A model with private information that supports conventional arguments for a government monopoly in supplying circulating media of exchange is constructed. The model also yields rate-of-return and velocity predictions which are consistent with observations from free banking regimes and fiat money regimes. In a laissezfaire banking equilibrium, fiat money is (essentially) not valued, and the resulting allocation is not Pareto optimal. However, if private agents are restricted from issuing circulating notes, there exists an equilibrium with valued fiat money that Pareto dominates the laissez-faire equilibrium and is Pareto optimal within a restricted class of allocations. Journal of Economic Literature Classification Numbers: 020, 310.