Title Symmetry and economic invariance / Ryuzo Sato, Rama V. Ramachandran

Edition Second enhanced edition Published Tokyo : Springer, [2014] ©2014

Table of Contents
pt. I	Introduction
1.	Introduction					3
1.1.	Group Theory and Classification of Mathematical Structure					4
1.2.	Lie Groups and Invariance					8
1.3.	Economic Applications of Lie Groups					12
2.	Technical Progress and Economies of Scale: Concept of Holotheticity					13
2.1.	A Reformulation of the Problem					13
2.2.	Lie Groups					22
2.3.	Holotheticity					24
2.4.	Conclusion					28
3.	Holothetic Production Functions and Marginal Rate of Technical Substitution					29
3.1.	Types of Technical Progress Functions and Holotheticity					30
3.2.	Marginal Rate of Transformation and Extended Transformation					34
3.3.	Holotheticity and Lie Bracket					37
3.4.	Conclusion					41
4.	Utility and Demand					43
4.1.	Integrability Conditions					47
4.2.	Conclusion					53
5.	Duality and Self Duality					55
5.1.	Duality in Consumer Theory					55
5.2.	Separability and Additivity					59
5.3.	Self-Duality in Demand Theory					62
5.4.	A Method of Deriving Self-Dual Demand Functions					66
5.5.	Empirical Estimation of Self-Dual Demand Functions					68
5.6.	Implicit Self-Duality of Production and Cost Functions					69
5.7.	Conclusion					72
6.	The Theory of Index Numbers					73
6.1.	Statistical Approach					73
6.2.	Test Approach					74
6.3.	Economic Index Numbers					79
6.4.	Divisia Index					82
7.	Dynamics and Conservation Laws					87
7.1.	The Variational Problem and the Ramsey Rule					88
7.2.	Steady State and the Golden Rules					93
7.3.	The Hamiltonian Formulation and Control Theory					94
7.4.	Noether Theorem and Its Implications					98
7.5.	Conservation Laws in von Neumann Model					101
7.6.	Measurement of National Income and Income-Wealth Ratios					104
7.7.	Conclusion					105
	References to Part I					107
pt. II	Recent Developments
8.	The Invariance Principle and Income-Wealth Conservation Laws					113
8.1.	Introduction					113
8.2.	Brief Summary of the Literature					114
8.3.	A Model with Heterogeneous Capital Goods					115
8.4.	Noether's Theorem (Invariance Principle)					116
8.5.	Income-Wealth Conservation Laws					119
8.6.	Special Cases					124
8.7.	Generalized Income/Wealth Conservation Laws					125
8.8.	Income-Capital (Wealth) Conservation Law in the von Neumann Model					128
8.9.	The Total Value Conservation Law of the Firm					132
8.10.	Empirical Applications					133
8.11.	Summary					138
	Appendix					139
	References					141
9.	Conservation Laws in Continuous and Discrete Models					143
9.1.	Introduction					143
9.2.	Continuous Models					144
9.2.1.	Review of the Noether Theorem					144
9.2.2.	Model 1: Zero Discount Rate					146
9.2.3.	Model 2: Fixed Discount Rate					148
9.2.4.	Model 3: Variable Discount Rate					150
9.2.5.	Model 4: Technical and Taste Change					151
9.2.6.	Model 5: "Local" Conservation Laws					152
9.2.7.	Total Value Conservation Law of the Firm					153
9.3.	Discrete Models (2012 Version) by Shigeru Maeda					154
9.3.1.	Introduction					154
9.3.2.	Model 6: Discrete Growth Models					154
9.3.3.	Quadratic Conservatives: A Mathematical Digression					157
9.3.4.	Economic Conservation Laws					163
9.4.	Summary					167
	Appendix					169
	References					175
10.	Quantity or Quality: The Impact of Labour Saving Innovation on US and Japanese Growth Rates, 1960--2004					177
10.1.	Introduction					177
10.1.1.	Recent Studies					179
10.2.	A Model of Biased (Labour Saving) Technical Change					179
10.2.1.	Importance of the Elasticity of Factor Substitution					180
10.2.2.	Why Do We Need Biased Technical Change?					183
10.2.3.	Equilibrium Growth and Stability Under Biased Technical Change					185
10.3.	Applications to the US and Japanese Data					187
10.3.1.	Tests of Non-unity of σ					187
10.3.2.	Estimates of Production Functions					189
10.3.3.	Simulation Results					193
10.3.4.	Biased Technical Change of Japan and the USA					195
10.3.5.	Contrast in Response to Oil Crises					197
10.3.6.	Economic Performance Revisited					199
10.4.	Conclusion					202
	Appendices					204
	References					207
11.	A Survey on Recent Developments					209
11.1.	Introduction					209
11.2.	Extensions of the Income-Wealth Conservation Law					209
11.3.	Externalities and Policy Interventions					211
11.4.	Stochastic Income and Wealth Conservation Law					213
11.5.	Warning					214
11.6.	Conservation Laws and Helmholtz Conditions					215
11.7.	Comparisons: Three Approaches					218
11.8.	Hartwick Rule and Conservation Laws					218
11.9.	Factor-Augmenting Technical Changes as the Magnification Type of Lie Group Transformations: Justification for Biased Technical Change					222
11.10.	Empirical Estimation of Biased Technical Change and Aggregate Production in Function					225
11.11.	More Abstract Applications of Group Theory to Economics and Finance					226
	References					228
12.	Appendix to Part II. Symmetry: An Overview of Geometric Methods in Economics					231
12.1.	Introduction					231
12.2.	Toolbox					236
12.2.1.	Mapping					236
12.2.2.	Charts and Manifolds					237
12.2.3.	Curves and Functions					238
12.2.4.	Vectors and Tangents					239
12.2.5.	1-Forms					242
12.2.6.	Tensors					244
12.2.7.	Vector Field, Connections and Covariant Derivatives					247
12.2.8.	Groups in Differential Equations					249
12.2.9.	Calculus of Variation and the Hamiltonian Formulation					253
12.2.10.	Conservation Laws and Noether Theorems					255
12.3.	Holotheticity: Symmetry of the Isoquant Map					258
12.4.	Examples of Conservation Laws in Economics					261
12.5.	Conclusion					264
	References					265
	Index					269

