Statistical Equilibrium Models in Economics

The concept of equilibrium states has played a decisive role in the development of quantitative sciences. The study of mechanical equilibrium, conceived as a balancing of forces in a static system, clarified the fundamental notions of force and mass in the course of the 17th century development of Newtonian physics. The 19th century saw the emergence of characteristically statistical descriptions and theories of mass phenomena (see Stephen Stigler, 1986; Theodore Porter, 1986) which migrated from the social sciences to physics, where they blossomed into the marvellously successful and equally marvellously puzzling methods of statistical mechanics (see Lawrence Sklar, 1993). These statistical theories eschew the goal of describing in detail the situation of all the subsystems that constitute a large system with many degrees of freedom in favor of drawing strong conclusions about the observable macro behavior of the system based on statistical considerations. As Edwin T. Jaynes (1978), following the approach of J. Willard Gibbs, realized, statistical equilibrium in all its various applications occurs when the appropriately defined entropy of the system is maximized subject to the appropriate constraints. The entropy is a strictly concave function of the probability distributions describing the system, and the constraints are typically linear or convex functions, so that this maximization implicitly calculates shadow prices (Lagrange multipliers) for each of the constraints, which are uniform over the subsystems and characterize its important properties in equilibrium. One might have expected that these statistical methods would be a natural basis for the attempt to put social theory, and particularly economic theory, on firm mathematical and quantitative foundations. It is a commonplace of social and economic methodology to point out that human behavior, no matter how idiosyncratic and unpredictable it is in individual human beings, is subject to statistical regularity and predictability in the aggregate. The MaxwellBoltzmann-Gibbs methods of statistical mechanics, furthermore, are based on