AN AXIOMATIC THEORY OF CONSUMER TIME PREFERENCE

THE CONCEPT of pure time preference of "impatience", which BdhmBawerk [1] and the Austrian school used as the cornerstone of the theory of interest and capital has, in spite of attacks by Knight [4] and others and in spite of a certain tendency by some of the neoutilitarians to regard impatience as "irrational", been widely used as a background concept. Little exact analysis of the consumer's behavior with respect to his time preference has, however, been carried out; the only rigorous treatment of the problem in a major way and in terms of modern consumer theory seems to be by Koopmans [2], [3] although some of the problems were discussed earlier by Strotz [5]. Koopmans was concerned with two main problems: the precise definition of impatience in terms of a rigorously defined ordinal utility function and the study of the ordering of infinite programs. The present paper is concerned with a simpler problem than that tackled by Koopmans, and a somewhat different one. It uses direct preference logic without a utility function which, coupled with the lesser complexity of the problem handled, leads, in the author's opinion, to a simpler exposition than Koopmans', with results more directly applicable to operational situations. This study does not overlap Koopmans', but the two analyses run parallel in some parts. The most important result here, which seems to be new to the literature, is the necessity for the static preference function to be homogeneous in order for a unique rate of time preference to exist for a given consumer. This condition does not arise in Koopmans' work because of the operation on utility indices rather than commodity vectors.