Question 4: Suppose that an economy is composed of three individuals with incomes y1 = 100, y2 = 50 and y3 = 150. All individuals have an identical utility function uj = In(y;). The government wants to implement an income redistribution programme which will result in individual 3 paying E20 to individual 2. Calculate the social welfare of this economy before and after the programme, and comment on the overall effect of the programme under the scenarios below. Highlight which features of the utility or welfare functions are responsible for the effect you find. a) The government is utilitarian b) The government is Rawlsian c) (Harder) The government applies the following social welfare function, proposed by Amartya Sen: W = U(1 - G) , where U is the average utility, and G is the Gini coefficient - a measure of inequality which, in this case, can be calculated as: G = lu1 - u2| + lu1 - u3| + |42 - 231 3(u1 + U2 + 23)