Externalities in a life-cycle model with endogenous survival

Michael Kuhn, Vienna Institute of Demography
Stefan Wrzaczek, Vienna University of Technology
Alexia Fürnkranz-Prskawetz, Vienna University of Technology
Gustav Feichtinger, Vienna University of Technology

We study socially vs individually optimal life-cycle 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 learning-by-doing (positive externality) or a deterioration in the quality of care through congestion (negative externality). We combine an age-structured optimal control model at population level with a conventional life-cycle 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 age-patterns of socially and individually optimal health expenditure and the transfer rate are derived. Numerical analysis illustrates the workings of our model.