The old age security hypothesis and optimal population growth

The old age security approach is used to study the relationship between the rate of growth of the population and capital accumulation, within a Samuelson-Diamond overlapping generations framework. It is shown that a decentralized economy will fail, in general, to achieve the Pareto optimal path. However, a pay-as-you-go social security scheme in which the old get transfers which are proportional to the number of their children may restore optimality. On the other hand, child support systems or subsidies to capital can guarantee the optimal capital: labor ratio, but not the optimal population growth rate, while a lump sum social security system can guarantee the optimal population growth rate, but not the optimal capital: labor ratio. Finally, in a monetary economy any policy aimed at correcting the interest rate will restore full optimality.