The Wage

The wage begins, in the history of the subject as in the life of any worker, not as a number read off a curve but as the outcome of a bargain — and Adam Smith, who opened the inquiry, opened it by insisting that the bargain is not struck between equals. In the eighth chapter of the first book of his great work, before any theory of marginal anything existed to complicate the matter, Smith set down the asymmetry that the rest of this volume will spend twelve plates trying to measure. The wage, he wrote, depends everywhere upon the contract made between two parties whose interests are by no means the same: the workmen desire to get as much, the masters to give as little, as they can. And in that contest the masters hold every advantage.

The advantages Smith named are worth listing, because they are not antique curiosities but the permanent architecture of the labor market. The masters are fewer, and so can combine the more easily, and the law and custom of his day tolerated their combinations while forbidding the workmen's. The masters can hold out the longer: a manufacturer with stores laid by can live a year or two without a single laborer, whereas few laborers could subsist a week, and not many a month, without employment. And so, in any dispute, it is the workmen who must yield first, driven by the plain necessity of the next meal. Smith granted that in the long run the master needs the workman as the workman needs the master — but the necessity, he observed, is not so immediate on the one side as on the other, and it is the immediacy of necessity, not its eventual symmetry, that settles a bargain.

What Smith described, in the language of his century, is exactly the bargaining problem that the ninth plate of The Surplus sets out in the language of ours. An exchange between two parties creates a surplus — the gain from the worker's labor over its cost to him, and to the master over its cost to hire — and where the market does not supply a crowd of competitors to fix the price, that surplus is divided by the bare relative strength of the two sides: by who has the better alternative, and who can the longer endure delay. Smith's masters, with their stores and their lawful combinations, have both the better alternative and the longer endurance; the workmen, with neither, take what is offered. The wage comes to rest near the lower bound of what the bargain might have yielded, and that lower bound is set, Smith saw, by subsistence: a man must always be able to live by his work, or there will soon be no workmen at all. Below subsistence the wage cannot durably fall; above it, how far above, is a question of power.

It is essential to see that this is a theory of the wage as a settlement, not as a measurement. Smith does not say the wage equals what the worker contributes; he says it equals what the worker can extract, given the weakness of his position — and these are the same number only by accident, or under conditions Smith did not assume. The orthodoxy of the very next plate will appear to abolish the asymmetry altogether, by showing that competition among many masters drives the wage up to the worker's full contribution whether any single master wishes it or not. That is the great consoling argument of the marginal revolution, and the volume gives it its due. But the doubt Smith planted is never quite uprooted, and when the volume reaches monopsony and search and the falling share of labor, it will find Smith's asymmetry waiting there, dressed in modern mathematics, looking very much as it did in 1776.

Against Smith's bargain the marginal revolution set a different picture of the wage — cleaner, more powerful, and far more consoling — and for the better part of a century it carried the field. Its architect, in the form that mattered for distribution, was John Bates Clark, who argued at the close of the nineteenth century that each factor of production is paid the value of its marginal product: the worth of what the last unit of it adds to the output it helps produce. Apply the principle to labor and the wage falls out at once. A firm will hire another worker so long as the value that worker adds — the marginal revenue product of labor — exceeds the wage it must pay him, and will stop hiring when the two are equal; to hire fewer would forgo a profitable worker, to hire more would employ an unprofitable one. In competitive equilibrium, therefore, the wage equals the marginal product of labor, exactly.

The figure is the competitive labor market, and its consolation is moral as much as analytical. Sum the hiring decisions of every firm and the downward-sloping marginal-product schedule becomes the demand for labor; its intersection with the supply of labor fixes the wage; and at that wage each worker receives the value of what he adds. Clark drew the implication in plain and pointed terms: the distribution of income is not a robbery to be remedied but the natural outworking of productivity, each factor taking what it creates. The wage measures the worker's worth, and the worth is what he is paid. Where Smith saw a contest settled by power, the orthodoxy sees an exchange governed by contribution — and it does so by an argument of real force, which the volume must answer rather than dismiss.

