Question: 3. One unit of cake has to be distributed between Ann and Bob, with their shares being respectively a and b. Both agents are

3. One unit of cake has to be distributed between Ann and Bob, with their shares being respectively a and b. Both agents are

3. 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 1 a + -b 3 Ua b+ -a 4 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 (10 points) (b) Find the egalitarian choice of a and b (15 points) (c) Find the Nash Collective choice of a and b (at least write the maxi- mization problem).(5 points)

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