One of the ethical objections made to inter-generational equity is the violation of consumer sovereignty. To address this concern, this paper presents a continuous-time Overlapping Generations Model (OLG) suitable for the treatment of sustainability issues, which distinguishes the intra- and inter-generational discount factor (see Calvo and Obstfeld, 1988) with taking into account heterogeneities of time preferences among individuals. We find that consumption for older patient individuals is always higher than older impatient agents while the social planner decides to allocate equally the consumption between patient and impatient young individuals. Along age t, the consumption of patient old agents always increases relatively, whichs speed depends on intertemporal elasticity of subtitution. Our results show that the consumption of patient and impatient young individuals are interdependent. We also show that the Hotelling rule for renewable resources is not affected regardless to the share of patient and impatient agents in society. Finally, we find that the effect of static increase of the individual discount rate of a patient or impatient agent on sustainable income depends on the level of aggregate consumption.