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}

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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.

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