Existence of competitive equilibrium when incomes may be zero (*)

In a pure exchange economy, there exists a price vector which is a quasi-equilibrium (Debreu 1962), but this may not be a competitive equilibrium if some individuals' demand functions are discontinuous because their incomes may be zero. We show nonetheless, in a pure exchange economy with free disposal, that there is a sequence of prices approaching the quasi-equilibrium along which total excess demands tend to a non-positive limit. <!--ID="" Correspondence to:J. Whittaker-->