Differential Topology And General Equilibrium With Complete And Incomplete Markets

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Differential Topology and General Equilibrium with Complete and Incomplete Markets

Author : Antonio Villanacci
Publisher : Springer Science & Business Media
ISBN 13 : 1475736193
Total Pages : 495 pages
Book Rating : 4.4/5 (757 download)

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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 .

Differential Topology and General Equilibrium with Complete and Incomplete Markets

Author : Antonio Villanacci
Publisher :
ISBN 13 : 9781475736205
Total Pages : 508 pages
Book Rating : 4.7/5 (362 download)

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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 . This book was released on 2014-01-15 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:

General Equilibrium Foundations of Finance

Author : Thorsten Hens
Publisher : Springer Science & Business Media
ISBN 13 : 1475753179
Total Pages : 313 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis General Equilibrium Foundations of Finance by : Thorsten Hens

Download or read book General Equilibrium Foundations of Finance written by Thorsten Hens and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a sound economic foundation of finance. Finance is a coherent branch of applied economics that is designed to understand financial markets in order to give advice for practical financial decisions. This book argues that for a sound economic foundation of finance the famous general equilibrium model which in its modern form emphasizes the incompleteness of financial markets is well suited. The aim of the book is to demonstrate that financial markets can be meaningfully embedded into a more general system of markets including, for example, commodity markets. The interaction of these markets can be described via the well known notion of a competitive equilibrium. We argue that for a sound foundation this competitive equilibrium should be unique. In a first step we demonstrate that this essential goal cannot of be achieved based only on the rationality principle, i. e. on the assumption utility maximization of some utility function subject to the budget constraint. In particular we show that this important lack of structure is disturbing as well for the case of mean-variance utility functions which are the basis of the Capital Asset Pricing Model, one of the cornerstones of finance. The final goal of our book is to give reasonable restrictions on the agents' utility functions which lead to a well determined financial markets model.

Essays in Dynamic General Equilibrium Theory

Author : Alessandro Citanna
Publisher : Springer Science & Business Media
ISBN 13 : 3540271929
Total Pages : 278 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Essays in Dynamic General Equilibrium Theory by : Alessandro Citanna

Download or read book Essays in Dynamic General Equilibrium Theory written by Alessandro Citanna and published by Springer Science & Business Media. This book was released on 2006-01-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the area of dynamic economics, David Cass’s work has spawned a number of important lines of research, including the study of dynamic general equilibrium theory, the concept of sunspot equilibria, and general equilibrium theory when markets are incomplete. Based on these contributions, this volume contains new developments in the field, written by Cass's students and co-authors.

General Equilibrium Analysis

Author : Monique Florenzano
Publisher : Springer Science & Business Media
ISBN 13 : 1475753152
Total Pages : 181 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis General Equilibrium Analysis by : Monique Florenzano

Download or read book General Equilibrium Analysis written by Monique Florenzano and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Equilibrium Analysis is a systematic exposition of the Walrasian model of economic equilibrium with a finite number of agents, as formalized by Arrow, Debreu and McKenzie at the beginning of the fifties and since then extensively used, worked and studied. Existence and optimality of general equilibrium are developed repeatedly under different sets of hypothesis which define some general settings and delineate different approaches to the general equilibrium existence problem. The final chapter is devoted to the extension of the general equilibrium model to economies defined on an infinite dimensional commodity space. The objective of General Equilibrium Analysis is to give to each problem in each framework the most general solution, at least for the present state of art. The intended readers are graduate students, specialists and researchers in economics, especially in mathematical economics. The book is appropriate as a class text, or for self-study.

General Equilibrium

Author : W. D. A. Bryant
Publisher : World Scientific
ISBN 13 : 9812818359
Total Pages : 492 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis General Equilibrium by : W. D. A. Bryant

Download or read book General Equilibrium written by W. D. A. Bryant and published by World Scientific. This book was released on 2010 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Equilibrium Theory studies the properties and operation of free market economies. The field is a response to a series of questions originally outlined by Leon Walras about the operation of markets and posed by Frank Hahn in the following way: OCyDoes the pursuit of private interest, through a system of interconnected deregulated markets, lead not to chaos but to coherence OCo and if so, how is that achieved?OCO This is always an apt question, but particularly so given the OCyGlobal Financial CrisisOCO that emerged from the operation of market economies in the Americas and Europe in mid to late 2008. The answer that General Equilibrium Theory provides to the Walras-Hahn question is that, under certain conditions coherence is possible, while under certain other conditions chaos, in various forms, is likely to prevail. The conditionality of either outcome is not always well understood OCo neither by proponents of, or antagonists to, the OCyfree market positionOCO. Consequently, this book attempts to show something of what General Equilibrium Theory has to say about the wisdom or otherwise of always relying on OCymarket forcesOCO to manage complex socio-economic systems. Sample Chapter(s). Chapter 1: General Equilibrium Theory: An Overview (138 KB). Contents: General Equilibrium Theory: An Overview; Existence of Equilibrium: Sufficient Conditions; Existence of Equilibrium: Necessary Conditions; Equilibrium and Irreducibility: Some Empirical Evidence; Existence of Equilibrium Under Alternative Income Conditions; Existence of Walrasian Equilibrium in Some NonOCoArrow-Debreu Environments; Uniqueness of Equilibrium; Stability of Equilibrium; Optimality of Equilibrium; Comparative Statics of Equilibrium States; Empirical Evidence on General Equilibrium; General Equilibrium Theory in Retrospect. Readership: Advanced undergraduates and graduate students in economics; economists interested in economic theory."

