(B.4), p. 42 — the mean-variance objective qq_N − (γ/2)q²q_D is maximized exactly at q = q_N/(γq_D)

Let $\gamma > 0$ be a risk aversion parameter, $q_D > 0$ the expected conditional variance of the net profit per share, and $q_N \in \mathbb R$ its conditional expectation. The mean-variance objective

attains its maximum over $q \in \mathbb R$ at $q$ if and only if

This is the first-order condition (B.4) of the investor problem (B.1): the optimal demand of each investor type is its expected net profit divided by $\gamma$ times its expected conditional variance. It identifies the maximizers required by market clearing in the model with the demand formulas (B.6).