Sometimes politicians propose a "flat" income tax, where everybody pays the same percentage of their income, no matter how much they make. They argue that this is more fair that a "progressive" income tax, which has richer people paying a higher percentage of their income than poorer people. Others argue that a flat tax is unfair, pointing to the Diminishing Marginal Utility of Wealth. What should be equalized, they claim, is not the percentage of income that people must pay, but the percentage of utility is costs them to pay whatever tax they owe. Someone making this argument could illustrate their point using Bernoulli's simple utility function (see p. 191 in the textbook). They might compare the tax burdens of two hypothetical people under a flat tax regime--Alice, who makes $100,000, and Bob, who makes $50,000. If we take one unit of wealth to be $10,000, that places Alice at 10 on Bernoulli's x-axis and Bob at 5. Suppose the flat tax is 20% of income. After paying it, Alice takes home $80,000 for the year, while Bob takes home $40,000. The opponent of the flat tax can point out that Bob has lost a higher percentage of his utility