How Are Income Tax and Sales Tax Calculated?
Inequality and poverty
What you will learn
- Tax each income slice at its own marginal rate.
- Apply the model to an original scenario and justify its limits.
Essential definitions
- Tax band
- A range of taxable income subject to a specified marginal rate.
- Tax-inclusive price
- The final price containing both the pre-tax value and the tax.
Define the income and the bands
Taxable income is the amount to which the tax schedule applies after any relevant allowances. Gross income is income before these deductions. Check which is given so an allowance is not subtracted twice. In a banded system, only income inside a band receives that band's marginal rate.
For annual taxable income of 50,000 currency units, suppose the first 10,000 is untaxed, the next 20,000 is taxed at 10%, and the remainder at 25%. The taxable slices are 10,000, 20,000 and 20,000. Multiply each slice by its decimal rate, then add the tax amounts. Applying 25% to the whole income would ignore the lower bands.
Interpret average and marginal rates
Total tax is 0 + 2,000 + 5,000 = 7,000. Average tax rate = total tax ÷ total income × 100 = 14%. The marginal rate remains 25%. If another 1,000 is earned inside the top band, tax rises by 250 and disposable income by 750.
Use annual tax with annual income, or monthly with monthly; mixing periods produces a meaningless burden. Keep currency amounts separate from rates and round at the final stage. The average rate measures the overall burden, while the marginal rate helps explain incentives for an extra unit of earnings.
Recover sales tax from the correct base
Let t be the sales-tax rate as a decimal and B the pre-tax price in currency units. Tax is B × t and the final price is B × (1 + t). A pre-tax price of 80 at 20% gives tax of 16 and a final price of 96.
If the supplied final price P is 120, first divide by 1.20 to find B = 100. The tax contained is 20, not 24. Equivalently, tax = P × t ÷ (1 + t). These calculations identify a statutory payment; judging the household's full burden also requires income, economic incidence and publicly financed benefits.
Hypothetical worked application
- Income-tax bill: 0 + 20,000 × 0.10 + 20,000 × 0.25 = 7,000 units.
- Average income-tax rate: 7,000 / 50,000 × 100 = 14%.
- Indirect tax within a final price of 120 at 20%: 120 × 0.20 / 1.20 = 20 units.
Marginal income-tax rate 25%; average rate 14%; tax-inclusive sales tax 20 units.
Apply and evaluate
- Tax computations need a stated tax base, period and treatment of allowances.
Common misconceptions
- Do not multiply a tax-inclusive price directly by the quoted tax rate.
Knowledge check
A final price is 110 including a 10% tax. What is the tax?
Real-world application
Poverty lines depend on a PPP vintage
5 June 2025: The World Bank’s June 2025 update set the international extreme-poverty line at $3.00 per person per day in 2021 PPP international dollars, replacing $2.15 in 2017 PPP dollars.
The change is not an ordinary market-exchange-rate conversion. PPP data and the national poverty lines underlying the benchmark changed. Comparing poverty counts across releases requires a consistent method; a statistical revision is not itself proof that living conditions suddenly worsened.
World Bank, June 2025 update to global poverty lines ↗Historical evidence checked 9 October 2026. The model interpretation is an original teaching application.
What to remember
Tax each income slice at its own marginal rate. For a tax-inclusive price, recover the pre-tax base before calculating the tax contained in it.
Completion is your own reflection on learning, not a test score. Syllabus references: 3.4.13, 3.4.14.
Sources and applications
Lessons in this section
- What Is Economic Inequality?
- How Do Lorenz Curves and Gini Coefficients Work?
- How Do We Draw a Lorenz Curve from Quintiles? · HL
- How Is Poverty Measured?
- Why Does Inequality Persist?
- How Do Taxes Affect Income Distribution?
- How Are Income Tax and Sales Tax Calculated? · HL
- How Can Transfers and Public Services Reduce Poverty?
- How Can Policy Support Incomes and Fair Access to Work?
Guest progress is saved on this browser. Log in to save across devices; import is optional.