The comforting answer, and the one the textbooks reach for first, is that you are paid exactly what you are worth. Where many employers compete for the same hands, the argument runs, none can pay a worker less than the value his last hour adds — a rival would outbid them — and none will pay more, for that is money thrown away; and so the wage comes to rest at the value of the marginal product, no higher and no lower. John Bates Clark, in 1899, drew from this a whole theory of justice: each factor paid its margin, the division of income neither robbery nor charity but arithmetic. It is a beautiful claim, and it rests entirely upon a single word — compete — which the world honors only sometimes, and never completely.
Set the moral of the claim aside for a moment and look only at its machinery, which is genuinely fine. An employer does not want workers for their own sake; he wants what they make, and what that will sell for — so the demand for labor is a demand derived from the demand for the product. Picture him deciding whether to take on one more hand. That hand will add some quantity to what the firm produces, and that addition, sold at its price, is worth some sum; if the sum exceeds the wage, the worker more than pays for himself and is hired; if it falls short, he is not. The employer goes on hiring while the value the next worker adds exceeds the wage, and stops at the worker for whom the two are equal. At that point the wage equals the value of the last worker's product — the value of the marginal product — and there the matter rests.
Two further steps complete the doctrine. The first: as more workers crowd onto the same fixed plant and land, each new one adds a little less than the last — the diminishing returns that grind the supply blade in the volume next door — so the value of the marginal product falls as employment rises, and the firm's appetite for labor has a definite stopping point. The second, and the bolder: since identical workers must be paid alike, every worker, not merely the last, is paid the value of what that last one adds. From here Clark took the leap that made his name. What holds for labor holds for every factor — capital and land no less than labor are paid the value of their marginal products — and, as Philip Wicksteed showed, under the right conditions these payments exactly exhaust the product, with nothing left over and nothing short. The whole of what is produced is parcelled out, each factor receiving the value of what it adds, the books balancing to the penny.
One must grant the theory its power before disputing its pretensions, for it explains a great deal, and explains it well. It tells us, rightly, why the skilled are paid more than the unskilled — their last hour adds more — and why the same worker earns more in a rich economy than a poor one, more beside good machines than bad, more when the thing he makes is keenly wanted than when it gluts the market. It predicts that a tax, a tariff, a new technology will move wages in particular directions, and the predictions are often borne out. For very large stretches of economic life it is the best first guess anyone has about why a wage is the size it is, and no honest account of the wage can dispense with it. The quarrel to come is not with what the theory explains. It is with what it claims to prove.
For the theory arrived freighted with a moral, and the moral was the point. Clark did not offer marginal productivity as a dry account of how wages happen to be set; he offered it as a vindication — a demonstration that the competitive market does each participant justice, paying every factor precisely the value it contributes and no less. The timing was not innocent. Marx had charged that labor is paid less than the worth of what it produces and robbed of the difference, and Clark's theory was, among other things, the reply: not robbery but desert, not exploitation but each rewarded by the exact measure of his product. To be paid your marginal product, on this telling, is to be paid what you are worth, and a system that does so is not merely efficient but fair. That moral has clung to the theory ever since, and it is the moral, far more than the mechanics, that the rest of this plate means to dispute.
It must be said, too, that the theory is not only the orthodoxy's banner but the whole subject's measuring rod, used as readily by those who attack it as by those who fly it. When the plate on the single buyer defined the employer's power as the gap between the wage and the value of the marginal product, it was measuring against this very theory's prediction — taking the competitive wage as the benchmark and reading the employer's advantage as the distance the actual wage fell beneath it. One may deny that the marginal product is a measure of justice and still need it as a measure of something: the wage a frictionless market would pay, against which every friction, every exercise of power, can be gauged. The orthodoxy is, in this sense, indispensable even to its critics. The question is only what its number means.
And the first thing its number means is: if the market is competitive. The whole apparatus — the rival who bids the worker away, the wage driven up to the value of the product — presumes the very thing the plates on either side of this one deny. Let there be few employers rather than many, or frictions that bind the worker to his place, and the wage no longer rises to the value of the marginal product but settles below it, by the margin of the employer's power; the bargain was unequal before the marginal product was ever reached. So the marginal-productivity wage is best understood not as the wage but as a ceiling and a benchmark — the most the competitive worker could win, the figure the actual wage approaches as power drains out of the market and recedes from as power floods in. The theory describes a limiting case. The wage lives at some distance from it, and the distance is this volume's true subject.
