On the existence of balanced growth equilibrium

We characterize the class of dynamic models that allow for the most commonly used types of sustained economic growth (balanced and asymptotically balanced). We show that, under a constant returns to scale technology, (asymptotically) constant discount rate and (asymptotically) constant elasticity of marginal felicity are not only necessary but also sufficient conditions for the existence of a(n) (asymptotically) balanced 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.