The plate before this one left the wage suspended within a range — above the worker's floor, below the value of his work — and pronounced its exact place undecided by the market, settled instead by power, by who at the table could afford to wait. This plate sets out the great theory that denies the suspension altogether: that competition does not leave the wage loose within a range at all, but drives it, as surely as water finds its level, to a single point — the value of the last hour worked. It is the marginal-productivity theory of wages, the central pillar of the orthodox account of how the social product comes to be divided, and it must be set down here at its full strength and granted its real force, for it is a far more formidable thing than the previous plate, intent upon the bargain, had any reason to allow. Its claim can be put in one sentence: the worker is paid his marginal product — the value of what his last hour adds — and the wage therefore measures not the employer's power but the worker's worth.
Consider the firm with one more worker it might hire, or might not. What that worker would add is the extra product of his labour, valued at the price it fetches in the market — his marginal revenue product. What he would cost is the wage. So long as the first exceeds the second, the firm gains by taking him on; it goes on hiring until the two have closed together, and stops at the point where the value the last worker adds is just equal to the wage he is paid. The schedule of those marginal products — declining as more and more hands are set to work with a fixed stock of plant and land, under the old law of diminishing returns — is nothing other than the firm's demand curve for labour, and the demand of the market is the sum of them all. Set that demand against the supply of labour, and the wage is determined; and it is determined at the value of the marginal hour. This was the deep achievement of the marginalist revolution of the eighteen-seventies: the very principle that had explained the price of a loaf by the worth of the last loaf to the last buyer was turned upon the factors of production themselves, and made to explain the wage by the worth of the last hour to the last employer. Value, for labour as for bread, was found at the margin.
The theory found its boldest and least guarded voice in the American economist John Bates Clark, whose Distribution of Wealth, published in 1899, made of it not merely an account of how wages happen to be set but a doctrine of how they ought to be — a theory, no less, of justice. Under free competition, Clark argued, each agent of production receives precisely what it contributes to the social product: labour is given what labour creates, capital what capital creates, the coordinating entrepreneur what his coordination creates. The wage, on this account, is not something subtracted from the worker, as Marx had thundered that it was; it is the worker's own product, handed back to him in full. There can be no exploitation in a competitive market, for each is paid exactly his creation, no more and no less, by the impersonal operation of a natural law. It was a claim of great power and greater consolation, aimed like a lance at the heart of the socialist indictment, and it lent the marginal-productivity theory a moral charge it has carried ever since — and, as this plate will argue, has never quite earned the right to carry.
The wage, Clark held, is not subtracted from the worker; it is the worker's own product, handed back to him in full.
And there was a piece of mathematics to set as a crown upon it. A natural doubt might arise: if every factor is paid the value of its marginal product, do the several payments come out right — does the whole product get parcelled out exactly, with nothing left over and nothing falling short? Philip Wicksteed showed, in a spare and elegant essay of 1894, that under one condition they do. If production exhibits constant returns to scale — double every input and you double the output — then by a theorem of Euler's on homogeneous functions the sum of each factor's marginal product, multiplied by the quantity of that factor, comes to exactly the total product. The thing adds up. The pie is divided to the last crumb by the marginal-product rule, leaving no residue to be fought over and no shortfall to be explained away. To its architects this product-exhaustion result seemed a profound confirmation: the competitive distribution was not merely determinate but consistent — a closed and self-balancing system, a natural order that gave an account of itself. It is worth marking, though, the slightness of the proviso on which the whole elegant edifice was made to rest — constant returns to scale — for it bears a good deal more weight than its modest appearance lets on, and we shall have cause to lean upon it before the plate is done.
It would be a grave error, and a common one, to mistake all this for mere apologetics — for a doctrine got up to flatter the propertied and quiet the discontented. As a positive account of what actually determines wages, the marginal-productivity theory has formidable evidence on its side, and an honest plate is bound to say so without flinching. Wages do track productivity, and track it closely, along very nearly every dimension one cares to examine. Across industries, the more productive pay the better. Across skills, the premium that schooling and training command follows, with fair fidelity, the marginal product of the skill. Across whole nations, the plain fact that the same task — driving a lorry, stitching a seam — earns a handsome wage in one country and a pittance in another is explained, more than by anything else, by the difference in marginal product that the surrounding capital, technology, and institutions confer upon the identical exertion. And across the long sweep of the last two centuries, real wages and output per worker have climbed so nearly in lockstep that no theory which severed the two could be entertained for an afternoon. The marginal product is no fiction. It sets the ceiling of the bargaining range the previous plate described — and it is that ceiling, rising decade upon decade with the productivity of labour, that has carried wages upward from the bare subsistence of Smith's day to the comfort, however unevenly shared, of our own. Whatever the limits of the theory — and they are real, and they are coming — it has hold of something true, and large, about why wages are what they are, and why they have grown as they have.
