We study socially vs individually optimal life cycle allocations of consumption and health, when individual health care 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 expenditures and the transfer rate are derived. Numerical analysis illustrates the working of our model.

中文翻译：

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具有内生生存的生命周期模型中的外部性

我们研究了消费和健康的社会与个人最佳生命周期分配，当个人医疗保健抑制自己的死亡率但也对其他人的生存产生溢出效应时。例如，当总体水平的医疗保健活动通过边做边学（正外部性）引发治疗改善或因拥挤（负外部性）导致护理质量下降时，就会出现这种溢出效应。我们将人口层面的年龄结构最优控制模型与传统生命周期模型相结合，推导出生命的社会和私人价值。然后，我们研究个人激励如何偏离社会激励，以及它们如何通过转移计划进行调整。推导出社会和个人最佳健康支出和转移率的年龄模式。