A well-known result with important policy implications is that an output increase is a necessary condition for social welfare to increase with third-degree price discrimination. In this paper, we explore the robustness of this result to the introduction of an assumption that is different than the conventional approach, namely preferences not being quasilinear. We show that in the presence of income differences among consumers, the aggregate utility of consumers may increase with price discrimination while total output remains constant. This result questions the general policy recommendation that third-degree price discrimination should be disapproved because it reduces welfare unless output increases. Our result highlights the crucial role of the assumption of quasilinear preferences in standard welfare calculations. In the presence of income differences, consumer surplus may be a biased welfare measure, thus potentially leading to incorrect conclusions when assessing the impact of specific policies.