Résumé en anglais

Given budget sets and consumer's consumption bundles, the economist deduces essential budgetary information, namely, whether every consumption bundle is available in every budget set and whether it exhausts the consumer's revenue. We show that rationalization of the original data is equivalent to the existence of budget sets compatible with the essential data together with a utility function rationalizing these budget sets. Hence the conclusion of the original rationalizability test automatically applies to a whole class of budget sets. Furthermore, in case of a positive answer, a single utility function, which rationalizes at once almost all compatible budget sets, can be constructed.