Pension Schemes and Falling Birth-Rates : Change in Customs or Microeconomic Optimization?

In this paper, we develop an overlapping generations model where fertility is endogenous. The utility of the parents is a function of the number of their children, and each child implies two types of fixed costs: the financial cost and the cost in terms of time. A "pay-as-you-go" pension scheme introduces an externality in that the number of children will be fewer than optimal because their favorable impact on the level of pension income is not taken into account. First, we define the competitive equilibrium dynamics and the steady state. This allows comparisons with the optimal stationary state, a notion which generalizes the golden rule. Two instruments, pensions and child benefits, are necessary to decentralize the optimal state. Next, we compare the scenario depicted by the model with historical fact. Variations in welfare allowances may explain the entire decrease in fertility rates