Mathematical Methods in Economics and Social Choice (Springer Texts in Business and Economics)

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. Sets, Relations, And Preferences -- Linear Spaces And Transformations -- Topology And Convex Optimisation -- Differential Calculus And Smooth Optimisation -- Singularity Theory And General Equilibrium -- Topology And Social Choice -- Review Exercises. Norman Schofield. Includes Bibliographical References And Indexes. Front Matter....Pages I-XV Sets, Relations, and Preferences....Pages 1-38 Linear Spaces and Transformations....Pages 39-75 Topology and Convex Optimisation....Pages 77-133 Differential Calculus and Smooth Optimisation....Pages 135-187 Singularity Theory and General Equilibrium....Pages 189-229 Topology and Social Choice....Pages 231-249 Review Exercises....Pages 251-256 Back Matter....Pages 257-262