Mathematical Methods in Economics and Social Choice
Published on 15. March 2004
Book
Paperback/Softback
XI, 300 pages
978-3-540-21138-9 (ISBN)
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.
More details
Edition
Softcover reprint of the original 1st ed. 2004
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
College/higher education
Research
Product notice
Paperback (trade)
Illustrations
biography
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 16 mm
Weight
980 gr
ISBN-13
978-3-540-21138-9 (9783540211389)
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
Shipment within 7-9 days
Additional editions
Norman Schofield
Mathematical Methods in Economics and Social Choice
Book
02/2003
1st Edition
Springer
€53.49
Shipment within 7-9 days
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.