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Economic Dynamics with Memoryкнига
- Авторы: Tarasov Vasily E., Tarasova Valentina V.
- Год издания: 2021
- Издательство: W. de Gruyter
- Местоположение издательства: Berlin, Germany
- Объём: 576 страниц
- ISBN: 978-3-11-062745-9
- Монография
- DOI: 10.1515/9783110627459
- Аннотация: PrefaceThe proposed book outlines the basic concepts, models and principles of Economics with Memory as one of the new modern branches of economic science. Economics with Memory is a science of the behavior and interaction of economic agents with memory, about economic processes with memory and non-locality over time. The presence of memory in the economic process means that this process depends on the history of changes of the process in the past during a finite time interval. Fractional calculus is used as the basic mathematical tool to take into account memory and nonlocality in time.For the first time, the importance of long-range time dependence in economic data was recognized in 1966 by Clive W.J. Granger, who received the Nobel memorial prize in economic sciences in 2003 "for methods of analyzing economic time series with common trends (cointegration)". In fact, the phenomenon of memory in modern economics was first discovered by Granger. Then, the first economic models with memory were proposed in the work of Clive W.J. Granger, Roselyne Joyeux, in 1980. These models are called the fractional ARIMA models, which generalize autoregressive integrated moving average (ARIMA) models by using non-integer values of orders of the differencing and integrating.Now, it is becoming more and more obvious that when describing the behavior of economic agents, we must take into account that agents may have memory. The description of economic processes should take into account that the behavior of economic agents may depend on the history of previous changes in economy. To describe this type of behavior, we need new economic concepts and notions that allow us to take into account the presence of memory in economic processes. New economic models and methods are needed to take into account that economic agents may remember the changes of economic indicators and factors in the past. The presence of memory can change the behavior of agents and the decisions they make. As a result, to describe economic processes with memory, we cannot use the standard tools of differential and difference equations of integer orders. In fact, the differential equations describe only such economic processes, in which agents actually have amnesia. In other words, economic models, which use only derivatives of integer orders, can be applied only when economic agents forget the history of changes in economic indicators and factors during an infinitely small time interval. Differential equations of integer orders describe an economy consisting of economic agents with amnesia. It is becoming clear that the use of such equations in models with continuous time holds back the development of the modern economics.At present time, a revolution is taking place in modern economics, which can be called the "Memory Revolution". This revolution is intended to include in the modern economic theory new economic concepts and notions that allow us to take into account the presence of memory in economic processes. The main mathematical tool designed to "cure amnesia" in economics is the theory of derivatives and integrals of non-integer order (the fractional calculus), fractional differential and difference equations. Note that the fractional calculus as a theory of integrals, derivatives, and differences of arbitrary (integer and non-integer) orders includes standard calculus as a special case. Derivatives and integrals of arbitrary (integer and non-integer) orders are well-known in mathematics more than three hundred years. In theory of economic processes with memory, fractional calculus should replace standard calculus of integrals, derivatives and differences of integer orders.To describe economic processes with long memory Clive W.J. Granger and Roselyne Joyeux in 1980 proposed the difference operators that were called the fractional differencing and fractional integrating. Approach, which is based on the discrete operators proposed by Granger and Joyeux, is now the most common among economists. In fact, these operators are the Grunwald-Letnikov fractional differences, which are well-known in mathematics for more than one hundred and fifty years. In modern mathematics, there are various types of fractional integral and differential operators that were proposed by such well-known mathematicians as Riemann, Liouville, Grunwald, Letnikov, Sonine, Marchaud, Weyl, Riesz, Kober, Erdelyi and other scientists. Obviously, the restriction of mathematical tools only to the Grunwald-Letnikov fractional differences significantly reduces the possibilities for studying economic processes with memory and nonlocality in time. Now is the time to use all the tools of fractional calculus in the modern economics, and not be restricted only by the discrete Grunwald-Letnikov operators.The "Memory Revolution" has led to the emergence of a new branch of economics, which can be called "Economics with Memory". The mathematical language of this branch of the economics is fractional calculus, which allows us to formulate new concepts and principles. However, this does not mean that the Economics with Memory can be considered as part of applied mathematics or mathematical economics. Economics with Memory focuses on the behavior and interactions of economic agents with memory and economic processes with memory and nonlocality in time. Economics with Memory should be a science based on new economic