A seller who has made his product distinctive has gained some room to choose its price. He has not thereby learned how much each customer would have paid. A single price still leaves the eager buyer a large surplus and sends the reluctant buyer away, even when supplying that buyer would cost less than she was prepared to give. Price discrimination is the seller's attempt to separate these customers: to charge more where a higher payment can be obtained without losing the sale, and less where a lower payment makes another sale worthwhile. The consumer's surplus is a prize the seller has reason to pursue, and the terms of sale determine how securely the buyer can keep it. But the pursuit can alter the size of the prize as well as its division. It may bring in an excluded customer, deter another, or change which buyer receives a scarce unit. The sorting therefore opens two accounts at once: the value created by the exchanges and the share of that value the seller keeps.
Begin with the limiting case, in which the seller knows each buyer's maximum willingness to pay and can charge it separately. Suppose three buyers each want one unit, value it at twelve, eight, and four pounds respectively, and cost two pounds each to serve. A single price of eight serves the first two and earns twelve pounds above production cost; prices of twelve or four earn only ten or six. The best uniform price therefore leaves the first buyer four pounds of surplus and excludes the third buyer, whose purchase could have created another two. Now allow separate charges of twelve, eight, and four, assuming the buyers accept a purchase when exactly indifferent. All three are served; the seller receives twenty-four, incurs six of cost, and keeps eighteen. The buyers keep nothing. The additional trade raises total surplus from sixteen to eighteen, while the seller's gain of six also includes the four previously retained by a buyer. This is Pigou's first-degree discrimination in miniature: with the stated knowledge, control, and cost conditions, every beneficial unit can be supplied and its entire surplus collected by one side.1
The knowledge is useful only if the seller can act on it and keep the cheaper offer from undoing the dearer one. A customer who can buy an identical service elsewhere on better terms does not have to surrender her whole valuation to this seller. A customer charged four who can freely resell to the customer charged twelve can make the price difference unsustainable. Pigou consequently treats the separation of markets as a substantive part of the problem. Sometimes the service is attached to the person: one cannot resell a haircut already received. Sometimes the separation depends on an enforceable condition, a costly journey, or a characteristic that is difficult to change. The seller must consider whether buyers can move between the categories as well as whether the product can move between them. A discount for carrying a pencil would invite everyone to carry one. A restriction that is costly to satisfy may sort customers, but the time and inconvenience spent satisfying it belong in the reckoning. Information, alternatives, and the practical durability of the dividing line determine how much of the imagined power can be exercised.2
A seller may also use the form of the bill to reach surplus that a price per unit leaves untouched. Walter Oi's amusement-park problem asks how to divide the charge between admission and rides. In a simple illustration, suppose one customer's demand for rides is eight minus the price per ride, and each ride costs two to supply. At a price of two the customer takes six rides and enjoys eighteen pounds of surplus before admission. An admission fee of eighteen can collect that surplus while leaving the price of another ride at its marginal cost. This works cleanly for the stipulated customer, or identical customers, with demand unchanged by the fee. With differing customers, the same admission charge can exclude someone whose total benefit is smaller; lowering it to retain that person leaves surplus with another. A menu gives the seller a further instrument: a low admission charge with dear rides can appeal to occasional users, while a larger fee with cheaper rides appeals to frequent users. Each customer must prefer the package intended for her to the alternatives actually offered. The seller cannot simply write a high charge beside the keen customer and assume that she will decline an available cheaper route.3
Sorting by an observable group can change the allocation even when it leaves the number of units sold unchanged. Consider two separated markets with demands of 100 minus price and 60 minus price, respectively, and a constant cost of twenty per unit. The best single price is fifty: fifty units go to the first group and ten to the second. Separate profit-maximizing prices are sixty and forty: the first group now receives forty units and the second twenty. Total output remains sixty. The seller's profit rises from eighteen hundred to two thousand, but consumers' surplus falls from thirteen hundred to one thousand. Total surplus has fallen by one hundred. Some buyers in the first group, willing to pay between fifty and sixty, have lost access, while buyers in the second, willing to pay between forty and fifty, have gained it. A unit that once went to a higher valuation now goes to a lower one, with no saving in production cost. A larger profit therefore does not establish a larger common benefit, and a lower price for one group does not establish that the aggregate gain exceeds the aggregate loss.4
An expansion of access can nevertheless outweigh the loss from a changed allocation. If a uniform price leaves an entire independent market unserved, the ability to supply it at a separate price above cost can add beneficial trades without changing the price in the market already served. That is one precise setting in which discrimination increases total surplus. It is a conditional result, not a verdict on every discount or every segmented market. Varian's welfare bounds show, under the stated money-surplus assumptions and constant marginal cost, that an increase in total output is necessary for a strict increase in total surplus when moving from a uniform price above cost to discriminatory prices. It is not sufficient. Additional units may add value while the reassignment of existing units loses more. Evaluating the change therefore requires both the amount sold and the valuations of those who gain or lose access. It also requires a separate account of distribution: the fact that a larger total is available does not mean every customer benefits, or that the customers who gain are the ones with the least income.5
The seller's sorting makes the distinction between producing a surplus and possessing it particularly sharp. Perfect knowledge and separate charges can bring production to the efficient quantity in the simple model while leaving the buyer no gain beyond her alternative. Imperfect knowledge produces a more varied result: some customers receive access they previously lacked, some surrender a larger payment, and some may be excluded. A fee, a menu, and a group price are different ways of working on those margins, and each must be judged against the terms that would otherwise prevail. The full price, the feasible alternatives, and the allocation of the good matter together. The volume can now separate two events that the language of a costly market often runs together. Surplus may leave the customer's hands and arrive in the seller's; it may also fail to arise because a worthwhile exchange never takes place. The next plate follows that second event, the loss that no recipient can be found enjoying.