This paper proposes a new welfare criterion which satisfies three desiderata: strong sensitivity to the least advantaged, sensitivity to the present, and sensitivity to the future. We develop necessary conditions for optimal paths under this new criterion, and demonstrate that, in a familiar dynamic model of capital accumulation, the optimal growth path exists. The optimal path converges to a steady state which is dependent on the initial stock of capital. Along this path, the minimum standard of living constraint, which is optimally chosen, is binding over some time interval. Optimal paths under the new criterion display properties that seem to be ethically appealing.