Sato / Shell Theory of Technical Change and Economic Invariance

Application of Lie Groups
1. Auflage 2014
ISBN: 978-1-4832-7649-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 456 Seiten, Web PDF

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.

Autoren/Hrsg.

Sato, Ryuzo

Shell, Karl

Inhaltsverzeichnis

1;Front Cover;1
2;Theory of Technical Change and Economic Invariance;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Foreword;12
7;Preface;14
8;Chapter 1. An Overview;18
8.1;I. Introduction: Why Lie Groups?;18
8.2;II. Holotheticity: Invariance of Production Function under Technical Change;23
8.3;III. Theory of Endogenous Technical Progress;25
8.4;IV. G (Group)-Neutral Technical Change;26
8.5;V. Comparative Statics and Integrability Conditions;27
8.6;VI. Implicit Technology;27
8.7;VII. Self-Duality;28
8.8;VIII. Dynamic Symmetries and Economic Conservation Laws;30
8.9;IX. Invariance of Index Numbers;31
8.10;X. The Group Structure of Observable Market Behavior;32
8.11;Appendix: A Brief Survey of Lie's Theory of Continuous Transformation Groups;33
8.12;References;34
9;Chapter 2. Holotheticity of a Technology;35
9.1;I. Introduction and Motivation: Relative Significance of the Scale Economies and Technical Progress (the Solow-Stigler Controversy);35
9.2;II. Holotheticity and the Group Properties of Technical Progress Functions;38
9.3;III. Existence of General Holothetic Technology;47
9.4;IV. Existence of a Lie Type of Technical Progress;51
9.5;V. Structures of Holothetic Technology;54
9.6;VI. Holothetic Technologies under Special Types of Technical Change;64
9.7;VII. Simultaneous Holotheticity;78
9.8;VIII. Multifactor Generalization;88
9.9;IX. Estimation of Technical Change;94
9.10;References;98
10;Chapter 3. A Theory of Endogenous Technical Progress;100
10.1;I. Introduction;100
10.2;II. Formulation of the Model;102
10.3;III. Solution of the Model;108
10.4;IV. Analysis of the Solution;114
10.5;Mathematical Appendix;126
10.6;References;130
11;Chapter 4. "G-Neutral" Technical Change, Comparative Statics, and Integrability Conditions;132
11.1;I. "G-Neutral" Types of Technical Change;132
11.2;II. Comparative Statics under r-Parameter Infinitesimal Transformations;150
11.3;III. Integrability Conditions;166
11.4;References;172
12;Chapter 5. Holotheticity of an Implicit Technology;174
12.1;I. Introduction and Motivation;174
12.2;II. Implicit Formulation of a Technology Holothetic under a Given Lie Type of Technical Progress;175
12.3;III. General Nonexistence Theorem of a Lie Type of Technical Progress for a Given Implicit Technology;180
12.4;IV. Special Types of Implicit Technologies;185
12.5;V. Analysis of Implicit Technology by r-Parameter Lie Type of Technical Change;189
12.6;VI. Two-Parameter Groups and Holotheticity of Degree 2;194
12.7;VII. Projective Holotheticity: Holotheticity of Degree 8;199
12.8;VIII. Classification of Implicit CES and Related Technologies;202
12.9;Mathematical Appendix;211
12.10;References;215
13;Chapter 6. Self-Dual Preferences and Technologies;217
13.1;I. Introduction: Why Self-Duality?;217
13.2;II. "Exact" (or Strong) Self-Duality;218
13.3;III. Uniform and Self-Dual Demand Functions;224
13.4;IV. Weakly Self-Dual Demand Functions;225
13.5;V. Special Cases of Self-Dual Demand Functions;228
13.6;VI. Method of Deriving Self-Dual Demand Functions by Infinitesimal Transformations;234
13.7;VII. Implicit Self-Duality: Duality of Production and Cost Functions;238
13.8;VIII. Uniformity and Implicit Self-Duality;244
13.9;IX. Duality of Scale Effect between Production and Cost Functions;247
13.10;References;249
14;Chapter 7. Dynamic Symmetries and Economic Conservation Laws;250
14.1;I. Introduction;250
14.2;II. Preliminaries: Noether's Theorem and Invariance Identities;253
14.3;III. Conservation Laws in Simple Models of the Ramsey Type;268
14.4;IV. Conservation Laws in "General" Neoclassical Optimal Growth Models;277
14.5;V. Conservation Laws When There Exists "Technical Change";291
14.6;VI. Conservation Laws in the von Neumann Model;296
14.7;References;307
15;Chapter 8. A Lie Group Approach to the Index Number Problems;309
15.1;I. Introduction;309
15.2;II. Axioms and Basic Tests;310
15.3;III. Economic Index Numbers;320
15.4;IV. Alternative Definition of the Quantity Index Number—''Dual Quantity Index";325
15.5;V. Invariant Index Numbers under Taste Change;329
15.6;VI. Dynamic Invariance (Symmetry) of Divisia Index Numbers;331
15.7;References;343
16;Chapter 9. The Group Structure and the Theory of Observable Market Behavior;345
16.1;I. Introduction;345
16.2;II. Preliminaries: Manifolds and Existence Theory;346
16.3;III. Revealed Preference, Integrability, and Lie Groups;353
16.4;IV. Economic Equilibrium as a Contact Transformation: Recoverability of a Mixed System;360
16.5;V. Simultaneous Recovery Problems: Externality of Production and Preference;368
16.6;VI. Recoverability of Dynamic Systems: Recovery of Optimal Growth Models;373
16.7;VII. The Group Structure of Optimal Dynamic Behavior;384
16.8;References;399
17;Appendix A: Brief Survey of Lie's Theory of Continuous Transformation Groups;402
17.1;I. Essential (or Effective) Parameters;403
17.2;II. Groups and Groups of Transformations;405
17.3;III. One-Parameter Groups;409
17.4;IV. Properties of Groups: Invariant Differential Equations and Extended Groups;417
17.5;V. Complete Systems of Linear Partial Differential Equations;424
17.6;VI. r- Parameter Group of Transformations;429
17.7;VII. Contact Transformations;436
17.8;References;440
18;Author Index;442
19;Subject Index;446