One of the fundamental themes in economic theory is the study of the role of prices in achieving an optimal allocation of resources in a competitive, decentralized economy.
The book begins with a review of the basic results on the rigorous elaboration of the Walras-Pareto theory (following the lead of Arrow and Debreu) in the context of a static economy with many agents. It summarizes some subsequent research in which the limits of the price-mechanism as a successful coordination device are recognized. When economic activity is allowed with no pre-assigned terminal period, the two fundamental theorems linking competitive equilibrium allocations to Pareto optimality are challenged and the question of decentralization is carefully re-examined. With incomplete markets, and sequential trading, the concept of a Radner equilibrium is next introduced, and some of the striking properties of this are summarized. In a large economy with random shocks to preferences and/or endowments of individual agents, the implications of the celebrated laws of probability theory are explored.
This book provides a clear and comprehensive analysis of the efficiency properties of general equilibrium, with many agents and an expanded list of commodities. It will be of particular interest to postgraduate and doctorate students of economic theory as well as scholars on Walrasian equilibrium, Pareto optimality and uncertainty theories.
Professor Majumdar has given us an admirable and unified account of general economic equilibrium theory, both as it was developed by Arrow and Debreu and their contemporaries, and beyond them to more recent developments. These latter topics comprise generalizations of the theory of "complete markets" in various directions, as well as developments of more realistic models embracing incomplete and sequential markets with stochastic perturbations. This volume will serve well, both as a reference book on this now voluminous subject, and a rigorous textbook for an advanced course on general equilibrium theory.
Stern School, New York University
This book contains an up to date and lucid presentation of all important topics in general equilibrium theory. It starts with the classical results of Arrow and Debreu and covers many dynamic models, general equilibrium under uncertainty, and economies with an infinite dimensional commodity space among other topics. The book is also unique in some respects: It contains chapters on infinite horizon economies and on axiomatization of the Walras correspondence. It is an excellent treatment of modern general equilibrium theory. In particular, it is one of the best available expositions of general equilibrium under uncertainty.
The Hebrew University of Jerusalem
1 Equilibrium and Welfare; 2 Finiteness and Comparative Statics; 3 Chaotic Tatonnement; 4 Special Structures; 5 Decentralization in Infinite Horizon Economies; 6 General Equilibrium under Uncertainty: Complete Markets; 7 Radner Equilibrium; 8 Survival: Random Exchange Economies; 9 Equilibrium with an Infinite Number of Commodities