In the setting of Proposition 3.24, for a given utility function \(u\), define \(\lambda^{*}\) by

\[\lambda^{*}=\frac{\operatorname{Cov}\left(\tilde{x}, u^{\prime}\left(w_{0}-\tilde{x}\right)\right)}{\mathbb{E}[\tilde{x}] \mathbb{E}\left[u^{\prime}\left(w_{0}-\tilde{x}\right)\right]}\]

Show that, if the insurance premium \(\lambda\) is greater than \(\lambda^{*}\), then the optimal insurance demand \(w^{*}\) consists in buying zero units of the insurance contract.