Twice now the volume has followed the surplus — watching it spring into being whenever a willing buyer meets a willing seller, and watching it parcelled out between them by the price they strike. There is a third thing that can befall a surplus, and it is the grimmest, for it is neither birth nor division but death. A surplus that might have existed can be prevented from existing; and, what is stranger, a surplus already counted upon can be made to vanish, not handed to anyone but simply abolished, struck from the sum of human satisfaction with no beneficiary anywhere. This destruction is the work of anything that drives a wedge between what a buyer pays and what a seller receives: a tax, a tariff, a quota, above all a monopoly. The vanished benefit has a name — the deadweight loss — and a shape, a small triangle that has done more to discipline the economics of policy than almost any other figure in the subject. This plate is about that triangle: what it measures, why it is so often smaller than one expects, and the unsettling argument that it is nonetheless far too small.
The essential thing is a distinction that untrained intuition almost always misses: between surplus that is moved and surplus that is destroyed. Lay a tax upon some good, and two quite different things happen to the surplus the market was generating. First, a part of it is transferred: buyers now pay more and sellers keep less, and the difference is collected by the government as revenue. This is a transfer, and from the standpoint of the society as a whole it is not a loss at all — the money has not vanished, it has merely changed hands, passing from buyers and sellers to the public purse, to be spent on something or returned to someone. Whether that transfer is good or bad is a question of who deserves the money, a question of distribution and not of waste. But a second thing happens too, and it is a genuine loss. The higher price the tax imposes drives some trades out of existence altogether — the trades of all those buyers who valued the good at more than its cost to produce, but at less than its cost plus the tax. These were mutually beneficial exchanges; they would have generated surplus; and now they do not occur at all. The surplus they would have created is not transferred to anyone, for the trades simply do not happen. It is destroyed. That destroyed surplus, and not the transfer, is the true social cost of the tax.
On the now-familiar diagram, the two pieces separate cleanly. Before the tax, the market trades the quantity at which supply meets demand, and the surplus is the whole area between the two curves. The tax opens a gap between the price buyers pay and the price sellers get, and the quantity traded shrinks to where that gap just fits between the curves. Of the surplus that used to fill the space out to the old, larger quantity, one part — a rectangle, as wide as the new and smaller quantity and as tall as the tax itself — is the revenue, the transferred portion, money moved from traders to treasury. The other part is a triangle, sitting just beyond the rectangle, bounded above by the demand curve and below by the supply curve and cut off at the new quantity: the surplus of the trades that the tax has killed, belonging now to no one. That triangle is the deadweight loss. Dupuit, the engineer of the first plate, had glimpsed it more than a century before, in the travellers his bridge-toll turned away; and it was Arnold Harberger who, in the nineteen-fifties, made it the standard instrument for measuring the cost of taxes and of monopolies, so that it bears his name to this day.
The revenue a tax collects is a rectangle, and that wealth is not lost but moved; the loss is the little triangle beside it — the trades the tax made no longer worth making, the surplus of bargains that now never occur, wealth that goes neither to the state nor to anyone, but simply ceases to be.
This triangle is what economists mean by the excess burden of a tax — the cost it imposes over and above the revenue it raises. A tax that brings in a hundred pounds does not cost the society a hundred pounds; it costs a hundred pounds plus the deadweight triangle, the surplus annihilated in the raising. Two features of the triangle govern the whole art of taxation. The first is that it grows with the square of the tax: double the rate and the deadweight loss roughly quadruples, for the triangle widens in both of its dimensions at once. Small taxes are therefore cheap in proportion to what they raise, and very large ones ruinously dear — which is the deep reason a broad tax at a low rate wastes less than a narrow one at a high rate. The second is that the triangle's size turns on elasticity, on how much the quantity traded responds to the wedge. Tax a good whose buyers and sellers will scarcely change their behaviour, and few trades are killed and little surplus lost; tax a good whose quantity collapses at the first hint of a higher price, and the destruction is great. From this follows the unsettling logic of efficient taxation — that one should tax most heavily the things people cannot or will not stop buying — a logic that runs hard against every instinct of fairness, since the goods most inelastic in demand are so often the very necessities of the poor.
