We develop a perpetual youth model to investigate how longevity affects economic growth and welfare. Life expectancy is determined by individuals' investments in healthcare. We find that improvements in the healthcare technology always increase the steady state growth rate. Although the effect is small, even for large increases in longevity, welfare gains may be substantial depending on the type of the technological improvement. We identify two externalities associated with healthcare investments and provide a condition when healthcare expenditures are inefficiently low in the market equilibrium. Finally, we discuss our results with respect to alternative spillover specifications in the production sector.