The nature of price dynamics has long been thought important for the origin and duration of business cycles. To investigate this topic, we construct a dynamic stochastic general equilibrium macroeconomic model in which monopolistically competitive firms face fixed costs of changing the nominal prices of final goods. These prices are thus changed infrequently and discretely. The framework captures major features of the price dynamics stressed by the New Keynesian research program, particularly work on (s, S) pricing rules. However, by treating firms as heterogenous with respect to the size of fixed costs of price adjustment, we are able to study a wider range of issues than in the prior literature. For example, we explore how the nature of optimal price-setting depends on (i) the extent of persistence of variations in the money stock and (ii) the interest elasticity of money demand. Further, our model can be used to study a wide range of aspects of the positive and normative economics of monetary policy. We illustrate these topics by considering the consequences of changing the rate of inflation and by evaluating alternative policy rules.