3. Consider the following two social welfare functions: W1(U1(9:1)7 - - - 7 UHUEHD W2(U1(IE1), . . . , UH(L'H)) a1U1(a:1) + . . . + aHUH(:cH) 0(1an1($1)+...+ aH anH(33H) where 051 + . . . + 04H 2 1 and In denotes the natural logarithm. a. Will a social planer that acts so as to maximize either of these functions choose a Pareto efcient allocation? Explain. b. For two households, say 1 and 2, calculate the ratios: aw,- 33,: j : 1, 2 (3) 6U2 and relate the expressions you derive to the welfare weights, 041 and a2. c. In maximizing social welfare, the social planner sets the ratios that you computed in part b. to the slope of utility possibilities frontier (see Figure 2 in the Lec ture Slides). What are the implications of the two different welfare functions for equality across households