  Because the \(U\)-function is unique up to positive affine transformations, we may without any loss of generality normalize it so that \(U(0) \ne 0\). It is then obvious that for all feasible \(\{C(t)\}\), \(V(0)\) in Ramsey Mark I diverges to minus infinity if \(U(0) \lt 0\), but diverges to plus infinity if \(U(0) \gt 0\). That an optimum policy does not exist in the cake-eating model can be seen if we now recall that \(U(C)\) has been assumed to be strictly concave. The assumption implies that any non-egalitarian distribution of consumption among the generations can be improved upon by a suitable redistribution. The ideal distribution would be equal consumption for all generations. The only consumption stream with the latter property is \(C(t) = 0\) for all \(t\). But that’s the worst possible distribution. QED