The same triangle measures the cost of monopoly, for a monopolist does to a market almost exactly what a tax does: he holds the price above the cost of production, the wedge in his case becoming his profit rather than the state's revenue, and the trades of all the buyers priced out by the markup are destroyed, their surplus lost. When Harberger turned his triangle upon the monopolies of American industry, in a famous calculation of 1954, he reached a conclusion that startled the profession and has unsettled it ever since: the deadweight loss from monopoly in American manufacturing came to something on the order of a tenth of one per cent of national income — a rounding error, far too small to justify the alarm with which monopoly was conventionally regarded. The result provoked an immediate and lasting reaction, and the most penetrating of the replies struck at the very distinction this plate began with. The monopolist's profit, Harberger had treated as a mere transfer, harmless to the social total. But that profit, his critics observed — Gordon Tullock foremost among them — is a prize, and prizes are competed for: firms will spend real resources, up to the whole value of the prize, in lobbying and manoeuvring and litigating to win their monopolies and to keep them, and those resources are not transferred but consumed. The great rectangle that Harberger had set aside as innocent is, on this view, partly or wholly burned in the contest to capture it, and the true cost of monopoly may be many times the little triangle he measured.
Harberger measured the triangle and found it astonishingly small, a tenth of a percent of all the nation made; but the triangle, his critics answered, is only the visible wound — the great rectangle of monopoly profit, which he had counted as a harmless transfer, is itself half-burned in the scramble to seize it.
The deadweight triangle is among the most powerful instruments in all of applied economics, the standard measure of the waste that any interference with a competitive market entails — the cost of taxes, tariffs, quotas, price controls, and monopolies alike, every one of them reckoned as the surplus its wedge destroys. But its power rests upon a deliberate narrowing of vision that is worth naming. The triangle counts only destruction and not transfer; it treats the rectangle of revenue or profit as socially neutral, a matter of mere bookkeeping. This is exactly right if one cares only about the size of the pie and not at all about its division — but no one really holds that view, for it is precisely the division that animates the politics of taxation and the resentment of monopoly. To say that a tax's only true cost is its deadweight triangle is to set aside, by methodological fiat, the question of who is made to bear it, which is the question most people are actually asking. The deadweight loss is a clean measure of inefficiency, purchased at the price of silence about distribution; and, like the consumer's surplus from which it descends, it inherits all the further difficulties of being an area drawn in money and summed, in the end, across persons whose satisfactions the theory forbids us to compare.
There is a final irony in the triangle, and it cuts in the opposite direction from the one its smallness suggests. Read naively, Harberger's tiny number says that monopoly and the milder taxes hardly matter, that the cost of departing from the competitive ideal is a trifle — and for moderate taxes upon competitive markets this is largely true, and a useful corrective to the reflex that any intervention whatever is a catastrophe. But the rent-seeking critique reveals the triangle to be, in the cases that matter most, a floor and not a ceiling on the loss. Where a wedge creates not merely a deadweight triangle but a fat rectangle of rents — a protected monopoly, a lucrative licence, a tariff that shelters an industry — the very existence of that rectangle summons a wasteful scramble to capture it, and the surplus that the simple diagram records as merely transferred is, in the world, substantially destroyed after all, dissipated in lobbying and litigation and the building of moats. The visible loss is the triangle; the invisible loss is the rectangle, slowly burning. So the deadweight loss both reassures and warns: it shows that the static cost of intervention is often smaller than feared, and it points, by way of its own most telling criticism, toward a far larger cost lying hidden in the very transfers it declines to count — a cost to which the volume will return at its end.
The deadweight loss exists, at bottom, because a single price is a blunt instrument: one price for all comers must turn away every buyer who would have paid something, but not the full price, and in turning them away it kills their surplus. This suggests a remedy that is also a menace. What if the seller need not name a single price at all — what if he could charge each buyer exactly what that buyer is willing to pay, a high price to the eager and a low one to the reluctant? Then no willing buyer is turned away, every beneficial trade is made, and the deadweight triangle vanishes entirely; the market becomes, in the technical sense, perfectly efficient. But the whole of the surplus, every last sliver of it, is now captured by the seller, and the buyers are left with nothing whatever. Such perfect price discrimination is a limiting case rarely reached, but the practice of charging different buyers different prices is everywhere, and it is the seller's great weapon against the surplus — the means by which the gains a market creates are extracted from the customers and gathered to the firm. To that extraction, and to the discriminating seller who leaves no surplus behind him, the next plate turns. As the table says of every quantity, first to last: the argument remains open.