Overview

This work 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.

Full Product Details

Author:   Ryuzo Sato ,  Rama V. Ramachandran
Publisher:   Springer
Imprint:   Springer
Edition:   1998 ed.
Volume:   3
Dimensions:   Width: 15.50cm , Height: 0.90cm , Length: 23.50cm
Weight:   0.860kg
ISBN:  

9780792380436

ISBN 10:   0792380436
Pages:   134
Publication Date:   30 November 1997
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Replaced By:   9784431544296
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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