Proportional Tax vs Regressive Tax

The dollar amount goes up while the rate comes down

Compare two illustrative households, one earning $30,000 and one earning $150,000. Under a proportional income tax of 10 percent the first pays $3,000 and the second pays $15,000. The second household hands over five times as many dollars, but both give up exactly 10 percent of income, so the tax is proportional by definition. Now switch to a 6 percent sales tax and assume the lower-income household spends 90 percent of its income while the higher-income household spends 50 percent and saves the rest. The first household spends $27,000 and pays $1,620, which is 5.4 percent of its income. The second spends $75,000 and pays $4,500, which is 3 percent of its income. The richer household still pays about 2.8 times as many dollars, yet its average tax rate is a little over half as high, and that falling rate is what makes the tax regressive. Saving is the mechanism. A tax whose base is spending misses the part of a large income that is not spent, so the base shrinks as a share of income as income rises. The same logic applies to any fixed charge, such as a flat license fee, which is a heavier share of a small income. Average rates are calculated at /calculate/effective-tax-rate.

Regressive describes the rate, not who writes the bigger check

Students lose points by calling a tax progressive because the rich pay more money under it. Progressivity is always about the share of income taken, so the comparison has to be a rate against a rate. That also explains the marginal and average relationship in the table above. When the extra dollar of income is taxed more lightly than the average dollar has been, the average rate is dragged down, and a falling average rate is the definition of regressive. A payroll tax charged only up to an earnings ceiling is the cleanest example of that design. Below the ceiling every extra dollar is taxed at the same rate, so the tax is proportional over that range, and above the ceiling extra dollars go untaxed, so the average rate slides downward as earnings climb. Two qualifications are worth carrying into an essay. First, the answer depends on what the tax is measured against. A consumption tax measured against annual income looks clearly regressive, while the same tax measured against lifetime income looks closer to proportional, because income saved in working years is eventually spent. Second, the distributional picture can be read off /glossary/lorenz-curve. A proportional tax scales everyone's income by the same factor, leaving the curve exactly where it was, while a regressive tax pushes it further from the diagonal and raises the summary number described at /glossary/gini-coefficient.

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