Schematic of the average tax rate against income for three taxes: a progressive tax whose average rate rises with income, a proportional tax with the same average rate at every income, and a regressive tax whose average rate falls as income rises.

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Download PNGThis schematic diagram shows the average tax rate (% of income) against income for three types of tax, drawn over the same range of income. The progressive line rises from left to right: the tax takes a larger percentage of income as income rises. The proportional line is flat: the tax takes the same percentage of income at every income. The regressive line falls: the tax takes a smaller percentage of income as income rises. The lines differ only in how the average rate changes with income.
Read the vertical axis: it shows the average tax rate, tax paid as a percentage of income, not the amount of tax paid. A regressive tax can still take more pounds from a high earner than from a low earner; what makes it regressive is that the percentage of income it takes falls as income rises. Check any example against that definition: UK income tax, with higher rates on higher bands of income, is progressive, while VAT is usually described as regressive because lower-income households spend a larger share of their income.
Students often call a tax regressive because richer people pay more of it, or progressive because they pay more in pounds. The test is the average rate: a tax is regressive when the percentage of income paid falls as income rises, even if richer people still pay more in total. Another slip is to judge a tax only by its marginal rate on the last pound earned; the lines on this diagram show the average rate on all income.
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