Chung (2023) purports to derive conditions under which a Utilitarian society, which maximizes total welfare, Pareto dominates a Rawlsian society, which maximizes the income of the least advantaged members of society. We show that Chung’s analysis is doubly flawed. First, his analysis assumes that a Rawlsian government chooses an inefficient tax rate when it could do otherwise. Second, his analysis violates his assumption that citizens must choose a non-negative amount of labour. We show that Chung’s headline result does not hold once we enforce this assumption.