Feldstein  posed the questions of what would be the optimal level of retirement benefit, and what would be the optimal mix between the pay-as-you-go system and the funded pension system under the assumption of an exogenous interest rate. We reconsider the problem with the addition of a flexible production function and, consequently, an endogenous interest rate. Moreover, we allow the contributions rate O to be negative as well. In the case of a negative O, the retired subsidize the workers out of their saved capital. This case turns out to be the optimal one in situations of low population growth.
Social security pay-as-you-go systems funded pensions retirement benefits welfare systems