Progressive taxation

Marginal and average rates

The most persistent misunderstanding about banded taxation is the belief that crossing into a higher band raises the rate on everything earned. It does not. Each band applies only to the slice of income that falls inside it, so the higher rate touches only the amount above the threshold. Earning one unit more can never leave someone worse off through the rate structure itself.

The rate charged on the next unit earned is the marginal rate. The share of total income actually paid is the average rate. In a banded system the average rate is always lower than the marginal rate and climbs slowly towards it, which is exactly what makes the structure progressive.

The arithmetic, with illustrative figures

Suppose a system with no charge on the first 10, a tenth charged on the next 20, and a fifth charged on anything above 30. Someone with an income of 50 pays nothing on the first 10, 2 on the next 20, and 4 on the final 20, making 6 in total. Their marginal rate is a fifth and their average rate is under an eighth.

The figures are chosen only to make the mechanism legible; no system is being described. What the example shows is structural: the average rate is a weighted blend of every band passed through, so it moves gradually even when the marginal rate jumps.

What progressivity does and does not settle

Progressivity describes the shape of one tax, not the fairness of a system. A system can pair a progressive income tax with heavy taxes on spending, which generally take a larger share from smaller incomes, and the combined effect may be much flatter than the headline structure suggests.

This is why arguments about tax burden are so difficult to settle in the abstract. The answer depends on which taxes are counted, over what period, and against which measure of capacity to pay, and reasonable people reach different conclusions from the same data by making different choices there.