Individual heterogeneity is an important source of variation in demand. Allowing for general heterogeneity is needed for correct welfare comparisons. We consider general heterogenous demand where preferences and linear budget sets are statistically independent. We find that the dimension of heterogeneity and the individual demand functions are not identified. We also find that the exact consumer surplus of a price change, averaged across individuals, is not identified, motivating bounds analysis. We use bounds on income effects to derive relatively simple bounds on the average surplus, including for discrete/continuous choice. We also sketch an approach to bounding surplus that does not use income effect bounds. We apply the results with income effect bounds to gasoline demand. We find little sensitivity to the income effect bounds in this application.