This paper develops a model of a monetary economy where firms face both aggregate inflation shocks and idiosyncratic productivity shocks, and can only change prices by incurring real "menu costs." The authors calibrate the model using a new dataset on individual prices from Klenow and Kryvtsov, and find that the model's predictions for the effects of high inflation on price change frequency align well with Israeli evidence. The model is then used to conduct numerical experiments on the economy's response to credible and non-credible disinflations and other shocks. The results show that monetary shocks do not induce large or persistent real responses. The model predicts that idiosyncratic shocks account for most price adjustments in the U.S., and simulations confirm this intuition. Despite the presence of idiosyncratic shocks, new prices reflect both firm-level and aggregate shocks, making it difficult to obtain significant persistence in monetary shocks. Simulations also demonstrate that even small inflationary shocks, if not sufficient to trigger a price change, are quickly reflected in new prices as firms react to other shocks. The economy exhibits very small real effects of monetary instability, with simulated time series showing a tenfold lower variance in aggregate output compared to recent U.S. data. The estimated Phillips curve is flat, indicating that a one percentage point reduction in the inflation rate depresses output by only 0.05%. Similar results hold for different policy experiments, suggesting that credible disinflations have no real effects, while non-credible disinflations result in a decline in production that never exceeds one percent of GDP.This paper develops a model of a monetary economy where firms face both aggregate inflation shocks and idiosyncratic productivity shocks, and can only change prices by incurring real "menu costs." The authors calibrate the model using a new dataset on individual prices from Klenow and Kryvtsov, and find that the model's predictions for the effects of high inflation on price change frequency align well with Israeli evidence. The model is then used to conduct numerical experiments on the economy's response to credible and non-credible disinflations and other shocks. The results show that monetary shocks do not induce large or persistent real responses. The model predicts that idiosyncratic shocks account for most price adjustments in the U.S., and simulations confirm this intuition. Despite the presence of idiosyncratic shocks, new prices reflect both firm-level and aggregate shocks, making it difficult to obtain significant persistence in monetary shocks. Simulations also demonstrate that even small inflationary shocks, if not sufficient to trigger a price change, are quickly reflected in new prices as firms react to other shocks. The economy exhibits very small real effects of monetary instability, with simulated time series showing a tenfold lower variance in aggregate output compared to recent U.S. data. The estimated Phillips curve is flat, indicating that a one percentage point reduction in the inflation rate depresses output by only 0.05%. Similar results hold for different policy experiments, suggesting that credible disinflations have no real effects, while non-credible disinflations result in a decline in production that never exceeds one percent of GDP.