There is a deeper trouble than the failure of competition, and it strikes at whether the marginal product can be found at all. The picture of a worker adding a clean, separable quantity to output suits a world of solitary laborers each tending his own row; it suits very badly the world of the modern firm, where work is done by teams and the product is joint — the assembly line's output, the office's, the hospital's, belonging to no single pair of hands and divisible into individual contributions by no honest accounting. When Armen Alchian and Harold Demsetz asked, in 1972, why firms trouble to employ supervisors at all, this was their answer: that team production hides the individual margin, and the firm must hire monitors precisely because it cannot read each worker's product off the output. But if the individual marginal product cannot be observed, the claim that each is paid it cannot be tested — and worse, it can quietly reverse, the marginal product no longer measured on its own and found to equal the wage, but simply inferred from the wage and pronounced equal to it. A theory that fixes its central quantity by reading back from the answer has stopped explaining the answer.
The labor case, for all that, is the theory's firm ground; it is when the doctrine reaches for capital that it nearly comes apart, and that unravelling belongs to another volume. Clark's justice required that capital, too, be paid the value of its marginal product — but capital, unlike an hour or an acre, is not a natural quantity. It is a sum of money, and the size of that sum already depends on the rate of profit the marginal product was meant to determine, so that the reasoning closes in a circle. The economists of Cambridge in England pressed exactly there, and wrung from Cambridge in Massachusetts a famous concession; the whole controversy, with its reswitching and its reversals, is the matter of the ninth and tenth plates of The Margin, the sixth volume of this table, of which the present plate is the labor-bound case. Here it is enough to mark that the doctrine is strongest where it speaks of labor and weakest where it speaks of the capital that labor works beside — and that its claim to deal out justice stands on the weaker leg.
Grant the theory everything, though — grant a market competitive enough, and a marginal product clean enough to measure — and the deepest objection still stands, for it is aimed not at the mechanics but at the moral drawn from them. Concede that the wage equals the value of the worker's marginal product. It does not follow that the worker is paid what he is worth, because the marginal product is not the worker's to begin with. What his last hour adds depends on everything arranged around him: on how many others stand at the same bench, since more hands mean a smaller margin for each though no one of them slackens; on the machines and the land he is given to work with, since the man with the excavator adds more than the same man with a spade, and the difference is the excavator's doing, not his; on how badly the world happens to want what he makes that season. Alter any of these and what he creates is altered, while the worker himself is exactly as he was. The marginal product measures what a worker is worth in one particular arrangement of everything else, and calls it what he is worth.
This is fatal to the theory's moral, though not to its mechanics, and in two ways. The first is a circle: what the worker's product is worth turns on who owns the machines and the land beside him, and on the demand for what he makes — which is to say, on the existing distribution of property and income. One cannot justify that distribution by appeal to marginal products that are themselves its creatures; the theory quietly assumes the justice of the arrangement it claims to vindicate. The second is the old worm at the root of every such valuation: the product is reckoned at what the market will pay, and the market weights each want by the purse behind it, so that the very same labor counts for more when it serves the rich and less when it serves the poor. The marginal product is not a measure of contribution to human welfare; it is a measure of contribution to salable value, in a world whose purchasing power is distributed as it is. What it tracks is want backed by money — the matter this volume returns to, and the burden of The Edge in the volume next door.
What the last hour adds is a fact about the worker's surroundings, not about the worker.
The marginal-productivity theory is the orthodoxy's proof that the wage is, after all, a fact — a fact about the worker, the measure of what he makes, read off by an impersonal market that plays no favorites. It is the most formidable answer the science has given to this volume's suspicion, and it must be met at its strongest, which is why it has been granted so much here. But its proof proves less than it claims. That the wage equals the marginal product, where it does, is a statement about a margin, not about a man; and that margin is fixed by the scarcity of his kind of labor, the capital that happens to stand beside it, the demand that happens to want its product, and the competition that happens to prevail — a contest among many parties, in which the worker is one. To call the result his worth, and the paying of it justice, is to mistake the outcome of that contest for the deserts of the person caught up in it. A price is a verdict on a hidden contest, mistaken for a fact of nature; the marginal-productivity wage is that mistake in its most respectable dress — the verdict gowned not merely as a fact but as a law of justice. The argument remains open.