1. An economy has $72, to divide between Hamlet and Ophelia. Hamlet has the utility function U[H](m[H]) = 7m[H], where m[H] denotes his quantity of money. Ophelia has the utility function u[O]= U[O](m[O]) = 42sqrt(m[O]), where m[O] denotes her quantity of money.
A different social welfare function is the “Rawlsian” function W(u[H],u[O]) = min(u[H],u[O]), meaning that welfare equals whichever of the utility values is smaller.
[H] means ("sub-H"), and [O] means ("sub-O")
(A) Calculate the allocation of money that maximizes utilitarian social welfare. In that allocation, what is the maximized value of social welfare? How much money does Hamlet receive? How much money does Ophelia receive?
(B) Calculate the allocation of money that maximizes Rawlsian social welfare. Explain how maximizing the Rawlsian social welfare does or does not achieve equality in this economy.
(C) Given Hamlet’s utility function, does he prefer the allocation that maximizes utilitarian social welfare or the allocation that maximizes Rawlsian social welfare?