Private Money and Reserve Management in a Random Matching Model

Some agents, which the authors identify as banks, are endowed with the technology to issue notes and to record-keep reserves with a central clearinghouse, which they call the treasury. The liabilities are redeemed according to a stochastic process that depends on the endogenous trades. The treasury removes the banking technology from banks that are not able to meet the redemptions in a given period. This, together with the market incompleteness, gives rise to a reserve management problem for the issuing banks. The authors demonstrate that "sufficiently patient" banks will concentrate on improving their reserve position instead of pursuing additional issue. The model provides a first attempt to reconcile limited note issue with optimizing behavior by banks during the National Banking Era.