A tax authority must decide on a social insurance scheme. It knows that half the population will unemployed this year with only $400 in income from odd jobs. The other half will earn $40000 each. Each individual has a utility function U = 2x^(1/2) where x is the individual’s income. Consider the following two possibilities.

(i) The tax authority taxes everyone with income at a flat rate of 10%. It then refunds an identical amount to each individual, independent of income.

(ii) The tax authority taxes everyone with income at a flat rate of 10%. It then refunds an identical amount to each individual according to the percentage of taxes paid. So for instance, if the high income group pays, on average, 60% of the taxes, then they would get 60% of the total revenue as a rebate.

Compare the proposals under the Benthamite (Utilitarian) and Rawlsian social welfare functions. How do these proposals rank under each SWF? (Note that all calculations can be done on a per-capita basis).