Jevons - The Mathematical School


Some seventeen years after the appearance of Gossen's book, yet quite independently, the English economist, Jevons, worked out similar ideas, and along similar lines. In an introduction to a collection of his essays another English econ­omist, and one whose opinion has no small weight, says: "But I do not think it too much to say that the future historian of the science . . . will trace the main sources of its advance in the writings of four men, each of marked genius — Petty, Cantillon, Ricardo, and Jevons; and of these four, the name of Jevons . . . will not, I think, rank last in order of fame." Though the words, "main sources," make the statement an exaggeration, it has its element of truth.

William Stanley Jevons was born in Liverpool, England, in. the year 1835. He was a shy and thoughtful man, much given to introspection, and possessed of a very inquiring turn of mind. He attended University College School and University College, London, and in 1854 was made assayer of the mint at Sydney in Australia. Returning, he became successively lecturer and professor at Owens College, and professor at University College (1876-1880). His untimely death in 1882 came by drowning, and men have always regarded it as a great loss to economic thought.

Jevons brought into the development of English economic thought more of the spirit and discipline of pure science than any predecessor. He was no "moral philosopher" or retired. business man or busy lawyer or social reformer. He was a social scientist who specialized in economic phenomena for the sake of ascertaining the laws which govern them. He was frankly a theorist. He sought the truth concerning fundamental principles, no matter where it might lead; and in his quest, he used the methods and technique which characterize the scientist in any field, and which are apt to be most highly de­veloped in academic life.

Though he wrote several books and numerous essays, his Theory of Political Economy, published in 1871, will be mainly considered here.

Jevons' political economy, while treating of the wealth of nations with the purpose of teaching how the poor can be made as few as possible and all be well paid for their work, inquires how wealth may be best consumed. Consumption he gives a distinct place, and puts it before production and distribution, in this departing from the practice of Mill and the Classical economists in general.

Thus wants, and their satisfaction by utilities, are empha­sized. "The most important law in the whole of political econ­omy" is the "law of variety" in human wants: each separate want is soon satisfied, yet there is no end to wants. (Note the idea of indefinite expansibility!) Banfield is quoted with ap­proval as saying: "The satisfaction of every lower want in the scale creates a desire of a higher character." A "law of suc­cession of wants" is also suggested, and is roughly illustrated by a range of utilities shading from air down through food, clothing, and lodging to amusements.

Jevons employs the word, "utility," "to denote the abstract quality whereby an object serves our purposes." He does not allow moral considerations to enter; mere pleasure and pain are the ultimate objects of the calculus of political economy.

He goes on to poit out that utility is not inherent. It is relative to wants, and too much of a good brings disutility. Utility decreases as the quantity increases. There is thus a difference between total utility and degree of utility, the degree of utility of successive units decreasing while total utility in­creases.

"There is a certain sense of esteem, of desirableness, which we may have with regard to a thing apart from any distinct consciousness of the ratio in which it would exchange for other things. I may suggest that this distinct feeling of value is prob­ably identical with the final degree of utility. While Adam Smith's often quoted value in use is the total utility of a com­modity to us, the value in exchange is defined by the terminal utility, the remaining desire which we or others have for pos­sessing more."

This final degree of utility is the degree of utility of the last or the next possible addition to a stock. It is the now famous term with which Jevons designated what we ordinarily call marginal utility. By it, exchange value is determined: "The ratio of exchange of any two commodities will be the reciprocal of the ratio of the final degree of utility of the quantities of commodity available after the exchange is completed." In fact, "The final degree of utility is that function upon which the whole Theory of Economy will be found to turn." To illus­trate, take water. Water has no value, for we have so much of it that its "final utility" is 0. But let the supply run short through drought, and we begin to feel a higher degree of util­ity, — and value comes into being.

Like Gossen, Jevons concluded that in consumption the tendency is to equalize final, or marginal, utilities.

He makes some further analyses: such as the distinction between actual, prospective, and potential utility; and the in­dication of three dimensions in utility — quantity, degree, and duration. He points out that the time element, too, must be allowed for, as an element of uncertainty. In this connection he undertakes to apply the idea of final degree of utility not only to current choices, but also to future choices — to the process of discounting the future use of goods. He emphasizes the fact that in appraising goods now, men consider not only the dura­tion of the period during which they will be consumed, but also the degree of certainty that consumption will be possible.

In developing his ideas Jevons endeavored to work out a theory of objective exchange value by applying mathematics. He argued that we do not need to employ units of measurement for quantities of feeling, because the individual makes direct comparisons in his mind. He does not assume that we can measure the utility of the last unit of a good, as a quantity of pleasure. He would deal only with relations — the ratio of final degrees of utility. His concept is of a ratio between (1) the changes in utility of a good and (2) the changes in the number of units of the good. He would thus avoid the assumption of an exact quantity of pleasure at the margin, and at the same time would provide a homogeneous basis for comparing the relative importance of all sorts of goods. This is an outstanding point in his theory.

In this way, Jevons deals with the difficulty that every mind is inscrutable to every other mind, and consequently no common denominator is to be found. This difficulty he endeavors to escape by turning to the "aggregate" of individuals, arguing that "the laws which We are about to trace out are to be con­ceived as theoretically true of the individual; they can only be practically verified as regards the aggregate transactions, pro­ductions, and consumptions of a large body of people. But the laws of the aggregate depend of course upon the laws apply­ing to individual cases."

He then works out his formula, based upon the ratio of final degrees of utility, for explaining the determination of exchange values,—with which values, regarded as mere "ratios of ex­change" Jevons was primarily concerned. It is as follows:

Jevons says that the only unknowns in this equation are x and y, i.e., the quantities of the two commodities exchanged.

Quite naturally Jevons attacked the labor-cost theory of value, and, for that matter, all cost theories. His brief runs something as follows. In the first place, many valuable things are not reproducible at any cost; hence all such goods are not subject to a cost-explained valuation, and a cost theory is at best partial. Again, the facts show that market values generally fluctuate either above or below cost, seldom equaling it. Finally, there seems to be little relation between the quantity of labor expended and the ultimate value of the product. Take the Great Eastern steamship, for example. In spite of its cost, what is its value when it is found impracticable to use it? In short, "labor once spent has no influence on the future value of any article:" its value on the contrary rises and falls according to the degree of its utility.

The obvious reply to Jevons is that this degree of utility de­pends partly upon supply, which in its turn is subject to limita­tions of cost. Indeed, Jevons himself goes on to admit that labor plays a part as a determining circumstance, reasoning that labor affects supply, supply affects degree of utility, value depends on degree of utility. This appears to be virtually an admission that the case for utility is overdrawn.

Jevons has been further criticized in two matters of impor­tance: first, he confuses demand price — what marginal pur­chasers will pay — with marginal utility, apparently assuming that the relations of the two to value are the same; and, in the second place, he is guilty at points of substituting the idea of social utility for that of individual utility, leaping the gulf which lies between the utility scales of different men.

In his theoretical writings, Jevons' method was deductive and mathematical, and, indeed, his conception of political econ­omy was not dissimilar to that held by Senior, whom he cites with approval. He believed, as Gossen had believed, that eco­nomics can and should be a science, and that the mathematical method is necessary to make it so, — a necessity inherent in the measurement of pleasures and pains.