Abstract 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.

The history of money has always been intertwined with the history of banking. Nevertheless, very few papers have studied banking in a rigorous monetary environment. This thesis demonstrates that it is crucial to integrate these two literatures. I present three theories of money and banking, each generating results that are drastically different from those of the traditional banking models without microfoundations for money. Chapter 1 addresses the problem of monitoring the monitor in a model with private information and aggregate uncertainty. There is no need to monitor a bank if it requires loans to be repaid partly with money. A market arises at the repayment stage and generates information-revealing prices that perfectly discipline the bank. The mechanism also applies when multiple banks exist. With multiple banks, a prohibition on private money issuing not only eliminates welfare-improving money competition but also triggers free-rider problems among banks. In Chapter 2, I develop a dynamic model to address the following question: when both individuals and banks have private information, what is the optimal way to settle debts? I establish two main results: first, markets can improve upon the optimal dynamic contract in the