TThis 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 \(U_{M}\) and his income is \(I_{M}\). Judy's utility function is \(U_{y}\) and her income is \(I_{y}\). Suppose that

\[ U_{M}=100 \times I_{M}^{1 / 2} \text { and } U_{y}=200 \times I_{J}^{1 / 2} \]

Let the social welfare function be

\[ W=U_{M}+U_{J} \]

What distribution of the total income between Mark and Judy maximizes social welfare?