Consider an economy as described at the beginning of Sect. 8.3, under the additional assumptions that \(a^{i}=a>0\) and \(\sigma_{\varepsilon^{i}}^{2}=1\), for all \(i=1, \ldots, I\). Assume furthermore that each agent has a random initial endowment \(\tilde{e}^{i}\) (in terms of units of the risky asset), which is normally distributed with zero mean and variance \(\sigma_{e}^{2}\), for all \(i=1, \ldots, I\). Show that this economy admits the partially revealing GreenLucas equilibrium price functional given in (8.23).