And yet the limits are real, and the first of them is struck at the very foundation of the theory, and struck by economists of the first rank. The marginal-productivity story speaks as easily of paying capital its marginal product as of paying labour: each factor, it says, receives the value of what its last unit adds. But here a question opens beneath the theory's feet — what is the quantity of capital? Labour can be reckoned in hours, alike enough to be added together. Capital is a miscellany of produced things — lathes and looms and ledgers and half-built ships — that have no common physical measure at all; the only way to gather them into a single magnitude is by their value; and their value is the discounted stream of their future earnings, which depends upon the rate of profit — which is the very thing the marginal product of capital was summoned to explain. The reasoning closes in a circle. In a long and bitter quarrel between two Cambridges — Joan Robinson and Piero Sraffa at the English one, Paul Samuelson and Robert Solow at the one in Massachusetts — the English side pressed this circularity until it gave up paradoxes the orthodox picture could not absorb: that techniques of production cannot in general be ranked by their capital-intensity independently of the rate of profit, and that one and the same technique might be the most profitable at a high rate of interest, then at a low one, then at the high again — the disconcerting phenomenon they named reswitching. The comfortable parable by which more capital brings a lower return to capital simply failed to hold. Samuelson, to his lasting credit, acknowledged the defeat in print in 1966. The controversy has a plate of its own in a later volume, and its full strangeness can wait for it; here the lesson is narrower, but it cuts deep. The marginal-productivity theory of distribution, offered as a general account of what every factor earns, rests upon a measure of capital that will not bear the moral weight John Bates Clark piled upon it.
Yet suppose we set the measurement of capital aside, and grant the theory everything else it asks — perfect competition, and labour counted cleanly in hours. Even then its moral version commits a quiet and consequential fallacy, and the fallacy is worth naming with precision, for it is the hinge upon which this entire volume turns. To say that a worker is paid his marginal product is to say that he is paid the amount by which his employer's output would fall if his hour were withdrawn and all else held just as it was. But that amount is not a property of the worker. It is a property of the whole arrangement in which he stands. It depends on how much capital is set beside him, on the sophistication of the technology he is given to work, on how many others labour alongside him, on the institutions and the demand that fix the price of what he helps to make. The identical worker, of identical skill and identical diligence, has a high marginal product in a well-capitalised firm in a wealthy country and a low one in a poor — and the vast gulf between the two wages he would earn is, by no stretch of the word, his own doing.
The marginal product, in short, is a relational and counterfactual quantity — the value of an hour at the margin of a particular configuration of the world — and not the measure of the worth of a person, nor of what he, as distinct from all that surrounds and equips him, has made. Joan Robinson pressed this until it could no longer be slipped past: production is an irreducibly joint affair, and to assign to the last hour of labour a separable product of its very own is a serviceable fiction for the firm deciding whom to hire, and an abuse the moment it is pressed into a verdict on what anyone deserves. Clark's leap — from the wage equals the marginal product to the worker is paid what he creates, and the result is therefore just — is the one step the theory has no power to license. The first proposition is a condition of equilibrium, true under competition and genuinely useful. The second is a moral judgment, smuggled in to stand beside it and to borrow its authority.
The marginal product is the value of an hour in a given arrangement of the world — not the measure of a person.
Return, a last time, to the question the volume exists to press. The Margin is the strongest case that can be made for worth, and its strength must be granted without grudging: under competition the wage does tend toward the value of the last hour, and that value — productivity — is the great engine that has lifted wages across the generations, and that explains, better than any rival, why one wage stands above another. The bargain of the previous plate is struck beneath a ceiling, and this is the theory of that ceiling, and a true one. But a ceiling is not a resting place, and the marginal product is not the measure of a person. It is the worth of an hour within a particular settlement of capital, technique, and institutions — a settlement the worker did not author and cannot claim as his creation. And where that settlement is not competitive — where the buyer of labour holds power, as a later plate will show he very often does — the wage sinks below even this ceiling, and the distance between them is no measure of worth at all, but the plain register of power. That, in the decades just past, the long and faithful marriage of productivity and the typical wage has visibly cooled — the matter of this volume's final plate — is the orthodoxy's own instrument testifying against its moral version: the ceiling has gone on rising while the wage beneath it has not, and something other than the marginal product has been pocketing the difference. The Margin answers the volume's question with its serene single word, worth; and the answer is true, and it is partial. It tells us what bounds the wage, and what has raised it. It does not tell us what a person is owed, nor where, in the wide room beneath the ceiling it so well describes, the wage will finally come to rest. For that, the volume must turn back — as it always turns back — to the bargain, and to the power exercised at the table where the price is set.