The Water — The Margin, Plate i

The volume's subject is the margin — the value of one more — and the discovery, made independently in three countries within a few years, that what governs a price is never the total or the average but the marginal unit, the last one. Begin where the marginalists began, with a paradox that had baffled economics for a century. Water, without which we die, is nearly free; a diamond, which we could live without, is dear. The classical economists, looking to the labor and the cost embodied in things, could not reconcile a good's usefulness with its price, and the puzzle stood as a standing reproach to the whole theory of value. William Stanley Jevons dissolved it with a single shift of attention — from the whole of a thing's usefulness to the usefulness of its last unit — and in doing so began the rebuilding of economics on a new foundation.

The puzzle was old. Adam Smith, in the founding text of the volume of the wage, had distinguished value in use from value in exchange and remarked on their strange divergence: nothing is more useful than water, yet it will purchase almost nothing; a diamond has scarcely any use, yet commands a great quantity of other goods. Unable to ground exchange value in usefulness, the classical economists grounded it instead in cost — in the labor required to produce a thing, or the resources its making consumed. On this view a diamond is dear because it is hard to find and harder to cut, water cheap because it falls from the sky. The labor theory of value had real power, and it governed economics for the better part of a century; but it left the role of usefulness an embarrassment, a quality everything must possess to be worth anything at all, and yet one that seemed to bear no steady relation to what anything actually cost.¹

1. Adam Smith (the volume of the wage) split value in use from value in exchange and noted the gap: water, supremely useful, buys almost nothing; a diamond, near useless, commands much. Unable to root exchange value in usefulness, the classicals rooted it in cost — labor and resources expended. So diamonds are dear (hard to find and cut), water cheap (it falls from the sky). The labor theory ruled for a century but left usefulness an embarrassment: needed for any worth, yet seemingly unrelated to price.

Jevons saw that the error lay in speaking of the usefulness of water, or of diamonds, as a whole. Usefulness is not a fixed quantity attached to a kind of thing; it varies with how much one already has. The first draught of water, to a man dying of thirst, is worth everything; the hundredth, to a man beside a river, is worth nothing. What governs his valuation of one more unit is therefore not the total usefulness of all the water he consumes but the usefulness of the last unit — what Jevons called the final degree of utility — and this falls as the quantity rises, in the principle of diminishing marginal utility. Now the paradox dissolves. Water is so abundant that its final degree of utility, the worth of one more glass when one already has plenty, is almost nothing, and so its price is almost nothing — though the total utility of all the water we drink is beyond reckoning. A diamond is so scarce that the worth of one more is great, and so its price is great, though its total utility is slight. Price answers to the margin, never to the whole.²

2. Jevons's correction: usefulness is not fixed to a kind of thing but varies with how much one holds. The first draught to the dying man is worth everything, the hundredth by the river nothing. What sets the value of one more is the worth of the last unit — the final degree of utility — which falls as quantity rises (diminishing marginal utility). So water is cheap (its last glass near worthless though its total worth is beyond reckoning) and diamonds dear (their last unit precious though their total worth slight). Price answers to the margin, not the whole.

⁂

The resolution carried with it a reorientation of the whole subject. The classical economists had sought the source of value on the side of supply, in the labor and the cost that went into a thing; Jevons relocated it to the side of demand, in the usefulness of the thing to the person who wants it. Value, on this view, is subjective — it resides not in the object but in the relation between the object and a valuer's wants — and it is bound to scarcity, for the marginal utility that fixes it depends on how much of the good is to be had. Jevons pressed the claim with a boldness that startled his contemporaries: that a thing's value depends wholly on its utility, and that labor, though it often determines how much of a thing is produced, is not the cause of its value. Cost might govern how much water or how many diamonds come to market; but what they are worth, once there, is settled at the margin, by the wants they meet.³

3. The deeper reorientation: the classicals sought value in supply (labor, cost); Jevons moved it to demand (a thing's usefulness to the wanter). Value is thus subjective — in the relation between object and want, not the object — and bound to scarcity, since marginal utility depends on quantity held. Jevons pressed it boldly: a thing's value depends wholly on its utility, and labor, though it governs how much is made, is not the cause of value. Cost sets how much reaches market; what it is worth there is settled at the margin, by the wants it meets.

Beneath the resolution lay a change of mathematical habit that would prove the revolution's deepest legacy. The classical economists had reasoned in totals and averages — the total labor embodied, the average cost of production, the whole stock of a commodity. The marginalists reasoned in increments — the value of one more, the cost of one more, the satisfaction of one more. The question was no longer what a thing is worth in sum, but what one additional unit is worth at the margin one happens to occupy; and because that marginal worth changes continuously with quantity, the natural language for it was the language of the derivative, the rate of change of one magnitude with respect to another. Jevons, trained in the sciences, saw this plainly and wrote his economics in the calculus of the margin. The shift from the total to the increment looks slight, but it remade every question in the subject, for nearly every economic decision — how much to buy, to sell, to make, to work — is a decision not about totals but about one more.⁴

4. The deepest legacy was a change of mathematical habit. The classicals reasoned in totals and averages (labor embodied, average cost, whole stock); the marginalists in increments (the value, cost, satisfaction of one more). The question shifted from what a thing is worth in sum to what one more unit is worth at one's current margin — and since that worth changes continuously with quantity, its natural language is the derivative. Jevons, science-trained, wrote economics in the calculus of the margin. Slight as it looks, the shift remade every question, for nearly every choice is about one more, not the total.

With the paradox of value dissolved, the marginal idea spread to rebuild the subject from its foundation, and the volume follows it outward. The principle that the last unit governs the value of the whole was not Jevons's alone; an obscure German had set down its underlying laws a generation earlier, and two others, in Austria and in Switzerland, were arriving at the same insight in the very years Jevons published. The next plate descends to that precursor, whose laws of diminishing utility and rational allocation underlie everything the marginalists built. After it the volume traces the subjective theory of value to its Austrian source, finds in opportunity cost the margin's account of cost itself, and rises at last to the grandest application of the marginal idea — the vision of the whole economy as a single system in which every price is settled, simultaneously, at the margin. But the foundation is the one Jevons laid: that value is marginal. The next plate is the increment.⁵

5. The marginal idea then spread to rebuild the subject, and the volume follows it: to the precursor whose laws of diminishing utility and rational allocation underlie it (the increment), to the Austrian source of subjective value (the subjective), to the margin's account of cost (the alternative), and at last to the whole economy as one system priced at the margin (the equilibrium). The principle was not Jevons's alone — Gossen had it a generation early, Menger and Walras in the same years. But the foundation is his: value is marginal. Next: the increment.

The marginal revolution began in the dissolving of a paradox. Water is useful and cheap, a diamond useless and dear, because price answers not to the total usefulness of a kind of thing but to the usefulness of its last unit — the final degree of utility, in Jevons's phrase — which abundance drives toward nothing in the water and scarcity holds high in the diamond. The resolution relocated the source of value from the side of supply, where the classical economists had sought it in labor and cost, to the side of demand, in the subjective wants of the valuer and the scarcity that makes the marginal unit precious; and it replaced the classical habit of reasoning in totals and averages with the marginalist habit of reasoning in increments, the value of one more. That shift, small as it appears, rebuilt the theory of value and with it the whole of economics. The next plate is the increment.