The force of the argument is this: it does not require any master to be generous. Even Smith's grasping employer, who would pay as little as he could, is compelled by competition to pay the worker his full marginal product — because if he paid less, a rival employer, finding that worker profitable at a higher wage, would bid him away, and would keep bidding until the wage reached the worker's product. The discipline of competition, not the goodwill of masters, is what protects the worker; the asymmetry of any single bargain is dissolved by the many bargains the worker might strike instead. This is a genuine and beautiful result, and where its conditions hold it is very nearly the truth. But the conditions are exactly the ones Smith's world lacked and most workers' world lacks still: many employers competing for each worker, and a worker free to move costlessly to whichever values him most. Remove the crowd of bidders, or make movement between them slow and dear, and the wage is no longer pinned to the marginal product; it drifts back down toward the floor of the bargain, and Smith's asymmetry returns. The remaining plates are, in large part, a survey of where the conditions fail — and they fail, it will turn out, nearly everywhere that people actually work.

Between Smith's bargain and Clark's margin lies a third account of the wage, older than the second and grimmer than the first, which determined the wage not from above, by what labor produces, but from below, by what it costs to keep a laborer in being. The classical economists called the resting point of the wage its natural price, and they identified that natural price with subsistence: the wage that allows the laboring population to maintain itself, neither growing nor dwindling. Above subsistence, Malthus's mechanism took hold — families grew, the supply of labor swelled, and competition pressed the wage back down; below it, want and mortality thinned the ranks until scarcity lifted the wage again. The market wage oscillated, on this view, around an iron floor set by the cost of human reproduction, and the floor itself owed nothing to the worker's productivity.

The strong form of the doctrine — Lassalle would later call it the iron law of wages — is simply false as a long-run prophecy, and its falsity is among the most important facts in economic history. Real wages in the industrializing world did not hover at subsistence; they rose, eventually enormously, as the demographic mechanism that was supposed to claw them back broke down and population growth decoupled from wages. Any theory that predicts the permanent immiseration of labor has been refuted by the simple prosperity of the descendants of those it was written about. And yet the classical account carried an insight the marginal orthodoxy mislaid and that the twentieth century had to relearn: that the wage has a floor set not by what labor makes but by what it costs to reproduce the laborer — and that this floor is only partly biological. What counts as subsistence, the classicals half-saw and Marx saw fully, is largely social and historical: it includes whatever custom, expectation, and past struggle have made into a necessity, so that the floor itself is an object of contest, not a fact of biology.

It was Marx who took this floor and made it the whole theory of the wage, in a move whose logic the fifth plate of The Surplus sets out in full and which need only be named here. The worker, in Marx's account, sells not his labor but his labor-power — his capacity to work — and like any commodity it sells at its value, which is the cost of its reproduction: the food, shelter, training, and rest required to return the worker to the gate each day fit to labor, and to raise the next generation. The wage equals that cost. But the labor the worker performs, once his power has been bought, produces a value greater than the cost of reproducing it, and the difference — surplus value — is kept by the one who bought the power. The wage and the surplus are thus two readings of one boundary: the wage is what labor receives; surplus value is what it makes and does not receive. The Wage and The Surplus meet exactly here, at the line between the cost of the worker and the value of his work.

The deep point is not the empirical fate of the subsistence theory but the direction of its determination. To fix the wage from below, by the cost of reproducing the worker, is a different intellectual act, with a different politics, from fixing it from above, by the value of his marginal product. The one makes the wage a cost of an input, set by what it takes to keep labor available, and treats any excess of product over that cost as a surplus to be claimed; the other makes the wage a price of an output, set by what labor contributes, and treats the whole product as already, justly, distributed. The same wage packet can be described both ways. Which description one reaches for is, in the end, a position on the very question this volume circles — whether the worker's pay is the reward of his contribution or the residue left after a stronger party has taken its share.

