A tractable menu cost model with an aggregate markup drift

This paper extends the menu cost model of Gertler and Leahy (2008) by introducing a drift in the aggregate markup. Assuming that the drift is always negative and not large, consistent with moderate and positive trend inflation, the paper analytically characterizes firms' value function and markup distribution. It derives explicit equations sufficient to close the model in general equilibrium, making the calculation of impulse responses to aggregate shocks as easy as in conventional representative-agent New Keynesian models. In addition, the paper shows two implications of the model. First, the model replicates the empirically observed positive correlation between the inflation rate and the frequency of price changes. Second, the model yields an explicit equation representing the Phillips curve, with additional terms that make the inflation rate more responsive to aggregate shocks.