Taxes are one side of fiscal policy, and how they are built matters too. Two rates describe any tax: the share of your total income you pay, and the rate on your next dollar. Both are percents of a number.
Key idea
Average tax rate = total tax ÷ income. Marginal tax rate = the tax rate on the next dollar of income. A tax is progressive if the average rate rises with income, regressive if it falls, and proportional (flat) if it stays the same.
Why it works
Under a bracket system, each rate applies only to the income inside its bracket. Picture buckets stacked on top of each other: your income fills the lowest bucket first, then the next. Only the dollars in the top bucket you reach face the top rate. So moving into a higher bracket raises the tax on the dollars above the line, never on the dollars below it. That is why, under bracket rates, a raise always leaves you with more after-tax income, and why the average rate stays below your marginal rate.
Worked examples
Worked example: Tax with brackets
A made-up tax: 10% on income up to \$20,000, 20% from \$20,000 to \$60,000, 30% above \$60,000. Find the tax, the average rate and the marginal rate on \$70,000.
- First bracket: $0.10 \times 20{,}000 = 2{,}000$.
- Second: $0.20 \times 40{,}000 = 8{,}000$. Third: $0.30 \times 10{,}000 = 3{,}000$.
- Total tax $= 13{,}000$. Average rate $= \dfrac{13{,}000}{70{,}000} \approx 18.6\%$. Marginal rate: 30%.
Answer: \$13,000; about 18.6% average; 30% marginal
Worked example: Crossing a bracket
Under the same tax, income rises from \$59,000 to \$62,000. Does after-tax income rise?
- Tax at \$59,000: $2{,}000 + 0.20 \times 39{,}000 = 9{,}800$. After tax: \$49,200.
- Tax at \$62,000: $2{,}000 + 8{,}000 + 0.30 \times 2{,}000 = 10{,}600$. After tax: \$51,400.
- After-tax income rises by \$2,200. Only the \$2,000 above \$60,000 is taxed at 30%.
Answer: Yes, by \$2,200
In the United States, the federal income tax is progressive. Sales taxes tend to be regressive, because lower-income households spend a larger share of their income. A tax that takes the same fixed dollar amount from everyone is regressive too.
Common mistake
Thinking that moving into a higher bracket taxes all of your income at the higher rate, so a raise could lower take-home pay. Only the dollars above the threshold face the higher marginal rate. Check: compute the tax at both incomes; after-tax income always rises under bracket rates.