Is there a trade-off between longevity and quality of life in Grossman's pure investment model?

The question is posed whether an individual maximizes lifetime or trades off longevity for quality of life in Grossman's pure investment (PI)-model. It is shown that the answer critically hinges on the assumed production function for healthy time. If the production function for healthy time produces a trade-off between life-span and quality of life, one has to solve a sequence of fixed time problems. The one offering maximal intertemporal utility determines optimal longevity. Comparative static results of optimal longevity for a simplified version of the PI-model are derived. The obtained results predict that higher initial endowments of wealth and health, a rise in the wage rate, or improvements in the technology of producing healthy time, all increase the optimal length of life. On the other hand, optimal longevity is decreasing in the depreciation and interest rate. From a technical point of view, the paper illustrates that a discrete time equivalent to the transversality condition for optimal longevity employed in continuous optimal control models does not exist.