The volume just closed measured the value of one more — the worth of the last and least-needed unit, which, the margin taught, is what sets the price of the whole. But a price, once set, conceals a second quantity, and it is the subject of the volume now beginning. When a thing sells at a single price, not everyone who buys it valued it equally; some would have paid far more than the price they were charged, and the difference between what they would have paid and what they did is a benefit they carry away unpaid for. That benefit is the surplus, the value an exchange creates over and above the price it settles at, and it is, in its way, the whole point of trade: were there no surplus — were each buyer charged exactly what the thing was worth to him, and not a penny less — exchange would enrich no one. This first plate is about the surplus's discovery, which came not from a philosopher pondering the nature of value but from an engineer trying to decide whether to build a bridge.
The engineer was Jules Dupuit, a Frenchman who, in the eighteen-forties, was occupied with the thoroughly practical business of public works — bridges, roads, canals, the infrastructure a state must decide whether and where to build. The decision turned on a comparison, of the cost of the work against its benefit; and the cost gave him no trouble, for the cost of a bridge is simply what it costs to build. The benefit was the difficulty. How does one put a number on the value a bridge confers upon the people who use it? The obvious candidate — the revenue the bridge collects in tolls — Dupuit saw at once to be inadequate, and inadequate in a specific and instructive way: it counts only what users actually pay, and most users would have been willing to pay more. A merchant who would have given ten francs to get his goods across, and is charged a toll of two, has had eight francs' worth of benefit that the toll-box never records. The toll revenue, in other words, systematically understates the worth of the bridge, by exactly the amount of benefit that the price fails to extract. To measure the true value of the work, Dupuit needed some way to capture that uncollected benefit, and to find it he was driven to invent a tool the economists of his day did not possess.
His insight was to picture the whole body of potential users arranged in order of what each would be willing to pay. A few would pay a great deal to cross, having urgent and valuable business on the far side; many would pay a moderate amount; and a long tail would cross only if it were nearly free. Plot the number who would cross against the toll that might be charged, and one obtains a downward-sloping line — the curve of demand, though Dupuit did not yet call it that — running from the few who would pay dearly down to the many who would cross only for a pittance. Now the toll revenue is merely a rectangle beneath this line: the toll, multiplied by the number who pay it. But the true benefit of the bridge is the whole area beneath the line, the sum of what every user would have been willing to pay, for that is the total worth the crossing holds for all of them together. And the benefit that goes uncollected — the value the bridge confers beyond what it charges — is the area beneath the demand curve and above the line of the toll: a triangle of unpaid-for worth sitting atop the rectangle of revenue. That triangle is the consumer surplus, and Dupuit was the first human being to draw it, and to grasp that it, and not the takings of the toll-box, was the true measure of what the bridge was worth.
The toll a bridge collects measures only what the crossing was worth to the last and most reluctant traveller; the value to all the others — who would gladly have paid more, and pocket the difference — is a benefit the toll-box never sees.
With this, Dupuit had founded, single-handed and decades before its time, the discipline we now call cost-benefit analysis. To judge whether a public work is worth building, he argued, one must set against its cost not the revenue it will earn but the whole surplus it will create — the entire area under the demand curve, the full benefit to all who will use it, whether or not they pay for the privilege. And this at once explained something the toll revenue had obscured: that a bridge might be very much worth building even if it could never pay for itself in tolls, because the benefit it confers, most of it uncollected, may vastly exceed both its cost and its takings. The same instrument cut the other way as well, and here Dupuit anticipated a result this volume will later take up in full. The toll, by turning away everyone who values the crossing at less than its price, destroys a portion of the benefit the bridge might have conferred — the surplus of all those who would have crossed at a lower charge, and now do not cross at all. Dupuit saw that this lost benefit was a real cost of the toll, a waste created by the very act of charging; and in seeing it he discovered, alongside the consumer's surplus, the welfare loss that pricing and taxation inflict.
All of this Dupuit set down in 1844, in a memoir published in a journal of civil engineering; and all of it the economists of his century comprehensively ignored. He was an engineer, not an economist; he wrote in the wrong place for the wrong audience; and the tools he had forged lay unused and unremarked for the better part of fifty years. When the consumer's surplus at last entered the body of economic doctrine, it did so through the work of Alfred Marshall, who arrived at the concept independently in his Principles of 1890, gave it the name it now bears, and made it one of the central instruments of the new economics. Marshall knew of Dupuit and credited him; but it was Marshall's version that the discipline learned, and to this day the surplus is taught as a Marshallian idea, with Dupuit relegated to a footnote of priority. It is a pattern this table has met before — in the marginal utility that Gossen discovered and died believing unread — the founder forgotten, the rediscoverer enshrined, the idea itself indifferent to which of its parents the world chooses to remember.
Dupuit found the surplus, and his century looked away; Marshall found it again fifty years on, and the discipline has not set it down since — the founder a footnote, the rediscoverer a landmark, as so often in this science.
It is worth pausing to see exactly how this new quantity stands to the one the previous volume was devoted to, for the relation is the deepest thing about it. Each point on Dupuit's demand curve is a marginal valuation — the worth of the crossing to one more user, the most that one further traveller would pay. The curve itself, the whole downward-sloping line, is nothing but the marginal values of all the users laid side by side, from the highest to the lowest. And the surplus is the area under that curve: which is to say, the surplus is the sum of all the margins. The quantity the marginal revolution taught the discipline to set aside — the whole, the total, the integral of value rather than its increment — returns here as the very thing the surplus measures, recovered by adding up the margins the previous volume had taught us to consider one at a time. The margin gives the curve; the surplus is the area beneath it. The two volumes are thus a single motion of thought: the first descends from the whole to the increment in order to explain the price, and the second climbs back from the increment to the whole in order to measure the benefit. The surplus is the margin, summed.
For all its power, the surplus carries from its very birth a set of difficulties that the rest of this volume will be largely occupied with, and honesty requires that they be named at the outset. To measure the surplus, one must know the demand curve — the willingness to pay of every user — and that curve is not handed to us; it must be inferred, estimated, guessed at, with all the error that implies. One must assume, further, that a franc of benefit means the same thing at every point on the curve, to the rich merchant and the poor carter alike — that the marginal utility of money is constant — for only then does the area, measured in money, faithfully track the benefit, measured in satisfaction; and this assumption, as a later plate will show, is not in general true. And the gravest difficulty of all lies in the innocent act of adding: to speak of the total surplus a bridge confers is to add one person's benefit to another's, and that addition, as the volume on the margin already warned, requires comparing the satisfactions of different people, an operation that the ordinal turn in the theory of utility declared to be without meaning. The surplus, in short, is indispensable and ill-founded at once — a quantity we cannot do without and cannot quite justify — and the tension between those two facts runs through everything that follows.
But these are troubles for later plates. What Dupuit accomplished, and what this opening plate has tried to honour, was to see that the value of an exchange is not exhausted by its price — that beneath every transaction conducted at a single price there lies a reservoir of unpaid-for benefit, the gap between what people would have given and what they were actually asked, and that this gap, far from being a curiosity, is the very measure of how much good a market does. He gave the gap its first quantity, drawing it as an area on a diagram, and in doing so handed the discipline a tool it has never since put down. The volume now follows that tool through its uses and its abuses: the form in which it became central, the surplus the seller earns as well as the buyer, the gains from trade entire, and the many ways the surplus can be destroyed, extracted, divided, and fought over. The next plate takes up the shape in which the consumer's surplus entered the mainstream of the subject and has lived there ever since — the triangle Marshall drew beneath the curve of demand. As the table says of every quantity, first to last: the argument remains open.