Changes in the legal and technological environment in the U.S. have created the possibility of private banknote issue, or its electronic equivalent. We wish to understand the implications of this possibility for economic performance. Accordingly, we construct and analyze a dynamic general equilibrium model in which privately-issued liabilities may circulate, either by themselves, or alongside a stock of outside money. In each case we provide results on the existence and multiplicity of equilibria, and we characterize local dynamics in a neighborhood of a steady state. Our results support Friedman's (1960) idea that circulating private liabilities as associated with endogenous (or "excess") volatility. But implementing Friedman's (1960) advice? the government should ban private issuance of close currency substitutes? causes significant inefficiency in our model. And implementing the polar opposite advice of Hayek (1976) and Fama (1980)? that the government should withdraw from currency issuance altogether in the presence of circulating private liabilities? also is often constrained suboptimal in our economies. Instead, our economies have both public and private circulating liabilities as part of an optimal monetary arrangement.