Crossing a tax-bracket threshold does not reprice the earlier dollars. The higher rate applies to the amount in the new layer. To read the bill, put each portion in its layer and add the results.
The IRS explanation of federal income tax brackets makes this distinction: the higher rate applies to the portion in the new bracket, not the whole income amount. The numbers below are wholly invented, not rates or thresholds for any actual tax year.
Put the dollars in their layers
Use this fictional annual schedule: the first $10,000 is taxed at zero percent; the portion over $10,000 through $20,000 at ten percent; and the portion over $20,000 at twenty percent.
Start with an amount already defined as taxable income. This model calculates only the invented tax. It does not model deductions, credits, benefit changes, withholding, payroll taxes or other taxes.
Compare two supplied annual taxable amounts, $19,000 and $21,000. The first $10,000 stays in the zero-percent layer in both. At $21,000, the ten-percent layer is full and the final $1,000 enters the twenty-percent layer.
Two taxable amounts under one invented annual schedule
Scroll across to see every column. Use the arrow keys when the table is focused.
| Taxable-income layer | Rate | Tax at $19,000 taxable income | Tax at $21,000 taxable income |
|---|---|---|---|
| First $10,000 | 0% | $10,000 × 0% = $0 | $10,000 × 0% = $0 |
| Portion over $10,000 through $20,000 | 10% | $9,000 × 10% = $900 | $10,000 × 10% = $1,000 |
| Portion over $20,000 | 20% | $0 × 20% = $0 | $1,000 × 20% = $200 |
| Total model tax | — | $900 | $1,200 |
Applying twenty percent to the full $21,000 would give $4,200. It would ignore the lower layers and overstate this model tax by $3,000.
Name the average and its denominator
At $19,000, total model tax divided by the whole taxable amount is $900 ÷ $19,000: about 4.74 percent. The next dollar is in the ten-percent layer.
At $21,000, the same whole-amount average is $1,200 ÷ $21,000: about 5.71 percent. The next dollar is now in the twenty-percent layer. That twenty percent is the marginal rate here, not the average on all $21,000.
These averages use taxable income as their denominator. A figure using gross income or another base would need its own label and calculation. Keep the denominator beside the rate.
An increase can cross more than one layer
The move from $19,000 to $21,000 adds $2,000. Its first $1,000 fills the rest of the ten-percent layer, adding $100 of tax. Its next $1,000 enters the twenty-percent layer, adding $200. Additional model tax is $300.
Divide that $300 change by the $2,000 increase: fifteen percent. This is the average tax on this particular increase. It differs from both the final next-dollar rate of twenty percent and the whole-$21,000 average of about 5.71 percent.
The amount remaining after this model tax moves from $18,100 to $19,800, an increase of $1,700. That result belongs to the supplied schedule and exclusions; it is not a calculation of real take-home pay.
Replace “The amount crossed $20,000, so all of it is taxed at twenty percent” with the calculation the layers support: “At $21,000, model tax totals $1,200. The next dollar faces twenty percent; the $2,000 increase added $300 of tax.” The bill, the next dollar and the increase no longer share one misleading rate.
If the next question concerns who gains from a payment funded through taxes, use the whole payment-and-funding comparison. Correct bracket arithmetic alone does not supply the rest of that proposal.
Read alongside the book
Original commentary and discussion material. Read the full personal accounts in Infinite Upside: Building Wealth With Room to Live, by Vijay Sheth.
Compare the payment with the taxes funding it
Who gains after a universal payment is funded?