Part I Introduction
1 Introduction
1.1 GROUP THEORY AND CLASSIFICATION OF MATHEMATICAL STRUCTURE
1.2 LIE GROUPS AND INVARIANCE
1.3 ECONOMIC APPLICATIONS OF LIE GROUPS
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
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 EXTENDED TRANSFORMATION
3.3 HOLOTHETICITY AND LIE BRACKET
3.4 CONCLUSION
4 Utility and Demand
4.1 INTEGRABILITY CONDITIONS
4.2 CONCLUSION
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
5.5EMPIRICAL ESTIMATION OF SELF-DUAL DEMAND FUNCTIONS
5.6 IMPLICIT SELF-DUALITY OF PRODUCTION AND COST FUNCTIONS
5.7 CONCLUSION
6 The Theory of Index Numbers
6.1 STATISTICAL APPROACH
6.2 TEST APPROACH
6.3 ECONOMIC INDEX NUMBERS
6.4 DIVISIA INDEX
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
Part II Recent Developments
8 The Invariance Principle and Income-Wealth Conservation Laws
8.1 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 LAW
IN THE VON NEUMANN MODEL
8.9 THE TOTAL VALUE CONSERVATION LAWOF THE FIRM
8.10 EMPIRICAL APPLICATIONS
8.11 SUMMARY
9 Conservation Laws in Continuous and Discrete Models --- In memory of Professor Mineo Ikeda
9.1 INTRODUCTION
9.2 CONTINUOUS MODELS
9.3 DISCRETE MODELS (2012 VERSION) BY SHIGERU MAEDA
9.4 SUMMARY
10 Quantity or Quality: The Impact of Labour Saving Innovation on US and Japanese Growth Rates, 1960–2004
10.1 INTRODUCTION
10.2 A MODEL OF BIASED (LABOUR SAVING) TECHNICAL CHANGE
10.3 APPLICATIONS TO THE US AND JAPANESE DATA
10.4 CONCLUSION
11 A Survey on Recent Developments
11.1 Introduction
11.2 Extensions of the Income-Wealth Conservation Law
11.3 Externalities and Policy Interventions
11.4 Stochastic Income and Wealth Conservation Law
11.5 Warning
11.6 Conservation Laws and Helmholtz Conditions
11.7 Comparisons: Three Approaches
11.8 Hartwick Rule and Conservation Laws
11.9 More Abstract Applications of Group Theory to Economics and Finance
12 Appendix to Part II---Symmetry: An Overview of Geometric Methods in Economics
12.1 INTRODUCTION
12.2 TOOLBOX
12.3 HOLOTHETICITY: SYMMETRY OF THE ISOQUANT MAP
12.4 EXAMPLES OF CONSERVATION LAWS IN ECONOMICS
12.5 CONCLUSION
