Mathematical methods in economics and social choice
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Bibliographic Information
Mathematical methods in economics and social choice
（Studies in economic theory, v. 17）
Springer, 2003
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Includes bibliographical references and indexes
Description and Table of Contents
Description
In recent years, the usual optimisation techniques have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behaviour of general economic and political systems. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.
Table of Contents
1: Sets, Relations and Preferences.- 1.1 Elements of Set Theory.- 1.2 Relations, Functions and Operations.- 1.3 Groups and Morphisms.- 1.4 Preferences and Choices.- 1.5 Social Choice and Arrow's Impossibility Theorem.- 2: Linear Spaces and Transformations.- 2.1 Vector Spaces.- 2.2 Linear Transformations.- 2.3 Canonical Representation.- 2.4 Geometric Interpretation of a Linear Transformation.- 3: Topology and Convex Optimisation.- 3.1 A Topological Space.- 3.2 Continuity.- 3.3 Compactness.- 3.4 Convexity.- 3.5 Optimization in Convex Sets.- 3.6 Kuhn-Tucker Theorem.- 3.7 Choice on Compact Sets.- 3.8 Political and Economic Choice.- 3.9 References.- 4: Differential Calculus and Smooth Optimisation.- 4.1 Differential of a function.- 4.2 Cr-Differentiable Functions.- 4.3 Constrained Optimization.- 4.4 The Pareto Set and Price Equilibria.- 4.5 References.- 5: Singularity Theory and General Equilibria.- 5.1 Singularity Theory.- 5.2 Transversality.- 5.3 Generic Existence of Regular Economies.- 5.4 Economic Adjustment and Excess Demand.- 5.5 Structural Stability of a Vector Field.- 5.6 Speculations on Chaos.- 5.7 References.- Review Exercises.- Name Index.
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