Food deserts are associated with lower quality diets and higher obesity rates. One hypothesis for their emergence is that retailers avoid food deserts because demand side factors such as low income limit demand for healthy foods. A competing hypothesis is that supply side factors cause prohibitively high costs of operation for grocers – leading to limited access to healthy foods and thus low expressed demand. The direction of causality has important implications for improving diets and health of food desert residents. This paper analyses Detroit food desert residents’ fresh vegetable purchasing behaviour using data from a non-profit grocer. The evidence confirms that these consumers respond to prices and income similarly to the average American, however, they face a different set of constraints. Both supply and demand side factors are at work – access problems are critical, but even with better access low incomes and other demand side issues limit vegetable consumption.