The last plate ended on a remedy for the deadweight loss that turned out to be a kind of theft. A single price, it observed, is a blunt instrument, turning away every buyer who would pay something but not the whole of it; and a seller who could instead charge each buyer his own private maximum would turn no one away, waste nothing — and keep every penny of the surplus for himself. That practice has a name, price discrimination, and it is the subject of this plate. It is the seller's standing campaign against the consumer's surplus, the array of devices by which the gains a market creates, which the earlier plates took such trouble to measure and to credit to the buyer, are prised loose from him and gathered instead to the firm. The consumer surplus is not a possession the buyer holds securely; it is a prize the seller is perpetually trying to take, and price discrimination is the means by which he tries.
Begin with the extreme case, the one the last plate glimpsed, which economists call first-degree or perfect price discrimination. Imagine a seller who knows each buyer's maximum willingness to pay and charges each one precisely that — the full ten to the buyer who values the thing at ten, the bare five to the one who values it at five, a different price for every customer, each set at the very top of what that customer will bear. Two things follow, and their combination is one of the most instructive paradoxes in the subject. First, the outcome is perfectly efficient: every buyer who values the good above its cost is served, since the seller is glad to sell to anyone at any price above cost, and so no mutually beneficial trade goes unmade and the deadweight triangle disappears entirely. But second, the entire surplus — the whole area between the demand curve and the cost, every scrap of value the market generates — is captured by the seller, and the buyers, one and all, are left with exactly nothing, each having paid away the last farthing of his own benefit. Here, starkly, are the two faces of the surplus that the volume has kept insisting are separate: perfect discrimination maximizes the size of the pie and simultaneously awards the whole of it to one party. It is at once the most efficient arrangement imaginable and the most unequal.
Perfect discrimination in its pure form is rare, for it asks the impossible — that the seller read the private mind of every buyer. What sellers actually do, A.C. Pigou observed in 1920, falls into three degrees, distinguished by how the seller comes to know, or to guess, what each buyer will pay. The first degree is the perfect case just described, knowledge of each buyer exactly, approached but seldom reached. The second degree dispenses with knowing the individual and instead offers everyone the same menu of options, designed so that buyers sort themselves: a lower price per unit for buying in bulk, a stripped-down version sold cheaply and a deluxe one dear, a fixed entry fee plus a charge for each use. The buyer is not asked who he is; he reveals it by what he chooses, the eager selecting the premium and the casual the budget tier, each sorting himself into the price the seller meant for him. The third degree sorts buyers not by their choices but by some visible badge that correlates with willingness to pay — age, occupation, location, the hour of purchase — and charges each group its own price: the student and the pensioner pay less, the business traveller booking late pays more, the same film costs differently by afternoon and evening. Knowledge read, knowledge coaxed, knowledge guessed: three roads to the one destination.
The seller's problem is always the same — to learn what each buyer would pay, and to charge him exactly that — and his three solutions differ only in how the knowledge is got: read from the buyer directly, coaxed out of him by a menu that makes him sort himself, or guessed from the group he visibly belongs to.
Three conditions must hold for any of this to work, and where they fail, discrimination fails along with them. The first is market power. A firm in perfect competition cannot discriminate at all, for competition has already driven its price down to its cost, leaving no margin to redistribute; only a seller with some power over his own price — a monopolist, or a firm with a differentiated product — has a surplus to extract and the latitude to vary what he charges. The second is information, or some workable substitute for it: the seller must be able to tell his buyers apart, whether by knowing them outright, by inducing them to sort themselves, or by reading off their groups, and the whole apparatus of discrimination is at bottom an apparatus for acquiring or simulating that knowledge. The third, and the one most often decisive in practice, is the prevention of resale. If the buyer charged a low price can simply turn around and sell to the buyer charged a high one, the scheme collapses, for the arbitrage erases the very price differences it depends upon. This is why discrimination flourishes in services that cannot be resold — a haircut, a flight, a doctor's hour — and in goods the seller can tie firmly to the individual, and why it struggles wherever what is sold can be cheaply passed from hand to hand.
