正常经济理论/THEORY OF REGULAR ECONOMIES

2004-07-31  

World Scientific Publishing Company  

Ryo Nagata  

216  

This book presents a comprehensive treatment of the theoryof regular economies, which is one of the most advancedtopics in modern general equilibrium theory, emphasizing thebasic ideas, the tools and the important applications. Althoughmany notions and tools of differential topology are required tounderstand the theory, the author chooses a minimum of themand heuristically arranges them; that is, instead of lumpingtogether all the necessary mathematics, the author puts at thebeginning of each chapter the minimum mathematics requiredfor the economic analysis of the chapter, so that the readerwill not only save much effort on the mathematics but alsodirectly understand howsuccessfully the mathematics is usedfor the economic issues.

PrefaceIntroductionPart 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 inthe General Formalization　 3.2.4 Specific Characterization of Regular Economies in theGeneral 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 EconomiesPart 2 Transversality and Regular Economies　6. Space of Utility Functions 　6.1 Mathematical Preliminaries　　　6.1.1 Jet Spaces　　……Part 2　Developments of Regular EconomiesBibliographyIndex

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