The previous plate set the puzzle and named the key: that the paradox of value dissolves the moment one stops asking after the worth of a thing entire and asks instead after the value of one more of it. This plate tells how that key came to be turned — and the telling is among the strangest stories in the history of thought, for the key was turned not once but three times over, in the same few years, by three men working in three countries, none of whom had heard of the others. Between 1871 and 1874, William Stanley Jevons in England, Carl Menger in Vienna, and Léon Walras in Lausanne each arrived, alone and by his own road, at the same fundamental insight into the nature of value. The same idea, discovered three times in the same decade, in mutual ignorance: it is the episode the historians call the marginal revolution, and it remade the whole of economics — though it took the discipline the better part of a generation to notice.
What the three men discovered was, at its core, identical, and it was precisely the thing the classical economists had been unable to supply. The worth of a good in exchange, each of them saw, is governed neither by its total usefulness — for then water would be priceless — nor by the labour and cost of producing it — for then a diamond's price would be a mystery and an old master's painting an impossibility — but by its marginal usefulness, the utility of the last unit acquired, which falls as one acquires more. A thing abundant has a low marginal utility however great its total usefulness, and so commands a low price; a thing scarce has a high marginal utility however trifling its total usefulness, and so commands a high one. With that single stroke the paradox of value dissolved, demand received at last the theory the cost theorists had denied it, and the whole question of price was recast as a question about the value of one more. The three differed in almost everything but this, and this was enough to found a science.
Jevons came to it first in print, and came to it as a mathematician and a utilitarian. His Theory of Political Economy, published in 1871, opened with the flat announcement that value depends entirely upon utility — a sentence aimed like a cannon at the labour theory that had reigned since Ricardo — and proceeded to build the whole of value upon what he called the final degree of utility, the usefulness of the last small increment of a thing, which he was at pains to distinguish from its usefulness in general. He wrote in the language of the calculus, treating utility as a magnitude that varied continuously with quantity and whose rate of change at the margin did the decisive work; he was, by temperament and conviction, a follower of Bentham, for whom pleasure and pain were quantities to be reckoned. Jevons had in fact glimpsed the whole idea nearly a decade earlier, in a paper of 1862 that fell, as he bitterly recorded, almost entirely flat; and he carried ever after an anxious concern for his priority, and a frustration at the slowness with which the world came round. From him would descend the English mathematical tradition that Marshall was presently to consolidate.
Value depends entirely upon utility, Jevons announced, against a century of economists who had lodged it in labour and cost — and the utility he meant was always the final degree of it, the worth of the last small increment, never the worth of the whole.
Menger reached the same core in the same year by a wholly different route. His Grundsätze, also of 1871, was innocent of mathematics altogether; where Jevons calculated, Menger reasoned, in prose, from the subjective wants of the acting individual and the importance he attaches to satisfying each of them in turn. Value, for Menger, was not a property of things but a judgement of persons — the significance a man assigns to a particular good, given the wants it can still meet — and from this he spun an apparatus, of goods of higher and lower order, and of the imputation of value backward from final wants to the means of producing them, that owed nothing to Jevons and would found the Austrian School, with its lasting suspicion of mathematics, its insistence on subjectivism, and its eye for the opportunity foregone. Walras, in Lausanne, reached it a few years later, in 1874, and reached it as the most ambitious mathematician of the three. For him the marginal utility of a good — its rareté, the intensity of the last want it satisfied — was one term in a vast system of simultaneous equations describing the whole economy at once, every price and every quantity in every market determined together in a general equilibrium. From Walras, by way of Pareto, would descend the equilibrium tradition that still sits at the centre of economic theory. Three men, then; one core; three sciences.
That three men should arrive at the same discovery in the same few years, each ignorant of the others, is a fact that demands an explanation, and the explanation is not that any one of them was a singular genius without whom the thing would have gone undiscovered. It is, rather, that the time for the discovery had come. The classical theory had reached a visible impasse, its paradox of value unresolved and its account of demand a blank; the mathematical tools that Jevons and Walras would use were by then to hand; the utilitarian temper that made utility seem a measurable quantity was in the air of the age. And the idea itself had been glimpsed before, again and again, by men whom almost no one had read — by Gossen in 1854, who had written its laws out in full; by Dupuit, by Cournot, by Bernoulli a century before, each of whom had seen some part of it and set it down where it lay neglected. When the ground has been so thoroughly prepared, the seed will germinate, and may germinate in several places at once; the historian of science Robert Merton argued that such multiples — the same discovery made independently by several hands — are not the exception in science but very nearly the rule, precisely because a discovery is the work of its moment as much as of its author. The marginal revolution is among the most striking cases on his roll.
When the time for a discovery has come it will be made — and made, as often as not, by several hands at once, in ignorance of one another, because the thing discovered was the work of the age and not of any single mind within it.
For all that, the revolution was a remarkably quiet one, and was not, at the time, recognized as a revolution at all. The three books met, at first, with coolness or silence. Jevons's was reviewed without much enthusiasm and made few converts in his lifetime; Menger's was little read beyond a circle in Vienna, and its author, wounded by the indifference, published almost nothing more of consequence; Walras's was too forbiddingly mathematical for most of his contemporaries to follow. None of the three lived to see his work installed at the foundation of the subject. That installation was the labour of a second generation — of Marshall in England, of Wieser and Böhm-Bawerk in Austria, of Pareto in Lausanne, of Edgeworth and Wicksell and others besides — who absorbed the marginal principle, refined it, and over some thirty years made it the common property of the discipline. Even the name came late: Jevons had said final degree of utility, Menger had said importance, Walras had said rareté, and the word marginal, with which we now describe the whole movement, was a later coinage that none of the founders had used. A revolution it was; but it conquered by slow infiltration rather than by sudden assault.
There is, indeed, a sense in which the single event we call the marginal revolution is partly the construction of those who came after. The three founders did not think of themselves as a movement; they had not collaborated, did not much cite one another even once they became aware of each other, and pursued aims so different that their heirs would spend the next century in disagreement. It was later historians, looking back, who gathered the three into one story and gave it a date — and some of those historians have since wondered whether the gathering does not impose more unity than the facts will bear, whether what happened around 1871 was one revolution or three distinct developments that happened to share a single insight. The insight was genuinely shared, and genuinely transformative, and in that the unity is real. But the marginal revolution is also a thing assembled in retrospect, a tidy name laid over an untidy convergence; and it is worth remembering that the men who made it did not know that this was what they were doing, nor that they were doing it together.
What is past dispute is the magnitude of what followed. The marginal principle, once absorbed, rebuilt economics from the foundation. It resolved the paradox of value; it gave demand the theory it had lacked; it shifted the subject's centre of gravity from the classical preoccupation with production and the division of the social product toward the modern preoccupation with allocation and choice, the disposing of scarce means among competing ends; and it bound the whole together with the calculus of the margin. The value of one more became the master concept of a science. Yet the founders, for all their achievement, had given the discipline a principle more than a law — they had established that value is settled at the margin, but the precise law by which the margin behaves, the law that marginal utility falls as quantity rises, they had stated rather than discovered, for it had been discovered already. It had been set down, with complete rigour and in full generality, seventeen years before any of their books, by a retired Prussian official whom not one of them had read, and whose name the next plate must finally restore. As the table says of every quantity, first to last: the argument remains open.