What is the difference between a progressive tax and a flat tax?

A progressive tax charges a higher rate as the amount being taxed grows, so someone with a bigger income pays a bigger share of it. A flat tax charges one single rate on the taxable amount, after any deductions or exemptions. The difference is whether the rate climbs with income or stays put.

Here is a made-up example. Suppose the first 10,000 of income is taxed at 0 percent, income from 10,000 to 50,000 at 20 percent, and anything above 50,000 at 40 percent. Each rate applies only to the slice of income inside its band. Someone earning 60,000 pays nothing on the first 10,000, 8,000 on the next 40,000 and 4,000 on the last 10,000: 12,000 in all. Their marginal rate, the rate on their last pound, is 40 percent, but their average rate is 20 percent. So crossing into a higher band never means paying the higher rate on all of your income, only on the part above the line. That gap between average and marginal rate is the mark of a progressive tax. The reverse is a regressive tax: sales taxes and tariffs, for instance, can take a larger share of a poor household's income, because food and basics cost the same whoever buys them.

Britain's first modern income tax already worked this way. William Pitt the Younger introduced it in December 1798 to pay for weapons for the war with revolutionary France. It began at about 0.83 percent on incomes over 60 pounds and climbed to 10 percent above 200 pounds. Pitt hoped to raise 10 million pounds, but 1799 receipts came to just over 6 million.

A flat tax is not always as flat as it sounds. A flat rate with a large exemption behaves like a progressive tax, because the first slice of income is not taxed at all. Which design is better is something people argue about: supporters of flat taxes stress simplicity, critics reply that a progressive tax can be simple too, and economists disagree about the wider effects of progressive taxation.