Solution
= Solution
Use the optimizer for $Z_0$ also with $Z_1$. Strict increase of $U$ and a strict inequality on a positive-probability event give $u(Z_1)>u(Z_0)$.
= Solution
Use the optimizer for $Z_0$ also with $Z_1$. Strict increase of $U$ and a strict inequality on a positive-probability event give $u(Z_1)>u(Z_0)$.