Numéraire
Volume the Sixth · of the table of twenty-six
The Quantities · Group II · № 06 · Mg

The Margin

the value of one more

The margin is the first of the quantities, the hinge on which all modern economics turns. It concerns the value of one more — 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. The volume opens with the paradox the marginalists dissolved: that water, supremely useful, is nearly free, while a diamond, of little use, is dear — a puzzle that vanishes once one sees that price answers to the usefulness of the last unit, the final degree of utility (Jevons), which abundance drives toward nothing and scarcity holds high. From there it builds. The laws beneath the marginal idea — that each added unit yields less satisfaction than the last, and that a person spends limited means best by equalizing the satisfaction won from the last unit of each good — were set down, a generation too early and ignored, by Gossen. The Austrian founder Menger grounded value not in measured pleasure but in ranked needs, and drew the inversion that finished the classical order: that the value of the means is imputed backward from the value of the ends, so that cost is a consequence of value and not its cause. His pupil Wieser named the cost that remained — opportunity cost, the value of the best alternative forgone, the marginal idea carried into the reckoning of cost itself. And the flagship takes the principle to its limit. Léon Walras conceived the whole economy as a single system of interlocking markets, in which the prices of all goods are determined together, simultaneously, at the margin — general equilibrium, the groping process by which a price system finds the numbers that reconcile every plan, and the numéraire, the one good against which all the others are measured, that gives this series its name. And the marginal idea did more than reorder the theory of value: recast as the derivative of the differential calculus, it turned economics from a verbal subject into a mathematical one, a transformation Paul Samuelson would carry to its conclusion, deriving all of price theory from the single act of maximizing a magnitude under constraint, for good and for ill (Samuelson). The question the author set the volume was this: why does the last unit, and not the whole, set the price of everything? Because the economy is one system, and in it every price is a marginal price, settled together with all the rest. With the margin, the quantities open on the idea that remade the whole of economics: that to understand any price, one looks not to the total or the average but to the value of one more.

in print · № VI · 12 of 12 plates
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The argument of the volume

Begin where the marginalists began, with the paradox of value. Water, without which we die, is nearly free; a diamond, which we could live without, is dear. The classical economists, grounding value in the labor and cost a thing embodied, could not reconcile its usefulness with its price. William Stanley Jevons dissolved the puzzle by looking to the last unit. Usefulness, he saw, is not fixed to a kind of thing but varies with how much one has; what governs the value of one more is the usefulness of the final unit, the final degree of utility, which falls as the quantity rises. Water is cheap because, being abundant, its last glass is worth almost nothing, though the whole of it is beyond price; a diamond is dear because, being scarce, its last unit is worth much. Price answers to the margin, never the whole — and value, on this view, springs not from the cost of making a thing but from the wants it meets, subjective and bound to scarcity.

The laws beneath the marginal idea had been set down, a generation too early and wholly ignored, by Hermann Heinrich Gossen: that each added unit of a good yields less satisfaction than the last, and that a person spends limited means best by equalizing, across all his wants, the satisfaction won from the last unit of money spent on each. The first is diminishing marginal utility; the second, the equimarginal principle, is the exact logic of rational allocation. The Austrian Carl Menger, arriving at the marginal insight independently, grounded value not in a measured quantity of pleasure but in the ranked needs of a purposive mind, and drew from it an inversion that finished the classical order: the value of the means of production is imputed backward from the value of the ends they serve, so that flour is dear because bread is wanted, and not the reverse. Cost is a consequence of value, not its cause. And Menger's pupil Friedrich von Wieser named the cost that remained — opportunity cost, the value of the best alternative a resource might have served and now cannot, the marginal idea carried into the reckoning of cost itself.

The flagship carries the principle to its limit. Léon Walras conceived the entire economy as a single system of interlocking markets, every price at once a cause and an effect of every other, and asked how all prices might be determined together. His answer was general equilibrium: a system in which the marginal conditions of every consumer and every producer are satisfied at once, every market clears, and the result, a later age would prove, is in a definite sense efficient — the invisible hand of the founding volumes given a mathematical body. He pictured the groping process by which a price system finds, without any central calculator, the numbers that reconcile every plan; and he chose one good as the unit of account, the numéraire, in whose units all value is reckoned — the device that gives this series its name. And what Walras did to the price system, the marginal idea did to the discipline entire: recast as the derivative of the calculus, the margin turned economics from a verbal subject into a mathematical one, a transformation Paul Samuelson carried to its conclusion, deriving all of price theory from the single premise that agents maximize under constraint — a gain in rigor and reach bought, his critics held, at a cost in realism and in readers. So the question the author set the volume is answered: the last unit sets the price of everything because the economy is one system, in which every price is a marginal price, all of them settled together. With the margin in print, the quantities open beside the utility, and the table gains the idea on which all the others rest — that to understand a price, any price, one looks not to the total or the average but to the value of one more.

The argument remains open. What follows is an attempt to fix its exact edges.

