Download or read book Convex Structures and Economic Theory written by Hukukane Nikaido and published by Elsevier. This book was released on 2016-06-03 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics in Science and Engineering, Volume 51: Convex Structures and Economic Theory consists of an account of the theory of convex sets and its application to several basic problems that originate in economic theory and adjacent subject matter. This volume includes examples of problems pertaining to interesting static and dynamic phenomena in linear and nonlinear economic systems, as well as models initiated by Leontief, von Neumann, and Walras. The topics covered are the mathematical theorems on convexity, simple multisector linear systems, balanced growth in nonlinear systems, and efficient allocation and growth. The working of Walrasian competitive economies, special features of competitive economies, and Jacobian matrix and global univalence are also covered. This publication is suitable for advanced students of mathematical economics and related fields, but is also beneficial for anyone who wishes to become familiar with the basic ideas, methods, and results in the mathematical treatment in economic theory through a detailed exposition of a number of typical representative problems.

Download or read book Convex Structures and Economic Theory written by and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematics in Science and Engineering written by H.. Nikado and published by . This book was released on 1968 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theory of Convex Structures written by M.L.J. van de Vel and published by Elsevier. This book was released on 1993-08-02 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology. Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

Download or read book Finite Dimensional Convexity and Optimization written by Monique Florenzano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications. The text is aimed at senior undergraduate students, graduate students, and specialists of mathematical programming who are undertaking research into applied mathematics and economics. The text consists of a systematic development in eight chapters, and contains exercises. The book is appropriate as a class text or for self-study.

Download or read book Convex Analysis and Mathematical Economics written by J. Kriens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: On February 20, 1978, the Department of Econometrics of the University of Tilburg organized a symposium on Convex Analysis and Mathematical th Economics to commemorate the 50 anniversary of the University. The general theme of the anniversary celebration was "innovation" and since an important part of the departments' theoretical work is con centrated on mathematical economics, the above mentioned theme was chosen. The scientific part of the Symposium consisted of four lectures, three of them are included in an adapted form in this volume, the fourth lec ture was a mathematical one with the title "On the development of the application of convexity". The three papers included concern recent developments in the relations between convex analysis and mathematical economics. Dr. P.H.M. Ruys and Dr. H.N. Weddepohl (University of Tilburg) study in their paper "Economic theory and duality", the relations between optimality and equilibrium concepts in economic theory and various duality concepts in convex analysis. The models are introduced with an individual facing a decision in an optimization problem. Next, an n person decision problem is analyzed, and the following concepts are defined: optimum, relative optimum, Nash-equilibrium, and Pareto-optimum.

Download or read book Convex Analysis and Mathematical Economics written by Jacobus Kriens and published by . This book was released on 1979-05-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Generalized Convexity and Generalized Monotonicity written by Nicolas Hadjisavvas and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which provides a basis for interesting existing and potential applications in different disciplines. The handbook offers an advanced and broad overview of the current state of the field. It contains fourteen chapters written by the leading experts on the respective subject; eight on generalized convexity and the remaining six on generalized monotonicity.

Download or read book General Equilibrium Models of Monetary Economies written by Ross M. Starr and published by Academic Press. This book was released on 2014-05-10 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Equilibrium Models of Monetary Economies: Studies in the Static Foundations of Monetary Theory is a collection of essays that addresses the integration of the theory of money and the theory of value by using a mathematical general equilibrium theory. The papers discuss monetary theory, microeconomic theory, bilateral trade, transactions costs, intertemporal allocation, and the value of money. The Arrow-Debreu model of Walrasian general equilibrium theory provides a framework to represent money as a device for facilitating trade among economic agents without the use of money as a medium of exchange and as a store of value. The essays analyze the rationale for using a medium of exchange, for using a store of value, and for holding of idle balances in equilibrium. The essays show that by explicit modeling of the structure and difficulties of trade, a powerful class of models which deny money and finance a role in the economy, has by itself shown to have provided the foundation for the structures of trade. The collection will prove helpful for economists, statistician, mathematicians, students or professors of economics and business.

Download or read book Discrete Convex Analysis written by Kazuo Murota and published by SIAM. This book was released on 2003-01-01 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.

Download or read book Mathematical Economics written by Akira Takayama and published by Cambridge University Press. This book was released on 1985-08-30 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic exposition and survey of mathematical economics emphasizes the unifying structures of economic theory.

