The previous plate left a question hanging, and it is the most awkward question that can be put to the whole apparatus of the margin: does anyone actually use it? Every plate so far has assumed that decisions are made at the margin — that the firm setting its output has its marginal cost and its marginal revenue before it and adjusts until they meet, that the consumer allocating her budget equates the satisfaction of the last penny across her purchases. But these are claims about how real people and real firms behave, and they can be checked; and when, in the middle of the twentieth century, economists began to check them, what they found set off a quarrel that has never entirely subsided. The quarrel was ostensibly about the theory of the firm; but underneath it lay a question about the nature of economic theory itself — about what we are entitled to assume, and what we must demonstrate, and whether a theory whose assumptions are false can nonetheless be true in the only way that matters. The margin was the occasion of the dispute. Its real subject was the standing of the entire discipline.
The trouble began when researchers did the obvious thing that economists had somehow never quite done: they asked businessmen how they actually decided what to charge and how much to make. The answers were not reassuring for the theory. Few of the businessmen had heard of marginal cost or marginal revenue; fewer still could be brought to recognize the concepts even when they were explained. What the firms reported doing instead was something far cruder and more comfortable: they reckoned up the average cost of a unit — the materials, the labour, a share of the overhead — and added to it a customary markup, a percentage for profit hallowed by habit or by the practice of the trade, and the sum was the price. This full-cost or markup pricing, documented in a celebrated Oxford study by Hall and Hitch in 1939, bore no visible relation to the delicate equating of margins the theory described. And Richard Lester, in an influential paper of 1946, pressed the point into a direct empirical indictment: firms, he argued from his surveys, simply do not behave as the marginal theory says — do not trim their workforces in response to a rise in wages the way marginal productivity predicts, do not have the marginal magnitudes in view at all. The theory of the firm, he concluded, was not a description of firms.
The reply, swift and formidable, came from Fritz Machlup, and it consisted in denying that the theory had ever claimed what Lester was refuting. The marginal theory does not assert that businessmen consciously compute marginal cost and marginal revenue, Machlup argued; it asserts that they behave, in the end, as though they had — and the two are entirely different claims. Consider, he said, a motorist deciding whether to overtake a lorry on a two-lane road. He does not solve, or even know, the equations governing the speeds and distances and accelerations involved; he glances, judges, and pulls out or holds back. Yet a physicist armed with those very equations could predict his decision with precision, and would be quite right to model the overtaking as if the driver had solved them. The businessman is in the same case: long experience and the steady pressure of profit and loss have taught him to do, by feel and by rule of thumb, very nearly what the marginal calculus prescribes, and the fact that he could not write the calculus down is neither here nor there. As for the surveys, Machlup regarded them as worthless on a point like this, for what a man says when asked to describe his own reasoning is a notoriously poor guide to the logic his behaviour actually follows.
The driver who overtakes does not solve the equations of motion, yet the equations predict him exactly; and the firm, Machlup said, need not know the calculus of the margin to be governed, in the end, by its results.
It was Milton Friedman who, in an essay of 1953 that became the most influential statement of method the discipline has produced, hardened Machlup's defence into a sweeping doctrine. The realism of a theory's assumptions, Friedman declared, is simply not a legitimate test of the theory; what matters, and all that matters, is the accuracy of its predictions. Indeed the most powerful theories, he held, are precisely those whose assumptions are the wildest simplifications of a tangled reality, for the whole art of theory is to abstract the few features that govern an outcome from the many that merely attend it. His illustration has grown as famous as the doctrine. An expert billiard player, Friedman observed, makes his shots exactly as though he knew the intricate formulae that give the optimal angle and force for each, could estimate the angles and distances by eye, could compute the formulae in his head, and could then direct the balls along the paths they prescribe — and we should predict his play excellently by assuming all of this, despite knowing that he does none of it. So with the firm: we predict its conduct by assuming that it maximizes profit, equating its margins, not because it performs these operations but because assuming that it does yields predictions that come true. The assumption is an instrument, justified by its results, and the question whether it is realistic does not arise. Friedman reinforced the case with an argument from selection: a firm that strays too far from maximizing profit will be competed into bankruptcy, so that the firms one actually observes are, by the very fact of their survival, the ones that behave as if they maximized, whether they intend to or not.
