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.

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.

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."

This book presents an original exposition of general equilibrium theory for advanced undergraduate and graduate-level students of economics. It contains detailed discussions of economic efficiency, competitive equilibrium, the first and second welfare theorems, the Kuhn-Tucker approach to general equilibrium, the Arrow-Debreu model, and rational expectations equilibrium and the permanent income hypothesis. Truman Bewley also treats optimal growth and overlapping generations models as special cases of the general equilibrium model. He uses the model and the first and second welfare theorems to explain the main ideas of insurance, capital theory, growth theory, and social security. It enables him to present a unified approach to portions of macro- as well as microeconomic theory. The book contains problems sets for most chapters.

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.

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.