Asset prices, liquidity, and monetary policy in an exchange economy

I formulate a model in which money coexists with equity shares on a risky aggregate endowment. Agents can use equity as a means of payment, so shocks to equity prices translate into aggregate liquidity shocks that disrupt the mechanism of exchange. I characterize a family of optimal monetary policies and find that the resulting equity prices are independent of monetary considerations. I also study a perturbation of the family of optimal policies that targets a positive constant nominal interest rate and find that in this case the real equity return includes a liquidity return that depends on monetary considerations.