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.

Productivity of inputs is an important determinant of the competitiveness of firms in national and international markets. Productivity growth arises from deliberate decisions to innovate but the technological opportunities could be such that different inputs would have different rates of growth. Previous literature has mostly concentrated on labor productivity but empirical studies indicate that productivity of capital is also increasing. One of the objectives of this book is to examine the difference or bias in the productivity growth of the two inputs. In this book, application of this general approach to study of biased technical change is developed and new empirical results presented for both macroeconomies and microeconomic firms.

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.

Economic Theory, Dynamics, and Markets. The collection of essays in honor of Ryuzo Sato, written by his colleagues and students, covers the many fields of economic theory and policy to which he has contributed. The first section pays tribute to his contributions to mathematical economics and economic theory. Ryuzo Sato is known for his work in growth theory and technical progress, and the second section has a number of papers on macroeconomics and dynamics. The third section has a number of papers on financial markets and their functioning in Japan and the United States. The next section examines various aspects of the economics of firms and industry. Ryuzo Sato has been very involved in analyzing the economic and business relations between Japan and the United States, and the last section is devoted to comparative analysis of economic systems.

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.

In this new volume it is argued that network effects are much more common than usually assumed, and that they have a profound impact on many aspects of economic systems, especially technological change and economic growth. The analysis and modelling of this interrelationship is the central focus of this book. While there exists a vast body of literature on economic growth, the theories put forward so far have had limited success in explaining observed patterns of economic growth. ‘Growth cycles’ in particular continue to elude standard economic models, though evolutionary economics has made some progress. Seeking to fill the gap, Torsten Heinrich’s innovative approach uses microeconomics to explain heterogeneous sectoral dynamics on the meso level, and then aggregating these to observed macroeconomic growth rates. In this way, it is shown that an evolutionary model of technological change with network effects can explain not only commonly observed asymmetric industry structures, monopolies and oligopolies but also ‘growth cycles’. The book includes a comprehensive account of the most influential economic growth theories, a discussion of the research on network effects as well as an introduction to the methodology, the model, and a case study on the recent emergence of information and communication technology. This important new volume will be relevant to all those interested in theoretical economics, growth theory, innovation economics, agent based modelling and industry dynamics.

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.