= Solution
<Risk neutrality> means indifference between a random <portfolio wealth> and its certain <expected value>. For increasing twice differentiable <expected utility> preferences, this corresponds to an <affine function> $u(w)=Aw+C$ with $A>0$ on the relevant wealth interval. Maximizing <expected utility> then amounts to maximizing <expected return>:
$$
\mathbb Ew=T[1+pg+(1-p)b]+x[r-pg-(1-p)b].
$$
The coefficient of $x$ is strictly negative. Consequently \b[the unique optimum is $x_*=0$: invest all initial wealth in equity]. <Risk neutrality> here is a preference property, distinct from the pricing use of a <risk-neutral measure>.
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