A model of private bank-note issue

A random-matching model (ofmoney) is formulated in which there is complete public knowledge of the trading histories of a subset of the population, called the banking sector, and no public knowledge of the trading histories of the complement of that subset, called the non bank sector. Each person, whether a banker or a non banker, is assumed to have the technological capability to create indivisible and durable objects called notes. If outside money is indivisible and sufficiently scarce, then the optimal mechanism is shown to have note issue and note destruction (redemption) by members of the banking sector.