In this paper, we consider an extension of the commonly used poverty gap measure that may be used to address the question of whether the elimination of poverty is a feasible objective, given sufficient political commitment. The resources potentially available to address poverty may be measured by the total amount by which the incomes of the non-poor exceed the same poverty line. The ratio of the poverty gap to the resources potentially available is equal to the proportional tax rate on incomes in excess of the poverty line that would be required to fund a transfer sufficient to raise the incomes of all poor people to the poverty line. We refer to this ratio as the ‘poverty burden’ (PB). We provide a formal definition of the poverty burden and an analysis of its properties as a poverty measure.