Contents -- Preface -- Introduction -- Part 1 Foundations of Regular Economies -- 1. What Is a Regular Economy? -- 1.1 Mathematical Preliminaries -- 1.1.1 Manifolds and Tangent Spaces -- 1.1.2 Differentiable Maps and Their Derivatives -- 1.1.3 Regular Values -- 1.2 Economical Analysis -- 1.2.1 Basic Model -- 1.2.2 The Space of Economies -- 1.2.3 Regular Economies -- 2. Regular Economies and Genericity -- 2.1 Mathematical Preliminaries -- 2.1.1 Preimage Theorem -- 2.1.2 Lebesgue Measure Zero -- 2.1.3 Sard's Theorem -- 2.1.4 Genericity -- 2.2 Economical Analysis -- 2.2.1 Regular Economies and Genericity -- 2.2.2 Local Uniqueness of Equilibria as a Generic Property -- 2.2.3 Finiteness of Equilibria as a Generic Property -- 3. Formalization of Regular Economies -- 3.1 Mathematical Preliminaries -- 3.1.1 Fibre Bundles -- 3.1.2 Vector Bundles -- 3.1.3 Family of Maps -- 3.2 Economical Analysis -- 3.2.1 Equilibrium Manifold and Regular Economies -- 3.2.2 Local Uniqueness and Finiteness of Equilibria in the General Formalization -- 3.2.3 Dependence of Equilibria on Regular Economies in the General Formalization -- 3.2.4 Specific Characterization of Regular Economies in the General Formalization -- 4. The Number of Equilibria in Regular Economies -- 4.1 Mathematical Preliminaries -- 4.1.1 Modulo 2 Degree -- 4.1.2 Manifolds with Boundary -- 4.1.3 Homotopy -- 4.2 Economical Analysis -- 4.2.1 Existence of Equilibria -- 4.2.2 The Number of Equilibria in Regular Economies -- 5. Stability of Equilibria in Regular Economies -- 5.1 Mathematical Preliminaries -- 5.1.1 Oriented Manifolds -- 5.1.2 Degree of Smooth Maps -- 5.1.3 Vector Fields and Index -- 5.1.4 Poincare-Hopf Theorem -- 5.1.5 Stability Conditions for Dynamical Systems -- 5.2 Economical Analysis -- 5.2.1 Walrasian Adjustment Mechanism.

5.2.2 Stability of Equilibrium Prices in Regular Economies -- Part 2 Transversality and Regular Economies -- 6. Space of Utility Functions -- 6.1 Mathematical Preliminaries -- 6.1.1 Jet Spaces -- 6.1.2 Compact Open Topology -- 6.1.3 Whitney Topology -- 6.2 Economical Analysis -- 6.2.1 Utility Functions and Demand Functions -- 6.2.2 Admissible Utility Functions and the Space of Economies -- 6.2.3 Extended Equilibrium -- 7. Transversality and Regular Economies -- 7.1 Mathematical Preliminaries -- 7.1.1 Geometrical Meaning of Transversality -- 7.1.2 Transversality with Maps -- 7.1.3 Generalization of Preimage Theorem -- 7.2 Economical Analysis -- 7.2.1 Transversality and Regular Economies -- 7.2.2 Properties of Regular Economies -- 8. Transversality Theorems and Regular Economies -- 8.1 Mathematical Preliminaries -- 8.1.1 Transversality Theorem -- 8.1.2 Thorn Transversality Theorem -- 8.1.3 Some Modifications of Transversality Theorems -- 8.2 Economical Analysis -- 8.2.1 The Transversality Theorem and Regular Economies -- 8.2.2 Thom Transversality Theorem and Regular Economies -- 9. The Number of Extended Equilibria in Regular Economies -- 9.1 Mathematical Preliminaries -- 9.1.1 Modulo 2 Intersection Number -- 9.1.2 Manifolds with Boundary and Transversality -- 9.1.3 Homotopy Invariance of the Modulo 2 Intersection Number -- 9.2 Economical Analysis -- 9.2.1 The Basic Idea and Its Attendant Considerations -- 9.2.2 The Number of Extended Equilibria in Regular Economies -- Part 3 Developments of Regular Economies -- 10. Production Economy with Linear Activities -- 10.1 Mathematical Preliminaries -- 10.1.1 Local Lefschetz Number and Index of Fixed Points -- 10.1.2 Index Theorem -- 10.2 Economical Analysis -- 10.2.1 The Basic Idea -- 10.2.2 The Model of Production Economies.

10.2.3 Regular Economies with Linear Production Technology -- 10.2.4 Computation of the Index of an Equilibrium in Regular Production Economies -- 11. Incomplete Markets I -- 11.1 Mathematical Preliminaries -- 11.1.1 Grassmann Manifolds -- 11.1.2 Modulo 2 Euler Number -- 11.1.3 Some Modifications of the Modulo 2 Euler Number -- 11.2 Economical Analysis -- 11.2.1 Uncertainty and Assets -- 11.2.2 Complete and Incomplete Markets -- 11.2.3 Generic Existence of Equilibria in Economies with Incomplete Asset Markets -- 12. Incomplete Markets II -- 12.1 Welfare Problem of Incomplete Markets: Pareto Efficiency and Inefficiency of Equilibria -- 12.2 Inefficiency of Equilibria of Incomplete Markets without Concavity -- 12.3 Constrained Optimality -- Bibliography -- Index.