One unit of cake has to be distributed between Ann and Bob, with their shares being respectively a and b. Both agents are altruistic, meaning that they care about the share of the other person. More precisely, their utility functions are ua = a + 1 /3 b, ub = b + 1 /4 a

Suppose that you can divide the cake in any way, so that 0 a; b 1; and a + b 1:

(a) Find the classical utilitarian choice of a and b

(b) Find the egalitarian choice of a and b

c) Find the Nash Collective choice of a and b (at least write the maximization problem).