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The Equilibrium Manifold
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Book Synopsis The Equilibrium Manifold by : Yves Balasko
Download or read book The Equilibrium Manifold written by Yves Balasko and published by MIT Press. This book was released on 2009-04-17 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: A leading scholar in the field presents post-1970s developments in the theory of general equilibrium, unified by the concept of equilibrium manifold. In The Equilibrium Manifold, noted economic scholar and major contributor to the theory of general equilibrium Yves Balasko argues that, contrary to what many textbooks want readers to believe, the study of the general equilibrium model did not end with the existence and welfare theorems of the 1950s. These developments, which characterize the modern phase of the theory of general equilibrium, led to what Balasko calls the postmodern phase, marked by the reintroduction of differentiability assumptions and the application of the methods of differential topology to the study of the equilibrium equation. Balasko's rigorous study demonstrates the central role played by the equilibrium manifold in understanding the properties of the Arrow-Debreu model and its extensions. Balasko argues that the tools of differential topology articulated around the concept of equilibrium manifold offer powerful methods for studying economically important issues, from existence and uniqueness to business cycles and economic fluctuations. After an examination of the theory of general equilibrium's evolution in the hundred years between Walras and Arrow-Debreu, Balasko discusses the properties of the equilibrium manifold and the natural projection. He highlights the important role of the set of no-trade equilibria, the structure of which is applied to the global structure of the equilibrium manifold. He also develops a geometric approach to the study of the equilibrium manifold. Applications include stability issues of adjustment dynamics for out-of-equilibrium prices, the introduction of price-dependent preferences, and aspects of time and uncertainty in extensions of the general equilibrium model that account for various forms of market frictions and imperfections. Special effort has been made at reducing the mathematical technicalities without compromising rigor. The Equilibrium Manifold makes clear the ways in which the postmodern” developments of the Arrow-Debreu model improve our understanding of modern market economies.
Book Synopsis Foundations of the Theory of General Equilibrium by : Yves Balasko
Download or read book Foundations of the Theory of General Equilibrium written by Yves Balasko and published by World Scientific. This book was released on 2016-05-11 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The economic theory of general equilibrium underpins the most important models used in economic theory in general and in its more specialized areas such as macroeconomics, international trade, environmental economics, growth theory, and developmental economics. In Foundations of the Theory of General Equilibrium, leading academic scholar, Yves Balasko offers a good introduction to the economic theory of general equilibrium and makes use of various mathematical tools as intuitive and easy as possible. The second half of the book addresses properties of the general equilibrium model that are still at the frontier of current research. These properties deal with the characterization of economies with a unique equilibrium and, more generally, with the relationships between the number of equilibria and the fundamentals of an economy. Contents:The Exchange ModelA Simple Linear Version of the Exchange ModelThe Exchange Model with Two Goods and Two ConsumersConsumer TheoryThe Equilibrium ManifoldThe Natural ProjectionEquilibrium Analysis for Fixed Total ResourcesThe Natural Projection and Envelope TheoryA Duality TheorySeveral Extensions of the General Equilibrium Model Readership: Graduate students in mathematics who want to specialize in economics and mathematical economics; researchers and professionals who will find in this book a detailed account of some of the most current developments of a difficult but essential theory.
Book Synopsis Applications of Centre Manifold Theory by : J. Carr
Download or read book Applications of Centre Manifold Theory written by J. Carr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope that this clarifies the use of centre manifold theory. The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. Dynamic bifurcation theory is concerned with topological changes in the nature of the solutions of differential equations as para meters are varied. Such an example is the creation of periodic orbits from an equilibrium point as a parameter crosses a critical value. In certain circumstances, the application of centre manifold theory reduces the dimension of the system under investigation. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions. Our use of centre manifold theory in bifurcation problems follows that of Ruelle and Takens [57) and of Marsden and McCracken [51).
Book Synopsis General Equilibrium Theory of Value by : Yves Balasko
Download or read book General Equilibrium Theory of Value written by Yves Balasko and published by Princeton University Press. This book was released on 2011-07-25 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. The mathematical tools and properties for this theory have developed over time to accommodate and incorporate developments in economic theory, from multiple markets and economic agents to theories of production. Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to which he has been a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary. General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field.
Book Synopsis General Equilibrium by : Yves Balasko
Download or read book General Equilibrium written by Yves Balasko and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the key pioneers in the field, this book offers an accessible introduction to general equilibrium theory. Written for undergraduates taking courses in economic theory and modelling who have limited mathematical proficiency, the book fills a gap between forbidding technical expositions and the less rigorous elementary ones.
