Inequality, welfare and monotonicity

We stablish a general relationship between the standard form of the individualistic social-welfare function and the "reduced-form" version that is expressed in terms of inequality and mean income. This shows the relationship between the property of monotonicity and the slope of the equity-efficient trade-off. Particularly simple results are available for a large class of inequality measures that includes the Gini. These results do not require differentiability of the social-welfare function.