Wages differ enormously among workers, and the orthodoxy of the second plate explains the differences as differences in marginal product — the more productive are paid more. But that only relocates the question: why are some workers so much more productive than others? The answer the mid-twentieth century gave, and built into a whole branch of the subject, is that productivity is itself produced — that a worker can invest in his own future output by schooling and training, forgoing earnings now to raise his earning power later, exactly as a firm invests in a machine. Theodore Schultz, Gary Becker, and Jacob Mincer made of this idea the theory of human capital, and it recast the wage gap between the schooled and the unschooled as, in good part, the return on an investment.

The empirical workhorse of the theory, the Mincer earnings function, relates the logarithm of earnings to years of schooling and, concavely, to years of work experience, and it has been estimated on more data, in more countries, across more decades, than almost any relationship in economics. It finds, with remarkable consistency, that an additional year of schooling is associated with earnings higher by several percent — a return comparable to what one might earn on financial capital, which is just what the theory predicts if schooling is an investment competing for the same scarce funds. The age-earnings profiles of the figure are the theory made visible: the schooled forgo earnings while in school, then rise more steeply and to a higher and later peak, the area of their early shortfall the cost of the investment and the height of their later advantage its return.

The theory is powerful and fits a great deal, but it has had to absorb two complications that bear directly on the volume's question, and neither is fully resolved. The first is the problem of ability. The schooled may earn more not only because schooling raised their productivity but because the people who get more schooling were more capable to begin with — so that the measured return to schooling is partly a return to a prior ability that the schooling merely accompanied. Economists have chased this confound with ingenuity, comparing twins, exploiting laws that compelled some cohorts to stay in school longer than others, and the causal return survives, diminished but real. The second complication is deeper and was named by Michael Spence: schooling may raise earnings not by building productivity at all but by signaling a productivity the worker already possessed. If employers cannot observe ability directly and the abler find schooling easier to complete, then a diploma can sort the able from the rest without adding a thing to anyone's skill — and the worker who pays for it is buying a credential, not a capability. Where signaling dominates, the private return to schooling is genuine but the social return is smaller, and education slides toward a positional race in which all run faster and none gains ground.

Two workers of equal skill may earn unequal wages because the work itself is unequal — one job safe and pleasant, the other dangerous, filthy, or precarious — and the wage must make up the difference. This is the theory of compensating, or equalizing, differentials, and it too is Adam Smith's, set down in the tenth chapter of his first book. Smith listed the circumstances that make the money wages of different employments diverge even where the skill required is the same: the agreeableness or disagreeableness of the work, the difficulty and expense of learning it, the constancy or inconstancy of employment, the trust that must be reposed in the worker, and the probability of succeeding at all. A trade that is hazardous, or irregular, or held in low esteem must pay a premium to draw workers who could earn as much elsewhere in comfort and security — and the premium is not a gift but a compensation, a payment for the disamenity that comes bundled with the job.

The theory is logically near-irresistible. If two jobs demanded the same skill but one were both better paid and more pleasant, workers would flood toward it and away from the other until the wages adjusted; in equilibrium, the worse job must pay enough more to leave the marginal worker indifferent between them, all things — money and conditions together — considered. It follows that the observed wage is never the whole of the reward: part of a low wage may be silently repaid in safety and ease, and part of a high wage may be the price of misery. To judge a wage by its number alone is to miss the bundle the number is attached to, and much that looks like inequality of pay is, on this account, equality of advantage differently composed.

