Banks as Suppliers of Medium of Exchange and Optimality of 100% Reserve Banking

There are three types of agents - households, firms and banks - in the model economy: Households supply labor to firms and banks, firms supply commodities to households, and banks receive deposits from households and make loans to firms. There are two types of medium of exchange, currency and deposit. Commodites can be purchased both by currency and by deposit at different transaction costs. In this economy, a stationary equilibrium is shown to exist for any given level of the reserve requirement ratio. The stationary equilibrium is optimal, if and only if it is associated with 100% reserve requirement ratio. The equilibrium deposit interest rate, when the reserve requirement ratio is 100%, is the negative of the marginal cost of servicing the deposit balance.