Externalities in a Life-Cycle Model with Endogenous Survival

We study socially vs. individually optimal lifecycle allocations of consumption and health care, when individual health expenditure curbs own mortality but also has a spillover effect on other persons' survival. Such spillovers arise, for instance, when health care activity at aggregate level triggers improvements in treatment through learningbydoing (positive externality) or a deterioration in the quality of care through congestion (negative externality). We combine an agestructured optimal control model at population level with a conventional lifecycle model to derive the social and private value of life. We then examine how individual incentives deviate from social incentives and how they can be aligned by way of a transfer scheme. The agepatterns of socially and individually optimal health expenditure and the transfer rate are derived. Numerical analysis illustrates the workings of our model.