And here the theory meets one of the most instructive embarrassments in empirical economics. The compensating differential, so compelling in logic, is remarkably hard to find in the data, and the premium for risk — the extra wage that dangerous work ought to command, from which economists try to infer the value people place on their own safety — comes out fragile, unstable, and often with the wrong sign altogether. In the raw numbers, dangerous and unpleasant jobs frequently pay less, not more. The reason is not that Smith was wrong but that another force overwhelms his in the data: the workers who take the worst jobs are disproportionately those with the fewest alternatives — the least skilled, the most desperate, the weakest in the bargain of the first plate — and their weakness drives both their low wages and their bad conditions at once. The disamenity and the low pay travel together, not because the job fails to compensate but because the worker lacks the power to demand that it should. To recover Smith's equalizing premium, the analyst must hold constant the worker's skill and bargaining position — precisely the things hardest to observe — and only then does the tradeoff peek through.

The same fact thus reads two ways, and the volume's whole quarrel is in the reading. To the orthodoxy, a dangerous job that pays little is a puzzle, to be dissolved by some unobserved difference in the workers who hold it. To Smith's older instinct, it is the asymmetry of the bargain made visible: the worst work goes to those with the least power to refuse it, and is paid least precisely because they cannot refuse. These are not exclusive — surely both operate — but their balance is the question, and the very difficulty of finding the compensating differential in the data is itself a quiet piece of evidence for how much the wage is shaped by power, and not only by the agreeable or disagreeable character of the work.

That workers alike in skill and effort are paid differently according to race, sex, or origin is among the best-documented facts in labor economics, and it sits awkwardly with the orthodoxy of the second plate, which has competition driving the wage to the marginal product regardless of who the worker is. Economics has produced two great theories of how a market can nonetheless discriminate, and they differ not in vocabulary but in their whole account of the thing — and, crucially, in what they imply competition will do about it.

The first is Gary Becker's, set out in 1957: discrimination as a taste. Some employers, or their customers, or their other workers, simply prefer not to deal with members of some group, and will forgo income to indulge the preference — paying the disfavored worker less than his product, or refusing him outright, at a cost to themselves. Becker's striking result is that competition should erode such discrimination. The employer who discriminates leaves money on the table; the employer who does not hires the disfavored workers cheaply, earns more, and expands at the discriminator's expense; in the long run the market competes the prejudiced out of business and the wage gap shrinks toward zero. On this account discrimination is a luxury the market punishes — which makes its stubborn persistence a genuine puzzle, and a sign, wherever it endures, that competition is somehow being held off.

The second theory, developed by Edmund Phelps and Kenneth Arrow around 1972, is darker, because it requires no prejudice at all. An employer who cannot observe a worker's productivity directly must predict it, and if group membership is correlated — or merely believed to be correlated — with the unobserved trait, it can be coldly rational to judge the individual by the group's average: to offer a member of a lower-averaging or higher-variance group a lower wage or a lesser chance, purely as a statistical inference. This is statistical discrimination, and it has two properties that taste-based discrimination lacks. It is not competed away, because it costs the employer nothing — it is, by construction, his best guess. And it can be self-fulfilling: if a group is paid less and promoted less on the strength of a belief about its productivity, its members may rationally invest less in the very skills the belief concerns, and so confirm the belief and lock it into a stable equilibrium from which no individual has an incentive to depart.

The distinction is not academic, for the two theories prescribe opposite remedies. If discrimination is taste-based, competition is the cure, and its persistence indicts the absence of competition. If it is statistical, competition is no cure and may entrench it, and the remedy must reach the information problem and the self-fulfilling expectations themselves — for the discriminating employer is not a bigot to be undersold but a forecaster whose forecast has become true by being believed. The evidence that discrimination is real and persistent is overwhelming: audit and correspondence studies, sending employers identical résumés that differ only in a name, find robust and durable gaps in who is called back. Disentangling how much of the gap is taste and how much statistical is far harder, and both plainly operate, alongside structural and historical forces that neither model fully captures.

