Currency and checking deposits as means of payment

We consider a record keeping cost to distinguish checking deposits from currency in a model where means-of-payment decisions and liquidity of assets are modeled explicitly. An equilibrium exists where checks are used only in big transactions while cash is used in all transactions. Higher inflation or lower reserve requirements raise the deposit interest rate, lower the currency deposit ratio and thereby increase the money multiplier and money supply. Monetary policy has differential impacts on the terms of trade in transactions using different means of payment. During high inflation, individuals economize on the holdings of nominal assets and use checks more frequently, implying higher liquidity of M1.