We examine the effect of introducing price stickiness into a stochastic growth model subject to a cash in advance constraint. As has been previously documented, the introduction of price rigidities provides a substantial source of monetary non-neutrality; leads to a strong positive correlation between inflation and output; and contributes significantly to output volatility. We find, however, that this increased volatility arises mostly at the higher than business cycle frequencies; leads to lower persistence in output fluctuations; and causes a deterioration in the ability of the model to explain UK data at all frequencies, but especially over the business cycle. As noted by Chari, Kehoe and McGratten (1996) this failure of exogenous price stickiness to cause persistent output fluctuations is due to strongly pro-cyclical marginal costs. Our results clearly show that, in the context of our model, adding price rigidities is not sufficient to account for business cycle fluctuations.