No prediction of the competitive model is sharper, more famous, or more readily falsifiable than its verdict on the minimum wage, and none has been more bruised by contact with the evidence. The logic is the clean machinery of the second plate. In a competitive labor market the wage rests where the demand for labor meets its supply; impose by law a wage above that resting point and you have a binding price floor. At the higher wage more workers wish to work, but firms — now facing a wage above the marginal product of the marginal worker — wish to hire fewer. The quantity of labor offered exceeds the quantity demanded, and the difference is involuntary unemployment: workers willing to work at the legal wage who can find no one to hire them.

The figure makes the verdict plain, and for decades it was textbook consensus and the standing economic case against minimum wages: a floor helps the workers who keep their jobs and harms those who lose them or are never hired, the harm larger the more elastic the demand for labor. It is a clean, quantitative, testable claim — which is precisely what makes its empirical fate so consequential. In 1994 David Card and Alan Krueger studied employment in fast-food restaurants on either side of the New Jersey–Pennsylvania line when New Jersey raised its minimum wage, and found no disemployment — if anything, a small increase — on the side that raised the wage. The finding detonated one of the most contested empirical debates the discipline has known.

A generation of studies has followed, with results ranging from modest job losses to none at all, and a methodological war over which comparisons can be trusted. The fair summary of the present state is this: moderate increases to the minimum wage, from low levels, appear to have small effects on employment, while very large increases relative to local wages remain genuinely risky, and the dispute over methods is not settled. What is no longer tenable is the confident textbook claim that a minimum wage must cause substantial job loss; the strong form of the competitive prediction has been refuted for moderate increases. And that refutation is the first hard evidence that the competitive model is simply the wrong model of the low-wage labor market — for if the model's central prediction fails just where it ought to be cleanest, the market it describes must not be the market that exists. The reconciliation does not require abandoning economics. It requires only the next plate.

Here the volume turns on its hinge. The orthodoxy of the second plate rests on a crowd of employers competing for each worker; remove the crowd, and the whole picture inverts. Joan Robinson, in 1933, gave the single buyer its name — monopsony, the mirror of monopoly — and with it the apparatus that recovers Smith's asymmetry from the very mathematics that seemed to have abolished it. A monopsonist in the labor market is not a price-taker but a price-maker: facing the whole upward-sloping supply curve of labor, it knows that to attract one more worker it must raise the wage, and — short of discriminating among them — raise it for every worker it already employs. The cost of an additional worker is therefore not merely that worker's wage but the wage plus the raise paid to all the rest, so that the marginal cost of labor lies above the wage.

From this single fact the inversion unfolds. The monopsonist hires up to the point where the marginal cost of labor equals the marginal revenue product — and because that marginal cost lies above the wage, it hires fewer workers than a competitive market would, and pays each of them a wage below the marginal product. The worker is paid less than the value of what he adds, not through anyone's malice and not as an anomaly, but as the ordinary equilibrium of a market with one buyer. The gap between the marginal product and the wage — Pigou and Robinson called it, in a precise technical sense, the rate of exploitation — is the measure of the employer's power. It is Smith's asymmetry given a diagram: the wage below the worth, and the shortfall the exact magnitude of who could afford to wait.

The inversion is total, and it shows most vividly at the minimum wage. In the competitive model of the seventh plate, a floor above equilibrium destroys jobs. Under monopsony, a floor set between the monopsony wage and the competitive wage raises employment — because once the wage is fixed by law, the employer no longer suffers the penalty of raising everyone's pay to hire one more, and so its motive to hold hiring back dissolves; the marginal cost of an added worker becomes simply the legal wage, and the firm expands toward the competitive level. The very policy that costs jobs in one model creates them in the other. And the empirical finding of the seventh plate — that moderate minimum wages do not destroy, and sometimes raise, employment — is exactly what monopsony predicts and the competitive model cannot abide. Card and Krueger's puzzle is monopsony's confirmation.

