Please solve this with in 1 hour

Question 4 (25 points)

A fixed amount of of a cake has to allocated between two individuals = 1,2 with utility functions Utah (with alpha ^ k > 0 ) where x is the amount of the cake allocated to individual h

a) Consider a utilitarian social welfare function, How do the optimal values of r' and r change among the cases alpha ^ 1 alpha ^ 2 ? Provide explanation. (9 points)

b) Consider the following Bernoulli-Nash social welfare function:

W = U ^ 1 * U ^ 2

(3)

What is the allocation maximizing the Bernoulli-Nash social welfare function? How do the optimal values of ' and z change with the preference parameters o' and o? Provide explanation. (9

A fixed amount of x of a cake has to allocated between two individuals h=1,2 with utility functions Uh=hxh (with h>0 ), where xh is the amount of the cake allocated to individual h. a) Consider a utilitarian social welfare function, How do the optimal values of x1 and x2 change among the cases 12 ? Provide explanation. (9 points) b) Consider the following Bernoulli-Nash social welfare function: W=U1U2 What is the allocation maximizing the Bernoulli-Nash social welfare function? How do the optimal values of x1 and x2 change with the preference parameters 1 and 2 ? Provide explanation. ( 9 points) A fixed amount of x of a cake has to allocated between two individuals h=1,2 with utility functions Uh=hxh (with h>0 ), where xh is the amount of the cake allocated to individual h. a) Consider a utilitarian social welfare function, How do the optimal values of x1 and x2 change among the cases 12 ? Provide explanation. (9 points) b) Consider the following Bernoulli-Nash social welfare function: W=U1U2 What is the allocation maximizing the Bernoulli-Nash social welfare function? How do the optimal values of x1 and x2 change with the preference parameters 1 and 2 ? Provide explanation. ( 9 points)