Health expenditures are on the rise in developed countries. This paper analytically studies how they affect capital accumulation in a Diamond model in which individuals can spend resources to live longer in second period. We rst derive the demand for health and show that the income share spent on health is an inverted U-shaped function of income. Second, we fully characterize the dynamic general equilibrium and determine the growth impacts of the health expenditures. Several cases can occur. Health expenditures can speed up or slow down economic growth. They can be a barrier to growth or they can be a necessity for growth to take place. A simple calibration of the model to OECD countries suggests that the latter case is the most likely one.