Many authors have recently emphasized the crucial role of income inequalities in the design of efficient policies aimed at reducing poverty. However, the link between variations in the degree of inequality and variations in poverty is not well documented. The literature, for instance, does not provide any satisfying tool for predicting how a small relative variation in the Gini index may be associated with a variation in the headcount index. In the present paper, we define a family of Lorenz curve transformations that can directly be interpreted in terms of relative variations of known inequality measures. Then, we extend Kakwani’s (Rev Income Wealth 39(2):121–139, 1993) methodology for the calculation of inequality elasticities of poverty. Improvements are threefold with respect to Kakwani’s work. First, our formulas are not confined to the sole Gini index. Secondly, they embrace the uncertainty and the complexity of the mechanical link between inequality and poverty. Third, using some flexible functional form, one can easily perform an accurate estimation of the point inequality elasticities of poverty corresponding to observed variations of a given income distribution. We also propose a simple measure that may be helpful to assess how “pro-poor” are inequality variations by comparing the observed elasticities with the set of theoretical elasticities that could be obtained from the initial income distribution.