3) During the recent election and resulting tax reform, there has been discussion about the wealthiest people in the nation. A Federal Reserve study indicates the following: The top 1 percent of earners receive about a fifth of the country's pre-tax income, about double their share 30 years ago. They controlled nearly a third of the nation's financial a and about 28 percent of non-financial assets. Money may not buy happiness, but the survey suggests it buys good health. About 90 percent of the 1 percenters describe themselves as being in excellent or good health, compared with 75 percent of everybody else. A Lorenz curve L(x) gives the proportion of the total income earned by the lowest r percent of population. Economists consider it to be a measure of social inequality. L(0.25) = 0.10 means that the poorest 25% of the households earn 10% of the total income L(0.90) = 0.55 means that the poorest % earn % of the total income. Equivalently, the richest % earn %. Properties of the Lorenz curve: (explain/justify each property) o The domain is [0, 1]. The range is [0, 1]. Thus, the graph lies inside the unit square in first quadrant. O L(0) = L(1) = o L(x) is an increasing function