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Theory of Technical Change and Economic Invariance
Application of Lie Groups
- 1st Edition - May 10, 2014
- Author: Ryuzo Sato
- Editor: Karl Shell
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 6 1 6 - 1
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 6 4 9 - 6
Theory of Technical Change and Economic Invariance: Application of Lie Groups presents the economic invariance problems observable behavior under general transformations such as… Read more
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Request a sales quoteTheory 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.
ForewordPrefaceChapter 1 An Overview I. Introduction: Why Lie Groups? II. Holotheticity: Invariance of Production Function under Technical Change III. Theory of Endogenous Technical Progress IV. G(Group)-Neutral Technical Change V. Comparative Statics and Integrability Conditions VI. Implicit Technology VII. Self-Duality VIII. Dynamic Symmetries and Economic Conservation Laws IX. Invariance of Index Numbers X. The Group Structure of Observable Market Behavior Appendix: A Brief Survey of Lie's Theory of Continuous Transformation Groups References 17Chapter 2 Holotheticity of a Technology I. Introduction and Motivation: Relative Significance of the Scale Economies and Technical Progress (the Solow-Stigler Controversy) II. Holotheticity and the Group Properties of Technical Progress Functions III. Existence of General Holothetic Technology IV. Existence of a Lie Type of Technical Progress V. Structures of Holothetic Technology VI. Holothetic Technologies under Special Types of Technical Change VII. Simultaneous Holotheticity VIII. Multifactor Generalization IX. Estimation of Technical Change ReferencesChapter 3 A Theory of Endogenous Technical Progress I. Introduction II. Formulation of the Model III. Solution of the Model IV. Analysis of the Solution Mathematical Appendix ReferencesChapter 4 "G-Neutral" Technical Change, Comparative Statics, and Integrability Conditions I. "G-Neutral" Types of Technical Change II. Comparative Statics under r-Parameter Infinitesimal Transformations III. Integrability Conditions ReferencesChapter 5 Holotheticity of an Implicit Technology I. Introduction and Motivation II. Implicit Formulation of a Technology Holothetic under a Given Lie Type of Technical Progress III. General Nonexistence Theorem of a Lie Type of Technical Progress for a Given Implicit Technology IV. Special Types of Implicit Technologies V. Analysis of Implicit Technology by r-Parameter Lie Type of Technical Change VI. Two-Parameter Groups and Holotheticity of Degree 2 VII. Projective Holotheticity: Holotheticity of Degree 8 VIII. Classification of Implicit CES and Related Technologies Mathematical Appendix ReferencesChapter 6 Self-Dual Preferences and Technologies I. Introduction: Why Self-Duality? II. "Exact" (or Strong) Self-Duality III. Uniform and Self-Dual Demand Functions IV. Weakly Self-Dual Demand Functions V. Special Cases of Self-Dual Demand Functions VI. Method of Deriving Self-Dual Demand Functions by Infinitesimal Transformations VII. Implicit Self-Duality: Duality of Production and Cost Functions VIII. Uniformity and Implicit Self-Duality IX. Duality of Scale Effect between Production and Cost Functions ReferencesChapter 7 Dynamic Symmetries and Economic Conservation Laws I. Introduction II. Preliminaries: Noether's Theorem and Invariance Identities III. Conservation Laws in Simple Models of the Ramsey Type IV. Conservation Laws in "General" Neoclassical Optimal Growth Models V. Conservation Laws When There Exists "Technical Change" VI. Conservation Laws in the von Neumann Model ReferencesChapter 8 A Lie Group Approach to the Index Number Problems I. Introduction II. Axioms and Basic Tests III. Economic Index Numbers IV. Alternative Definition of the Quantity Index Number—"Dual Quantity Index" V. Invariant Index Numbers under Taste Change VI. Dynamic Invariance (Symmetry) of Divisia Index Numbers ReferencesChapter 9 The Group Structure and the Theory of Observable Market Behavior I. Introduction II. Preliminaries: Manifolds and Existence Theory III. Revealed Preference, Integrability, and Lie Groups IV. Economic Equilibrium as a Contact Transformation: Recoverability of a Mixed System V. Simultaneous Recovery Problems: Externality of Production and Preference VI. Recoverability of Dynamic Systems: Recovery of Optimal Growth Models VII. The Group Structure of Optimal Dynamic Behavior ReferencesAppendix A Brief Survey of Lie's Theory of Continuous Transformation Groups I. Essential (or Effective) Parameters II. Groups and Groups of Transformations III. One-Parameter Groups IV. Properties of Groups: Invariant Differential Equations and Extended Groups V. Complete Systems of Linear Partial Differential Equations VI. r- Parameter Group of Transformations VII. Contact Transformations ReferencesAuthor IndexSubject Index
- No. of pages: 456
- Language: English
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- Paperback ISBN: 9781483246161
- eBook ISBN: 9781483276496
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Karl Shell
Affiliations and expertise
Cornell UniversityRead Theory of Technical Change and Economic Invariance on ScienceDirect