It is the rarest thing in the life of a science: the same correction, reached independently, in three languages, inside three years. In 1871 the Englishman William Stanley Jevons and the Austrian Carl Menger each set it down, in plain ignorance of the other — that value is governed at the margin; three years later, at Lausanne, Léon Walras cast the identical proposition as a system of simultaneous equations and believed he had founded a mechanics of exchange. That three minds should arrive so precisely at one place is the kind of coincidence that is not one. It suggests the idea was not invented but found — that it had lain all along in the shape of the problem, waiting only for someone to stop staring at the whole and look instead at the last.
Consider how little the three men had in common beyond the answer. They wrote in different languages, in different countries, for different readers, out of different intellectual worlds; they would never collaborate, and two of them would go to their graves barely acknowledging the third. What they shared was a single seismic perception — that the worth of a thing is set by the usefulness of its last and least-needed unit — and a willingness to rebuild the whole of economics upon it. To watch one idea surface in three such unlike minds is to suspect that the mind was not, in the end, the decisive thing.
In England the idea came dressed as arithmetic. Jevons proposed to treat economics as a calculus of pleasure and pain — Bentham's utilitarian psychology made into mathematics — and gave the marginal quantity a name of his own: the final degree of utility, the usefulness of the last increment a person troubles to consume. From this he mounted a frontal assault on the reigning doctrine. Value does not come from labor, he insisted; labor once spent is gone and can compel no price. Value comes from utility, and utility is reckoned at the margin. It was a clean, combative, thoroughly mathematical case — and it landed, though Jevons knew better than anyone how nearly it had not.
In Vienna the same idea came without a single equation. Carl Menger reached the margin not through mathematics but through a patient psychology of wanting. A person, he saw, ranks his wants by urgency and meets the most pressing first; as a good grows more abundant it is put to ever less urgent uses, and its value is fixed by the least urgent want its supply is called upon to satisfy. The water that first slakes thirst, then washes, then merely cools the air is worth, at each unit, only what that last and idlest use is worth. Menger never wrote the word "marginal"; he had no need of it. But he had the principle entire, and from his Grundsätze of 1871 would grow the Austrian school — the one heir of the revolution to keep its distance from the mathematics the others made their pride.
At Lausanne the idea came as a machine. Léon Walras, the least patient of the three with half-measures, was not content to price one good at the margin; he meant to price every good at once. He conceived the entire economy as a single interdependent system — each market bound to every other, each price a function of all the rest — and set out to show, in a great lattice of simultaneous equations, that the whole might come to rest together in one general equilibrium. Marginal utility, which he called rareté, was the cornerstone of demand; upon it he raised the most ambitious structure economics had yet attempted. Where Jevons argued and Menger described, Walras built — and the thing he built would outlast its scaffolding by a century.
A moralist's calculus, a philosopher's psychology, an engineer's mechanics: three temperaments that agreed on almost nothing about how economics ought to be done, and on exactly one thing about what it had got wrong. Each had taken the riddle the classical economists could not crack — why the useful thing is cheap and the useless thing dear — and dissolved it the same way, by refusing to ask after the worth of the whole and asking instead after the worth of the last. That such different men should converge so exactly is the central fact of the episode, and the one most in need of explaining.
For there was a fourth man, and he was first, and he was nobody. Twenty years before the three, in 1854, a retired Prussian civil servant named Hermann Heinrich Gossen had published a book setting out the whole of it: that the worth of successive units of a good declines, and that a person spends his means best when the last coin laid out on each good buys him an equal measure of satisfaction. The two propositions are the foundation stones of the entire theory; they are taught today as Gossen's first and second laws. The book sold almost nothing. The world had no use for it, and Gossen, stung, had the remaining copies withdrawn from sale.
He died four years later, in 1858, certain that his life's work had come to nothing. It is among the quietly terrible stories in the history of thought: a man who had seen, whole and early, what a discipline would spend the next century groping toward, and who went to his grave believing he had failed. The vindication came, as it so often does, too late to reach him — and from the unlikeliest quarter. Jevons, alerted by a correspondent some years after his own book had appeared, found that this forgotten German had anticipated him entirely, and said so without reservation in his second edition; Walras paid the same debt. The first man to the truth was hauled back out of oblivion by the very men who had, in complete ignorance of him, re-discovered it for themselves.
And behind Gossen the roots run deeper yet, for the marginal idea had been glimpsed and let fall many times before he gathered it. Obscure lecturers had stated it at Oxford and Dublin in the 1830s; a French engineer had drawn it from a demand curve in 1844; and more than a century before any of them, in 1738, a mathematician had reached its very heart while puzzling over a game of chance. The principle, in short, was never hard to discover. It was hard to keep. It had been found and forgotten so many times that its eventual triumph looks less like the dawning of a new truth than the moment a very old one finally refused to be put back down.
