The Optimum

A tax distorts, and its burden shifts; given both, how should a tax be laid? This is the problem of optimal taxation, and it is a problem of conflict — between two things a good tax should be, which pull against each other. A tax should be efficient: it should raise its revenue with the least deadweight loss, the smallest destruction of trades. And a tax should be fair: it should fall more heavily on those better able to bear it. The trouble is that the efficient tax and the fair tax are often opposites, and the art of taxation is the management of their conflict.

Take efficiency first. The plate on the wedge showed that the deadweight loss grows with the square of the rate, so efficiency calls for broad bases at low rates. But it calls for something more pointed, which the plate on the shift prepared: tax the inelastic. For the deadweight loss comes from the trades a tax destroys, and a tax destroys few trades when the taxed parties cannot escape — when demand or supply is inelastic, the quantity barely falls, and little surplus is lost. So the most efficient taxes fall on the most inelastic things: necessities no one can forgo, labor that must be sold, land that cannot move. This is the efficiency rule — tax what does not budge — and it has a cruel corollary, joining efficiency to incidence. For the inelastic parties are not only those who distort least when taxed; they are also, as the shift showed, those who bear the tax most fully, being unable to escape it. So the most efficient tax is borne most heavily by those least able to avoid it — and the inelastic necessities are, very often, the necessities of the poor, who cannot forgo bread or rent or fuel. Efficiency, pursued alone, taxes the staples of the poor, because the poor cannot retreat from them; the efficient tax is frequently the regressive one.¹

Against efficiency stands equity — the demand that a tax be fair, falling more on those better able to bear it. Fairness in taxation is usually understood in two ways. Horizontal equity asks that those in like circumstances be taxed alike — that two people equally able to pay should pay the same, whatever the source of their means. Vertical equity asks that those better able to pay should pay more — and, in its stronger form, that they should pay a larger share, the principle of progressivity, by which the tax rate rises with income or wealth. The case for vertical equity rests on the diminishing value of money: a dollar taken from the rich costs its bearer less, in real well-being, than a dollar taken from the poor, for whom each dollar buys more urgent things; so a tax that takes more from the rich and less from the poor imposes less total sacrifice for the same revenue. Equity, so understood, calls for progressive taxation — for taxing the able and the affluent more than proportionally, and the struggling less. But here equity collides with efficiency, for the income and effort of the able are precisely the things that respond to taxation — and to tax them heavily is to discourage the very industry that produces the income.²

James Mirrlees gave the conflict its deepest formulation, and in doing so connected taxation to the problem of hidden information the volume on the asymmetry studied. The state wishes to tax by ability — to take more from the more capable, who can bear it, and less from the less capable, who cannot. But ability is hidden: the state cannot observe how able a person is, only how much income he earns. And income is not ability alone, but ability times effort: a high income may mean great ability lightly exercised, or modest ability strenuously applied. So when the state taxes income to reach ability, it taxes effort too — and a high tax on income, meant to fall on the able, falls also on the effort by which income is made, discouraging the able from exercising their ability. This is the Mirrlees problem: the state must redistribute, which is equity, by taxing income, but in taxing income it discourages effort, which is the loss to efficiency, and it cannot separate the two, because it cannot see ability behind income. The optimal income tax is the schedule that best balances the gain from redistribution against the loss from discouraged effort — taking enough from the able to help the unable, but not so much as to make the able stop trying. And Mirrlees's striking finding was that the optimal schedule is far less steeply progressive than equity alone would suggest, for the disincentive to effort bites hard at high rates: the very top rate, he argued, should not be confiscatory, lest it kill the effort that produces the income the state means to redistribute.³

The Mirrlees problem is the sharpest case, but the optimal-tax question runs through every choice of what to tax. Tax income, and you discourage earning; tax saving, and you discourage thrift, and tax the patient twice, once when they earn and again when their savings grow; tax consumption, and you spare saving but burden the present; tax wealth, and you reach the accumulated but may drive it abroad. Each base has its distortion — for what you tax, you get less of — and the art is to choose bases whose distortions are least costly and whose burdens fall most fairly, knowing the two criteria conflict. The broad conclusions of the optimal-tax literature are a compromise: tax broadly and at moderate rates, to keep the squared deadweight loss low; lean toward taxing consumption over saving, to spare the thrift that funds investment; tax the inelastic where it can be done without injustice — land, especially, which the later plates revisit; and pursue redistribution through the income tax and transfers, but with rates tempered by the disincentives they create. The optimum is never a single perfect tax but a portfolio of imperfect ones, each chosen to do the least harm for the revenue and the fairness it secures.⁴

The optimum, then, is a balance struck between efficiency and equity — between the tax that distorts least, falling on the inelastic who cannot escape, and the tax that is fairest, falling on the able who can best bear it — two criteria that conflict, because the inelastic are often the poor and the able are precisely those whose effort taxation discourages. Mirrlees gave the conflict its deepest form, in the optimal income tax that redistributes without destroying the incentive to earn. But all of this — the wedge, the shift, the optimum — has assumed that a tax is a necessary evil, distorting in order to raise revenue, the deadweight loss a cost to be minimized. The next plate turns to the remarkable exception: the tax that is not an evil at all, but a good — the tax that corrects a distortion rather than creating one, and whose deadweight loss is negative. For when the thing taxed is itself a harm — pollution, congestion, the externality the market overproduces — the tax that discourages it does not destroy good trades but prevents bad ones, and the wedge becomes a cure. The next plate is the corrective.⁵

The optimum is the resolution, always imperfect, of the conflict at the heart of tax design: that the efficient tax and the fair tax pull in opposite directions. Efficiency says tax the inelastic, which destroys the fewest trades — but the inelastic bear the tax most fully and are often the poor. Equity says tax the able, who can best bear it — but their effort is what taxation discourages, and to tax it heavily is to kill the industry that makes the income. Mirrlees gave the conflict its sharpest expression: the state, unable to see ability behind income, must trade redistribution against the disincentive to earn, and the optimal schedule is gentler than fairness alone would ask. The optimum is a portfolio of imperfect taxes, each doing the least harm for the good it secures. But all of this assumes the tax a necessary evil — and there is one tax that is a positive good. When what is taxed is a harm the market overproduces, the tax corrects rather than distorts. The next plate is the corrective.