Recursive preferences and balanced growth

We study a class of utility functions that are defined recursively by an aggregator Wx,y where ut=Wct,ut+1. In single-agent economies it is known that a sufficient condition for the existence of a balanced growth path is that utility should be homogenous of degree γ. In the context of a multi-agent economy we show that this restriction implies that either a balanced growth equilibrium fails to exist or all agents have the same constant discount factor. We suggest a generalization of recursive preferences wherein the intertemporal utility function is time dependent. Within this class we establish that there may exist a balanced growth equilibrium even if agents are different.