In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

This volume is the result of a conference held at the Institute for Advanced Studies, Vienna. There is still a gap reflected both in fundamental meth odological differences and in the style of analysis between the Walrasian (and Edgeworthian) tradition of general equilibrium theory and the theo retical and policy problems raised in the framework of Keynesian and post-Keynesian macroeconomics. The conference succeeded in bringing together economic theorists working in fields ranging from abstract prob lems of mathematical equilibrium analysis to applied macroeconomic theory, and it is hoped that the present volume will contribute to bridging the above-mentioned hiatus. As organizer of the meeting and editor of its proceedings I want to thank the Institute for Advanced Studies for providing facilities and funds. I am also sincerely grateful to all my colleagues from the Institute for their generous help, in particular to Mrs Monika Herkner without whose assistance and organizational talent the conference would certainly not have been the success it in fact - in the opinion of all participants - turned out to have been. Furthermore, I wish to express my gratitude towards all participants in the meeting and contributors to the volume whose patient support of the whole enterprise proved indispensable. To Mrs Elfriede Auracher I am deeply indebted for her skillful and effective general management of the editorial work and her invaluable assistance in compiling the indexes.

This book deals with the effect of public and semi-public companies on economy. In traditional economic models, several private companies – interested in maximizing their profit – interact (e.g., compete) with each other. Such models help to avoid wild oscillation in production and prices (typical for uncontrolled competition), and to come up with a stable equilibrium solution. The problems become very complex if we take into account the presence of public and semi-public companies – that are interested in public good as well as in the profit. The book contains theoretical results and numerical techniques for computing resulting equilibria. As a case study, it considers the problem of selecting optimal tolls for the public roads – tolls that best balance the public good and the need to recover the cost of building the roads. It is recommended to specialists in economics as well as to students interested in learning the corresponding economic models.

This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.

The Welfare Economics of Public Policy is a great book that should be of interest to all economists interested in applied welfare analysis. It is a good reference book for economists studying the effects of public policy. Finally, it should be a useful textbook for students studying economic policy and applied welfare economics. Jean-Paul Chavas, American Journal of Agricultural Economics . . . a very comprehensive overview of the state of the art in welfare economics. It can be used as a teaching book for advanced students as well as a reference volume for researchers. This duality of possible uses is supported by the fact that very complex issues are presented in an easily readable manner. More technical aspects are then outlined in the appendices of the relevant chapters, offering colleagues the option to study formal considerations in more detail. . . a welcome addition to and expression of the knowledge base of agricultural economics. Stefan Mann, Journal of Agricultural Economics I am absolutely delighted that the authors have revised and republished this text. I have used the previous version for years in my graduate environmental economics course; usually I had to share the one copy I have with students and I felt it was a shame that these students did not have the opportunity to purchase the book since every serious environmental economist should have this volume on their shelf. It has been a continuous reference volume for me over the years and I am sure this is true of many others in the discipline. In the field of applied welfare analysis (spanning environmental economics, international trade, agricultural policy, etc.) there is no need for further elaboration when Just, Hueth and Schmitz is referenced. Everyone knows the book that is being referred to: the bible of applied welfare economics. Catherine Kling, Iowa State University, US For the record, I am one of the people who requested that the authors revise and re-issue their textbook. It is an extremely valuable book for applied economists; as with the previous edition, I will use it extensively in two of my courses and consult it frequently in my own research endeavors. Richard Adams, Oregon State University, US The original book is very well known in our profession and is still used in many classes. It will be wonderful to have a revised edition of this classic book. Colin Carter, University of California, Davis, US This outstanding text, a follow-up to the authors award-winning 1982 text, provides a thorough treatment of economic welfare theory and develops a complete theoretical and empirical framework for applied project and policy evaluation. The authors illustrate how this theory can be used to develop policy analysis from both theory and estimation in a variety of areas including: international trade, the economics of technological change, agricultural economics, the economics of information, environmental economics, and the economics of extractive and renewable natural resources. Building on willingness-to-pay (WTP) measures as the foundation for applied welfare economics, the authors develop measures for firms and households where households are viewed as both consumers and owner/sellers of resources. Possibilities are presented for (1) approximating WTP with consumer surplus, (2) measuring WTP exactly subject to errors in existing econometric work, and (3) using duality theory to specify econometric equations consistent with theory. Later chapters cover specific areas of welfare measurement under imperfect competition, uncertainty, incomplete information, externalities, and dynamic considerations. Applications are considered explicitly for policy issues related to information, international trade, the environment, agriculture, and other natural resource issues. The Welfare Economics of Public Policy is ideal for graduate and undergraduate courses in applied welfare economics, public policy, agricultural policy, and environmental economi

'Since the extraordinary impact of networks is self-evident today both in the field of telecommunications and transportation as well as in the field of economic and financial equilibria, the scientific work carried out by Patrizia Daniele appears as an outstanding resource. The author employs with uncommon competence mathematical topics that are at the forefront of the science, while at the same time enabling the reader to understand the matter treated without any difficulty. Moreover the reader is fascinated by the clarity, depth and soundness with which the evolutionary equilibria problems are studied and by the original efficient computational procedures which allow for the solving of many significant examples and concrete problems. Without any doubt the book represents a shining light and a necessary tool for scholars of pure and applied mathematics, for economists and engineers as well as for practitioners, general managers and managing directors.' - Antonino Maugeri, Università di Catania, Italy This book offers a comprehensive analysis of dynamic networks and evolutionary variational inequalities, a topic of growing prominence in the study of networks. The extraordinary importance of networks in finance, mathematics, computer science and other areas is well known but the relatively new concept of 'dynamic' networks is less well understood. They become dynamic when the constitutive elements of the phenomena associated with the fixed geometry of networks are considered to be evolving over time. Patrizia Daniele offers many numerical examples to illustrate the issues discussed and provides a broad appendix to enrich this challenging but deeply informative book.