Antonio Villar – författare

These lectures aim to help readers understand the logics and nature of the main indicators of inequality and poverty, with special attention to their social welfare underpinnings. The key approach consists in linking inequality and poverty measurement with welfare evaluation. As concern for inequality and poverty stems from ethical considerations, the measurement of those aspects necessarily involves some value judgments. Those value judgments can be linked, directly or indirectly, to welfare assessments on the distribution of personal and social opportunities. Inequality and poverty are thus considered to be partial aspects of the welfare evaluation of the opportunities in a given society. The volume includes two applications that illustrate how the models can be implemented. They refer to inequality of opportunity and poverty in education, using PISA data.

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.

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.

This book is a substantially revised and enlarged version of the monograph General Equilibrium with Increasing Returns, published by Springer-Verlag as a Lecture Notes volume in 1996. It incorporates new topics and the most recent developments in the field. It also provides a more systematic analysis of the differences between production economies with and without convex production sets. Five out of twelve chapters are new, and most of the remaining ones have been reformulated. An outline of contents appears in chapter 1. As its predecessor, this book contains a formal and systematic exposition of the main results on the existence and efficiency of equilibrium, in production economies where production sets need not be convex. There is an explicit attempt at making of it a suitable reference both for graduate students and researchers interested in theory (not necessarily specialists in mathematical economics). With this twofold purpose in mind, the work has been written according to three key principles: (i) To provide a uhified approach to the problems involved. For that we construct a basic model that is rich enough to encompass the different models appearing throughout, and to derive all the results as coroilaries of a reduced number of general theorems. (ii) To maintain a relatively low mathematical complexity. Thus, when the estimated cost of generality exceeds the benefit of simplicity, we shall state and prove the theorems under assumptions that need not be the most general ones.

This book is a substantially revised and enlarged version of the monograph General Equilibrium with Increasing Returns, published by Springer-Verlag as a Lecture Notes volume in 1996. It incorporates new topics and the most recent developments in the field. It also provides a more systematic analysis of the differences between production economies with and without convex production sets. Five out of twelve chapters are new, and most of the remaining ones have been reformulated. An outline of contents appears in chapter 1. As its predecessor, this book contains a formal and systematic exposition of the main results on the existence and efficiency of equilibrium, in production economies where production sets need not be convex. There is an explicit attempt at making of it a suitable reference both for graduate students and researchers interested in theory (not necessarily specialists in mathematical economics). With this twofold purpose in mind, the work has been written according to three key principles: (i) To provide a uhified approach to the problems involved. For that we construct a basic model that is rich enough to encompass the different models appearing throughout, and to derive all the results as coroilaries of a reduced number of general theorems. (ii) To maintain a relatively low mathematical complexity. Thus, when the estimated cost of generality exceeds the benefit of simplicity, we shall state and prove the theorems under assumptions that need not be the most general ones.