Consider two households h = A, B and two goods i = 1, 2. Preferences of household A are described by the utility function uA = X1, AX2, A, those of household B by ub = 21,0 + 2x2,B. Use the following three possible allocations x = (X A, XB), y = (YA, YB), and z (2A, 2B) and determine, through pairwise comparison, which allocation is a Pareto-improvement to another or if they are Pareto-noncomparable. X A = (2,3) - (4,2) ZA = (3,3) YA = YB = XB = (5,6) (6,3) - (4,7) ZB = (a) Calculate the corresponding social welfare of the three allocations x,y, and z using i. a (equally weighted) utilitarian social welfare function, ii. a (equally weighted) Nash' social welfare function, iii. a Rawlsian social welfare function. (b) Check if the ranking in the three approaches correspond to the Pareto-criterium (if possible)