The first family of this table weighed the five fundamental prices and found each of them, in the end, to be a verdict — on a contest, a power, a history — rather than a fact of nature. This second family turns from the verdicts to the things they are verdicts about: the magnitudes a market is forever trying to count, the quantities beneath the prices. The first of those quantities is the strangest and the most important, the one whose discovery remade the whole of economics — the value of one more. Not the value of a thing in general, nor the value of all of it that exists, but the value of a single additional unit: one more hour, one more loaf, one more ton. That economics should turn on this quantity, and not on the totals it seems so much more natural to count, is the great counterintuitive finding of the discipline, and the gateway to it is a puzzle older than the finding itself — a paradox the classical economists could state with perfect clarity and could not, for the life of them, resolve. It is the paradox of value, and this plate is its statement; the next will be its undoing.
The paradox is easily put, and its emblem is a comparison between two things. Water is the most useful substance on earth: nothing whatever can live without it, and a person deprived of it dies in days. A diamond is among the most useless: it sustains no life, performs no labour, serves no purpose beyond ornament and the cutting of glass. By every measure of usefulness, water is incomparably the more valuable of the two. And yet in the market the ranking is exactly reversed. Water is nearly free — so cheap that in most places it is scarcely priced at all — while a diamond commands a fortune, exchangeable for houses, for years of labour, for quantities of almost anything else one might name. The most useful thing in the world is the cheapest; one of the most useless is among the dearest. Here is the puzzle in its starkest form: the price of a thing, the rate at which it exchanges for other things, bears no evident relation to its usefulness, and often runs flatly against it. If value in exchange followed value in use, water would be priceless and diamonds worthless; instead the world has arranged things the other way about, and the question is why.
Adam Smith saw the paradox clearly and named its two terms. There were, he wrote, two different senses of the word value: value in use, the utility of a thing, its capacity to satisfy a want; and value in exchange, the power of purchasing other goods that the possession of it conveys. The two, he observed, not only differed but could diverge to opposite extremes. Nothing was more useful than water, yet it would purchase scarcely anything; a diamond had hardly any use, yet a great quantity of other goods could commonly be had in exchange for it. Having drawn the distinction, however, Smith could not explain it — could not say why the two values parted, nor what governed the exchange value that so plainly was not governed by use. He set the puzzle down with admirable honesty and walked past it, turning to a different account of exchange value altogether: that a thing's worth in trade was determined, in the end, by the labour required to produce it. Diamonds were dear because they were hard to find and harder to win from the earth; water was cheap because it lay everywhere to hand. This was an answer of a kind, and it would anchor the classical theory of value for the better part of a century. But it answered only half the question, and the half it left untouched was the half that mattered.
Nothing is more useful than water, Smith saw, yet it will purchase almost nothing; a diamond is good for almost nothing, yet it will purchase almost anything — and he could say that this was so, but never why.
The answer Smith reached for, and Ricardo after him refined into a system, was a theory of value built upon cost — upon the labour, and the other expenses of production, embodied in a thing. On this view the natural price of a good was the sum of the wages, profits, and rents required to bring it to market, and its market price hovered around that natural price as supply adjusted to demand. For a great range of goods this worked admirably. Most of what is traded can be produced in greater quantity if its price rises, and the cost of producing it therefore sets, over time, the price at which it settles; the cloth and the corn and the iron of the classical world obeyed the law of cost well enough. And the theory had the great virtue of locating value in something solid and measurable — the labour and resources a thing consumed — rather than in the shifting and subjective business of how much someone happened to want it. The classical economists built an imposing edifice on this foundation, and for many purposes it stood. But it rested on a suppression, and the paradox of value was the crack through which the suppressed thing would eventually return.
What the cost theory suppressed was demand — the side of the market on which wanting, not making, does the work. By grounding value in the cost of production, the classical economists had given a complete account of supply and almost none of demand; they could say what a thing took to make, but not what it was worth to the one who wanted it, and so they could not explain the cases where price plainly answered to desire rather than to cost. The paradox of value was the sharpest of these cases. The labour theory could indeed say why diamonds cost more to produce than water — but it could not say why anyone should give a fortune for a stone that did nothing, and the price of a diamond is, in the end, a fact about how much people will pay for it, which is to say a fact about demand. Worse, the theory stumbled outright on the goods that cannot be produced at all: an old master's painting, a vintage long since drunk down to its last bottles, a parcel of land in a particular place. For these, cost determined nothing, because no quantity of labour could make another; their prices were set entirely by desire meeting scarcity, and of that meeting the cost theory had nothing to say. The demand side was a darkness the classical lamp could not light, and the paradox of value was a fact that lived squarely within it.
The classical theory could say what a thing cost to make, but never what it was worth to the one who wanted it; demand was a darkness its lamp could not light, and the paradox of value lived squarely within it.
The resolution, when it came, would not abandon usefulness but refine it — and the refinement turned on a single word the classical economists had failed to attach to the right quantity. The mistake had been to ask after the usefulness of water as such, against the usefulness of diamonds as such, and to find the ranking absurdly at odds with the prices. But no one in a market ever chooses between all the water in the world and all the diamonds; one chooses, always, whether to acquire a little more of this or a little more of that, here and now, given what one already has. And the usefulness that bears on that choice is not the total usefulness of the thing but the usefulness of the particular increment in question — the value of one more unit. Water has an immense total usefulness and a vanishing marginal one: because it is abundant, the worth of one more cupful, to someone who already has plenty, is almost nothing, and it is that worth, not the worth of water in general, that sets what one will pay for it. Diamonds have a trivial total usefulness and a high marginal one: because they are scarce, the worth of one more, to someone who has few or none, is great, and that worth sets the price. The paradox dissolves the instant the question is asked of the margin rather than of the whole.
This is the marginal principle, and the reach of it is hard to overstate, for what looks at first like a clever escape from a single puzzle turns out to be the hinge on which the entire subject swings. The classical economists had not been wrong to look for value in usefulness; they had only looked at the wrong usefulness, the total instead of the marginal, and the error had driven them to abandon demand for cost and to leave half of economics in the dark. To restore the margin was to restore the whole — to give demand a theory at last, to reunite it with supply, and to recast every question of price and quantity as a question about the value of one more. Once the discipline learned to think in this way, it could not stop, for the principle proved to govern not only the price of diamonds but the wage of an hour, the rent of an acre, the allocation of a budget, the optimum of a firm: everywhere a quantity had to be settled, it was settled at the edge, by weighing one more against its cost, and the totals that had seemed the natural objects of attention turned out to decide nothing. How that single shift of attention came to be made — and made three times over, in the same few years, by three men in three countries who had never heard of one another — is the story the next plate tells. The volume's question is already in view: why the last unit, and not the whole, sets the price of everything.
The paradox of value, then, is the door through which this volume enters its subject. Stated by Smith and left unresolved, it stood for more than a century as a small embarrassment at the foundation of the discipline — a thing every economist knew and none could quite explain, the most useful substance cheap and the most useless dear. Its persistence was the symptom of a theory that understood the cost of things but not their worth, that had built a complete account of making upon the suppression of wanting. The cure was not to think harder about totals but to stop thinking about them — to see that price answers not to the value of a thing entire but to the value of one more of it, and that this marginal value depends on how much one already has, falling as abundance rises and climbing as scarcity bites. That cure, administered almost simultaneously in 1871 by three economists working in ignorance of one another, is the subject to which this volume now turns, and the revolution it worked is nothing less than the quiet, total rebuilding of economics around the margin. As the table says of every price, and now of every quantity, first to last: the argument remains open.