Demand for cash balances in a cashless economy

We study the demand for cash balances in the year 2050, when people exclusively use debit cards for all transactions. Money no longer serves as a medium of exchange. However, money still retains its roles as unit of account, numeraire and store of value. We capture these roles in a multi-period model with intertemporal uncertainty regarding prices and the interest rate on bonds, the alternative asset. A key result of our analysis is that the standard negative relationship between money demand and the bond interest rate is seen to be part of a larger economic reality encompassing a broader range of empirically testable implications, including the possibility that the relationship may be positive. We develop formal structural restrictions under which the positive relationship between cash balance demand and the bond interest rate is not only a possible outcome, but an explicit prediction of the model.