We characterize the class of dynamic models that allow for the most co
mmonly used types of sustained economic growth (balanced and asymptoti
cally balanced). We show that, under a constant returns to scale techn
ology, (asymptotically) constant discount rate and (asymptotically) co
nstant elasticity of marginal felicity are not only necessary but also
sufficient conditions for the existence of a(n) (asymptotically) bala
nced growth equilibrium path. We provide examples of recursive utility
models that accept a(n) (asymptotically) balanced growth equilibrium
and discuss their implications on cross-country differences in growth
rates, as well as on savings behavior and wealth distribution.