Old age or dependence. Which social insurance?

We consider a society where individuals differ according to their pro- ductivity and their risks of mortality and dependency. We show that according to the most reasonable estimates of correlations among these three characteristics, if one had to choose between a public pension sys- tem and a long-term care social insurance, the latter should be chosen by a utilitarian social planner. For a Rawlsian planner, the balance between the two schemes does depend on a comparison of the ratio of the survival probability to the dependence risk of the poor with its population average.