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Author: Ryuzo Sato
Publisher: Springer Science & Business Media
ISBN: 4431544305
Category : Business & Economics
Languages : en
Pages : 278
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Book Description
Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.
Author: Ryuzo Sato
Publisher: Springer Science & Business Media
ISBN: 4431544305
Category : Business & Economics
Languages : en
Pages : 278
Get Book Here
Book Description
Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.
Author: Ryuzo Sato
Publisher: Springer Science & Business Media
ISBN: 1461555132
Category : Business & Economics
Languages : en
Pages : 140
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Book Description
Symmetry and Economic Invariance: An Introduction explores how symmetry and invariance of economic models can provide insights into their properties. While the professional economist is nowadays adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered.
Author: R. Sato
Publisher: Springer Science & Business Media
ISBN: 364245545X
Category : Business & Economics
Languages : en
Pages : 104
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Book Description
The theory of Lie groups has proven to be a most powerful analytical tool in many areas of modern scientific endeavors. It was only a few years ago that economists discovered the usefulness of this approach in their study of the frontiers of modern economic theory. These frontiers include the areas of technical change and productivity, technology and preference, economic conservation laws, comparative statics and integrability conditions, index number problems, and the general theory of ~ observable market behavior (Sato [1980, 1981], Nono [1971], Sato and N~no [1983], Russell [1983]). 1 In Nono [1971] and Sa to [1981, Chapter 4] the concept of "G-neutral" (group neutral) technical change was first introduced as a natural extension of the well-known concepts of Hicks, Harrod, Solow and Sato-Beckmann-Rose neutrality. The present monograph contains a further extension of the G-neutral technical change to the case of non-constant-returns-to-scale technology and to the case of multiple factor inputs. The methodology of total productivity estimation by means of Lie group transformations is also developed in this monograph. We would like to express our sincere thanks to many individuals notably to Professor M. J. Beckmann, Professor F. Mimura, Professor G. Suzawa, T. Mitchell, K. Mino and P. Calem, for their numerous contributions at various stages of this work. We are also grateful to Marion Wathey for her usual superb typing of this difficult manuscript. Providence, R. I. , U. S. A.
Author: Ryuzo Sato
Publisher: Springer Science & Business Media
ISBN: 9401711453
Category : Business & Economics
Languages : en
Pages : 312
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Book Description
Modem geometric methods combine the intuitiveness of spatial visualization with the rigor of analytical derivation. Classical analysis is shown to provide a foundation for the study of geometry while geometrical ideas lead to analytical concepts of intrinsic beauty. Arching over many subdisciplines of mathematics and branching out in applications to every quantitative science, these methods are, notes the Russian mathematician A.T. Fomenko, in tune with the Renais sance traditions. Economists and finance theorists are already familiar with some aspects of this synthetic tradition. Bifurcation and catastrophe theo ries have been used to analyze the instability of economic models. Differential topology provided useful techniques for deriving results in general equilibrium analysis. But they are less aware of the central role that Felix Klein and Sophus Lie gave to group theory in the study of geometrical systems. Lie went on to show that the special methods used in solving differential equations can be classified through the study of the invariance of these equations under a continuous group of transformations. Mathematicians and physicists later recognized the relation between Lie's work on differential equations and symme try and, combining the visions of Hamilton, Lie, Klein and Noether, embarked on a research program whose vitality is attested by the innumerable books and articles written by them as well as by biolo gists, chemists and philosophers.
Author: Olav Kallenberg
Publisher: Springer Science & Business Media
ISBN: 9780387251158
Category : Mathematics
Languages : en
Pages : 536
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Book Description
This is the first comprehensive treatment of the three basic symmetries of probability theory—contractability, exchangeability, and rotatability—defined as invariance in distribution under contractions, permutations, and rotations. Originating with the pioneering work of de Finetti from the 1930's, the theory has evolved into a unique body of deep, beautiful, and often surprising results, comprising the basic representations and invariance properties in one and several dimensions, and exhibiting some unexpected links between the various symmetries as well as to many other areas of modern probability. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book. Olav Kallenberg received his Ph.D. in 1972 from Chalmers University in Gothenburg, Sweden. After teaching for many years at Swedish universities, he moved in 1985 to the US, where he is currently Professor of Mathematics at Auburn University. He is well known for his previous books Random Measures (4th edition, 1986) and Foundations of Modern Probability (2nd edition, 2002) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991–94, he served as the Editor in Chief of Probability Theory and Related Fields. Professor Kallenberg is an elected fellow of the Institute of Mathematical Statistics.
