Currency and Debit Cards as Means of Payment

We consider a search monetary model with currency and a bank deposit-based payment instrument such as debit cards, in which means-of-payment decisions and liquidity of assets are modeled explicitly. Currency is subject to thefts, while costly technology of record keeping and monitoring is needed for accepting debit cards. When the acceptability of debit cards (which implies liquidity of bank deposits) is endogenously determined, there may exist multiple equilibria. In the equilibrium with a lower acceptance rate of debit cards, higher inflation raises the liquidity of bank deposits and output, in contrast to the case in which the acceptability of debit cards is exogenously imposed. Hence, the question of whether to endogenize the acceptability of means of payment has monetary policy implications.