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This paper uses revealed preference inequalities to provide tight nonparametric bounds on consumer responses to price changes. Price responses are allowed to vary nonparametrically across the income distribution by exploiting microdata on consumer expenditures and incomes over a finite set of discrete relative price changes. This is achieved by combining the theory of revealed preference with the semiparametric estimation of consumer expansion paths (Engel curves). We label these expansion path based bounds as E-bounds. Deviations from revealed preference restrictions aremeasured by preference perturbations which are shown to usefully characterise taste change.