Money, unit of account, and nominal rigidity

In order to characterize the properties required to fulfill the roles of money as a unit of account (UoA) as well as a medium of exchange (MoE), we consider the choice of a UoA in the context of a micro-founded model where inflation uncertainty exists and some conversion cost is incurred in using a UoA that is different from an MoE. We show that it is not the level of inflation but its volatility that matters for the choice of a UoA. In the presence of inflation uncertainty, money can still become both an MoE and a UoA as long as the conversion cost is higher than its maximum buyers are willing to bear for ensuring stable consumption against inflation uncertainty. Also, the choice of a UoA in the presence of fiat money as an MoE determines endogenously the nominal price rigidity or flexibility. An economy adopting money as a UoA yields the short-run nominal rigidity and the Phillips-curve relationship.