Before revision:  This model is appropriate whenever a consumer's demand over a  strict subset of all available goods is being analyzed . For the random utility extension of the model, we devise nonparametric statistical procedures for testing and welfare comparisons. The latter requires the development of novel tests of linear hypotheses for partially identified parameters .
After revision:  This model is appropriate whenever a consumer's demand over a  strict subset of all available goods is being analyzed ; it can also be extended to settings with discrete goods and nonlinear prices. To illustrate its use, we apply our model to a single-agent data set and to a data set with repeated cross-sections. We develop a novel test of linear hypotheses for partially identified parameters .