Mathematical Methods In Economics And Social Choice - Schofield Norman | Libro Springer 02/2003 - HOEPLI.it


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schofield norman - mathematical methods in economics and social choice

Mathematical Methods in Economics and Social Choice




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 02/2003
Edizione: 2003





Trama

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.





Sommario

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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Altre Informazioni

ISBN:

9783540000860

Condizione: Nuovo
Collana: Studies in Economic Theory
Dimensioni: 235 x 155 mm Ø 641 gr
Formato: Copertina rigida
Pagine Arabe: 300
Pagine Romane: xi






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