A discovery made by three men at once is not three strokes of genius. It is one idea, grown ripe, finding every unlocked door.
Why, then, 1871? If the idea was so often had and so easily lost, what made it stick at last — and stick in three places at once? The answer is not chance but ripeness. By the third quarter of the century three conditions had quietly converged. The great classical edifice was cracking under its own weight, the labor theory strained by anomalies it could not absorb, and John Stuart Mill, its last and ablest synthesizer, had in 1869 publicly abandoned one of its central doctrines. The mathematical cast of mind — the habit of reasoning in increments and at the margin — had spread through the sciences and stood ready to hand. And the turn toward the valuing subject, toward the chooser rather than the thing chosen, was everywhere in the air. When a question's structure and the tools to answer it align in this way, the answer ceases to wait upon genius and begins, instead, to announce itself through whoever happens to be standing nearest.
This is the pattern the historians of science know best. The most famous discoveries are very often made twice or three times over, independently, within a few years: the calculus by Newton and by Leibniz, natural selection by Darwin and by Wallace, the conservation of energy by half a dozen hands at once. Such multiples are the strongest evidence that discoveries ripen — that they are made not when a singular mind appears but when the accumulated state of a field renders the next step all but unavoidable, and therefore available to several minds together. The marginal revolution is economics' cleanest case. The idea was, as the opening of this plate had it, lying in the shape of the problem; 1871 was simply the year the shape became impossible to overlook.
That it was a revolution, in one sense, is past dispute. It moved the seat of value from the object to the subject, from the labor congealed in a thing to the satisfaction a chooser draws from it; it dethroned cost and crowned utility; it made the optimizing individual, weighing one more unit against its price, the atom from which the whole science would henceforth be built. The classical economists had asked what things cost to make. Their successors asked what things were worth to have — and answered at the margin. That is as deep a change of subject as a discipline can undergo.
And yet "revolution" flatters the suddenness of it. The books of 1871 were themselves largely ignored at first; it took some twenty years for the new view to consolidate, and the man who consolidated it did so by denying that any overthrow had occurred. Alfred Marshall, gathering the threads in 1890, insisted that the marginalists had not refuted the classics but completed them: cost of production still governs what sellers will supply, marginal utility governs what buyers will demand, and price is settled by the two together, as a sheet of paper is cut by both blades of a scissors. The labor theorists, on this telling, had not been wrong so much as half-right — they had described one blade and mistaken it for the whole instrument. A revolution that takes a century of false starts to begin, twenty years of aftermath to win, and ends by absorbing rather than annihilating the doctrine it replaces is a strange sort of revolution: more a change of vantage than a change of facts.
There is, too, a reading of the turn that its champions seldom volunteer. In moving the science from cost and class and distribution toward the satisfactions of the individual chooser, the marginalists also moved it away from the questions that had animated the classical economists, and would animate Marx — who gets what, and why, and whether the getting is just. The new economics had a great deal to say about how a solitary agent might best spend a fixed income, and rather less to say about how the income came to be fixed where it was. Whether this was the natural unfolding of a truer theory or a quiet turning-away from uncomfortable ground is itself a matter of argument, and not one to be settled here — but the question deserves to be named, and is taken up again at this volume's far edge.
One idea, then, refracted through three unlike minds, and seeding three unlike sciences. From Jevons, by way of Marshall, descended the Anglo-American mainstream — the supply and demand, the curves and equilibria, that every student meets in a first week. From Menger descended the Austrian line — Wieser and Böhm-Bawerk, then Mises and Hayek — keeping faith with subjectivism and with a deep suspicion of the equations the others loved, and turning the discipline's gaze toward knowledge, expectation, and time. From Walras descended the Lausanne line — Pareto, and in the fullness of time the entire grand apparatus of general equilibrium — pursuing the dream of the whole economy solved at once as a single system. They argue with one another still. The marginal insight was one; its heirs were three, and they have never wholly reconciled.
The revolution of 1871 discovered no new fact about diamonds or water. It discovered a new place to stand — the margin — from which Smith's ancient riddle, and a hundred riddles after it, simply dissolved. What looks in the retelling like a single bold stroke was in truth the slow ripening of a question, found and forgotten across a century and more, until the field and its tools had grown ready and the answer announced itself, all at once, through three men who had never met. The price of a thing was always a verdict struck at the margin; eighteen seventy-one was merely the year the science learned, at last and in triplicate, where to look. The argument remains open.