Banking in the Lagos-Wright Monetary Economy

We introduce banks in a monetary economy and analyze the effect of monetary friction on the banking sector. The basic model is a cash-in-advance economy which is a simplified version of Lagos and Wright's (2005) model. We introduce the banks using Diamond and Rajan (2001) in this economy: Bankers can produce goods more efficiently than depositors but cannot pre-commit to the use of human capital on behalf of the latter. Demand deposit contracts work as a commitment device for bankers, while leaving banks susceptible to bank runs. We show that as the inflation rate increases, the size of the banking sector expands, and the probability of bank runs occurring rises.