Social choice and justice: Collected papers of Kenneth J. Arrow

Abstract

General equilibrium theory serves as a comprehensive framework for analyzing the coordination of individual economic decisions through price mechanisms. Central to this inquiry is the mathematical proof of the existence of competitive equilibrium, utilizing fixed-point theorems and convex set analysis to demonstrate that a consistent set of prices can balance supply and demand across all markets. This theoretical structure clarifies the relationship between competitive markets and Pareto efficiency, establishing that market outcomes are optimal under specific assumptions while identifying how externalities and transaction costs necessitate non-market allocation strategies. The model further integrates uncertainty by treating commodities in different states of nature as distinct goods, thereby elucidating the role of securities in the optimal allocation of risk. Production is examined through both static Leontief models and dynamic frameworks where the firm acts as an autonomous agent making intertemporal decisions based on expectations. Stability analysis addresses the paths by which systems return to equilibrium, particularly when governed by Metzler matrices or quantity adjustments. Ultimately, the transition from individual optimization to social choice reveals the logical tensions in collective decision-making, where the aggregation of diverse preferences often conflicts with fundamental requirements for consistency and non-dictatorship. – AI-generated abstract.