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.