The question is as follows

Consider a twoperson household. These two people have very similar preferences (that's why they enjoy living together), which are described by the following utility function: 1.5,:(117, y) = :17 + day, where i is the index of a person and a parameter a, is a positive real number (which may or may not be the same for different people). For example, if :11 = 5, then person 1 prefers (1,1) to (5,0) and prefers (0,2) to (1,1) (mm, 2) = 10 > u1(1, 1) = 6 > u1(5,0) = 5). Sometimes they need to make joint decisions. They decide very simply: for any two alternatives, (m',g/) and {:v\the household prefers (1", 3;"). If they pick di'erent alternatisz (say person 1 picks (r' , y') and person 2 picks (3\We switch now to a three- person household (with preferences 1($,'y} = $+c1y, 11.2 (3:? y] = x | (1211;, v.3 (my) 2 x | (1311;). They also decide by voting: if bundle (1",y') collects more votes than the bundle (3",y"), then (1",y'} is selected. A person who is indi'erent does not cast a vote. That is, if 1 and 2 prefer my}, it will be selected regardless of what 3 prefers. If 1 prefers (3," ,y'}, 2 is indierent, and 3 prefers (3\