Dynamic Model of the Individual Consumer

This paper presents an alternative formulation of consumer theory that allows consumer behavior to be modeled as a dynamic process. Rather than simply predicting the optimal choices a consumer will make, this formulation provides a time dependent process by which the consumer arrives at equilibrium with the market and maintains stability with it. This formulation is built upon multivariate integral (vector) calculus and is formally analogous to the theory of electric fields in classical physics. This approach allows the consumer’s Marginal Rates of Substitution (MRS) to be accepted as a theoretical given, rather than derived from hypothetical quantities such as utility or preference. Using a basic set of axioms, a vector function giving the consumer’s (observable) Marginal Values is defined from his (her) MRS. Using an additional axiom regarding the reciprocity of substitute and/or complementary goods, a scalar Use Value function is defined as the integral of the Consumer’s Marginal Values using Stokes’ Theorem. While functionally equivalent to utility, the consumer’s Use Value is measurable and unique to constants of integration that correspond to observable quantities. With an additional assumption that guarantees convexity of Use Value’s isotimic surfaces, the formulation developed here is used to solve the traditional consumer choice problem. It is shown that, whenever the consumer holds a bundle of goods that is not his or her “optimal†one, the consumer will undergo a tatonnement–like process consisting of a series of incremental exchanges with the market until her optimal bundle is obtained.