Which distribution is preferred by a rawlsian social

Question

Consider the three alternative allocations of money (m) in an economy composed of three people, with people labeled A, B, C, and alternative allocations labeled X, Y, Z. The values in the 9 cells are the moneys accruing to each person under each alternative allocation (You may wish to look back at Chapter 18):

Person	A	B	C
Allocation X	5	5	5
Allocation Y	7	5	4
Allocation Z	11	6	0

a) Which distribution is preferred by a Rawlsian Social Welfare Function? Assume that utility is defined as u_i = m_i and recall that Rawlsian Social Welfare function would be equal to the minimum utility experienced by any person under the allocation.

b) Which distribution is preferred by a Utilitarian Social Welfare Function that is defined as Σ(u_i) where u_i = m_i, ?

c) Which distribution is preferred by a different Utilitarian Social Welfare Function that is defined as Σ(u_i), where u_i = m_i^1/2?