Two-sided altruism and time inconsistency

In this study, we examine dynamic allocation of resources and consumption over an infinite time horizon in an overlapping-generations model with two-sided altruism. Each generation cares not only about its own consumption and the utility of its successor, but also about the utility of its parental generation. The consumption decisions of different generations could display time-inconsistency in a model of two-sided altruism. Consequently, the outcome solutions could differ depending on whether members of the current generation are naive and falsely believe that the future generation will comply with their, or are sophisticated and know exactly how the future generation will choose to behave. We assume that the young generation is naive and behaves as a central planner in allocating capital resources. The capital stocks inherited by each generation from the parental generation are actually realized and used in the joint production of capital stocks and consumption goods. We refer to a sequence of such capital stocks as a two-sided altruistic path. This study examines a more general production function than earlier models of two-sided altruism, and our results prove that any two-sided altruistic path will eventually converge to the two-sided altruistic stationary path.