This paper investigates the response of the price level to random monetary shocks through a model of the fixed cost of changing a nominal price. It shows that, in an inflationary environment, an expansionary monetary shock is accommodated faster than a contractionary monetary shock. Furthermore, when the average rate of monetary expansion increases, the lag in response to a positive shock decreases. The study also proves that the relationship between the expected rate of inflation and the variance of real prices is positive only above a critical level of expected inflation. Copyright 1993 by The Review of Economic Studies Limited.