Optimal Economic growth with recursive preferences: decreasing rate of time preference

In the field of optimal growth theory, since Ramsey's time it is frequent to maximize a welfare function consisting of the discounted sum of instantaneous utilities. Such an optimality criterion implies that preferences are independent over time. Following in the tradition of Irwing Fisher, Koopmans presented postulates for recursive preferences for which the rate of time preference is variable. In a later study with Beals he showed that the implications are that even in the simplest situations described by the neoclassical growth model initial conditions affect the long run optimal path. These authors assumed a quasiconcave welfare function. In the present essay their analysis is extended to the case of a discounted sum of instantaneous utilities when the discount rate decreases as consumption increases, and the welfare function need not be concave.