Food demand parameters are necessary for informed food policy making. In this paper we specify a Quadratic Almost Ideal Demand System and estimate a complete demand system for rice, sorghum, millet and maize in rural and urban Mali using Mali’s 2006 household budget survey data. Elasticities are estimated by per capita income groups and by rural and urban residence. We use these estimates to measure the welfare effects of cereals price shocks observed from 2008 to 2011 by means of a proportional compensating variation that allows for second-order demand responses to price changes.