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 the presence of paternalistic altruism. This note shows that the specification of the central planner objective is crucial for optimal capital accumulation and growth. When paternalistic altruism enters the social welfare function, we depart from the standard Modified Golden Rule. Capital intensity is no more determined by the equality between optimal returns on human and physical capital, and the optimal growth rate is higher when we consider altruism enters in the social welfare function. We calibrate the model for several countries and emphasize large differences on optimal growth rate, according to the specification of the social welfare function.