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This paper provides an analysis of the role of prices in determining food purchases and nutrition using very detailed transaction-level observations for a large, nationally-representative sample of US consumers over the period 2002-2007. Using product-specific nutritional information, we develop a new method of partitioning the product space into relevant nutritional clusters that define a set of nutritionally-bundled goods, which parsimoniously characterize consumer choice sets. We then estimate a large utility-derived demand system over this joint product-nutrient space that allows us to calculate price and expenditure elasticities. Using our structural demand estimates, we simulate the role of product taxes on soda, sugar-sweetened beverages, packaged meals, and snacks, and nutrient taxes on fat, salt, and sugar. We find that a 20% nutrient tax has a significantly larger impact on nutrition than an equivalent product tax, due to the fact that these are broader-based taxes. However, the costs of these taxes in terms of consumer utility are not higher. A sugar tax in particular is a powerful tool to induce healthier nutritive bundles among consumers.