Author: Ryuzo Sato
Publisher: Academic Press
ISBN: 148327649X
Category : Business & Economics
Languages : en
Pages : 458
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Book Description
Theory of Technical Change and Economic Invariance: Application of Lie Groups presents the economic invariance problems observable behavior under general transformations such as taste change or technical change. This book covers a variety of topics in economic theory, ranging from the analysis of production functions to the general recoverability problem of optimal dynamic behavior. Organized into nine chapters, this book begins with an overview of the theory of observable behavior by analyzing the invariant relationships among economic variables. This text then examines the Lie group theory which provides one of the most efficient methods of studying invariance properties. Other chapters consider the analysis of exogenous technical change, a process partly due to dynamic market forces of supply and demand. This book discusses as well the topics closely related to parametric changes under Lie groups and related transformations. The final chapter deals with mathematical foundations of the theory of observable market behavior. This book is a valuable resource for economists.
Author: Shigeyuki Hamori
Publisher: Springer Science & Business Media
ISBN: 1441992081
Category : Business & Economics
Languages : en
Pages : 140
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Book Description
An Empirical Investigation of Stock Markets: The CCF Approach attempts to make an empirical contribution to the literature on the movements of stock prices in major economies, i.e. Germany, Japan, the UK and the USA. Specifically, the cross-correlation function (CCF) approach is used to analyze the stock market. This volume provides some empirical evidence regarding the economic linkages among a group of different countries. Chapter 2 and Chapter 3 analyze the international linkage of stock prices among Germany, Japan, the UK and the USA. Chapter 2 applies the standard approach, whereas Chapter 3 uses the CCF approach. Chapter 4 analyzes the relationship between stock prices and exchange rates. Chapter 5 analyzes the relationship among stock prices, exchange rates, and real economic activities. Chapter 6 summarizes the main results obtained in each chapter and comments on the possible directions of future research.
Author: Ryuzo Sato
Publisher: Springer Science & Business Media
ISBN: 1461551099
Category : Business & Economics
Languages : en
Pages : 589
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Book Description
Global Competition and Integration offers varied perspectives on the changing international economy. The book is divided into four main sections covering world trade and competition, innovation and growth, financial markets and globalization, and regulation, distribution, and the role of government.
Author: Toshihiro Ihori
Publisher: Springer Science & Business Media
ISBN: 1475735286
Category : Business & Economics
Languages : en
Pages : 172
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Book Description
Government Deficit And Fiscal Reform In Japan presents a theoretical-based comprehensive analysis of economic consequences of government deficits and fiscal reform in Japan. Particular emphasis is directed at developing tools that can be applied to theoretically and empirically clarify essential economic concerns in Japan such as generational incidence of fiscal reform and a growing dependence on government bonds for covering financial deficits. This book evaluates the recent movement of Japanese fiscal reform and government deficit. The authors first summarize fiscal policy in 1990's. Then, they move on to investigate the macroeconomic impact of government dept and the sustainability problem, and then discuss benefits and costs of public investment. The political aspect of fiscal reconstruction movements in Japan is also examined. Finally, the authors investigate the behavior of central government's control on local governments' debt issuance and its effect on the real activities of local governments. This book points out that the long-run structural fiscal reform is more important than the short-run Keynesian fiscal policy in Japan.
Author: E. Agliardi
Publisher: Springer
ISBN: 0230376215
Category : Business & Economics
Languages : en
Pages : 159
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Book Description
The objective of this book is to study the economy as a complex system and to show that the presence of self-reinforcing mechanisms in very different economic problems gives rise to common regularities and common qualitative properties. Dynamic systems of the self-reinforcing type are considered, that is, systems with local positive feedbacks. Economic theory maintains that positive feedbacks can cause multiple equilibria and possible inefficiency. This book concentrates on the less familiar properties of lock-in, path-dependence and symmetry-breaking.
