Relative Price Distortions and Inflation Persistence *

Sticky‐price models often suggest that relative price distortion is a major cost of inflation. We provide an intuition for this: Even at low rates, inflation strongly affects price dispersion which in turn has an impact on the economy qualitatively similar to, and of the order of magnitude of, a negative shift in productivity. The utility cost of price dispersion is quantified and its impact on optimal monetary policy discussed. Price dispersion is incorporated into a linearised model. Strikingly, a contractionary nominal shock has a persistent, negative hump‐shaped impact on inflation but may have a positive hump‐shaped impact on output.