This paper proposes a two-step aggregation method for measuring long-term income inequality and income mobility, where mobility is defined as an equalizer of long-term income. The first step consists of aggregating the income stream of each individual into a measure of permanent income, which accounts for the costs associated with income fluctuations and allows for credit market imperfections. The second step aggregates permanent incomes across individuals into measures of social welfare, inequality and mobility. To this end, we employ an axiomatic approach to justify the introduction of a generalized family of rank-dependent measures of inequality, where the distributional weights, as opposed to the Mehran-Yaari family, depend on income shares as well as on population shares. Moreover, a subfamily is shown to be associated with social welfare functions that have intuitively appealing interpretations. Further, the generalized family of inequality measures provides new interpretations of the Gini-coefficient.