This article assesses the e¤ects of a "fat tax" on the nutrient intake of French households across di¤erent income groups using a method that estimates the nutrient elasticities of French households. The incompleteness of our data requires the use of a cohort model. We estimate a complete demand system by aggregating an individual demand system over cohorts. We fnd that a "fat tax" would have ambiguous and extremely small effects on the nutrient intake of French households, and its associated economic welfare costs would be similarly weak.