We compare supermarket price setting in the US and the euro area and assess its impact on food inflation. We introduce a novel scanner dataset of Germany, the Netherlands, France, and Italy (EA4) and contrast it with an equivalent dataset from the US. We find that both higher frequency and stronger state dependence of price changes contribute to higher flexibility of supermarket inflation in the US relative to the euro area. We argue that the driving force behind both factors is higher cross-sectional volatility in the US. Larger product-level fluctuations both force retailers to adjust prices more frequently and increase price misalignments, which increase the selection of large price changes. Both facts are well represented by a mildly state-dependent price-setting model, and they jointly explain over a third of the difference in food-inflation volatility between the US and the euro area as well as around a third of the difference between the inflation responses to the COVID-19 shock in Germany and Italy.