This article concerns an infinite horizon economy where trade must occur pairwise, using a double auction mechanism, and where fiat money overcomes lack of double coincidence of wants. Traders are anonymous and lack market power. Goods are divisible and perishable, and are consumed at every date. Preferences are defined by utility‐stream overtaking. Money is divisible and not subject to inventory constraints. The evolution of individual and economywide money holdings distributions is characterized. There is a welfare‐ordered continuum of single price equilibria, reflecting indeterminacy of the price level rather than of relative prices.