It would be a small thing if monopsony required a literal single employer, a company town with one mill. Its modern revival, owed above all to Alan Manning, is the recognition that it requires no such thing. Any friction that makes it costly for a worker to move from one employer to another — the time and expense of searching, skills specific to a firm, the ties of home and family to a place, the sheer difficulty of finding the rival who would value him most — hands every employer a slice of monopsony power, because a worker cannot instantly flee a wage cut, and an employer who knows it can pay a little under the mark. On this view monopsony is not the exception but the rule; the frictionless competition of the second plate is the special case, the limit of zero frictions that no actual labor market reaches. Where employers are few and the labor market concentrated — a profession with a handful of buyers, a town with one large firm — the markdown is large and plain; everywhere else it is smaller, but it is rarely nothing. The structures that confer and entrench such power are the subject of The Power, the table's tenth element.

The worker's answer to the asymmetry of the first plate, and to the monopsony of the eighth, is the oldest in the history of labor: to stop bargaining one at a time. If the masters are few and can combine, and the workman is one and cannot wait, then let the workmen combine too, and meet the single buyer of labor with a single seller of it — a union, monopoly raised against monopsony. John Kenneth Galbraith gave the idea its modern name in 1952: countervailing power. In concentrated markets, he argued, the effective check on one side's power is often not competition, which is absent, but the organized power of the other side; and the union is countervailing power in the labor market, the institutional reply to the employer who would otherwise set the wage alone.

The economics of unions wears two faces, and the long quarrel over whether unions help or harm turns on which face one is looking at. The first is the monopoly face: by restricting the supply of labor, or by threatening to withhold it altogether, a union can raise the wage above what the market — competitive or monopsonistic — would set, and capture for its members a larger share of the surplus the firm's activity creates. In a competitive labor market this is the textbook monopoly-union story, with the textbook cost: a wage above the competitive level reduces employment, helping those who keep their union jobs at the expense of those shut out. The second is the collective-voice face, drawn out by Richard Freeman and James Medoff: a union is also the institution through which workers express grievances, negotiate conditions, reduce the turnover that costs firms dearly, and bring information up the hierarchy that would otherwise never arrive — and through these channels a union can raise productivity, making the firm more efficient rather than less. The net effect on the wage is a premium, historically substantial; the net effect on employment and efficiency depends on which face dominates, and on how the bargain is struck.

The decisive point, for this volume, is what the union does under monopsony — for that, the eighth plate has shown, is the condition of most labor markets. Against a monopsonist, a union's wage demand behaves exactly as a minimum wage does: by fixing the wage above the monopsony level, it strips the employer of its motive to hold hiring back, and can raise employment and pay together, clawing back the markdown without the disemployment the competitive model would predict. Collective bargaining against an employer with wage-setting power is not a distortion of an efficient market but a correction of an inefficient one — the workers' device for recovering the share that monopsony had quietly transferred away. Whether the bargain reaches that happy result, or instead the monopoly-union outcome with its lost jobs, depends on its structure: whether union and firm bargain over employment as well as wages (and so can find the efficient agreements on the contract curve of The Surplus's ninth plate), or whether the firm sets employment alone once the wage is fixed. The union, in the end, is a machine for altering the worker's outside option and his patience — the two levers the bargaining theory of the surplus identified. The strike fund is precisely the store laid by that Smith said the single workman did not possess: the manufactured ability to hold out.

The competitive market of the second plate is an auction: every worker and every job present themselves at once, and the wage is called out for all to take. No real labor market is anything of the kind. Workers and jobs must find each other, at a cost, one offer at a time, through a fog of partial information — and the moment the search for work is admitted to the theory, the wage acquires a new determinant that the auction concealed. George Stigler opened the economics of information in 1961; the sequential-search model that followed gave the worker a reservation wage: the lowest offer he will accept. He samples offers from some distribution, accepts any that clears his reservation wage, and rejects the rest to keep looking. And what he is willing to accept depends on what sustains him while he searches.

