Rational Choice Functions and Orderings

Abstract

The language of the theory of consumers' demand is still somewhat confused despite the great progress that has been made in recent years.2 The basic purpose of the theory is to explain the demand vector d (p, M) chosen by an individual when faced with a price vector p and an income M. Cournot, who introduced the concept of the demand function, and others, simply postulated some properties such as monotonic decrease of demand for any commodity with respect to its own price. The development of utility theory in the second half of the 19th century by Gossen, Jevons, Menger, and Walras and its subsequent reinterpretation on an ordinal basis by Pareto led to an alternative formulation in terms of an ordering of all conceivable commodity bundles. The demand vector for a particular p and M is that vector among all those compatible with the budget limitation which is most preferred. The derivation of demand functions from orderings (expressed as indifference maps or utility functions) became standard and its fruitfulness in yielding implications for demand functions was made evident by the work of Slutzky [14], Hicks and Allen [7], Hotelling [8], and