Quasi-linear integrability

Applied researchers often work with demand systems that do not depend on income, with the implicit assumption that preferences are quasi-linear and income sufficiently large. The classic approach to the integrability of demand does not readily apply in this case. Adopting a much simpler approach that is based on integrating the vector field defined by the demand system and on duality, we provide necessary and sufficient conditions for the quasi-linear integrability of such (continuous) demand systems. We also derive results on the associated utility function and its domain, and provide an application to the analysis of demand systems in the presence of measurement errors.