The purpose of this paper is to provide some microeconomics tools to discuss and evaluate public policies that imply transfers of income from the public sector to the poor and their impact on their food demand and calories and nutrient intakes. This study is concerned with the differences in subsistence expenditures, own-price elasticities and income elasticities for two households groups segmented by income: those people below the poverty guideline and those above it. The attention of our research is focused on a demand system for all food groups included in a National Consumption Survey and examines the household food consumption behavior by partitioning the sample. A complete system of demand equations, the Linear Expenditure System (LES), has been used due to its relative empirical expediency. Some additional econometric techniques to correct the bias in the parameter estimates were also applied because of the large number of zero observations in the data. Preliminary estimations following the procedure suggested in the Park et al. (1996) paper, gave some results that they were not as good as we expected and we finally use an alternative one based on Shonkwiler and Yen (1999).