The twelve plates of this volume

  1. i The Waterin print Jevons; the diamond-water paradox dissolved — price answers not to a thing's total usefulness but to the usefulness of its last unit, the final degree of utility. Read the plate →
  2. ii The Laborin print the classical theory the margin overthrew; value sought in the labor and cost a thing embodied, and the usefulness it could never quite explain. Read the plate →
  3. iii The Incrementin print Gossen; the two laws beneath it all — that each added unit yields less satisfaction than the last, and that means are spent best by equalizing the satisfaction of the last unit of each. Read the plate →
  4. iv The Subjectivein print Menger; value grounded in ranked needs, not measured pleasure, and the inversion that follows — that the worth of the means is imputed backward from the worth of the ends. Read the plate →
  5. v The Alternativein print Wieser; opportunity cost — the cost of any use of a resource is the value of the best alternative use forgone, the marginal idea carried into the reckoning of cost. Read the plate →
  6. vi The Scissorsin print supply meets demand; if marginal utility governs what buyers will pay, marginal cost governs what sellers will take, and the price is settled where the blades cross. Read the plate →
  7. vii The Methodin print the marginal rule generalized; do a little more of a thing while its marginal benefit exceeds its marginal cost, and stop just where the two meet. Read the plate →
  8. viii The Equilibriumin print Walras; the whole economy as one system of interlocking markets, all prices settled together at the margin — general equilibrium, and the numéraire that gives this series its name. Read the plate →
  9. ix The Calculusin print the marginal quantity is a derivative; how the margin turned a verbal subject into a mathematical one, for good and for ill. Read the plate →
  10. x The Efficiencyin print the welfare theorems; in what exact sense an economy that reckons at the margin wastes nothing, and the demanding conditions under which the claim holds. Read the plate →
  11. xi The Revolutionin print why three men, in three countries, lit on the margin within a few years of one another, and what it means that an idea has its moment. Read the plate →
  12. xii The Returnin print diminishing returns in production; why each added hand or acre yields a little less than the last, and how the margin governs what is made as well as what is wanted. Read the plate →

In closing

This volume took up the margin, the first of the quantities and the hinge on which all modern economics turns — the value of one more, and the discovery that what governs a price is never the total or the average but the marginal unit. Its subject was the marginal revolution: the resolution of the paradox of value, the laws of diminishing utility and rational allocation, the subjective theory of value and its inversion of cost, opportunity cost, and the vision of the whole economy as one system priced at the margin. And the question the author set it was this: why does the last unit, and not the whole, set the price of everything?

The volume built from a single good to the whole economy. William Stanley Jevons dissolved the diamond-water paradox by looking to the last unit, relocating the source of value from the cost of making a thing to the wants it meets. Hermann Heinrich Gossen, ignored a generation earlier, had set down the laws beneath it: diminishing marginal utility, and the equimarginal principle that is the logic of rational allocation. Carl Menger grounded value in ranked needs and imputed the worth of the means backward from the worth of the ends, dissolving the classical cost theory; and his pupil Friedrich von Wieser named the cost that remained, opportunity cost, the value of the best alternative forgone. At each step the principle was the same: look not to the total but to the margin, the value, and the cost, of one more.

The flagship carried the principle to its limit. Léon Walras conceived the entire economy as a single system of interlocking markets and showed that, when every agent reckons at his own margin, the prices of all goods are determined together, simultaneously, in a general equilibrium that clears every market at once and, a later age would prove, wastes nothing at the margin. He gave the invisible hand a mathematical body, pictured the groping by which a price system finds the numbers that reconcile every plan, and chose the one good against which all the others are measured — the numéraire that gives this series its name. And the marginal idea, cast as the derivative of the calculus, did to the discipline what Walras did to the price system: Paul Samuelson made the maximizing of a magnitude under constraint the single engine of economic theory, turning a verbal subject into a mathematical one, for good and for ill. So the question is answered: the last unit sets the price of everything because the economy is one system, every price a marginal price, all settled together. With the margin joining the utility in print, the quantities stand two volumes deep; and the table gains the idea on which all its others rest — that to understand any price, one looks not to the total or the average, not to the labor sunk or the cost incurred, but to the value of one more.

The marginal revolution was so complete that its language is now simply the language of economics: every student learns to set marginal benefit against marginal cost, to reckon opportunity cost, to find the optimum where the margins meet. Yet the very completeness raises a doubt the volume leaves open. The marginal account assumes a person who can weigh the value of one more against the value of one more of everything else — who knows his own wants, computes his margins, and chooses the point where they balance. Real people, the volume of the choice has shown, are not always such reckoners; they lean on rules of thumb, are swayed by how a choice is framed, and cannot always say what they want until they have chosen it. So the question the margin leaves is whether its triumph describes how people actually decide, or only how a perfectly rational agent would — whether the economy truly reckons at the margin, or merely behaves, often and roughly, as if it did.