  We present, solve and numerically simulate a simple model that describes the
consequences of increased longevity on 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
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.
