The previous plate closed on a debt. The founders of the marginal revolution, it said, had given economics a principle more than a law — they had established that value is settled at the margin, but the law by which the margin actually behaves they had stated rather than discovered, because it had been discovered already, seventeen years before any of their books, by a man none of them had read. This plate pays the debt and names the law. The law is that the marginal utility of a good diminishes as one has more of it — that each successive unit yields less satisfaction than the unit before — and the line it traces, of utility falling as quantity rises, is the gradient on which the whole of marginalism is built. The man was Hermann Heinrich Gossen, and the story of how he found the law, and lost it, and was found again too late to know it, is among the most poignant in the history of the subject.
The law is as homely as any in economics, and as easily felt. Consider a thirsty traveller and a series of glasses of water. The first glass is worth a great deal to him — it may be worth, in the limit, his life. The second is welcome too, but less urgently; the thirst is already half quenched. The third he drinks with mild pleasure, the fourth out of mere completeness, and by the tenth the water has become a matter of indifference, by the twentieth a positive burden he would pay to be spared. The total usefulness of the water has risen with every glass; but the additional usefulness of each successive glass — its marginal utility — has fallen steadily away, from the life-saving worth of the first to the nuisance of the twentieth. Plot that additional worth against the quantity already drunk and the points descend in a line from upper left to lower right: the gradient, the downward slope of marginal utility against quantity. It is the simple shape of a satiable want, and nearly every want is satiable; there is almost nothing of which the hundredth unit is as dear as the first.
What looks like a modest observation about thirst is in fact the engine of the entire theory, the single mechanism from which the marginal apparatus draws its power. Set the gradient in place and the paradox of value resolves itself without further effort: water is abundant, and abundance pushes one far down the gradient to where the marginal utility, and hence the price, is near zero, while a diamond is scarce, and scarcity holds one near the top of the gradient where the marginal utility, and hence the price, is high. Set the gradient in place and the demand curve acquires its downward slope, for if each additional unit is worth less than the last, a buyer will take more only as the price falls to meet that declining worth. Set it in place and the gains from trade follow, and the consumer's optimum, and the whole logic of allocation, for all of these are arguments about how a falling marginal worth is to be weighed against a cost. Remove the gradient and the apparatus seizes; with it, the machine turns over and runs. Diminishing marginal utility is not one law of the theory among several. It is very nearly the theory's beating heart.
It is the homeliest of laws — that the second glass means less than the first — and almost the whole of marginalism is built upon it: the falling demand curve, the resolved paradox, the gains of every trade, each of them the gradient at work.
The man who first set the law down in full was not an economist by trade but a disenchanted Prussian official. Hermann Heinrich Gossen, born in 1810, spent unhappy years in the tax and administrative service of the Prussian state before abandoning it to work out, in solitude, a mathematical theory of human satisfaction. In 1854 he published the result at his own expense, under a title of forbidding length — usually rendered as The Development of the Laws of Human Intercourse — in which he laid out, with a rigour decades ahead of his contemporaries, not one fundamental law but two: the first, that the marginal utility of a good diminishes as one consumes more of it; the second, that a person divides his means among competing goods so as to equalise the marginal utility of the last unit of each, which is the rule that defines the optimum. He believed, and said in so many words, that he had done for the moral world of economics what Copernicus had done for the heavens. He was, in substance, correct.
The book fell into a silence almost total. It was self-published, by an unknown man, in a dense and heavily mathematical style that the economics of 1854 — still Ricardian, still suspicious of mathematics, still preoccupied with cost and production — was wholly unprepared to receive; and the grandeur of its author's claims for himself, the comparison to Copernicus and the rest, did nothing to recommend it to the few who opened it. It found no reviewers of consequence, no readers who understood it, no champions. Wounded by the indifference, and persuaded that his life's work had failed, Gossen withdrew the book from circulation, recalling the unsold copies from the publisher; most were destroyed. He died of consumption in 1858, four years after publication, in the settled belief that he had accomplished nothing. It is the precise fate reserved for a true thing said too soon — not refutation, which is at least a kind of attention, but silence, and the slow conviction of the one who said it that he must after all have been wrong.
He had done for economics what Copernicus did for the heavens, and he knew it; but the book fell dead, and he withdrew it, and died sure he had wasted his life — which is the fate of a true thing said a generation too early.
The vindication came, as it so often does, just too late to be of use to the man who had earned it. In the years around 1870 the three founders rediscovered, independently and in ignorance of Gossen as of one another, the very laws he had set down. It was not until 1878, twenty years after Gossen's death, that a copy of his book surfaced — pointed out to Jevons by a correspondent, Robert Adamson, who had chanced upon it — and Jevons, to his great credit, responded not with defensiveness but with generosity, devoting a passage of the second edition of his own Theory to Gossen and acknowledging without reservation that this forgotten German had completely anticipated him in the general principle and method of the whole theory. Walras went further still, writing some years afterward an essay expressly to rescue Gossen's name, under a title that says everything: an unknown economist. By these acts the priority was at last assigned where it belonged. But Gossen himself never knew that he had been right, and the laws that bear his name were made famous by men who reached them two decades after he had died despairing of them.
Gossen's fate is more than a sad story; it is the decisive piece of evidence for the claim the previous plate advanced. If a discovery were simply the achievement of an individual mind, then Gossen, who made the discovery fully and first, should have carried the day, and the marginal revolution should bear the single date 1854 and the single name Gossen. It bears neither, and the reason is that a discovery is also, and perhaps mostly, the work of its moment — and Gossen's moment was wrong. In 1854 the ground was unprepared: the classical theory had not yet reached the visible impasse that would make a new approach seem necessary, the mathematical temper had not yet entered economics, the readers who could have understood him did not yet exist. The very same truth, carried to a world that was ready for it, was found by three men at once; carried to a world that was not, it was found by one man and buried with him. Gossen is the control case that proves the experiment: he had the idea entire, and the idea was not enough, because an idea arrives only when its time has come.
The gradient, then — diminishing marginal utility, the first of Gossen's two laws — is the foundation beneath the whole marginal structure, the downward slope without which none of the rest would stand. But it is, by itself, only a description of how the worth of a thing falls as one acquires more of it; it does not yet tell a person facing many goods and a limited purse what he ought to do. For that one needs Gossen's second law, which takes the gradient as given and asks how, across all the goods competing for one's means, the spending should be arranged to wring from it the most satisfaction attainable — and which answers, with a precision that still defines what economists mean by an optimum, that the last unit of money laid out on each good must yield the same marginal utility as the last laid out on every other. The first law gives the slope; the second uses it to find the summit. That second law is the subject of the next plate. As the table says of every quantity, first to last: the argument remains open.