Book Synopsis Introduction to Applied Nonlinear Dynamical Systems and Chaos by : Stephen Wiggins
Download or read book Introduction to Applied Nonlinear Dynamical Systems and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
Book Synopsis Differential Topology and General Equilibrium with Complete and Incomplete Markets by : Antonio Villanacci
Download or read book Differential Topology and General Equilibrium with Complete and Incomplete Markets written by Antonio Villanacci and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: General equilibrium In this book we try to cope with the challenging task of reviewing the so called general equilibrium model and of discussing one specific aspect of the approach underlying it, namely, market completeness. With the denomination "general equilibrium" (from now on in short GE) we shall mainly refer to two different things. On one hand, in particular when using the expression "GE approach", we shall refer to a long established methodolog ical tradition in building and developing economic models, which includes, as of today, an enormous amount of contributions, ranging in number by several 1 thousands • On the other hand, in particular when using the expression "stan dard differentiable GE model", we refer to a very specific version of economic model of exchange and production, to be presented in Chapters 8 and 9, and to be modified in Chapters 10 to 15. Such a version is certainly formulated within the GE approach, but it is generated by making several quite restrictive 2 assumptions • Even to list and review very shortly all the collective work which can be ascribed to the GE approach would be a formidable task for several coauthors in a lifetime perspective. The book instead intends to address just a single issue. Before providing an illustration of its main topic, we feel the obligation to say a word on the controversial character of GE. First of all, we should say that we identify the GE approach as being based 3 on three principles .
Book Synopsis The Input Parameterized Linearization Around the Equilibrium Manifold Approach to Modeling and Identification by :
Download or read book The Input Parameterized Linearization Around the Equilibrium Manifold Approach to Modeling and Identification written by and published by . This book was released on 2006 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of General Economic Equilibrium by : Andreu Mas-Colell
Download or read book The Theory of General Economic Equilibrium written by Andreu Mas-Colell and published by Cambridge University Press. This book was released on 1985 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the author's pioneering work, written over the last twenty years, on the use of differential methods in general equilibrium theory.
Book Synopsis Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds by : Taeyoung Lee
Download or read book Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds written by Taeyoung Lee and published by Springer. This book was released on 2017-08-14 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.
Book Synopsis Mathematical Foundations of Game Theory by : Rida Laraki
Download or read book Mathematical Foundations of Game Theory written by Rida Laraki and published by Springer Nature. This book was released on 2019-09-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text. Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.
Author :Alexander N. Gorban Publisher :Springer Science & Business Media ISBN 13 :9783540226840 Total Pages :524 pages Book Rating :4.2/5 (268 download)
Book Synopsis Invariant Manifolds for Physical and Chemical Kinetics by : Alexander N. Gorban
Download or read book Invariant Manifolds for Physical and Chemical Kinetics written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2005-02-01 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: By bringing together various ideas and methods for extracting the slow manifolds, the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.
Download or read book Advances in Applied Mechanics written by and published by Academic Press. This book was released on 2009-09-26 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Applied Mechanics book series draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. Covers all fields of the mechanical sciences Highlights classical and modern areas of mechanics that are ready for review Provides comprehensive coverage of the field in question
Book Synopsis Continuous and Discrete Dynamics Near Manifolds of Equilibria by : B. Aulbach
Download or read book Continuous and Discrete Dynamics Near Manifolds of Equilibria written by B. Aulbach and published by Lecture Notes in Mathematics. This book was released on 1984-04 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Manifolds of Preferences and Equilibria by : Graciela Chichilnisky
Download or read book Manifolds of Preferences and Equilibria written by Graciela Chichilnisky and published by . This book was released on 1976 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This work is concerned with the study of local and global properties of spaces of preferences and their applications to general equilibrium, utility and demand analysis. Differential topology and global analysis tools are used to study the mathematical aspects of these problems, adding further results and techniques to an approach introduced in mathematical economics by Gerard Debreu in 1970"--Preface.
Download or read book Shock Waves written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 2021-10-12 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws. The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters. The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.
Book Synopsis Addresses and Papers Delivered ... Annual Meeting by : American Petroleum Institute
Download or read book Addresses and Papers Delivered ... Annual Meeting written by American Petroleum Institute and published by . This book was released on 1927 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
