A growing literature has emphasized the role of firm heterogeneity within sectors in accounting for nominal income inequality. This paper explores the implications for household price indices across the income distribution. Using detailed matched US home and store scanner microdata, we present evidence that rich and poor households source their consumption from different parts of the firm size distribution within disaggregated product groups. We use the microdata to examine alternative explanations, write down a quantitative model featuring two-sided heterogeneity across producers and consumers that rationalizes the observed moments, and calibrate it to explore general equilibrium counterfactuals. We find that larger, more productive firms endogenously sort into catering to the taste of wealthier households, and that this gives rise to asymmetric effects on household price indices. These effects amplify observed changes in nominal income inequality over time, and lead to a more regressive distribution of the gains from international trade.
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