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Symmetry and Economic Invariance

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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 5.5 EMPIRICAL 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