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 MU m = 600 - 2I m , while for Ms. Fleming, marginal utility is MU f = 600 - 3I f , where I m and I f 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 Mu m = 250 = MU f . (This one is subtle.)
The setup should be I m + I f = 500 and 600 - 3I f = 600 - 2I m
(A) Solving this system of two equations and two unknowns gives I m = 300 and I f = 200.
(B) Since these two lines intersect at 0, the optimal distributions would remain I m = 300 and I f =
200.
(C) Since they are constant horizontal lines at $250, any distribution of the $500 will be
optimal.
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