Consider a normally distributed loss (tilde{x} sim mathscr{N}left(mu, sigma^{2} ight)) with (mu>0) and an agent with exponential

Consider a normally distributed loss \(\tilde{x} \sim \mathscr{N}\left(\mu, \sigma^{2}\right)\) with \(\mu>0\) and an agent with exponential utility function \(u(x)=-\exp (-a x) / a\), for \(a>0\). Verify that, in the setting of Proposition 3.24, if \(\lambda>0\), then the optimal insurance demand \(w^{*}\) is less than one.