We consider a one-sector growth model which combines overlapping generations of finite lived agents and infinite lived consumers. We show that two types of equilibrium may exist. A first type corresponds to the modified golden rule if the stationary consumption of infinite lived agents is strictly positive. A second type of steady state in which infinite lived agents do not consume may also exist. We give sufficient conditions for local determinacy of the interior steady state which does not depend on the "size"
of infinitely lived agents. An example finally shows that the equilibrium may be locally indeterminate when both types of agents are present while the associated DIAMOND model has one unique equilibrium.

This paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal twoperiod cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.

[eng] This paper investigates the dynamical properties of optimal paths in an exam­ple of one-sector overlapping generations model in which the utility function of the representative agent is non-separable. We show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogenous fluctuations.

[fre] On étudie les propriétés dynamiques des sentiers optimaux dans un exemple du modèle à générations imbriquées à un secteur dans lequel la fonction d'utilité de l'agent représentatif est non separable. On montre dans cet exemple que le sentier optimal de croissance peut osciller et que des cycles optimaux de période deux peuvent exister. En appliquant ces résultats au modèle avec altruisme, on montre que la condition de legs positif s est parfaitement compatible avec des fluc­tuations endogènes.