There is real power in this, and it would be a mistake to wave it away as mere evasion, for it captures something true and important about how theories work. We genuinely do not need an agent to perform a calculation in order for a model that assumes the calculation to predict him well; the billiard player and the motorist are not sophistries but sound examples of a real and pervasive phenomenon. The selection argument, too, has genuine force: competition does press upon firms, and over time it does tend to eliminate the grossly inefficient and to spare the roughly optimal, so that a population of surviving firms may behave much as the maximizing model says even if no single firm maximizes by design. And prediction is, after all, the discipline of an empirical science; a model that forecasts what firms and markets will do has earned a great deal of respect regardless of the tale it tells about why. On these grounds the marginal theory emerged from the controversy not defeated but transformed — no longer, perhaps, a portrait of the deliberating mind, but a remarkably serviceable instrument for predicting the behaviour of firms and markets in the aggregate and over the long run.
A theory, Friedman insisted, is to be judged not by the truth of its assumptions but by the accuracy of its predictions — a doctrine that rescued the margin as an instrument by quietly surrendering it as a description.
And yet the doctrine, taken to the hilt, proves too much, and its critics have never been silenced. The first objection is that it threatens to place the theory beyond the reach of evidence altogether: if no fact about how firms actually decide can ever count against a theory of how they decide, because the theory claims only an as-if, then the theory risks becoming unfalsifiable, immune by construction to the very disconfirmation that is supposed to discipline it — and Samuelson, among others, argued at length that the unrealism of an assumption is not always harmless, since an assumption carries implications of its own that can be tested and found wanting. The second objection is that prediction is not the whole of understanding: a model that forecasts an outcome without capturing the mechanism that produces it cannot tell us why the outcome occurs, and will mislead us the moment we move to a situation the mechanism would handle differently than the as-if summary suggests. The selection argument, examined closely, is weaker than it first appears — competition is often too slack, and selection too slow and too noisy, to grind every survivor into an optimizer, and firms that merely muddle through survive in great numbers. And most tellingly of all, the departures of real behaviour from the maximizing ideal have turned out not to be the random, self-cancelling scatter that the as-if defence requires, but systematic, patterned, and predictable — which means that the realistic model and the as-if model make different forecasts, and that in the cases where they differ it is increasingly the realistic one that proves correct.
The most searching alternative came from Herbert Simon, who proposed that the whole picture of decision as maximization be replaced by something he believed far closer to the truth of how minds and organizations actually work. Real deciders do not optimize, Simon argued, for optimizing would require surveying every option and computing the best of them, a labour beyond the powers and the patience of any actual agent. They satisfice: they fix upon a level of outcome that would be good enough, search until they find an option that meets it, and then stop, the search itself being costly and the perfect being the enemy of the workable. Decisions are made by rules of thumb, by routines, by aspiration levels that rise and fall with experience — a bounded rationality, fitted to creatures of limited attention operating in a world far too complex to optimize against. This was not a refinement of the marginal theory but a rival to it, a descriptive account of the very process the as-if defence had declared off-limits, and it has proved its worth in its own predictions, anticipating the patterned departures from maximization that the later behavioural economics would document in such abundance. The firm of the evolutionary economists who followed Simon is not a calculator of margins but a bundle of habits, selected and revised; and that firm, it turns out, often behaves in ways the maximizing fiction does not foresee.
Where, then, does the controversy leave the margin? Not refuted, but qualified, and qualified in a way worth stating with care. As an instrument for predicting the broad behaviour of firms and markets — especially in the aggregate, under competition, and over a span long enough for selection and adjustment to do their work — the marginal theory remains powerful, and the as-if defence of it is, within those limits, entirely legitimate. But it is not a faithful account of how any particular decision is reached, and the as-if defence becomes an evasion the moment it is used to forbid all inquiry into the mechanism, or to explain away the systematic ways in which real choosers depart from the maximizing ideal. The margin, in the end, is something like a useful fiction — false in the detail of any single deliberation, illuminating in the mass, in the manner of the frictionless plane and the point mass and the other fruitful lies by which sciences make tangled realities tractable. And it leaves us with a question that no amount of predictive success can settle: how much should we ask that a theory be true, and how much is it enough that it merely works? The volume has one plate left, and it turns from this question about how the margin is used back to the deepest tension in what the margin teaches. For the margin's whole instruction was to attend to the increment and forget the whole — to ask always after one more, and never after the total. There are domains, though, in which that instruction fails most spectacularly: where one more changes everything, where the advantage grows with size, where a system crosses a threshold and tips. To the return of the whole, and the close of the volume, the final plate now turns. As the table says of every quantity, first to last: the argument remains open.