Mathematical Methods in Economics and Social Choice

This book presents an overview of mathematical techniques useful in mathematical economics, general equilibrium theory and social choice theory.

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.

Inhalt
Sets, Relations and Preferences.- Linear Spaces and Transformations.- Topology and Convex Optimisation.- Differential Calculus and Smooth Optimisation.- Singularity Theory and General Equilibria.- Topology and Social Choice.