In this paper I show that a lax anti-counterfeiting policy is inconsistent with price stability. I use a deterministic matching model with no commitment and no enforcement. An intrinsically worthless but perfectly durable object called a ‘note’ can be produced by banks at a given cost, but also by nonbanks at a (possibly) higher cost. Counterfeiting occurs when nonbanks produce notes in equilibrium. When it is cheap for nonbanks to produce notes, or the technology used to detect counterfeits is poor, counterfeits are circulating in equilibrium and trade is only implemented with a growing stock of notes (thus creating inflation). Finally, I show that the highest welfare level is achieved when counterfeiting is costly, or when the detection of counterfeits is of high quality.