Operator Theorems with Applications to Distributive Problems and Equilibrium Models

by Antonio Villar

Overview

Presentation Many economic problems, as equilibrium models, input-output analysis, rational behaviour, etc. , are usually modelled in terms of operators in Euclidean spaces. This monograph deals with the analysis of a number of formal problems involving this kind of operators (with particular reference to complementarity problems and variational inequalities), and their applications to distributive problems and equilibrium models. Thus the purpose of this work is to provide a set of new results on the solvability of those problems, and a number of economic applications that will illustrate the interest of these results in economics. It is worth stressing from the very begining that our analysis concentrates on the existence (and in some cases optimality) of solutions. That is what is meant here by solvability (in particular, nothing will be said with respect to the uniqueness, stability, sensitivity analysis or computation of solutions). The results on the solvability of operator problems presented here, were actually arrived at as a way of solving specific economic models. Yet we are going to relate this case by somehow reversing the way it happened, that is, starting with the formal results and then presenting a number of economic models which appear as applications of VIII these formal results. The rationale for this approach is twofold. First, it provides a neat track via which to go through the whole work. Then, because I would like to emphasize the interest of complementarity and variational inequalities problems in economic modelling.

Product Details

ISBN-13:	9783540550877
Publisher:	Springer Berlin Heidelberg
Publication date:	03/25/1992
Series:	Lecture Notes in Economics and Mathematical Systems , #377
Edition description:	Softcover reprint of the original 1st ed. 1992
Pages:	160
Product dimensions:	6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

First Part: Operator Theorems.- I. Operators in Euclidean Spaces: Eight Selected Problems.- I.1.- Introduction.- I.2.- Eight Selected Problems.- I.3.- Relationships between the Solvability of the Eight Selected Problems.- I.4.- Further References to the Literature.- I.5.- Final Remarks.- II. The Main Formal Results: Some Theorems on Operators in Euclidean Spaces.- II.1.- Introduction.- II.2.- Zk -Functions and k-fold Complementarity Problems.- II.3.- Two Theorems on Variational Inequalities for Set-Valued Mappings.- II.4.- Extensions and Interconnections.- Second Part: applications to distributive problems and Equilibrium Models.- III. Efficient Allocations with Consumption Externalities.- III.1- Introduction.- III.2.- The Basic Model: Distributing a Bundle of “Goods”.- III.3.- Egalitarian Allocations and Informational Frameworks.- III.4.- Final Remarks.- IV. Market Equilibrium with Nonconvex Technologies.- IV.1.- Introduction.- IV.2.- The Model.- IV.3.- Pricing Rules.- IV.4.- The Existence of Market Equilibrium.- V. Further Applications.- V.1.- Introduction.- V.2.- Egalitarian Allocations: The General Case.- V.3.- The Existence of Lindahl Equilibria in a Model with Several Public Goods and Price Externalities.- V.4.- Nonlinear Input-Output Models.- References.