Foundations of mathematical economics (Q2768979)

This textbook provides a comprehensive introduction to the mathematical foundations of economics. It concentrates on the mathematical principles that underlie economics, and gives an extended presentation of separation theorems and their applications. It includes a thorough treatment of some material often omitted from introductory texts, such as correspondences, fixed point theorems, and constraint qualification conditions. Some recent developments such as supermodularity and monotone comparative statics are shown. The mathematical concepts are illustrated with economic examples which perfectly complement the theory. The Book is designed to be used as a graduate text or as a research reference for professional economists. The wide range of mathematical methods is essential reading for graduate students of economics. The book may also be used for a course emphasizing microeconomic theory rather than mathematical methods.NEWLINENEWLINEContents:NEWLINENEWLINE Ch. 1: Sets and Spaces (Ordered Sets, metric spaces, linear spaces, preference relations).NEWLINENEWLINE Ch. 2: Functions (Functions as mappings, examples, classes of functions; Monotone functions, supermodular functions, monotone maximum theorem, continuous functionals, semicontinuity, continuity of correspondences, continuity maximum theorem, fixed point theorems).NEWLINENEWLINE Ch. 3: Linear Functions (Properties, linear functionals, bilinear functions, linear operators, systems of linear equations and inequalities; Convex functions, homogeneous functions, separation theorems).NEWLINENEWLINECh. 4 Smooth functions (Properties of differentiable functions, polynomial approximation, Taylor's theorem; Systems of nonlinear equations, inverse function theorem, implicit funnction theorem, convex and homogeneous functions).NEWLINENEWLINE Ch. 5: Optimization (Unconstrained optimization, equality constraints, inequality constraints).NEWLINENEWLINE Ch. 6: Comparative Statics (Envelope theorem, optimization models, equilibrium models).