Principles of Macroeconomics / Unit 14 MAC 1309 worked example, 60 to 90 seconds
Classifying a Tax from a Table
The idea
Given incomes and tax paid, classify each tax. Compute tax as a share of income at each level and read the direction of the shares. Rising shares mean progressive, constant shares proportional, falling shares regressive. Do not classify from the dollar amounts, which rise under all three.
In practice
Take incomes of 20,000, 50,000 and 100,000. The first tax collects 2,000, 5,000 and 10,000: shares of 10, 10 and 10 percent, so it is proportional. The second collects 1,000, 4,000 and 12,000: shares of 5, 8 and 12 percent, so it is progressive. The third collects 1,600, 3,000 and 4,000: shares of 8, 6 and 4 percent, so it is regressive. Notice that the dollars collected rise with income under all three, including the regressive one.
Where people slip
That last observation is the whole trap. The regressive tax took 4,000 from the highest earner and 1,600 from the lowest, and it is still regressive, because 4,000 is a smaller slice of 100,000 than 1,600 is of 20,000. Anyone classifying by the dollar column gets all three wrong in the same way.
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