- 27 Consider A Distribution Of Income For Three People With Incomes 1 2 3 A Verify That The Gini Index Is 0 22 1 (26.3 KiB) Viewed 10 times
27. Consider a distribution of income for three people with incomes (1, 2, 3).< (a) Verify that the Gini index is 0.22. Draw the Lorenz curve. How would it change if the distribution became (1.5, 1.5, 3)? How would it change if the distribution became (1, 2, 2, 3)? Consider the implications for inequality in each case, as compared to the (1, 2, 3) distribution.< (b) Starting from the (1, 2, 3) distribution, consider a redistribution toward the middle, such that the new distribution is (0.75, 2.5, 2.75). Do you think inequality is higher or lower?< ( 28. The Gini index is very insensitive to even large changes in the income of the richest person. Imagine doubling the income of the richest person, giving (1, 2, 2x). Show that the new Gini index is 0.66. At the other extreme, imagine doubling the income of either of the poorest two people, to give the distribution (2, 2, x) or (1, 4, x). Show that (either way) the new index only drops to 0.64.<