Overlapping generations and idiosyncratic risk: can prices reveal the best monetary policy?

Incomplete markets in overlapping generations leaves room for Pareto improve-ment. I analyze a model with two goods and idiosyncratic shocks. Intervention can make agents better off in two different situations: one in which agents face shocks on endowments and the other in which shocks affect preferences. I compare market equilibrium with the constrained efficient equilibrium allocation and show that, when shocks are symmetric either only on endowments or only on prefer-ences, prescription of optimal monetary policy depends exclusively on information about relative prices. Monetary policy may be expansionist or contractionist in order to bring prices to their constrained optimal point