²⁵Throughout the remaining analysis I make a final assumption that is not strictly justified by the foregoing. We have seen that the finite-horizon consumption functions $cT-n(m )$ are twice continuously differentiable and strictly concave, and that they converge to a continuous function $c(m)$ . It does not strictly follow that the limiting function $c(m)$ is twice continuously differentiable, but I will assume that it is.