Symmetry and Economic Invariance: An Introduction
Published on 6. December 2012
VIII, 134 pages
978-1-4615-5513-1 (ISBN)
Description
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.
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Ryuzo Sato | Rama V. Ramachandran
Symmetry and Economic Invariance: An Introduction
Book
10/2012
Springer
€106.99
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Book
11/1997
Kluwer Academic Publishers
€105.50
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Content
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.- 2.1 A Reformulation of the Problem.- 2.2 Lie Groups.- 2.3 Holotheticity.- 2.4 Conclusion.- 3. Holothetic Production Functions.- 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.- 8. Bibliography.
