How much a household suffers from inflation depends on what it consumes. We show that this simple observation links household expenditure behavior to inflation inequality, welfare losses, and poverty. Building on a non-homothetic CES demand system, we derive household-specific exact cost-of-living indexes and apply them to the 2022 European energy crisis in Spain and Italy. Using household expenditure microdata, we estimate non-homothetic preferences and show that the same expenditure patterns governing Engel curves also determine households' welfare sensitivity to inflation. Consequently, poorer households face substantially larger welfare losses than would be implied by inflation differentials alone, while Italian households exhibit systematically greater welfare sensitivity than comparable Spanish households. Under an anchored poverty line, a common price deflator conceals 1.6 million newly poor in Spain, while in Italy it is nearly innocuous, because the shock is already large enough to push the same households below the line. Our results caution against relying on a single representative-agent price index to assess the distributional consequences of large relative-price shocks.