e) What allocation(s) would be chosen according to this criterion? Consider a new optimality criterion that we will call the “inequality-averse utilitarian” criterion. This social welfare function penalizes inequality in the following way: SIAU (u1,u2) = u1 + u2??|u1?u2|. where ?>0 is a number that determines the strength of inequality aversion, and |.| is the absolute value function. i. Write social welfare under each allocation as a function of ? ii. Find the best allocation(s) when ?= 0 iii. Find the best allocation(s) when ?= 1 iv. Find the best allocation(s) when ?= 0.5 v. Are there any values of ?>0 for which (0,0) would be chosen according to this criterion? If so, which ones? If not, show that there are no values of ? for which (0,0) would be chosen.