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Apart from the underlying theme that all the contributions to this volume pertain to models set in an infinite dimensional space, they differ on many counts. Some were written in the early seventies while others are reports of ongoing research done especially with this volume in mind. Some are surveys of material that can, at least at this point in time, be deemed to have attained a satisfactory solution of the problem, while oth ers represent initial forays into an original and novel formulation. Some furnish alternative proofs of known, and by now, classical results, while others can be seen as groping towards and exploring formulations that have not yet reached a definitive form. The subject matter also has a wide leeway, ranging from solution concepts for economies to those for games and also including representation of preferences and discussion of purely mathematical problems, all within the rubric of choice variables belonging to an infinite dimensional space, interpreted as a commodity space or as a strategy space. Thus, this is a collective enterprise in a fairly wide sense of the term and one with the diversity of which we have interfered as little as possible. Our motivation for bringing all of this work under one set of covers was severalfold.
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.
This monograph is a systematic exposition of the authors' research on general equi librium models with an infinite number of commodities. It is intended to serve both as a graduate text on aspects of general equilibrium theory and as an introduction, for economists and mathematicians working in mathematical economics, to current research in a frontier area of general equilibrium theory. To this end, we have pro vided two introductory chapters on the basic economic model and the mathematical framework. The exercises at the end of each section complement the main exposition. Chapter one is a concise but substantiative discussion of the questions of exis tence and optimality of competitive equilibria in the Walrasian general equilibrium model of an economy with a finite number of households, firms and commodities. Our extension of this model to economies with an infinite number of commodities constitutes the core material of this book and begins in chapter three. Readers fa miliar with the Walrasian general equilibrium model as exposited in [13], [23J or [52J may treat chapter one as a handy reference for the main economic concepts and notions that are used throughout the book.
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.
This volume contains papers on Economic Theory and International Trade: The papers on Economic Theory cover the existence and structure of competitive equilibrium in various settings: non-convexities, non-transitivity of preferences, and absence of differentiability or free-disposal assumptions, the role of the compensating variation as a welfare measure, oligopoly under bounded rationality, and regulation of a public utility. The papers on International Trade offer analyses of the "Dutch disease" or the Atlantic Slave Trade, or treat the influence of economic growth on import demand, the terms of trade, and other economic variables, as well as theoretical and empirical evidence for the validity of the Heckscher-Ohlin model. The papers, rigorous and often requiring mathematical sophistication, variously reflect Trout Rader's work.
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.