Symmetry and Economic Invariance [electronic resource] /
Sato, Ryuzo.author.
Ramachandran, Rama V.author.
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.
Description based upon print version of record.
""Preface""; ""Contents""; ""Part I Introduction""; ""Chapter 1: Introduction""; ""1.1 Group Theory and Classification of Mathematical Structure""; ""1.2 Lie Groups and Invariance""; ""1.3 Economic Applications of Lie Groups""; ""Chapter 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""; ""Chapter 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 ExtendedTransformation""""3.3 Holotheticity and Lie Bracket""; ""3.4 Conclusion""; ""Chapter 4: Utility and Demand""; ""4.1 Integrability Conditions""; ""4.2 Conclusion""; ""Chapter 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""
""Chapter 6: The Theory of Index Numbers""""6.1 Statistical Approach""; ""6.2 Test Approach""; ""6.3 Economic Index Numbers""; ""6.4 Divisia Index""; ""Chapter 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""; ""References to Part I""; ""Part II Recent Developments""
""Chapter 8: The Invariance Principle and Income-Wealth Conservation Laws""""8.1 Introduction""; ""8.2 Brief Summary of the Literature""; ""8.3 A Model with Heterogeneous Capital Goods""; ""8.4 Noether'S Theorem (Invariance Principle)""; ""8.5 Income-Wealth Conservation Laws""; ""8.6 Special Cases""; ""8.7 Generalized Income/Wealth Conservation Laws""; ""8.8 Income-Capital (Wealth) Conservation Lawin the von Neumann Model""; ""8.9 The Total Value Conservation Law of the Firm""; ""8.10 Empirical Applications""; ""8.11 Summary""; ""Appendix""; ""References""
""Chapter 9: Conservation Laws in Continuous and Discrete Models""""9.1 Introduction""; ""9.2 Continuous Models""; ""9.2.1 Review of the Noether Theorem""; ""9.2.2 Model 1: Zero Discount Rate""; ""9.2.3 Model 2: Fixed Discount Rate""; ""9.2.4 Model 3: Variable Discount Rate""; ""9.2.5 Model 4: Technical and Taste Change""; ""9.2.6 Model 5: ``Local'' Conservation Laws""; ""9.2.7 Total Value Conservation Law of the Firm""; ""9.3 Discrete Models (2012 Version) by Shigeru Maeda""; ""9.3.1 Introduction""; ""9.3.2 Model 6: Discrete Growth Models""
""9.3.3 Quadratic Conservatives: A MathematicalDigression""
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.
Economic theory.
Economic history.
Economic Theory/Quantitative Economics/Mathematical Methods.
History of Economic Thought/Methodology.