A three-person society has a Rawlsian social welfare function U =min u1(c1), u2(c2), u3(c3)

defined over the utilities of the three citizens. ci is the consumption of citizen i. Suppose

u1(c1) = c1, u2(c2) = c2, and

u3(c3) = 2(c3)^0.5

. The society has total 100 units of consumption to divide among

the three citizens. What allocation will this society choose to maximize social

welfare if the government has full control to allocate the units of consumption as

it likes? Suppose instead that initially 80 units belong to citizen 1 with 10 units

belonging to each of citizens 2 and 3 (this is called an endowment). The gov-

ernment loses $0.50 for each unit it takes away from citizen 1 to give to others.

Will the government still raise social welfare by implementing the solution you

found above or would it be better off leaving the citizens to consume their initial

endowment? Why?