Symmetry and Economic Invariance

<p>Part I  Introduction</p><p>1  Introduction</p><p>1.1 GROUP THEORY AND CLASSIFICATION OF MATHEMATICAL STRUCTURE</p><p>1.2 LIE GROUPS AND INVARIANCE</p><p>1.3 ECONOMIC APPLICATIONS OF LIE GROUPS</p><p> </p><p>2  Technical Progress and Economies of Scale: Concept of Holotheticity</p><p>2.1 A REFORMULATION OF THE PROBLEM</p><p>2.2 LIE GROUPS</p><p>2.3 HOLOTHETICITY</p><p>2.4 CONCLUSION</p><p> </p><p>3  Holothetic Production Functions and Marginal Rate of Technical Substitution</p><p>3.1 TYPES OF TECHNICAL PROGRESS FUNCTIONS AND HOLOTHETICITY</p><p>3.2 MARGINAL RATE OF TRANSFORMATION AND EXTENDED TRANSFORMATION</p><p>3.3 HOLOTHETICITY AND LIE BRACKET</p><p>3.4 CONCLUSION</p><p> </p><p>4 Utility and Demand</p><p>4.1 INTEGRABILITY CONDITIONS</p><p>4.2 CONCLUSION</p><p> </p><p>5  Duality and Self Duality</p><p>5.1 DUALITY IN CONSUMER THEORY</p><p>5.2 SEPARABILITY AND ADDITIVITY</p><p>5.3 SELF-DUALITY IN DEMAND THEORY</p><p>5.4 A METHOD OF DERIVING SELF-DUAL DEMAND FUNCTIONS</p><p>5.5EMPIRICAL ESTIMATION OF SELF-DUAL DEMAND FUNCTIONS</p><p>5.6 IMPLICIT SELF-DUALITY OF PRODUCTION AND COST FUNCTIONS</p><p>5.7 CONCLUSION</p><p> </p><p>6  The Theory of Index Numbers</p><p>6.1 STATISTICAL APPROACH</p><p>6.2 TEST APPROACH</p><p>6.3 ECONOMIC INDEX NUMBERS</p><p>6.4 DIVISIA INDEX</p><p> </p><p>7  Dynamics and Conservation Laws</p><p>7.1 THE VARIATIONAL PROBLEM AND THE RAMSEY RULE</p><p>7.2 STEADY STATE AND THE GOLDEN RULES</p><p>7.3 THE HAMILTONIAN FORMULATION AND CONTROL THEORY</p><p>7.4 NOETHER THEOREM AND ITS IMPLICATIONS</p><p>7.5 CONSERVATION LAWS IN VON NEUMANN MODEL</p><p>7.6 MEASUREMENT OF NATIONAL INCOME AND INCOME-WEALTH RATIOS</p><p>7.7 CONCLUSION</p><p> </p><p>Part II  Recent Developments</p><p>8  The Invariance Principle and Income-Wealth Conservation Laws</p><p>8.1 INTRODUCTION</p><p>8.2 BRIEF SUMMARY OF THE LITERATURE</p><p>8.3 A MODEL WITH HETEROGENEOUS CAPITAL GOODS</p><p>8.4 NOETHER’S THEOREM (INVARIANCE PRINCIPLE</p><p>8.5 INCOME-WEALTH CONSERVATION LAWS</p><p>8.6 SPECIAL CASES</p><p>8.7 GENERALIZED INCOME/ WEALTH CONSERVATION LAWS</p><p>8.8 INCOME-CAPITAL (WEALTH) CONSERVATION LAW</p><p>IN THE VON NEUMANN MODEL</p><p>8.9 THE TOTAL VALUE CONSERVATION LAWOF THE FIRM</p><p>8.10 EMPIRICAL APPLICATIONS</p><p>8.11 SUMMARY</p><p> </p><p>9  Conservation Laws in Continuous and Discrete Models---In memory of Professor Mineo Ikeda</p><p>9.1 INTRODUCTION</p><p>9.2 CONTINUOUS MODELS</p><p>9.3 DISCRETE MODELS (2012 VERSION) BY SHIGERU MAEDA</p><p>9.4 SUMMARY</p><p> </p><p>10  Quantity or Quality: The Impact of Labour Saving Innovation on US and Japanese Growth Rates, 1960–2004</p><p>10.1 INTRODUCTION</p><p>10.2 A MODEL OF BIASED (LABOUR SAVING) TECHNICAL CHANGE</p><p>10.3 APPLICATIONS TO THE US AND JAPANESE DATA</p><p>10.4 CONCLUSION</p><p> </p><p>11  A Survey on Recent Developments</p><p>11.1 Introduction</p><p>11.2 Extensions of the Income-Wealth Conservation Law</p><p>11.3 Externalities and Policy Interventions </p><p>11.4 Stochastic Income and Wealth Conservation Law</p><p>11.5 Warning</p><p>11.6 Conservation Laws and Helmholtz Conditions</p><p>11.7 Comparisons: Three Approaches</p><p>11.8 Hartwick Rule and Conservation Laws</p><p>11.9 More Abstract Applications of Group Theory to Economics and Finance</p><p> </p><p>12  Appendix to Part II---Symmetry: An Overview of Geometric Methods in Economics</p><p>12.1 INTRODUCTION</p><p>12.2 TOOLBOX</p><p>12.3 HOLOTHETICITY: SYMMETRY OF THE ISOQUANT MAP</p><p>12.4 EXAMPLES OF CONSERVATION LAWS IN ECONOMICS</p><p>12.5 CONCLUSION</p>