In the context of the model considered by Grossman [840] (as presented in Sect. 8.2), prove that there exists a Green-Lucas equilibrium price functional \(\phi^{*}: \mathscr{Y} \rightarrow \mathbb{R}^{N}\) which is a sufficient statistic if and only if there exists an equilibrium price functional \(p^{a *}: \mathscr{Y} \rightarrow \mathbb{R}^{N}\) of the artificial economy (where every agent observes the full set of private signals) which is a sufficient statistic.