Equilibrium, Welfare and Uncertainty: Beyond Arrow-Debreu

Majumdar Mukul has been a recognized authority in the field of general equilibrium theory for some years now. In this important new book, he takes the pulse of the field – still fundamental to economic theory as a whole.

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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.