The hypothesis that consumers use a two-stage procedure to maximize a utility function in which food items are strongly separable from non-food items is combined with prior information about food price correlations to derive statistically manageable demand equations for fresh oranges and frozen orange concentrate. Special attention is given to the problem of measuring demand when all the variables are measured with error. A new statistical method, which yields consistent demand parameter estimates when such errors are present, is used to compute price and income elasticities of demand.