№ VI
The twelve plates
For the better part of a century, economics asked what a thing was worth and answered by looking backward, to the labor and the cost that had gone into it. Then, in the space of three years and three countries, a single correction undid the question: what governs a price is never the whole or the average, but the value of one more — one more hour, one more loaf, one more ton. This volume follows that correction, the most quietly total in the history of the science, from the paradox it dissolved to the distribution it was built to justify, and to the exact points where the last unit explains everything, and where it explains too much.
why does the last unit, and not the whole, set the price of everything?
A glass of water will save your life; a diamond will not. Yet the diamond commands a fortune and the water is very nearly free. Adam Smith set this puzzle down in 1776 and could not answer it, and for a hundred years neither could the great science he founded. The question what is a thing worth? was answered by looking backward — to the labor and the cost that had gone into making it — a theory with the considerable virtue of seeming to reward effort, and the fatal defect of getting the plainest facts exactly wrong. Water is cheap to provide and beyond price in use; the diamond is useless and dear. Cost looked the wrong way down time. Worth, it turned out, was a matter of the future, and of one thing only: how much you would give for one more.
The correction arrived three times at once. In 1871 William Stanley Jevons published it in England and Carl Menger in Vienna, neither aware of the other; in 1874 Léon Walras set the same proposition out in Lausanne in the language of equations. Three men, three countries, one idea — and behind them a fourth, Hermann Gossen, a retired Prussian tax official who had stated the whole of it in 1854, sold almost no copies, had the book withdrawn from sale, and died believing he had failed. What the four of them saw was this. The worth of a thing is not fixed in it like a weight. It depends on how much of it you already hold. The first glass of water, to a man dying of thirst, is worth everything; the second a great deal; the hundredth, used to wash a step, almost nothing. Utility falls as quantity rises — Gossen's first law — and so the value of any unit is set not by the whole stock but by the last one, the marginal one, the one whose loss would be felt least. Water is cheap not because it is unimportant but because it is abundant: there is always a hundredth glass, and that glass prices all the rest. The diamond is dear because it is scarce, and the last diamond is still badly wanted. The paradox was never a paradox. It was a confusion of the total with the margin.
Once seen, the principle could not be unseen, and it proved astonishingly complete; it rebuilt the subject room by room. If value lies at the margin, then the careful chooser spends so that the last penny laid out on bread yields exactly the satisfaction of the last penny laid out on wine, and on everything else besides — for otherwise he would move a penny to where it did more. This is Gossen's second law, the equimarginal rule, and it is the entire theory of the consumer in a single line. The same logic governs the producer, who hires one more worker, plants one more acre, runs the line one more hour only so long as the added product covers the added cost, and stops precisely where the two meet. Alfred Marshall, who gave the new economics its settled form in 1890, closed the long quarrel between the utility theorists and the older cost theorists with an image no one has bettered: asking whether value is governed by utility or by cost, he said, is like asking whether it is the upper or the lower blade of a pair of scissors that does the cutting. Both blades, always, meeting at the margin.
And because every one of these statements is a statement about a rate — satisfaction per penny, product per hour, the slope of a curve at a point — the whole of it could be written in the calculus. The margin is a derivative. To maximize anything, set its marginal benefit equal to its marginal cost; at the summit, the slope is zero. With that, economics became a mathematical science of constrained optimization, and has remained one. There was a price for the completeness, and the science paid it slowly. The early marginalists wrote as though utility could be measured, as though pleasure came in countable units they called utils — an embarrassment, since no instrument has ever read a single one. The cure, begun by Pareto and finished by Hicks and the young Paul Samuelson, was to throw the units away and keep only the ranking. You need not know how much a man prefers coffee to tea, only that he does; and from the order of his choices alone, revealed in what he actually buys, the entire apparatus rebuilds itself without ever naming a quantity of feeling. The ghost was exorcised; the slope of the indifference curve did all the work the old utils had pretended to. Want itself receded into something inferred and never seen — a matter taken up in its own volume, The Utility.
But the marginal principle made one further claim, and it is the one that has never stopped being argued. If the producer pays each worker, each acre, each machine the value of what one more of them adds, then — the American economist John Bates Clark announced in 1899 — every factor receives exactly the value of its marginal product, and the division of income into wages and profits and rents is neither robbery nor charity but a kind of natural justice: each is paid what it is worth. Here the cool geometry of the margin turns warm, and political. For if the claim holds, the existing distribution of the world's product is simply what productivity dictates, and to protest it is to protest against arithmetic. The trouble is that the claim rests on saying how much one more unit of capital produces — and capital, unlike an hour or an acre, is not a natural quantity but a sum of money whose size already depends on the rate of profit the theory was meant to explain. The economists of Cambridge in England — Joan Robinson, Piero Sraffa — pressed exactly there through the 1950s and 1960s, against the economists of Cambridge in Massachusetts, and showed, by the strange phenomenon of reswitching, that the parable breaks: there is no general sense in which more capital must earn less, no clean marginal product on which to hang a wage or a profit. Samuelson conceded the logic in 1966. The profession noted the concession and carried on. And so the margin arrives, by its longest road, at the same doubt that opens The Wage: whether the last unit measures a worker's worth, or merely names the going rate of a contest he did not set.
This is the line the volume walks. The marginal principle is the most powerful instrument the science possesses, and within its proper country it explains very nearly everything — why prices are what they are, why people choose as they do, why one more is the only quantity that ever decides. It also has edges. It falters where things come in lumps that cannot be halved, and it inverts where one more grows cheaper rather than dearer, as it does wherever ideas and networks rule. It asks of a starving man and a glutton the same question — what will you give for one more loaf? — and weights their answers by their purse, so that it can value a whim above a need and call the sum efficient. The twelve plates that follow trace the principle from the paradox that bore it to the exact frontier where description shades into apology. What the last unit explains, it explains completely. What it cannot, it tends to hide. The argument remains open.