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RESEARCH PRODUCT

Median vs. Mean in Poverty Alleviation

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When evaluating poverty, the relative poverty line may be taken as a percentage of either normalized median or normalized mean income. It is proved that, for any family of non-intersecting Lorenz curves, when the poverty line is set relative to the normalized median income, reducing poverty become less costly in proportion to the total income when inequality is great and increasing; a counter-example proves that such a change may be associated with greater poverty. However, when the poverty line is set relative to the normalized mean income, the relative cost of poverty alleviation always increases with inequality and poverty, as expected. One concludes that the poverty line should be taken relative to the normalized mean income rather than the normalized median income even if the median is generally preferred.