Symmetry and Economic Invariance Book

	Preface
1	Introduction	1
1.1	Group Theory and Classification of Mathematical Structure	3
1.2	Lie Groups and Invariance	6
1.3	Economic Applications of Lie Groups	12
2	Technical Progress and Economies of Scale	15
2.1	A Reformulation of the Problem	16
2.2	Lie Groups	27
2.3	Holotheticity	29
3	Holothetic Production Functions	35
3.1	Types of Technical Progress Functions and Holotheticity	36
3.2	Marginal Rate of Transformation and Extended Transformation	41
3.3	Holotheticity and Lie Bracket	46
4	Utility and Demand	51
4.1	Integrability Conditions	55
5	Duality and Self Duality	65
5.1	Duality in consumer theory	66
5.2	Separability and Additivity	69
5.3	Self-Duality in Demand Theory	74
5.4	A Method of Deriving Self-Dual Demand Functions	80
5.5	Empirical Estimation of Self-Dual Demand Functions	81
5.6	Implicit Self-Duality of Production and Cost Functions	82
6	The Theory of Index Numbers	87
6.1	Statistical approach	88
6.2	Test Approach	88
6.3	Economic Index Numbers	93
6.4	Divisia Index	96
7	Dynamics and Conservation Laws	101
7.1	The Variational Problem and the Ramsey Rule	103
7.2	Steady State and the Golden Rules	108
7.3	The Hamiltonian Formulation and Control Theory	110
7.4	Noether Theorem and Its Implications	115
7.5	Conservation Laws in von Neumann Model	119
7.6	Measurement of National Income and Income-Wealth Ratios	123
8	Bibliography	125