This paper examines the health effects of a fiscal food policy based on a combination of fat taxes and thin subsidies. The fat tax is based on the saturated fat content of food items while the thin subsidy is applied to select fruit and vegetable items. The policy is designed to be revenue neutral so the subsidy exactly offsets the revenue from the fat tax. A model of food demand is estimated using Bayesian methods that accounts for censoring and infrequency of purchase (the problem of unit values is also discussed). The estimated demand elasticities are used to compute nutrient elasticities which demonstrate how consumption of specific nutrients changes based on price changes in particular foods from the fiscal policy. Results show that although the fat tax decreases saturated fat intake, consumption of other important nutrients is also decreased, which may lead to negative health outcomes.