The Bracket

The bracket divides income into slices, and much of the fear it arouses comes from imagining that it divides people into separate kinds of taxpayer. A worker crosses a threshold and hears that she has entered a higher rate, as though the whole of her earnings had suddenly been carried into another room and taxed there. In an ordinary graduated schedule, the higher rate attaches to the additional slice. The money earned below the threshold keeps its earlier treatment. That small piece of arithmetic opens a larger distinction: the marginal rate asks what happens to the next unit earned; the average rate asks what share of the whole income goes in tax. One describes an incentive at the edge, the other a burden spread across the account.

Take a hypothetical schedule that exempts the first twenty thousand units, taxes the next thirty thousand at twenty percent, and taxes income above fifty thousand at forty percent. At forty thousand, the tax is four thousand and the average rate ten percent. At sixty thousand, the bill is six thousand on the middle slice and four thousand on the top slice: ten thousand altogether, or one-sixth of income. The marginal rate is now forty percent, while the average rate is about sixteen and two-thirds percent. An additional thousand leaves six hundred after this tax. Crossing the boundary preserves the treatment of earlier earnings and alters the division of additional earnings between the worker and the treasury. Each rate is correct, and each answers a different question.¹

A schedule can become progressive without a staircase of rising marginal rates. Exempt twenty thousand and tax every unit above it at twenty percent. A person earning forty thousand pays four thousand, or ten percent of income; one earning one hundred thousand pays sixteen thousand, or sixteen percent. The marginal rate is the same for both, but the untaxed allowance occupies a smaller part of the larger income. Progressivity, in this comparison, means a rising average share. Nor does the smooth-bracket result rule out every loss from earning more under a wider system. Suppose a hypothetical benefit of three thousand disappears entirely when income rises from fifty thousand to fifty thousand and one. The extra unit leaves sixty cents after our first schedule, while the lost benefit costs three thousand. That is a benefit cliff added to the schedule, with a different mechanism.²

The ethical case for a larger share asks how the capacity to pay should affect the common claim. A thousand units may secure essentials for one household and scarcely alter another's choices. That difference supports a familiar argument for progression, but it supplies no uniquely correct percentage. Need, family responsibilities, accumulated wealth, and the time over which income is measured complicate the comparison. Two people with the same annual earnings may have very different resources; one may be recovering from a lean decade while the other receives a steady stream. Horizontal equity asks how comparable positions should be treated; vertical equity asks how the burden should vary across unequal positions. Choosing the positions and the measure of inequality is already part of the judgment, before a rate has been entered in a table.³

The cost in effort depends on the choices a taxpayer can actually change. At a gross hourly reward of one hundred, a twenty-percent marginal charge leaves eighty; a forty-percent charge leaves sixty. An additional task requiring seventy units of personal sacrifice is worthwhile in the first case and unattractive in the second. A task costing fifty remains worthwhile under both. These examples establish a possible substitution response, without predicting how many hours a population will surrender. People may also work more to restore a desired income, have little control over their hours, change careers, defer a receipt, or rearrange how earnings are reported. The response that matters for output is therefore not identical to every movement observed on a tax return. The schedule reaches an economy of constraints and opportunities, not a single worker free to adjust every hour.⁴

The full distribution of the burden requires more than the income-tax table. Other levies, transfers, deductions, and the shifting of taxes through prices can change the result. Consider two hypothetical households, each with one hundred units of economic income. One owes twenty units under a wage schedule; another recognizes only fifty units in a favored taxable category charged at ten percent, and owes five. The difference comes from both base and rate. It cannot be read from the wage schedule's top bracket. Equally, a payment for a public service may change a household's resources beyond what its tax receipt records. A distributional account must say whether it measures annual or lifetime income, legal payments or estimated incidence, taxes alone or taxes with transfers. Otherwise a precise percentage may describe an imprecisely chosen object.⁵

The bracket makes a political judgment legible, but the judgment becomes meaningful only when the arithmetic and the comparison are sound. A higher marginal rate can coexist with a much lower average share; an allowance can create progression beneath a flat marginal rate; an unrelated cliff can reverse what the smooth schedule alone would imply. The question of effort then asks which opportunities are forgone and which receipts merely change form. None of this dissolves the choice over what the fortunate owe. It clears the ground on which that choice must be made. The Burden returns to the gap between the person sending the payment and the person reduced by it, carrying the schedule out of the printed table and into the prices, wages, and positions through which its consequences travel.