Suppose there are only two people, Mr. Mullinax and Ms. Fleming, who must split a fixed income of $500. For Mr. Mullinax, the marginal utility of income is MUm=600-2Im, while for Ms. Fleming, marginal utility is MUf=600-3If , where Im, If are the amounts of income to Mr. Mullinax and Ms. Fleming, respectively.

a) What is the optimal distribution of income if the social welfare function is additive?

b) What is the optimal distribution if society values only the utility of Ms. Fleming? What if the reverse is true? Comment on your answer.

c) Finally, comment on how your answers change if the marginal utility of income for both Mr. Mullinax and Ms. Fleming is constant such that MUm=250= MUf.