Let us consider an economy with two agents \(a, b\), two possible states of the world with strictly positive probabilities \((\pi, 1-\pi)\) and a single consumption good. Suppose that the endowments of agents \(a\) and \(b\) satisfy \(e_{1}^{a}+e_{1}^{b}>e_{2}^{a}+e_{2}^{b}\), so that there is aggregate risk. Show that the prices \(p_{1}, p_{2}\) of the contingent goods in correspondence of an interior Pareto optimal allocation satisfy \(p_{1} / p_{2}<\pi /(1-\pi)\).