasily E. Tarasov |
| author_facet | Vasily E. Tarasov |
| author_sort | Vasily E. Tarasov |
| collection | DOAJ |
| description | In this article, two well-known standard models with continuous time, which are proposed by two Nobel laureates in economics, Robert M. Solow and Robert E. Lucas, are generalized. 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. |
| first_indexed | 2024-03-10T14:41:03Z |
| format | Article |
| id | doaj.art-7c36c71ef8af4a18902a8cffde3b0e23 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:41:03Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-7c36c71ef8af4a18902a8cffde3b0e232023-11-20T21:49:11ZengMDPI AGMathematics2227-73902020-11-01811207810.3390/math8112078Non-Linear Macroeconomic Models of Growth with MemoryVasily E. Tarasov0Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, RussiaIn this article, two well-known standard models with continuous time, which are proposed by two Nobel laureates in economics, Robert M. Solow and Robert E. Lucas, are generalized. 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.https://www.mdpi.com/2227-7390/8/11/2078fractional differential equationgrowth modelfading memoryfractional derivativesolow model |
| spellingShingle | Vasily E. Tarasov Non-Linear Macroeconomic Models of Growth with Memory Mathematics fractional differential equation growth model fading memory fractional derivative solow model |
| title | Non-Linear Macroeconomic Models of Growth with Memory |
| title_full | Non-Linear Macroeconomic Models of Growth with Memory |
| title_fullStr | Non-Linear Macroeconomic Models of Growth with Memory |
| title_full_unstemmed | Non-Linear Macroeconomic Models of Growth with Memory |
| title_short | Non-Linear Macroeconomic Models of Growth with Memory |
| title_sort | non linear macroeconomic models of growth with memory |
| topic | fractional differential equation growth model fading memory fractional derivative solow model |
| url | https://www.mdpi.com/2227-7390/8/11/2078 |
| work_keys_str_mv | AT vasilyetarasov nonlinearmacroeconomicmodelsofgrowthwithmemory |