In standard macroeconomic models, the costs of inflation are tightly linked to the price dispersion of identical goods. Therefore, understanding how price dispersion empirically relates to inflation is crucial for welfare analysis. In this paper, I study the relationship between steady-state inflation and price dispersion for a cross section of U.S. retail products using scanner data. By comparing prices of items with the same barcode, my measure of relative price dispersion controls for product heterogeneity, overcoming an important challenge in the literature. I document a new fact: price dispersion of identical goods increases steeply around zero inflation and becomes flatter as inflation increases, displaying a ?-shaped pattern. Current sticky-price models are inconsistent with this finding. I develop a menu-cost model with idiosyncratic productivity shocks and sequential consumer search that reproduces the new fact and exhibits realistic price-setting behavior. In the model, inflation-induced price dispersion increases shoppers' incentives to search for low prices and thus competition among retailers. The positive welfare-maximizing inflation rate optimally trades off the efficiency gains from lower markups and the resources spent on search.