Equity and efficiency as components of a social welfare function

An income distribution-based abbreviated social welfare function is an increasing function of equity and efficiency. When inequality is of relative type, we characterize variants of the Atkinson-Kolm-Sen and the Shorrocks abbreviated welfare functions, where the variation results from the existence of a corresponding trade-off parameter, and in each case if the parameter becomes one the two forms coincide. When the value of the parameter increases, equity gains more weight in the equity-efficiency trade-off. For absolute inequality, we characterize the Blackorby-Donaldson-Kolm welfare function. Some implications of the lexicographic-type equity used in the paper are also considered.