Symmetry and Economic Invariance [Hardcover]

Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is 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. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.

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

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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

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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

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4 Utility and Demand

4.1 INTEGRABILITY CONDITIONS

4.2 CONCLUSION

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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 SELlC