Theory of Technical Change and Economic Invariance: Application of Lie Groups / Edition 2

Theory of Technical Change and Economic Invariance: Application of Lie Groups / Edition 2

by Ryuzo Sato
     
 

ISBN-10: 1840640774

ISBN-13: 9781840640779

Pub. Date: 01/01/1999

Publisher: Elgar, Edward Publishing, Inc.

Product Details

ISBN-13:
9781840640779
Publisher:
Elgar, Edward Publishing, Inc.
Publication date:
01/01/1999
Series:
Economic Theory, Econometrics and Mathemat
Pages:
456
Product dimensions:
6.30(w) x 9.06(h) x (d)

Table of Contents

Forewordxi
Prefacexiii
Chapter 1An Overview
I.Introduction: Why Lie Groups?1
II.Holotheticity: Invariance of Production Function under Technical Change6
III.Theory of Endogenous Technical Progress8
IV.G(Group)-Neutral Technical Change9
V.Comparative Statics and Integrability Conditions10
VI.Implicit Technology10
VII.Self-Duality11
VIII.Dynamic Symmetries and Economic Conservation Laws13
IX.Invariance of Index Numbers14
X.The Group Structure of Observable Market Behavior15
AppendixA Brief Survey of Lie's Theory of Continuous Transformation Groups16
References17
Chapter 2Holotheticity of a Technology
I.Introduction and Motivation: Relative Significance of the Scale Economies and Technical Progress (the Solow-Stigler Controversy)18
II.Holotheticity and the Group Properties of Technical Progress Functions21
III.Existence of General Holothetic Technology30
IV.Existence of a Lie Type of Technical Progress34
V.Structures of Holothetic Technology37
VI.Holothetic Technologies under Special Types of Technical Change47
VII.Simultaneous Holotheticity61
VIII.Multifactor Generalization71
IX.Estimation of Technical Change77
References81
Chapter 3A Theory of Endogenous Technical Progress
I.Introduction83
II.Formulation of the Model85
III.Solution of the Model91
IV.Analysis of the Solution97
Mathematical Appendix109
References113
Chapter 4"G-Neutral" Technical Change, Comparative Statics, and Integrability Conditions
I."G-Neutral" Types of Technical Change115
II.Comparative Statics under r-Parameter Infinitesimal Transformations133
III.Integrability Conditions149
References155
Chapter 5Holotheticity of an Implicit Technology
I.Introduction and Motivation157
II.Implicit Formulation of a Technology Holothetic under a Given Lie Type of Technical Progress158
III.General Nonexistence Theorem of a Lie Type of Technical Progress for a Given Implicit Technology163
IV.Special Types of Implicit Technologies168
V.Analysis of Implicit Technology by r-Parameter Lie Type of Technical Change172
VI.Two-Parameter Groups and Holotheticity of Degree 2177
VII.Projective Holotheticity: Holotheticity of Degree 8182
VIII.Classification of Implicit CES and Related Technologies185
Mathematical Appendix194
References198
Chapter 6Self-Dual Preferences and Technologies
I.Introduction: Why Self-Duality?200
II."Exact" (or Strong) Self-Duality201
III.Uniform and Self-Dual Demand Functions207
IV.Weakly Self-Dual Demand Functions208
V.Special Cases of Self-Dual Demand Functions211
VI.Method of Deriving Self-Dual Demand Functions by Infinitesimal Transformations217
VII.Implicit Self-Duality: Duality of Production and Cost Functions221
VIII.Uniformity and Implicit Self-Duality227
IX.Duality of Scale Effect between Production and Cost Functions230
References232
Chapter 7Dynamic Symmetries and Economic Conservation Laws
I.Introduction233
II.Preliminaries: Noether's Theorem and Invariance Identities236
III.Conservation Laws in Simple Models of the Ramsey Type251
IV.Conservation Laws in "General" Neoclassical Optimal Growth Models260
V.Conservation Laws When There Exists "Technical Change"274
VI.Conservation Laws in the von Neumann Model279
References290
Chapter 8A Lie Group Approach to the Index Number Problems
I.Introduction292
II.Axioms and Basic Tests293
III.Economic Index Numbers303
IV.Alternative Definition of the Quantity Index Number--"Dual Quantity Index"308
V.Invariant Index Numbers under Taste Change312
VI.Dynamic Invariance (Symmetry) of Divisia Index Numbers314
References326
Chapter 9The Group Structure and the Theory of Observable Market Behavior
I.Introduction328
II.Preliminaries: Manifolds and Existence Theory329
III.Revealed Preference, Integrability, and Lie Groups336
IV.Economic Equilibrium as a Contact Transformation: Recoverability of a Mixed System343
V.Simultaneous Recovery Problems: Externality of Production and Preference351
VI.Recoverability of Dynamic Systems: Recovery of Optimal Growth Models356
VII.The Group Structure of Optimal Dynamic Behavior367
References382
AppendixA Brief Survey of Lie's Theory of Continuous Transformation Groups
I.Essential (or Effective) Parameters386
II.Groups and Groups of Transformations388
III.One-Parameter Groups392
IV.Properties of Groups: Invariant Differential Equations and Extended Groups400
V.Complete Systems of Linear Partial Differential Equations407
VI.r-Parameter Group of Transformations412
VII.Contact Transformations419
References423
Author Index425
Subject Index429

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