<p>This paper develops a theoretical framework for evaluating poverty-reducing tax policies in endowment economies. Using a comprehensive class of poverty measures, we characterize the complete set of tax schedules that reduce both absolute and relative poverty, regardless of the underlying distribution of income or wealth. Our main theorems establish necessary and sufficient conditions for universal poverty reduction through taxation. For relative poverty reduction, we show that tax schedules must preserve ranks and exhibit average-rate progressivity among the poor, while maintaining the non-poor status of all individuals. Absolute poverty reduction requires these conditions plus the additional requirement that tax liabilities be non-decreasing among the poor. These results provide insights into effective tax policy design for poverty alleviation.</p>