Click on the following:
Springer eBooks
Springer Business and Economics eBooks

Copies

Description 1 online resource (xi, 273 pages) : illustrations Series Advances in Japanese business and economics Advances in Japanese business and economics. Contents Preface -- Contents -- Part I Introduction -- Chapter 1: Introduction -- 1.1 Group Theory and Classification of Mathematical Structure -- 1.2 Lie Groups and Invariance -- 1.3 Economic Applications of Lie Groups -- Chapter 2: Technical Progress and Economies of Scale:Concept of Holotheticity -- 2.1 A Reformulation of the Problem -- 2.2 Lie Groups -- 2.3 Holotheticity -- 2.4 Conclusion -- Chapter 3: Holothetic Production Functions and Marginal Rate of Technical Substitution -- 3.1 Types of Technical Progress Functions and Holotheticity 3.2 Marginal Rate of Transformation and ExtendedTransformation3.3 Holotheticity and Lie Bracket -- 3.4 Conclusion -- Chapter 4: Utility and Demand -- 4.1 Integrability Conditions -- 4.2 Conclusion -- Chapter 5: Duality and Self Duality -- 5.1 Duality in Consumer Theory -- 5.2 Separability and Additivity -- 5.3 Self-Duality in Demand Theory -- 5.4 A Method of Deriving Self-Dual Demand Functions -- 5.5 Empirical Estimation of Self-Dual Demand Functions -- 5.6 Implicit Self-Duality of Production and Cost Functions -- 5.7 Conclusion Chapter 6: The Theory of Index Numbers6.1 Statistical Approach -- 6.2 Test Approach -- 6.3 Economic Index Numbers -- 6.4 Divisia Index -- Chapter 7: Dynamics and Conservation Laws -- 7.1 The Variational Problem and the Ramsey Rule -- 7.2 Steady State and the Golden Rules -- 7.3 The Hamiltonian Formulation and Control Theory -- 7.4 Noether Theorem and Its Implications -- 7.5 Conservation Laws in von Neumann Model -- 7.6 Measurement of National Income and Income-Wealth Ratios -- 7.7 Conclusion -- References to Part I -- Part II Recent Developments Chapter 8: The Invariance Principle and Income-Wealth Conservation Laws8.1 Introduction -- 8.2 Brief Summary of the Literature -- 8.3 A Model with Heterogeneous Capital Goods -- 8.4 Noether'S Theorem (Invariance Principle) -- 8.5 Income-Wealth Conservation Laws -- 8.6 Special Cases -- 8.7 Generalized Income/Wealth Conservation Laws -- 8.8 Income-Capital (Wealth) Conservation Lawin the von Neumann Model -- 8.9 The Total Value Conservation Law of the Firm -- 8.10 Empirical Applications -- 8.11 Summary -- Appendix -- References Chapter 9: Conservation Laws in Continuous and Discrete Models9.1 Introduction -- 9.2 Continuous Models -- 9.2.1 Review of the Noether Theorem -- 9.2.2 Model 1: Zero Discount Rate -- 9.2.3 Model 2: Fixed Discount Rate -- 9.2.4 Model 3: Variable Discount Rate -- 9.2.5 Model 4: Technical and Taste Change -- 9.2.6 Model 5: ̀̀Local'' Conservation Laws -- 9.2.7 Total Value Conservation Law of the Firm -- 9.3 Discrete Models (2012 Version) by Shigeru Maeda -- 9.3.1 Introduction -- 9.3.2 Model 6: Discrete Growth Models Summary 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 Bibliography Includes bibliographical references and index Notes Print version record Subject Economics, Mathematical. Group theory. Lie groups. BUSINESS & ECONOMICS -- Economics -- General. BUSINESS & ECONOMICS -- Reference. Science économique. Affaires. Economics, Mathematical Group theory Lie groups Form Electronic book Author Ramachandran, Rama V., author. ISBN 9784431544302 4431544305

  Permalink