Now to the question that matters most and answers least cleanly: is price discrimination good or bad for the world as a whole? On distribution the answer is plain enough — it shifts surplus from buyers to the seller, which is rather the point of it. But on efficiency, on the size of the total pie, the answer is genuinely and surprisingly undecided. The perfect case, we have seen, is efficient, and so improves upon the single-price monopoly it would replace, for it serves the very customers that the monopolist's single high price would have turned away. And this points to a defense of the practice that cuts hard against the intuition that it is mere exploitation. A single price, set high enough to be profitable, abandons every buyer who cannot meet it; a discriminating seller, free to charge those buyers a lower price without lowering it for everyone, may bring the good to people a uniform price would never have reached. The drug priced out of reach in a poor country and sold there cheaply, the student fare that fills a seat which would otherwise have flown empty, the off-peak ticket that serves the traveller of modest means — in each, discrimination widens the circle of those served. The rigorous result, worked out by Robinson and refined by Schmalensee and Varian, is that third-degree discrimination improves welfare when, and largely only when, it raises total output. The practice that takes the most from some may be the very thing that brings the good to others at all.
The single price is not the friend of the poor it appears: it turns away everyone who cannot meet it, and the discriminating seller, charging the rich man much and the poor man little, may serve them both where one price would have served only the one — so that the practice which extracts the most from some can also be the one that includes the most.
For all that, no clean verdict on price discrimination is to be had, and the reason is precisely the gap between efficiency and equity that the practice throws into its sharpest relief. Perfect discrimination is the efficient ideal and the distributive nightmare in a single object — the whole pie made and the whole pie taken — and there is no rate of exchange between those two facts that the theory can supply, no formula telling us how much extra efficiency is worth how much extra inequality. The imperfect, real-world forms are murkier still: some raise output and serve the excluded, and are by that much to the good; others merely sort the willing from the desperate and squeeze the latter harder, and are by that much to the bad; and which of the two a given scheme is doing is an empirical question rarely easy to settle. Price discrimination is thus one of those practices on which economics can be scrupulously clear about the considerations and still decline to render a final judgment, because the considerations genuinely conflict and the weighing of them is not the economist's to do. It can say what is gained and what is lost, and to whom; it cannot say whether the trade is worth it.
There is a reason the perfect case, long treated as a textbook fiction too demanding ever to be realized, has begun of late to feel less fictional. Its single impossible requirement was knowledge — the seller's knowledge of each individual buyer's private willingness to pay — and knowledge of exactly that kind is now being assembled, on a scale and at a granularity that would have seemed fantastical to Pigou, out of the vast records of what each of us searches and buys and lingers over. A seller who knows enough about a buyer can begin to estimate the figure that buyer would pay, and to quote him that figure and no less; personalized pricing, set by algorithm from a dossier of past behaviour, is first-degree discrimination creeping out of the textbook and toward the checkout. The limit it approaches is the one this plate began with: every buyer charged his exact maximum, the whole of the consumer surplus extracted, the customer left with nothing. We are nowhere near that limit, and resale, regulation, reputation, and the sheer difficulty of the estimate all stand in its way. But the direction is unmistakable, and it lends a sudden practical edge to what was for a century an abstraction. The consumer surplus the volume has spent its plates measuring is not merely a thing that sellers would like to take; it is a thing they are learning, with every passing year, to take more of.
Through all of this — the surplus shifted from buyer to seller, the welfare of the world said to rise or to fall, the rich man's loss set against the poor man's gain — there has run a quiet assumption so constant that it has escaped examination, and it is now time to examine it. Every claim of the kind this volume has been making rests on adding surplus up: on treating the buyer's surplus and the seller's as quantities in the same currency, to be summed into a single total; on weighing one person's gain against another's loss and pronouncing the net. But can satisfaction be added across persons at all? Is my surplus and yours the sort of thing that can be placed on a common scale and totalled, or are we measuring, when we sum them, things that were never commensurable — adding, as it were, my warmth to your hunger? This is the deepest scruple lying beneath the whole edifice of consumer surplus and deadweight loss and welfare, and the volume can defer it no longer. To the interpersonal comparison, and the question of whether one person's surplus can be added to another's at all, the next plate turns. As the table says of every quantity, first to last: the argument remains open.