  We study existence, uniqueness and computability of solutions for a class of
discrete time recursive utilities models. By combining two streams of the
recent literature on recursive preferences---one that analyzes principal
eigenvalues of valuation operators and another that exploits the theory of
monotone concave operators---we obtain conditions that are both necessary and
sufficient for existence and uniqueness of solutions. We also show that the
natural iterative algorithm is convergent if and only if a solution exists.
Consumption processes are allowed to be nonstationary.
