The optimal trade-off between quality and quantity with uncertain child survival

The present paper investigates a standard model of endogenous fertility when child survival to adulthood is uncertain. In this framework, I first show that facing the risk their children die before reaching adulthood, parents don’t always formulate a precautionary demand for children. Indeed, there exists a non-empty set of utility functions for which parents undershoot their number of children rather than overshooting it. Second, the properties of the optimal economic policy will crucially depend on the manner the Social Welfare Function takes uncertainty into account. More precisely, if Social Welfare is evaluated after the resolution of uncertainty, the parental response to uncertainty is a source of social inefficiency. Then, individual decisions have to be corrected through tax or transfer on both births and education. This property becomes crucial to determine the optimal public response to a mortality crisis in presence of positive externalities on education.