Theory of Incomplete Markets

Author : Michael Magill
Publisher : MIT Press
ISBN 13 : 9780262632546
Total Pages : 566 pages
Book Rating : 4.6/5 (325 download)

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Book Synopsis Theory of Incomplete Markets by : Michael Magill

Download or read book Theory of Incomplete Markets written by Michael Magill and published by MIT Press. This book was released on 2002 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of incompl. markets/M. Magill, M. Quinzii. - V.1.

General Equilibrium Theory

Author : Gerard Debreu
Publisher : Edward Elgar Publishing
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis General Equilibrium Theory by : Gerard Debreu

Download or read book General Equilibrium Theory written by Gerard Debreu and published by Edward Elgar Publishing. This book was released on 1996 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-volume work provides a collection of essays on general equilibrium theory, illustrating its role as one of the major theoretical developments in economics since 1945. The aim is to improve access to the literature on this subject, which is not always readily available.

General Equilibrium Theory of Value

Author : Yves Balasko
Publisher : Princeton University Press
ISBN 13 : 1400838916
Total Pages : 192 pages
Book Rating : 4.4/5 (8 download)

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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.

Theory of Regular Economies

Author : Ryō Nagata
Publisher : World Scientific
ISBN 13 : 9789812794765
Total Pages : 242 pages
Book Rating : 4.7/5 (947 download)

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Book Synopsis Theory of Regular Economies by : Ryō Nagata

Download or read book Theory of Regular Economies written by Ryō Nagata and published by World Scientific. This book was released on 2004 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive treatment of the theory of regular economies, which is one of the most advanced topics in modern general equilibrium theory, emphasizing the basic ideas, the tools and the important applications. Although many notions and tools of differential topology are required to understand the theory, the author chooses a minimum of them and heuristically arranges them; that is, instead of lumping together all the necessary mathematics, the author puts at the beginning of each chapter the minimum mathematics required for the economic analysis of the chapter, so that the reader will not only save much effort on the mathematics but also directly understand how successfully the mathematics is used for the economic issues. Contents: Foundations of Regular Economies: What Is a Regular Economy?; Regular Economies and Genericity; Formalization of Regular Economies; The Number of Equilibria in Regular Economies; Stability of Equilibria in Regular Economies; Transversality and Regular Economies: Space of Utility Functions; Transversality and Regular Economies; Transversality Theorems and Regular Economies; The Number of Extended Equilibria in Regular Economies; Developments of Regular Economies: Production Economy with Linear Activities; Incomplete Markets I; Incomplete Markets II. Readership: Upper level undergraduates, graduate students and researchers involved with the application of mathematics to economic analysis.

General Equilibrium Theory

Author : Ross M. Starr
Publisher : Cambridge University Press
ISBN 13 : 9780521564731
Total Pages : 280 pages
Book Rating : 4.5/5 (647 download)

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Book Synopsis General Equilibrium Theory by : Ross M. Starr

Download or read book General Equilibrium Theory written by Ross M. Starr and published by Cambridge University Press. This book was released on 1997-07-13 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory of Regular Economies

Author : Ryo Nagata
Publisher : World Scientific
ISBN 13 : 981448265X
Total Pages : 236 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Theory of Regular Economies by : Ryo Nagata

Download or read book Theory of Regular Economies written by Ryo Nagata and published by World Scientific. This book was released on 2004-07-14 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' This book presents a comprehensive treatment of the theory of regular economies, which is one of the most advanced topics in modern general equilibrium theory, emphasizing the basic ideas, the tools and the important applications. Although many notions and tools of differential topology are required to understand the theory, the author chooses a minimum of them and heuristically arranges them; that is, instead of lumping together all the necessary mathematics, the author puts at the beginning of each chapter the minimum mathematics required for the economic analysis of the chapter, so that the reader will not only save much effort on the mathematics but also directly understand how successfully the mathematics is used for the economic issues. Contents:Foundations of Regular Economies:What Is a Regular Economy?Regular Economies and GenericityFormalization of Regular EconomiesThe Number of Equilibria in Regular EconomiesStability of Equilibria in Regular EconomiesTransversality and Regular Economies:Space of Utility FunctionsTransversality and Regular EconomiesTransversality Theorems and Regular EconomiesThe Number of Extended Equilibria in Regular EconomiesDevelopments of Regular Economies:Production Economy with Linear ActivitiesIncomplete Markets IIncomplete Markets II Readership: Upper level undergraduates, graduate students and researchers involved with the application of mathematics to economic analysis. Keywords:General Equilibrium Theory;Regular Economy;Finiteness of Equilibria;Genericity;Transversality;Activity Analysis;Incomplete MarketReviews:“Professional mathematical economics, as well as second-year PhD students who have mastered, will enjoy this book. The presentation is clear throughout, and the proofs clean.”Mathematical Reviews “This small book, rich in content concerning the theory of regular economies and (some of) its applications, represents successfully connections between economical analysis and its purely mathematical counterpart … The book is equipped with a lot of improvements and supplements. It is highly interesting to those, who live in the big and beautiful world of mathematical economics.”Zentralblatt MATH '

