  We take an axiomatic approach to study redistribution problems when agents
report income and needs. We formalize axioms reflecting ethical and operational
principles such as additivity, impartiality and individual rationality.
Different combinations of those axioms characterize three focal rules (laissez
faire, full redistribution, and need-adjusted full redistribution) as well as
compromises among them. We also uncover the structure of those compromises
exploring the Lorenz dominance criterion as well as majority voting. Our
analysis provides an axiomatic justification for a linear income tax system. We
conclude our analysis resorting to Eurostat's Household Budget Survey from
where we illustrate the different redistribution patterns accounting for needs
across European countries.