concepts, notions, principles, rules, and models to take into account a memory. The modern revolutionary situation in economic theory means the importance of developing new economic concepts, notions, models, principles. This is especially important due to the fact that the Economics with Memory is now only being formed as new branch of science.We can assume that Economics with Memory can include, as a special case, the standard economics. The standard economic model, which does not take into account the fading memory, can be considered as a special case of the economic model with memory, when the parameters of memory fading take integer values. This statement is based on the fact that fractional differential equations of economic models with memory include differential equations of integer orders, which describe standard models, as a special case. The situation is similar for generalized economic concepts. For example, a marginal value with power-law memory contains the standard marginal and average values as special cases corresponding to the fading parameter equal to zero and one, respectively.In writing this book, an ambitious task was set to create and describe the foundation of the Economics with Memory as a new branch of the economics. For this purpose, generalizations of basic economic concepts, models, and principles of economic dynamics were proposed. It is obvious that such an ambitious task cannot be completely solved within the framework of one book, despite its volume. Many questions, concepts, notions, models and parts of economics remained beyond the scope of this book. However, the authors hope that the proposed book will lead to new publications of articles and books on Economics with Memory. In this case, we will consider that the proposed book has achieved its purpose. We hope that the Economics with Memory will become an actively developing branch of economics. Perhaps in the future, standard economics will become a part of the Economics with Memory, in the same way as classical physics became a part of quantum and relativistic physics.In this book, we proposed the construction of the Economics with Memory as new branch of economics, we offer new notions, concepts, effects, phenomena, principles and models, which take into account the features of economic processes with memory. This book is based on our works written in the period from 2016 to 2020.The following economic concepts and notions were proposed between 2016 and 2020: the marginal values of non-integer order with memory and nonlocality; the economic multiplier with memory; the economic accelerator with memory; the exact discretization of economic accelerators and multipliers based on exact fractional differences; the accelerator with memory and periodic sharp bursts; the duality of the multiplier with memory and the accelerator with memory; the accelerators and multipliers with memory and distributed lag; the elasticity of fractional order for processes with memory and nonlocality; the measures of risk aversion with nonlocality and with memory; the warranted (technological) rate of growth with memory; the nonlocal methods of deterministic factor analysis; the productivity with fatigue and memory; the chronological memory ordering; and some other.Using these concepts, the following economic models were proposed: the natural growth model with memory; the growth model with constant pace and memory; the Harrod-Domar model with memory; the Keynes model with memory; the dynamic Leontief (intersectoral) model with memory; the model of dynamics of fixed assets (or capital stock) with memory; the model of price dynamics with memory; the logistic growth model with memory; the model of logistic growth with memory and periodic sharp splashes (kicks); the time-dependent dynamic intersectoral model with memory; the Phillips model with memory and distributed lag; the Harrod-Domar growth model with memory and distributed lag; the dynamic Keynesian model with memory and distributed lag; the model of productivity with fatigue and memory; the Solow–Swan model with memory; the Kaldor-type model of business cycles with memory; the Evans model with memory; the Cagan model with memory; the Lucas models with memory; and some other economic models.Some of these generalized economic concepts and models for processes with memory are described in the proposed book on economic dynamics with memory.We hope that the book will be useful to anyone interested in modern economics and applied mathematics. Preliminary knowledge of fractional calculus for reading the book is not expected. However, knowledges of standard calculus and the introductory course of economics are necessary. Chapters of the Advanced Parts of the book may be skipped by economists on their first reading.In conclusion of this preface, the authors want to thank the Editor-in-chief of the book series, Professor Changpin Li, for supporting us in writing this book. The authors also express their gratitude to the members of the Editorial Board, Professors Virginia Kiryakova, Francesco Mainardi, Dragan Spasic, Bruce Ian Henry, YangQuan Chen.
- Добавил в систему: Тарасов Василий Евгеньевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Обложка | Cover (Обложка) | Cover_9783110624601.jpg | 100,6 КБ | 19 января 2021 [VasilyTarasov] |
| 2. | Preface (Предисловие) | Economic_Dynamics_with_Memory_Preface.pdf | 40,5 КБ | 19 января 2021 [VasilyTarasov] | |
| 3. | Обложка | Flyer.pdf | 234,4 КБ | 19 января 2021 [VasilyTarasov] | |
| 4. | Contents (Оглавление) | Economic_Dynamics_with_Memory_Contents.pdf | 46,5 КБ | 19 января 2021 [VasilyTarasov] | |
| 5. | Introduction (Введение) | Economic_Dynamics_with_Memory_Introduction_economics_with_m… | 65,3 КБ | 19 января 2021 [VasilyTarasov] |