The previous two plates measured a surplus on each side of the market and then set them together, and in doing so they brought the volume to the edge of a claim it has so far approached only obliquely. The claim is this: that a voluntary exchange, simply by occurring, makes both parties to it better off, and therefore that trade creates value — not by manufacturing anything, but by the bare act of moving goods from those who value them less to those who value them more. It is among the most consequential propositions in all of economics, the intellectual foundation of the case for markets and for commerce of every kind, and it is at the same time among the most counterintuitive, for it appears to conjure benefit out of nothing at all. This plate sets out the claim at its full strength, gives it the name the economists gave it, and then asks, with as much honesty as the subject allows, what the claim does and does not establish.
The argument is disarmingly simple, and rests on a single observation about why people trade at all. No one enters a voluntary exchange expecting to come out behind; each party trades because he values what he will receive more than what he must give up, or he would not trade. When you sell me your apple for a pound, you do so because, to you, the pound is worth more than the apple; and I buy it because, to me, the apple is worth more than the pound. The apple passes from a hand that valued it less to one that values it more; the pound passes the other way, on the same terms; and both of us, by our own reckoning, are better off than we were a moment before. Nothing has been produced — there is exactly one apple before the trade and one apple after — and yet the total of satisfaction has risen, because the apple now sits with the person who wanted it most and the pound with the person who wanted it most, which was not the case before. This rise in total satisfaction is the gain from trade, and the surpluses of the previous plates, summed, are its measure: the whole area between the curves is the value that the trading, and nothing but the trading, brought into being.
There is something that genuinely puzzles people here, and it is worth facing squarely, because the resolution of the puzzle is the deepest idea in the plate. How can value be created without anything being made? The intuition that resists this is ancient and stubborn: it is the feeling that trade is a zero-sum affair, that in any exchange one party's gain must be the other's loss, that the pie is of fixed size and bargaining merely a fight over the slices — the conviction that animated the mercantilists, who saw foreign trade as a contest to be won, and that animates protectionists and hagglers still. The error in it is an error about the nature of value. Value is not a fixed quantity residing in things, the same for everyone; it is subjective, a relation between a thing and a particular person's wants, and the very same apple is worth more to the hungry than to the sated, more to one who has no apples than to one with a barrelful. Because value lives in the valuer and not in the object, the identical physical stuff can be worth more in one arrangement than in another, and trade, by rearranging who holds what, raises the total without adding a thing to the stock. The pie grows not because there is more matter in it but because the matter has been moved to where it counts for more.
Nothing is made, and yet there is more: the apple is the same apple and the coin the same coin, but each has passed to the hand that holds it dearer, and the sum of satisfactions is larger than before — value conjured not out of matter but out of the mere difference in how two people weigh the very same things.
What the market does, on this account, is to find and exhaust these gains wholesale. Every mutually beneficial trade that can be made, the competitive market tends to make: goods flow, through a chain of voluntary exchanges, toward those who value them most, until no further trade can make anyone better off without making someone else worse off — a condition the economists, after Vilfredo Pareto, call efficient. This is the content of the first fundamental theorem of welfare economics, the formal descendant of Adam Smith's most famous image: that the individual, "led by an invisible hand," pursuing only his own gain through voluntary exchange, is brought to promote an end that was no part of his intention — an allocation of the society's goods from which no costless improvement remains. Arrow and Debreu and their successors gave the theorem its rigorous modern form, specifying the precise conditions under which a competitive equilibrium is provably efficient. It is the most powerful single argument the discipline possesses in favour of markets: not that they are kindly, or fair, or wise, but that, under the right conditions, they leave none of the available gains from trade upon the table.
And here the honest qualifications must begin, for the theorem establishes something narrower than its admirers sometimes claim. It speaks to the size of the pie and says nothing whatever about its division. To call an allocation efficient is only to say that no one can be made better off without making someone worse off; it is emphatically not to say that the allocation is good, or just, or even tolerable. An arrangement in which a single person owns everything and the rest of humanity starves is, by the strict definition, perfectly efficient — for the starving cannot be fed without taking something from the one who has it all, which would make him worse off — and yet no one would call it anything but monstrous. Efficiency, in the technical sense, is a remarkably weak virtue: it rules out only sheer waste, the leaving of gains unrealised, and is entirely compatible with any distribution of the realised gains, however lopsided. How the surplus a market generates is actually divided between the parties — what share the buyer keeps and what share the seller, and behind them what share labour and what share capital — depends on prices and on bargaining power, and is the subject of the plate that follows. The gains from trade are real; who ends up with them is a wholly separate question, on which the theorem is, by design, silent.
Efficiency speaks only to the size of the pie, never to the cutting of it; an arrangement in which one man holds everything and the rest go hungry is efficient in the strict sense — for none can be made better off without making him worse — which is reason enough never to mistake the efficient for the just.
There is a second set of qualifications, concerning not what the theorem omits but what it assumes, for the whole sunny conclusion depends upon the exchange being of a particular kind. It must be voluntary in fact and not merely in form: a trade made at gunpoint, or under a duress that leaves no real alternative, does not leave both parties better off, and the consent the argument leans on is then a fiction. It must be informed: if I sell you a horse I know to be lame and you believe to be sound, you do not gain by the bargain, and fraud, deception, and hidden defects break the logic at its root, for the buyer's expected gain and his actual one come apart. And it must be confined in its effects to the two parties who make it: if our exchange visits a cost upon some third party who had no say in it — the smoke that the factory's sale of its wares sends drifting over the neighbours — then the fact that buyer and seller both gain tells us nothing about whether the world as a whole is better off, for the surplus they divide between them may be smaller than the harm they have exported. Where exchange is coerced, or deceived, or laden with such spillovers, it can destroy value as readily as create it, and the gains-from-trade theorem, which had assumed these troubles away, simply does not apply.
What survives all this is still a great deal, and it would be as much a mistake to lose the insight in the qualifications as to forget the qualifications in the insight. The core discovery is true and profound: voluntary exchange, where it is genuine, is positive-sum; the zero-sum intuition is wrong; trade between persons, between regions, between nations can and routinely does make both sides better off at once, and the suspicion that one party must lose for the other to gain has done incalculable harm wherever it has been allowed to guide policy. That a market, left to find its own equilibrium, will wring out the available gains is a result of real beauty and real force. But it is a result about the magnitude of the gains and not their sharing, and a result that holds only where exchange is free, informed, and contained — conditions that real markets meet partially, and sometimes hardly at all. The theorem is thus a powerful argument for markets and an incomplete one: it shows what they accomplish at their best, leaves entirely open who shall enjoy it, and falls silent precisely where coercion, ignorance, and spillover begin. To hold the discovery and its limits together — neither inflating the first into a blanket endorsement nor letting the second dissolve a genuine truth — is very nearly the whole of wisdom on the matter.
The pie, then, is real, and the market makes it as large as it can be made; that much the volume may now take as established. What remains entirely unsettled is how it is to be carved. The surplus an exchange creates does not come labelled with the names of its owners; it must be divided between buyer and seller, and the price at which they happen to trade decides the division, sliding the boundary between the buyer's share and the seller's as it moves. Where, within the whole range of prices that would leave both parties better off, the price actually settles — and what determines whether the buyer or the seller captures the larger part of the gains they jointly create — is a question of bargaining, and it has a geometry of its own, first drawn by Edgeworth in the diagram that bears his name. To the division of the surplus, and the bargain over it, the next plate turns. As the table says of every quantity, first to last: the argument remains open.