Sherry's utility is \(U_{S}\) and her income is \(Y_{S}\). Marsha's utility is \(U_{M}\) and her income is \(Y_{M}\).

Suppose it is the case that:

\(U_{S}=100 Y_{S}^{1 / 2}\), and \(U_{M}=100 Y_{M}^{1 / 2}+0.8 U_{S}\)

Define the Pareto efficient redistribution, and explain why the concept is relevant in this situation. Suppose that initially Sherry and Marsha both have incomes of \(\$ 100\). Assuming that the social welfare function is additive, what happens to social welfare if \(\$ 36\) is taken away from Marsha and given to Sherry?