In the setting of Exercise 5.3, remove the assumption that asset returns are normally distributed and assume instead that the \(I\) agents have quadratic utility functions of the form

\[u^{i}(x)=a_{i} x-\frac{b_{i}}{2} x^{2}, \quad \text { for all } i=1, \ldots, I\]

Assume furthermore that the initial endowments of the agents and the asset returns are such that the optimal consumption plans of the agents always remain in the range where the utility functions are increasing (i.e., \(\widetilde{W}^{i *}