Walrasian General Equilibrium and Nonlinear Dynamics

Abstract

Investigations of the structural stability of the general equilibrium model show that within a nonlinear framework, the differential equation governing price adjustment requires two conditions: (a) The number of agents must be greater than or equal to the number of commodities; and (b) severe restrictions on the nature of preferences must be placed. These restrictions are the same as the restrictions on preferences that are required by Chipman and Moore (1980) in order to obtain an exact and an invariant measure of consumer surplus, which is the measure and standard of value in neoclassical economics. When the Chipman-Moore conditions are examined, it is clear that the required restrictions on preferences can also be understood as requiring the constancy of the marginal utility of money, either with respect to all prices (homothetic preferences), or with respect to income and all prices except the numeraire commodity (parallel preferences). The constancy of the marginal utility between the rich and the poor implies an unintended interpersonal comparison of utility. This makes the theory of value rather special, and has implications for much applied work such as benefit-cost analysis or other social decision-making, which requires a general theory of value. It is the utilitarian formulation of welfare, which by definition means that only utility information is taken into account, that leads to the restrictive theory of value. Consequently, avoiding utilitarianism requires an approach to social choice theory that takes other information about well-being into account in social decision-making.