A note on the essentiality of money under limited memory

I use a simplified version of Trejos and Wright's (1995) random matching environment to make a point about when fiat money is essential – that is, when the set of equilibrium outcomes is strictly larger with money than without. Under two natural forms of limited memory, money becomes essential when small, idiosyncratic shocks to production costs are introduced. Monetary equilibria approach full efficiency in the limit as agents become patient, while without money no trade is possible in equilibrium for any discount factor.