We present, solve and numerically simulate a simple model that describes the consequences of increased longevity for fertility rates, population growth and the distribution of wealth in developed societies. We look at the consequences of the repeated use of life extension techniques and show that they represent a novel commodity whose introduction will profoundly influence key aspects of the economy and society in general. In particular, we uncover two phases within our simplified model, labeled as 'mortal' and 'immortal'. Within the life extension scenario it is possible to have sustainable economic growth in a population of stable size, as a result of dynamical equilibrium between the two phases.