Mathematical Methods in Economics and Social Choice
1st Edition
Published on 12. February 2003
Book
Hardback
XI, 300 pages
978-3-540-00086-0 (ISBN)
Description
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 behavior 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.
More details
Series
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Professional and scholarly
Research
Illustrations
XI, 300 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
641 gr
ISBN-13
978-3-540-00086-0 (9783540000860)
DOI
10.1007/978-3-642-55867-2
Schweitzer Classification
Other editions
New editions
Norman Schofield
Mathematical Methods in Economics and Social Choice
Book
10/2013
2nd Edition
Springer
€53.49
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Additional editions
Norman Schofield
Mathematical Methods in Economics and Social Choice
Book
03/2004
Springer
€80.20
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Content
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.