We study optimal monetary policy in an environment in which money plays a basic role in facilitating exchange, aggregate shocks affect households asymmetrically and exchange may be conducted using either bank deposits (inside money) or fiat currency (outside money). A central bank controls the stock of outside money in the long-run and responds to shocks in the short-run using an interest rate policy that manages private banks’ creation of inside money and influences households’ consumption. The zero bound on nominal interest rates prevents the central bank from achieving efficiency in all states. Long-run inflation can improve welfare by mitigating the effect of this bound.