The Wedge

in print · The Tax · plate i

A tax is laid on one person and borne by another. The statute names who must hand the money to the state; but the burden, driven as a wedge between the price a buyer pays and the price a seller keeps, settles where the law cannot reach. This plate sets out the first fact of incidence — that who is charged and who pays are decided by separate things, and only the price tells which is which.

To tax and to please, no more than to love and to be wise, is not given to men. Edmund Burke, Speech on American Taxation, 1774

A tax is a wedge. Before it is imposed, a single price joins the buyer and the seller — the buyer pays exactly what the seller receives. The tax drives a wedge between them: the buyer now pays more than the seller keeps, and the difference goes to the state. Everything that is puzzling about who bears a tax follows from a single fact about this wedge — that how it divides, how much falls on the buyer and how much on the seller, has nothing whatever to do with which of the two the law commands to pay. The statute names a payer; the market names a bearer; and they are seldom the same person. To understand a tax is to learn to read the second name, which is written not in the law but in the price.

The distinction the wedge forces upon us has two names, and the difference between them is the whole of the subject. Statutory incidence is the legal fact: it names the person on whom the law lays the duty to pay, who must compute the tax, withhold it, and remit it, and it is set down in black letter for anyone to read. Economic incidence is the consequence: it names the person whose command over real goods is actually diminished by the tax — whose wage is lower, whose profit thinner, whose purchases dearer — and it is written nowhere, for it must be worked out from the way the tax disturbs the market. John Stuart Mill drew the line as sharply as anyone, dividing taxes into the direct, demanded from the very persons meant to bear them, and the indirect, demanded from one person in the settled expectation that he will reimburse himself at the expense of another. The customs duty and the excise are the plain cases: laid on the importer or maker, they are meant from the first to be passed down the chain to the consumer, who pays them without ever being named. But Mill's insight runs deeper than the cases he gave, for nearly every tax, on inspection, turns out to be indirect in his sense — shifted, in some degree, from the party the law charges to some other the law never mentions.

To see how the shifting works, hold the wedge itself in view. In a market without the tax, supply and demand meet at a single price, and at that price the quantity buyers wish to take equals the quantity sellers wish to give: the buyer's outlay and the seller's receipt are one and the same number. Introduce a tax of a fixed amount on each unit sold, and that single price splits in two. The price the buyer pays rises; the price the seller keeps falls; and the gap between them, holding the tax, is handed to the state. The two prices are tied together — their difference is exactly the rate — but where, within that gap, the old single price ends up is not fixed by the tax at all. The buyer's price may rise by nearly the whole of the tax, the seller's receipt falling hardly at all; or the seller's receipt may fall by nearly the whole, the buyer's price barely moving; or the two may share it evenly. David Ricardo had worked the cases one by one; Alfred Marshall, drawing supply and demand as the two blades of a scissors, showed in general that the burden divides according to the shapes of those curves, and incidence became the question of how far each blade gives way when the wedge is driven between them.

Here is the fact that overturns the plain reading of every tax statute: it makes no difference, to where the burden finally rests, which side of the market the law orders to pay. Lay the tax on the seller, requiring a dollar on each unit, and he treats it as a cost, supplies less at any given price, and the buyer's price rises; lay the identical tax on the buyer, and he treats it as an addition to the price, demands less, and the seller's price falls. Work the two cases through, and they end in exactly the same place: the same price paid by buyers, the same price kept by sellers, the same quantity traded, the same division of the burden between them. The wedge is the same wedge, opened to the same width on the same side, whichever party the law appoints to carry the money to the treasury. The choice of remitter is a matter of administrative convenience — of whom it is easier to collect from — and nothing more; it is bookkeeping, not burden. The party named in the law and the party reduced by the tax are settled by two separate things, and there is no reason on earth they should be the same.

If the law does not decide the split, something else must, and the something else is the relative power of the two sides to escape. When the tax drives its wedge, each side tries to avoid the part of it that would otherwise fall on them — the buyer by buying less, or buying something else, or going without; the seller by selling less, or shifting his effort and capital to some other line. Whichever side finds escape easier forces more of the burden onto the side that finds it harder, for the party that can readily walk away will not accept a worse price, and so the worse price must be borne by the party that cannot. The capacity to escape has a technical name, elasticity, and the working out of how it governs the division of the wedge is the burden of the plate that follows, on the escape itself. Here it is enough to have established the negative half of the truth: that the division is not fixed by the statute. What fixes it is a contest between the parties over who can do without the exchange — and the wedge opens toward the one who cannot, as the Physiocrats saw of land, which cannot flee at all.