This is the double-edged link the plate's title names. The reservation wage rises with the value of continued search and with whatever supports the worker through it — his savings, a spouse's income, and, most pointedly, the social safety net, and above all unemployment insurance. By keeping a roof over the worker who turns down a low offer, unemployment insurance raises his reservation wage and so his bargaining power: it lets him hold out, manufacturing the very patience that the first plate said the single workman lacked, and pulling the wage up the bargaining range. The same raised reservation wage, of course, can lengthen the spell of unemployment — the classic moral hazard of any insurance — and the tension between the two is real. But the framing matters as much as the tradeoff. The safety net is not merely charity laid over a labor market that would otherwise run cleanly; it is itself a determinant of the wage, the institution that gives the worker the means to say no, and so shifts the division of every match's surplus in his favor.

The mature theory, owed to Peter Diamond, Dale Mortensen, and Christopher Pissarides, set the search on both sides at once. Workers and jobs meet through a matching process; each match, once made, creates a surplus — the gap between what the worker produces in the job and the value of his next-best alternative — and the wage is settled by bargaining over that surplus, which is to say by the Nash bargain of The Surplus's ninth plate, rising with the worker's outside option and his patience. And here the deepest connection of the volume closes: the search frictions that give this theory its wage are the very same frictions that give the eighth plate its monopsony. Because finding a job takes time and offers arrive singly, a worker cannot instantly abandon an employer who cuts his pay — and that inability is exactly what lets the employer pay below the marginal product. Search theory and monopsony are two descriptions of one fact, the frictional, one-at-a-time character of the labor market, and both place the wage somewhere in the bargaining range rather than at the competitive point the auction imagined.

The oldest fear about the wage is that the machine will do for nothing what the worker was paid to do, and since the first power loom the question has been whether technology destroys the wage or remakes it. The reassuring answer, long the orthodoxy, is that machines are complements as much as substitutes: automating one task raises the productivity, and hence the wage, of the labor that remains to work alongside the machine, and the new wealth it creates calls forth demand for kinds of work that did not exist before. Historically the reassurance has largely held — real wages rose with mechanization rather than falling — because the complementing and the new-task-creating effects have, in the long run, outrun the displacing one. The Luddites smashed the looms and lost; their grandchildren earned more than they had.

But the long run concealed a darker passage that economists have learned to take seriously, because it shows the reassurance is neither automatic nor swift. For roughly the first half-century of the British Industrial Revolution — the period Robert Allen and others have studied as the "Engels' pause" — output and profits climbed steeply while the real wages of workers stagnated. The displacement ran ahead of the compensation; the new wealth accrued to capital, and only after decades did wages begin to share in it. The lesson is exact: technology's benefit to labor depends on the balance of its effects and on the horizon over which one measures, and there is no law guaranteeing that the balance favors workers in any given generation, however well it has come out across centuries.

The modern frame is sharper than the old fear. The hypothesis of skill-biased technological change, developed by Lawrence Katz, Kevin Murphy, Claudia Goldin, and others, holds that technology has tended to complement skilled labor and substitute for unskilled, raising the relative demand for skill — so that the skill premium, the extra a college wage commands, rises unless the supply of skilled workers rises faster. It is a race between education and technology, and the figure shows its mechanism: when education won the race, in the decades after the war, the premium fell and wages compressed; when technology pulled ahead, from around 1980, the premium climbed and the wage distribution pulled apart. The task-based refinement of David Autor, Daron Acemoglu, and others made the picture more precise still: automation substitutes for labor in the particular tasks it can codify — routine work, whether of the hand or of the calculating mind — displacing the workers who did them, while elsewhere creating new tasks that labor can perform. The net effect on the wage turns on the balance of the displacement and the reinstatement, and nothing guarantees the balance runs labor's way in any given era.

