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 than Alice has, which they claim is unfair. Figure out what percentage of utility Alice and Bob lose under this hypothetical flat tax. For each person, figure out their utility before the tax is levied and then after they pay the 20%. Subtract one figure from the other, then divide the difference by their pre-tax utility. In other words, for each person, calculate the following: (Utility before tax - utility after tax) Utility before tax