The classical and early neoclassical economists knew that the essential function of money was its role as a medium of exchange. Recently, this idea has been formalized using search-theoretic noncooperative equilibrium models of the exchange process. The goal of this paper is to use a simple model of this class to analyze four substantive issues in monetary economics: the interaction between specialization and exchange, dual fiat currency regimes, the welfare improving role of money, and the susceptibility of monetary economies to extrinsic uncertainty.