Solution
= Solution
At the optimal terminal wealth, normalized marginal utility defines an <equivalent martingale measure> $Q$ and hence a marginal utility price
$$
p_Q(Y)=\frac1{1+r}\mathbb E_QY.
$$
This is an arbitrage-free price, so $p_Q(Y)\in I$. Concavity of utility implies that the finite-quantity indifference bid does not exceed its marginal price:
$$
\pi(Y)\leq p_Q(Y).
$$
Consequently
$$
\boxed{\pi(Y)\leq\sup\{p:p\in I\}}.
$$