So the perennial question is reframed, not answered: not "will the machines take the jobs," which the long history answers in the negative, but "will the new tasks the machines create employ, at decent wages, the workers the old tasks displaced" — and that is contingent, a matter of how fast the displacement comes and how fast the new work and the new skills arrive to meet it. It is, once again, the volume's question in another guise. A technology that complements a worker raises the value of his labor and his wage; a technology that substitutes for him removes his product from the bargaining table altogether. Which a given innovation does is partly a matter of the innovation and partly a matter of choice — for the direction of invention is itself shaped by the relative price of labor and capital, and by the policies that tilt it. The machine has never been simply fate.

The volume ends where its question can be asked of a whole economy at once. Add up all the wages and salaries a nation pays; divide by everything the nation produces; the ratio is labor's share, the fraction of the total product that goes to those who work rather than to those who own. For most of the twentieth century it was thought roughly constant — one of the "stylized facts" of growth that Nicholas Kaldor catalogued, a reassuring sign that labor and capital rose together and that the marginal-productivity story of the second plate held at the level of the aggregate. Since around 1980, in the United States and across much of the advanced world, labor's share has fallen, and the decline is the macroeconomic face of everything this volume has examined plate by plate.

The logic of the inference is what makes the fact so charged. If wages tracked marginal products and labor markets were competitive — if the second plate were the whole truth — labor's share would be pinned down by technology and would not drift. That it has fallen is evidence that something other than productivity is moving the wage, and the candidates are precisely the themes of the preceding plates: the decline of unions and the erosion of countervailing power; the rise of monopsony and of product-market concentration, with the increasing markups that recent work has documented; the cheapening of capital and the automation that shifts production toward machines; and a globalization that has handed bargaining power to mobile capital and taken it from rooted labor. Each is a way the wage might fall below the worker's product; together they are the macroeconomic shadow of the markdown.

The most arresting single version of the fact is the decoupling the figure shows. In the United States, since roughly 1973, the productivity of the average hour of work has gone on rising while the compensation of the typical — the median — worker has risen far more slowly, the two lines that once climbed together pulling steadily apart. If the orthodoxy of the second plate were the whole truth, this could not occur: pay would follow product. That it has occurred is the empirical heart of the case that the wage has come to measure the worker's power more, and his product less, than it did in the decades after the war, when the lines moved as one.

Here the two readings that have run through every plate — worth and power — meet their decisive test, and the test runs straight into the deepest theoretical question of all. In the 1950s and 1960s, the economists of Cambridge in England — Joan Robinson, Piero Sraffa, and their circle — pressed against the economists of Cambridge in Massachusetts a challenge to the aggregate marginal-productivity theory of distribution, the claim that capital and labor each receive their marginal products in the economy as a whole. They showed that the notion of an aggregate quantity of "capital," with a well-defined marginal product, is in general incoherent: the paradoxes of reswitching and capital-reversing break the simple link between the price of a factor and its scarcity, and Paul Samuelson, for the Massachusetts side, conceded the logical point in 1966. If there is no well-defined marginal product of capital in the aggregate, then the claim that the factor shares are fixed by marginal products — technologically, and so fairly — loses its foundation, and the door swings open to the older view: that the division of the product between labor and capital is set by social and institutional power, by the bargain and the combination and the law, and not by any technological given. Labor's falling share, on that reading, is not a movement along a marginal-product schedule but a shift in the balance of power.

And so the volume closes by handing its question on. The Wage has taken the marginal-productivity orthodoxy at its full strength, given it every due, and tested it at every seam — and found, at seam after seam, that the equality of the wage and the worker's product is a property of a frictionless, competitive, well-organized world, and that the world most workers inhabit departs from it, by a margin that is the measure of the employer's power. How large that margin is, how much of any wage is worth and how much is power, is the open and consequential question that this volume cannot close and was never meant to. It belongs, at the scale of the whole economy, to The Share — the table's twenty-second element — to which The Surplus, from the other side, hands the very same question; for the wage is what labor receives, and the surplus is what its labor creates, and the distance between them is the contest this entire table exists to read. The wage looks like a fact. It is a verdict. And no diagram, however elegant, has ever closed the argument over what the verdict should be.