Average Tax Rate vs Sales Tax
Average Tax Rate and Sales Tax are two Public Finance & Taxation concepts in AP Economics that students often mix up. The average tax rate is total taxes paid divided by total income. A sales tax is a tax on goods and services collected at the point of sale as a percentage of the price. Here is how they compare side by side.
It measures the overall share of income paid in tax, while the marginal rate applies only to the last dollar. In a progressive system the average rate is below the marginal rate.
It is generally considered regressive because lower-income households spend a larger share of their income on taxed consumption. It is a major revenue source for U.S. state and local governments.
Average Tax Rate vs Sales Tax: A Ratio You Compute Against a Tax You Compute It On
| Average Tax Rate | Sales Tax | |
|---|---|---|
| What the term names | A ratio, tax paid divided by a chosen denominator | A levy charged as a percentage of the price of a purchase |
| Whether the posted number is the answer | Nothing is posted, it has to be computed after the fact | The posted rate applies to the pre-tax price, so it is not the share of what you hand over |
| Denominator | Whatever you name: income, spending, or a lifetime of either | The pre-tax price of the goods bought |
| Treatment of saving | Income saved pulls the income-based ratio down | Untouched until the money is spent |
| What it settles about progressivity | Everything, since the labels are defined by how it moves with income | Nothing on its own, since every buyer faces the same posted rate |
| Who produces the number | The analyst, after choosing what to divide by | The register, automatically, at the moment of sale |
| Where each appears in a question | Compare two taxpayers, or label a system progressive or regressive | Compute tax on a purchase, or shade revenue on a market diagram |
A 25 percent sales tax takes 20 percent of what you actually hand over
Two denominators are in circulation and they give different numbers for the same tax. A good priced 80 before tax, charged a sales tax of 25 percent, costs 100 at the register, and the tax inside that purchase is 20. Quoted on the pre-tax price, which is how a register-added sales tax is normally advertised, the rate is 20 divided by 80, or 25 percent. Quoted on the total handed over, which is how a value-added tax buried in a shelf price is normally described, the average rate on that purchase is 20 divided by 100, or 20 percent. Converting between them is mechanical. The tax-inclusive figure equals the posted rate divided by one plus the posted rate, and 0.25 divided by 1.25 is 0.20. Going the other way, 0.20 divided by 0.80 gives 0.25 back. Neither number is wrong, and a comparison between two countries that mixes the conventions is. For an average tax rate the lesson is that the ratio means nothing until the denominator is named, and a sales tax is the cleanest place to see it, since one purchase supports two defensible answers five percentage points apart.
One household, three denominators, three different verdicts on the same tax
Take a household with income of 120,000 facing a sales tax of 20 percent on pre-tax prices. It buys goods with a pre-tax value of 75,000, so the tax is 15,000, the total outlay is 90,000, and 30,000 is saved. Now compute the average rate three ways. Against pre-tax spending it is 15,000 divided by 75,000, or 20 percent, which simply recovers the posted rate. Against the total handed over it is 15,000 divided by 90,000, or 16.7 percent. Against income it is 15,000 divided by 120,000, or 12.5 percent. The tax did not change and the household did not change. Only the question changed. That is why a consumption tax looks regressive against annual income, since households saving less have a higher ratio, and roughly proportional against consumption, since everyone meets the same posted rate on what they buy. Whoever eventually spends the 30,000 pays the tax then, which is the lifetime version of the same argument. One exam convention is worth memorizing: progressive, proportional and regressive are defined by what the average rate does as income rises, so income is the denominator unless a question says otherwise. See /glossary/regressive-tax, and compute one at /calculate/effective-tax-rate.
Frequently asked questions
How do you calculate the average tax rate for a sales tax?
Divide the sales tax paid by whichever total you are judging the tax against, then say which one you used. A household paying 15,000 of sales tax on income of 120,000 has an average rate of 12.5 percent measured against income, 16.7 percent measured against the 90,000 it actually handed over, and 20 percent measured against the 75,000 of pre-tax prices. All three are correct arithmetic, and only the first one answers a question about progressivity.
Why is the sales tax rate different from the share of your spending it takes?
Posted sales tax rates are charged on the pre-tax price, so the tax is a smaller fraction of the larger total you end up paying. A 25 percent tax on a good priced 80 adds 20 and brings the bill to 100, which is 20 percent of the money handed over. Converting is one line: the posted rate divided by one plus the posted rate. Value-added taxes are usually quoted the other way round, inside the shelf price, so two identical taxes can be advertised with different-looking numbers.
Which denominator should you use to decide whether a tax is regressive?
Income, whenever the question uses the words progressive, proportional or regressive, because those labels are defined by what the average rate does as income rises. Consumption or lifetime income is the denominator policy analysts reach for when arguing that a sales tax is less regressive than it looks, since savings are taxed once they are eventually spent. Naming the denominator before arguing is the whole trick, and answers that skip it tend to contradict themselves.
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