# Question

[This problem is for readers who know some calculus.] Suppose that there are only two people in society, Mark and Judy, who must split a fixed amount of income of \$ 300. Mark’s utility function is UM and his income is IM . Judy’s utility function is UJ and her income is IJ . Sup-pose that
UM = 100 × IM 1/ 2 and UL = 200 × IJ 1/ 2
Let the social welfare function be
W =UM + UJ
What distribution of the total income between Mark and Judy maximizes social welfare?

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