VI

Preface.

The equations in Chapter IV, 5 10, -were found by me two years ago,when I had read no mathematical economist except Jevons . They were anappropriate extension of Jevons ’ determination of exchange of two com-modities between two trading bodies to the exchange of any number ofcommodities between any number of traders and were obtained as the in-terpretation of the mechanism which I have described in Chapter IV. Thatis, the determinateness of the mechanism was expressed by writing asmany equations as unknowns. These equations are essentially those ofWalras in his Elements d’economie politique pure. The only fundamentaldifferences are that I use marginal utility throughout and treat it as afunction of the quantities of commodity, whereas Prof. Walras makesthe quantity of each commodity a function of the prices. That similar re-sults should be obtained independently and by separate paths is certainlyan argument to be weighed by those skeptical of the mathematical method.It seemed best not to omit these analytical portions of Part I, both becausethey contribute to an understanding of the other portions of the work andbecause they were in a proper sense my own.

Three days after Part II was finished I received and saw for the firsttime Prof. Edgeworth ’s Mathematical Psychics. I was much interested tofind a resemblance between his surface on page 21 and the total utilitysurfaces* described by me. The resemblance, however, does not extend far.It consists in the recognition that in an exchange, utility is a function ofboth commodities (not of one only as assumed by Jevons ), the use of thesurface referred to as an interpretation thereof and the single phrase(Math. Psych., p. 28) “and similarly for larger numbers in hyperspace”which connects with Part II, Ch. II, <5 5.

There is one point, however, in which, as it seems to me, the writer ofthis very suggestive book has gone far astray. Mathematical economistshave been taunted with the riddle: What is a unit of pleasure or utility?Edgeworth , following the Physiological Psychologist Feclmer, answers:“Just perceivable increments of pleasure are equatable” (p. 99). I havealways felt that utility must be capable of a definition which shall con-nect it with its positive or objective commodity relations. A physicistwould certainly err who defined the unit of force as the minimum sensibleof muscular sensation. Prof. Edgeworth admits his perplexity: “It mustbe confessed that we are here leaving the terra firma of physical analogy”

* His result, which translated into my notation is/dUN /ro\ _ /dU\ /dU\

\dAi/ \<m 2 J \ t mJ \dAj

becomes by transposition and division identical with part of the continuous pro-portion, Hart I, Ch. IV, $3.