And with that, the tax falls into the pattern this work has traced through every price it has examined. The new price the tax brings into being — the price the buyer pays, raised above what the seller keeps — wears the look of a simple sum: the old price, with the tax added on. A price is a verdict on a hidden contest, mistaken for a fact of nature; and this after-tax price is a verdict of precisely that kind. For how much of the tax actually shows itself in the buyer's price, and how much disappears instead into the seller's diminished receipt, is no arithmetical necessity at all but the settled result of the contest just described — a silent trial of strength between the two sides over which of them can bear to walk away. The arithmetic of the rate tells us only the width of the wedge; it is the contest that tells us on which side it opens, and so who is really taxed. The price reports the verdict — this much to the buyer, that much to the seller — and reports it as though it were a fact about the goods, disclosing nothing of the struggle that decided it.

It may be objected that this makes too little of the law — that surely it cannot be wholly indifferent who is charged, and the equivalence must be an artifact of the economist's idealizations. The objection has real force, in three directions. The first is salience: people do not always see through to the true burden, and a tax they notice may change their behavior differently from an identical tax they do not — a charge added visibly at the register weighs on the buyer's mind in a way the same charge folded into the shelf price does not, so that who remits, by changing what is seen, can change what is done. The second is friction and time: the equivalence holds once prices have fully adjusted, but adjustment is not instant, and in the interval before wages and prices move — which may be long — the party the law charges does bear the tax, the statutory and the economic incidence coinciding until the market has worked. The third is the imperfect market: where a seller has power over his price, or contracts fix terms, or the costs of changing prices are real, the remitter's identity can leave a trace that perfect competition would have erased. Under full information, instant adjustment, and perfect competition the law is indeed irrelevant to the burden; loosen any of these, and a residue of relevance returns.

Each of these qualifications is true, and none of them restores the plain reading. Grant that salience matters: it shifts behavior at the margin, but it does not repeal the deeper forces, and a tax the buyer is fooled into ignoring is still, once the market adjusts, borne according to who can escape, not according to who was fooled. Grant that adjustment takes time: the short run belongs to the statute, but the medium and the long run belong to elasticity, and a burden that rests on the legal payer for a season and on the inelastic party thereafter is, in any reckoning that outlasts the season, the latter's. Grant that frictions and market power leave a trace: they bend the result, sometimes far enough to matter for a particular tax, but they bend it around the elasticities, which remain the center of gravity — the remitter's identity a second-order correction, not the first-order fact. The qualifications make the naive reading less wrong in the short run and at the margins; they do not make it right. The burden still goes, in the main and in the end, where the power to escape sends it — and the law's choice of payer still tells us, by itself, almost nothing about who pays.

This is why the wedge is the volume's first lesson: it dissolves the illusion that the statute creates and the public believes. A price is a verdict on a hidden contest, mistaken for a fact of nature; and the price a tax produces is such a verdict, the resting place of a burden read off a figure that looks like arithmetic and is in truth the record of a struggle the law names no party to. The statute's confident designation of a payer — the seller, the employer, the corporation — is a kind of fiction, useful precisely to whoever profits from the belief that the named payer is the real one: the politician who can lay a burden on the unpopular while it settles quietly on someone else, the advocate who can call a tax a charge on the rich while the market passes it down to the poor. To read a tax honestly is to decline the name the law offers and to look instead at the prices, asking of each whose has moved and by how much; for that, and not the statute, is where the bearer's name is written.

The law names who hands over the money. The price names who is poorer for it. They are rarely the same — and only the price tells the truth.

The wedge, then, is driven, and the burden it carries does not stay where the law sets it down. What the law cannot decide, the power to escape decides — and that power, elasticity, is the subject of the companion plate, on the escape, where the negative truth established here, that the statute does not fix the burden, is met by the positive one, that the burden falls on whoever cannot flee. From there the volume follows the consequences of the moving burden: the value the wedge destroys beyond the revenue it yields, the rule by which efficiency would aim it at the captive, the ladder by which fairness would graduate it, and the bases and instruments through which a society lays it down. Through all of them the wedge remains the elementary figure — two prices where there was one, a gap held by the state, and a burden that settles where no statute can command. The argument remains open.