Download or read book Theory of Cost and Production Functions written by Ronald William Shephard and published by Princeton University Press. This book was released on 2015-03-08 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production. The approach is axiomatic for a definition of technology, by mappings of input vectors into subsets of output vectors that represent the unconstrained technical possibilities of production. To provide a completely general means of characterizing a technology, an alternative to the production function, called the Distance Function, is introduced. The duality between cost function and production function is developed by introducing a cost correspondence, showing that these two functions are given in terms of each other by dual minimum problems. The special class of production structures called Homothetic is given more general definition and extended to technologies with multiple outputs. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Download or read book Prices Cycles and Growth written by Hukukane Nikaidō and published by MIT Press. This book was released on 1996 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hukukane Nikaido is an economic theorist whose work helped lead the way for modern research in dynamic economics. Prices, Cycles and Growth provides a selection of his major papers since the 1970s. They offer uncommon insights into problems of instability and their effects on growth, income distribution, and unemployment, among other fundamental issues in macroeconomics.

Download or read book Fixed Points and Economic Equilibria written by Ken Urai and published by World Scientific. This book was released on 2010 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction. 1.1. Mathematics is language. 1.2. Notes on some mathematical tools in this book. 1.3. Basic mathematical concepts and definitions -- 2. Fixed-point theorems. 2.1. Classical results and basic extensions. 2.2. Convexity and duality for general spaces. 2.3. Extension of classical results to general spaces -- 3. Nash equilibrium and abstract economy. 3.1. Multi-agent product settings for games. 3.2. Nash equilibrium. 3.3. Abstract economy -- 4. Gale-Nikaido-Debreu's theorem. 4.1. Gale-Nikaido-Debreu's theorem. 4.2. Market equilibria in general vector spaces. 4.3. Demand-supply coincidence in general spaces -- 5. General economic equilibrium. 5.1. General preferences and basic existence theorems. 5.2. Pareto optimal allocations. 5.3. Existence of general equilibrium -- 6. The C̮ech type homology theory and fixed points. 6.1. Basic concepts in algebraic topology. 6.2. Vietoris-Begle mapping and local connectedness. 6.3. Nikaido's analogue of Sperner's lemma. 6.4. Eilenberg-Montgomery's theorem -- 7. Convex structure and fixed-point index. 7.1. Lefschetz's fixed-point theorem and its extensions. 7.2. Cohomology theory for general spaces. 7.3. Dual-system structure and differentiability. 7.4. Linear Approximation for Isolated Fixed Points. 7.5. Indices for compact set of fixed points -- 8. Applications to related topics. 8.1. KKM, KKMS, and core existence. 8.2. Eaves' theorem. 8.3. Fan-Browder's coincidence theorem. 8.4. L-majorized mappings. 8.5. Variational inequality problem. 8.6. Equilibrium with cooperative concepts. 8.7. System of inequalities and affine transformations -- 9. Mathematics and social science. 9.1. Basic concepts in axiomatic set theory. 9.2. Individuals and rationality. 9.3. Society and values -- 10. Concluding discussions. 10.1. Fixed points and economic equilibria. 10.2. Rationality and fixed-point views of the world

Download or read book Mathematical Optimization and Economic Analysis written by Mikulás Luptácik and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical Optimization and Economic Analysis" is a self-contained introduction to various optimization techniques used in economic modeling and analysis such as geometric, linear, and convex programming and data envelopment analysis. Through a systematic approach, this book demonstrates the usefulness of these mathematical tools in quantitative and qualitative economic analysis. The book presents specific examples to demonstrate each technique’s advantages and applicability as well as numerous applications of these techniques to industrial economics, regulatory economics, trade policy, economic sustainability, production planning, and environmental policy. Key Features include: - A detailed presentation of both single-objective and multiobjective optimization; - An in-depth exposition of various applied optimization problems; - Implementation of optimization tools to improve the accuracy of various economic models; - Extensive resources suggested for further reading. This book is intended for graduate and postgraduate students studying quantitative economics, as well as economics researchers and applied mathematicians. Requirements include a basic knowledge of calculus and linear algebra, and a familiarity with economic modeling.

Download or read book Advances in Mathematical Economics written by Shigeo Kusuoka and published by Springer Science & Business Media. This book was released on 2000-01-14 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the second volume of the series, Advances in Mathematical Economics, which was launched in 1999. Each volume does not to have volume title like each volume of usual journal. This volume consists of only invited and refereed papers to keep high standard of this series.

Download or read book Complex Economic Dynamics An introduction to macroeconomic dynamics written by Richard Hollis Day and published by MIT Press. This book was released on 1994 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The two volumes of Complex Economic Dynamics show that, far from being a passing trend in economic research, complex dynamics belongs at the heart of the subject. Although they can be read independently, the volumes follow a logical sequence. Volume 1 contained nontechnical introductions to the basics of economic change and to the mathematical and theoretical tools used to describe them. Volume 2, which is concerned with macroeconomic dynamics, looks at the economy as a whole. Topics include business cycles, economic growth, economic development, and dynamical economic science and policy. The book concludes with the author's reflections on the implications of complex dynamics for economic theory, quantitative research, and government policy."--Pub. desc.