Mathematical Methods in Economics and Social Choice

Norman Schofield

300 pages, parution le 24/02/2003

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Résumé

In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, 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. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. 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.

Contents

Chapter 1: Sets, Relations and Preferences

Elements of Set Theory
Relations, Functions and Operations
Groups and Morphisms
Preferences and Choices
Social Choice and Arrow's Impossibility Theorem

Chapter 2: Linear Spaces and Transformations

Vector Spaces
Linear Transformations
Canonical Representation
Geometric Interpretation of a Linear Transformation

Chapter 3: Topology and Convex Optimization

A Topological Space
Continuity
Compactness
Convexity
Optimization in Convex Sets
Kuhn-Tucker Theorem
Choice on Compact Sets
Political and Economic Choice
References

Chapter 4: Differential Calculus and Smooth Optimization

Differential of a function
C-Differentiable Functions
Constrained Optimization
The Pareto Set and Price Equilibria
References

Chapter 5: Singularity Theory and General Equilibria

Singularity Theory
Transversality
Generic Existence of Regular Economies
Economic Adjustment and Excess Demand
Structural Stability of a Vector Field
Speculations on Chaos
References

L'auteur - Norman Schofield

Washington University, St. Louis, MO, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Norman Schofield
Parution	24/02/2003
Nb. de pages	300
Format	16 x 24
Couverture	Relié
Poids	569g
Intérieur	Noir et Blanc
EAN13	9783540000860