The authors examine Walras' general equilibrium models, tracing their development through his major work Elements of Pure Economics, and also placing them in the broader context of his design for optimal economic order.

In his fourth edition of Éléménts d'économie politique pure (1900), León Walras introduced the device of written pledges to eliminate path dependency: sellers of products and services write out commitments to supply certain quantities at suggested prices with no commodities actually produced and supplied until a set of prices is found at which supply and demand are equal simultaneously in every market. This brought about very serious alterations to the character of the book. Unfortunately, these changes resulted in an incomplete, internally contradictory, and occasionally incoherent text. This translation, therefore, by two leading scholars of León Walras' work, Donald A. Walker and Jan van Daal, revisits the third edition of this seminal work, including Walras' brilliant explanation of his comprehensive model, with all its richness derived from reality. Growing research into Walras' work indicates that it was this third edition that contained his best theoretical research and a translation of this edition of the book is now a necessity.

Elements of Pure Economics was one of the most influential works in the history of economics, and the single most important contribution to the marginal revolution. Walras' theory of general equilibrium remains one of the cornerstones of economic theory more than 100 years after it was first published.

2010 marks the hundredth anniversary of the death of Léon Walras, the brilliant originator and first formaliser of general equilibrium theory – one of the pillars of modern economic theory. In advancing much derided practical solutions Walras also displayed more concern for the problems of living in a second best world than is common in modern pure theories of the invisible hand, efficient market hypothesis, DSGE macroeconomics or the thinking of some contemporary free market admirers all based on general equilibrium theory. This book brings contributions from the likes of Kenneth Arrow, Alan Kirman, Richard Posner, Amartya Sen and Robert Solow to share their thoughts and reflections on the theoretical heritage of Léon Walras. Some authors reminisce on the part they played in the development of modern general economics theory; others reflect on the crucial part played by general equilibrium in the development of macroeconomics, microeconomics, growth theory, welfare economics and the theory of justice; others still complain about the wrong path economic theory took under the influence of post 1945 developments in general equilibrium theory.

In order to understand the various strands of general equilibrium theory, why it has taken the forms that it has since the time of Léon Walras, and to appreciate fully a view of the state of general equilibrium theorising, it is essential to understand Walras's work and examine its influence. The first section of this book accordingly examines the foundations of Walras's work. These include his philosophical and methodological approach to economic modelling, his views on human nature, and the basic components of his general equilibrium models. The second section examines how the influence of his ideas has been manifested in the theorising of his successors, surveying the models of theorists such as H. L. Moore, Vilfredo Pareto, Knut Wicksell, Gustav Cassel, Abraham Wald, John von Neumann, J. R. Hicks, Kenneth Arrow, and Gerard Debreu. The treatment also examines models of many types in which Walras's influence is explicitly acknowledged.

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 book focuses on the foundations of general equilibrium theory, more specifically on the existence, uniqueness, stability, optimality and comparative static properties of equilibrium states. It also explores the question of the empirical relevance of equilibrium states. It highlights a series of 'relationship conditions' which are essential for the existence of equilibrium, but appear in optimality results." -- PUBLISHER WEBSITE.