Summary
We address the question of the measurement of pure health inequalities and achievement in the context of welfare decreasing variables. We adopt a general framework whereby the health variable is reported on an interval, from an optimum level m to a critical survival threshold b. There are two problems that require some departures from the usual framework used to measure inequality and social welfare. Firstly, we show that for welfare decreasing variables, the equally distributed equivalent value is decreasing in progressive transfers (instead of being increasing). Accordingly, appropriate achievement and inequality indices for welfare decreasing variables are introduced. Secondly, because the Lorenz curve and the associated inequality indices are not robust to alternative values of the survival threshold, we argue that the family of translation invariant social welfare functions and related absolute Lorenz curve allow us to undertake inequality comparisons between distributions that are robust to the chosen level of the survival threshold. An illustrative application of the methodology is provided.