A definition of a transactions medium is proposed. This is that a transactions medium permits the attainment of otherwise unattainable resource allocations. It is shown that by this definition money can be a transactions medium in a pure exchange, overlapping generations economy. It is also shown that money is a transaction medium only if there are informational asymmetries of a particular type. Finally, it is shown that the set of economies for which money is a transactions medium is not isolated, in a well-defined sense.