Operator Theorems with Applications to Distributive Problems and Equilibrium Models
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 t
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377
Antonio Villar
Operator Theorems with Applications to Distributive Problems and Equilibrium Models
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Author Prof. Dr. Antonio Villar Department of Economics University of Alicante E-03071 Alicante, Spain
ISBN-13: 978-3-540-55087-7 001: 10.1007/978-3-642-45711-1
e-ISBN-13: 978-3-642-45711-1
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1992 Typesetting: Camera ready by author 42/3140-543210 - Printed on acid-free paper
"Some of the so-called technical issues are really of the essence of the so-called deep issues and you really can't separate them at all. Each one illuminates the other. In fact they fuse together
and
in
some
cases
they're
identical."
K. J. ARROW
(!la.cW1 rghaice and. WcllaJte, nO 1, 19Er1)
FOREWORD
Presentation
Many analysis,
economic
problems,
rational behaviour,
as
equilibrium
models,
input-output
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
inequalities),
and
to
their
complementarity
problems
applications
distributive
to
and
variational
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. To under
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