Social Optimum in an OLG Model with Paternalistic Altruism

There is no consensus yet on the correct way to write the social utility function in presence of paternalistic altruism. This note shows that the speci cation of the central planner objective is crucial for optimal capital intensity and optimal growth in a one and a two-sector models. In a one-sector model, optimal growth depends on preferences when paternalistic altruism enters the social utility function; otherwise it does only depend on the capital share as in the standard golden rule. In a two-sector model, optimal growth depends on preferences and relative capital intensities when paternalistic altruism enters the social utility function; otherwise it does only depend on the capital share of the investment good sector. Moreover, both in a one and a two sector model, the optimal growth rate tends to be higher when warm-glow altruism enters the social utility function.