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Topological Methods In Walrasian Economics
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Book Synopsis Topological Methods in Walrasian Economics by : E. Dierker
Download or read book Topological Methods in Walrasian Economics written by E. Dierker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In winter 71/72 I held a seminar on general equilibrium theory for a jOint group of students in mathematics and in econo mics at the university of Bonn , w.Germany1~ The economists , how ever , had a mathematical background well above the average • Most of the material treated in that seminar is described in these notes. The connection between smooth preferences and smooth demand func tions [ see Debreu (1972) ] and regular economies based on agents with smooth preferences are not presented here • Some pedagogical difficulties arose from the fact that elementary knowledge of algebraic topology is not assumed although it is helpful and indeed necessary to make some arguments precise • It is only a minor restriction , at present , that functional ana lysis is not used • But with the development of the theory more economic questions will be considered in their natural infinite dimensional setting • Economic knowledge is not required , but especially a reader without economic background will gain much by reading Debreu's classic "Theory of Value" (1959) • Although the formulation of our economic problem uses a map between Euclidean spaces only , we shall also consider ma- folds • Manifolds appear in our situation because inverse images under differentiable mappings between Euclidean spaces are very often differentiable manifolds • ( Under differentiability assump tions , for instance , the graph of the equilibrium set correspon
Book Synopsis Topological Methods in Walrasian Economics by : Egbert Dierker
Download or read book Topological Methods in Walrasian Economics written by Egbert Dierker and published by Berlin ; New York : Springer-Verlag. This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Methods in Economics and Social Choice by : Norman Schofield
Download or read book Mathematical Methods in Economics and Social Choice written by Norman Schofield and published by Springer Science & Business Media. This book was released on 2013-10-11 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behavior of general economic and political systems. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.
Book Synopsis Mathematical Methods in Economics and Social Choice by : Norman Schofield
Download or read book Mathematical Methods in Economics and Social Choice written by Norman Schofield and published by Studies in Economic Theory. This book was released on 2003-02-12 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behavior of general economic and political systems. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.
Book Synopsis Mathematical Methods in Economics by : Norman Schofield
Download or read book Mathematical Methods in Economics written by Norman Schofield and published by Routledge. This book was released on 2018-03-05 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1984. Since the logic underlying economic theory can only be grasped fully by a thorough understanding of the mathematics, this book will be invaluable to economists wishing to understand vast areas of important research. It provides a basic introduction to the fundamental mathematical ideas of topology and calculus, and uses these to present modern singularity theory and recent results on the generic existence of isolated price equilibria in exchange economies.
Book Synopsis Mathematical Methods of Game and Economic Theory by : Jean-Pierre Aubin
Download or read book Mathematical Methods of Game and Economic Theory written by Jean-Pierre Aubin and published by Courier Corporation. This book was released on 2007-01-01 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.
Book Synopsis Mathematical Economics by : Gerard Debreu
Download or read book Mathematical Economics written by Gerard Debreu and published by Cambridge University Press. This book was released on 1986-10-31 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twenty papers written by the influential economic theorist Professor Gerard Debreu.
Book Synopsis From Topology to Computation: Proceedings of the Smalefest by : Morris W. Hirsch
Download or read book From Topology to Computation: Proceedings of the Smalefest written by Morris W. Hirsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati cians working in the many fields to which Smale has made lasting con tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.
Book Synopsis Fixed Point Theory by : Andrzej Granas
Download or read book Fixed Point Theory written by Andrzej Granas and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS
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 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 Mathematical Methods in Theoretical Economics by : Erwin Klein
Download or read book Mathematical Methods in Theoretical Economics written by Erwin Klein and published by . This book was released on 1973 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Equilibrium Analysis by : W. Hildenbrand
Download or read book Introduction to Equilibrium Analysis written by W. Hildenbrand and published by Elsevier. This book was released on 2014-07-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.
Book Synopsis Game-Theoretic Methods in General Equilibrium Analysis by : J.F. Mertens
Download or read book Game-Theoretic Methods in General Equilibrium Analysis written by J.F. Mertens and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: JEAN-FRANQOIS MERTENS This book presents a systematic exposition of the use of game theoretic methods in general equilibrium analysis. Clearly the first such use was by Arrow and Debreu, with the "birth" of general equi librium theory itself, in using Nash's existence theorem (or a generalization) to prove the existence of a competitive equilibrium. But this use appeared possibly to be merely tech nical, borrowing some tools for proving a theorem. This book stresses the later contributions, were game theoretic concepts were used as such, to explain various aspects of the general equilibrium model. But clearly, each of those later approaches also provides per sea game theoretic proof of the existence of competitive equilibrium. Part A deals with the first such approach: the equality between the set of competitive equilibria of a perfectly competitive (i.e., every trader has negligible market power) economy and the core of the corresponding cooperative game.
Book Synopsis Theory of Moduli by : Edoardo Sernesi
Download or read book Theory of Moduli written by Edoardo Sernesi and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions making up this volume are expanded versions of the courses given at the C.I.M.E. Summer School on the Theory of Moduli.
Book Synopsis New Quantitative Techniques for Economic Analysis by : Giorgio P. Szegö
Download or read book New Quantitative Techniques for Economic Analysis written by Giorgio P. Szegö and published by Academic Press. This book was released on 2014-05-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic Theory, Econometrics, and Mathematical Economics: New Quantitative Techniques for Economic Analysis provides a critical appraisal of the results, the limits, and the developments of well-established quantitative techniques. This book presents a detailed analysis of the quantitative techniques for economic analysis. Organized into four parts encompassing 16 chapters, this book begins with an overview of the general questions concerning models and model making. This text then provides the main results and various interesting economic applications of some quantitative techniques that have not been widely used in the economic field. Other chapters consider the principle of optimality in dynamic programing wherein the infinite sequence of consumption-saving decisions can be reduced to one decision. This book discusses as well the methods for online control and management of large-scale systems. The final chapter deals with special problems. This book is a valuable resource for economists, social scientists, epistemologists, economic historians, and research workers.
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.