The Theory of General Economic Equilibrium

Author : Andreu Mas-Colell
Publisher : Cambridge University Press
ISBN 13 : 9780521388702
Total Pages : 396 pages
Book Rating : 4.3/5 (887 download)

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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.

The Equilibrium Manifold

Author : Yves Balasko
Publisher : MIT Press
ISBN 13 : 0262262045
Total Pages : 245 pages
Book Rating : 4.2/5 (622 download)

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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.

Fundamentals Of General Equilibrium Analysis

Author : Takashi Suzuki
Publisher : World Scientific
ISBN 13 : 981121963X
Total Pages : 436 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Fundamentals Of General Equilibrium Analysis by : Takashi Suzuki

Download or read book Fundamentals Of General Equilibrium Analysis written by Takashi Suzuki and published by World Scientific. This book was released on 2020-09-03 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to incorporate Marshallian ideas such as external increasing returns and monopolistic competitions into the general equilibrium framework of Walrasian tradition. New chapters and sections have been added to this revised and expanded edition of General Equilibrium Analysis of Production and Increasing Returns (World Scientific, 2009).The new material includes a presentation of equilibrium existence and core equivalence theorems for an infinite horizon economy with a measure space of consumers. These results are currently the focus of extensive studies by mathematical theorists, and are obtained by an application of an advanced mathematical concept called saturated (super-atomless) measure space.The second major change is the inclusion of a simple toy model of a liberal society which implements the difference principle proposed by J Rawls as a principle of distributive justice. This new section opens up a possibility to connect theoretical economics and political philosophy.Thirdly, the author presents the marginal cost pricing equilibrium and discusses welfare properties of the external increasing returns, which also belong to Marshall/ Pigou tradition of the Cambridge school.Finally, a new mathematical appendix treats basics of singular homology theory. Although the fixed point theorem is originally a theorem of algebraic topology, most economic students know its proof only in the context of the differentiable manifold theory presented by J Milnor. Considering the significance of the fixed point theorem and its playing a key role in general equilibrium theory, the purpose of this new appendix is to provide readers with the idea of a proof of Brower's fixed point theorem from the 'right place'.This volume will be helpful for graduate students and researchers of mathematical economics, game theory, and microeconomics.

Mathematical Analysis in Interdisciplinary Research

Author : Ioannis N. Parasidis
Publisher : Springer Nature
ISBN 13 : 3030847217
Total Pages : 1050 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Mathematical Analysis in Interdisciplinary Research by : Ioannis N. Parasidis

Download or read book Mathematical Analysis in Interdisciplinary Research written by Ioannis N. Parasidis and published by Springer Nature. This book was released on 2022-03-10 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

Equilibrium, Markets and Dynamics

Author : Cars H. Hommes
Publisher : Springer Science & Business Media
ISBN 13 : 3642561314
Total Pages : 344 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Equilibrium, Markets and Dynamics by : Cars H. Hommes

Download or read book Equilibrium, Markets and Dynamics written by Cars H. Hommes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains essays in honour of Claus Weddepohl who, after 22 years, is retiring as professor of mathematical economics at the Department of Quantitative Economics of the University of Amsterdam. Claus Weddepohl may be viewed as th~ first Dutch mathematical economist in the general equi librium tradition of Arrow, Debreu and Hahn. The essays in this book are centered around the themes Equilibrium, Markets and Dynamics, that have been at the heart of Weddepohl's work on mathematical economics for more than three decades. The essays have been classified according to these three themes. Admittedly such a classification always is somewhat arbitrary, and most essays would in fact fit into two or even all three themes. The essays have been written by international as well as Dutch friends and colleagues including Weddepohl's former Ph. D. students. The book starts with a review of Claus Weddepohl's work by Roald Ramer, who has been working with him in Amsterdam for all those years. The review describes how Weddepohl became fascinated by general equilibrium theory in the early stages of his career, how he has been working on the theory of markets throughout his career, and how he turned to applications of nonlinear dynamics to price adjustment processes in a later stage of his career. The first part of the book, Equilibrium, collects essays with general equilib rium theory as the main theme.