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Author: G. Isac Publisher: Springer Science & Business Media ISBN: 1475736231 Category : Mathematics Languages : en Pages : 458
Book Description
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.
Author: G. Isac Publisher: Springer Science & Business Media ISBN: 1475736231 Category : Mathematics Languages : en Pages : 458
Book Description
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.
Author: Ross M. Starr Publisher: Cambridge University Press ISBN: 9780521564731 Category : Business & Economics Languages : en Pages : 280
Book Description
General Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear first as (point-valued) functions, then optionally as (set-valued) correspondences. The mathematics presented (with elementary proofs of the theorems) includes a real analysis, the Brouwer fixed point theorem, and separating and supporting hyperplane theorems. Optional chapters introduce the existence of equilibrium with set-valued supply and demand, the mathematics of upper and lower hemicontinuous correspondences, and the Kakutani fixed point theorem. The treatment emphasizes clarity and accessibility to the student through use of examples and intuition.
Author: Emilio Barucci Publisher: Springer Science & Business Media ISBN: 1447100891 Category : Business & Economics Languages : en Pages : 473
Book Description
A presentation of classical asset pricing theory, this textbook is the only one to address the economic foundations of financial markets theory from a mathematically rigorous standpoint and to offer a self-contained critical discussion based on empirical results. Tools for understanding the economic analysis are provided, and mathematical models are presented in discrete time/finite state space for simplicity. Examples and exercises included.
Author: Antonio Villar Publisher: Springer Science & Business Media ISBN: 3642457118 Category : Business & Economics Languages : en Pages : 166
Book Description
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.
Author: Trout Rader Publisher: Academic Press ISBN: 1483268926 Category : Business & Economics Languages : en Pages : 382
Book Description
Theory of General Economic Equilibrium provides information pertinent to the general economic equilibrium theory. This book covers a variety of topics, including efficiency, economic systems analysis, welfare economics, and international trade. Organized into three parts encompassing eight chapters, this book begins with an overview of the theory of efficient production and growth where consumer preferences play a subordinate role. This text then examines that for the case where preferences satisfy appropriate conditions, efficiency theory is superseded as normative analysis by optimality theory. Other chapters consider the optimization of consumer preferences that leads to the decline of many families. This book discusses as well the existence of equilibrium, which is of importance to both normative and positive economics. The final chapter deals with the question of the speed with which the economic system attains its equilibrium state, which is assumed to be stationary. This book is a valuable resource for professional economists and advanced graduate students in economics.
Author: Antonio Villar Publisher: Springer Science & Business Media ISBN: 3642596703 Category : Business & Economics Languages : en Pages : 283
Book Description
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.
Author: Truman F. Bewley Publisher: Harvard University Press ISBN: 0674020928 Category : Business & Economics Languages : en Pages : 615
Book Description
This book presents an original exposition of general equilibrium theory for advanced undergraduate and graduate-level students of economics. It contains detailed discussions of economic efficiency, competitive equilibrium, the first and second welfare theorems, the Kuhn-Tucker approach to general equilibrium, the Arrow-Debreu model, and rational expectations equilibrium and the permanent income hypothesis. Truman Bewley also treats optimal growth and overlapping generations models as special cases of the general equilibrium model. He uses the model and the first and second welfare theorems to explain the main ideas of insurance, capital theory, growth theory, and social security. It enables him to present a unified approach to portions of macro- as well as microeconomic theory. The book contains problems sets for most chapters.
Author: Donald M. Topkis Publisher: Princeton University Press ISBN: 9781400822539 Category : Business & Economics Languages : en Pages : 288
Book Description
The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity. This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.
Author: Panos M. Pardalos Publisher: Springer Science & Business Media ISBN: 0387772472 Category : Mathematics Languages : en Pages : 872
Book Description
This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of 29 survey chapters written by distinguished researchers in the above areas.
Author: G. Isac
Author: G. Isac
Author: Alan Sussmann Manne
Author: Ross M. Starr
Author: Emilio Barucci
Author: Antonio Villar
Author: Trout Rader
Author: Antonio Villar
Author: Truman F. Bewley
Author: Donald M. Topkis
Author: Panos M. Pardalos