Part I: Lorenz-Curve and Gini Coefficient (0.5 mark) Consider the following (very roughly measured) distribution of income in the economy, Share of Households Cumulative Share of Income 0 0 1/2 1 1 Thus, the distribution function says that the lower half of the households earns one fourth of the total income in the society. 1. Draw the Lorenz-curve for the economy. 2. Calculate the Gini-coefficient. Part II: Redistributing Income (0.5 mark) Suppose that in an economy composed of three people we can measure each person's utility cardinally. Suppose, too, that we can use three possible institutions - A, B, and C- to organize economic activity in this economy. The problem is to choose one of the three institutions. The utility of each person under each institution is given below. Institution Person I's utility Person 2's utility Person 3's utility A 45 45 45 B 75 60 30 C 78 63 21 1. According to Rawls's difference principle, which institution is preferred? 2. Suppose that you would be one of the three people in this economy, but you don't know which one. Which institution would you choose? If each person maximizes expected utility and if each attaches probability 1/3 to being any one person, which is the preferred institution? 3. Now suppose that each of the three does know which person he or she will be. If the institution is chosen by majority rule, which one will be chosen by self-interested individuals