We analyze the role played by the Supplemental Nutrition Assistance Program (SNAP) in alleviating or exacerbating inequality across racial and ethnic groups in food expenditures and in the resources needed to meet basic food needs (the "food resource gap"). To do this, we propose a simple framework that decomposes differences across groups in SNAP benefit transfer levels into three components: eligibility, participation, and generosity. This decomposition is then linked to differences in food expenditures and the food resource gap. Our results reveal that among the three components, differences in eligibility contribute the most to SNAP benefits differentials for Black and Hispanic households relative to White households. Given that SNAP is often a target of policy changes, we employ the framework to provide counterfactual analyses of how selected SNAP policy changes can impact group differences in benefits and, ultimately, disparities in food expenditures and the food resource gap. The proposed framework can be applied to analyze other safety net programs.