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Symmetry and Economic Invariance : An Introduction - Ryuzo Sato

Symmetry and Economic Invariance

An Introduction

Hardcover Published: 30th November 1997
ISBN: 9780792380436
Number Of Pages: 134

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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.

Prefacep. vii
Introductionp. 1
Group Theory and Classification of Mathematical Structurep. 3
Lie Groups and Invariancep. 6
Economic Applications of Lie Groupsp. 12
Technical Progress and Economies of Scalep. 15
A Reformulation of the Problemp. 16
Lie Groupsp. 27
Holotheticityp. 29
Conclusionp. 34
Holothetic Production Functionsp. 35
Types of Technical Progress Functions and Holotheticityp. 36
Marginal Rate of Transformation and Extended Transformationp. 41
Holotheticity and Lie Bracketp. 46
Conclusionp. 49
Utility and Demandp. 51
Integrability Conditionsp. 55
Conclusionp. 62
Duality and Self Dualityp. 65
Duality in consumer theoryp. 66
Separability and Additivityp. 69
Self-Duality in Demand Theoryp. 74
A Method of Deriving Self-Dual Demand Functionsp. 80
Empirical Estimation of Self-Dual Demand Functionsp. 81
Implicit Self-Duality of Production and Cost Functionsp. 82
Conclusionp. 86
The Theory of Index Numbersp. 87
Statistical approachp. 88
Test Approachp. 88
Economic Index Numbersp. 93
Divisia Indexp. 96
Dynamics and Conservation Lawsp. 101
The Variational Problem and the Ramsey Rulep. 103
Steady State and the Golden Rulesp. 108
The Hamiltonian Formulation and Control Theoryp. 110
Noether Theorem and Its Implicationsp. 115
Conservation Laws in von Neumann Modelp. 119
Measurement of National Income and Income-Wealth Ratiosp. 123
Conclusionp. 124
Bibliographyp. 125
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792380436
ISBN-10: 0792380436
Series: Research Monographs in Japan-U.S. Business & Economics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 134
Published: 30th November 1997
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 0.97
Weight (kg): 0.39

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