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What are the unequal effects of changes in consumer prices on the cost of living? In the context of changes in import prices, most analyses focus on variation across households in initial expenditure shares on imported goods. However, the unequal welfare effects of non-marginal foreign price changes also depend on differences in how consumers substitute between imported and domestic goods, on which there is scant evidence. Using data from Switzerland surrounding the 2015 appreciation of the Swiss franc, we provide evidence that lower income households have higher price elasticities. These differences in elasticities contribute significantly to the unequal welfare effects of large import price changes