Transfers within a three generations family : when the rotten dids turn into altruistic parents

We study exchanges between three overlapping generations with non-dynastic altruism. The middleaged choose informal care provided to their parents and education expenditures for their children. The young enjoy their education, while the old may leave a bequest to their children. Within each period the three generations play a "game" inspired by Becker's (1974, 1991) rotten kids framework, with the added features that the rotten kids turn into the altruistic parent in the next period and that parents invest in the education of their children. We show that Becker's rotten kids theorem holds for the single period game in that informal aid is set according to an efficient rule. However, education is distorted upwards. In the stationary equilibrium the levels of both transfers are inefficient: education is too large and informal aid is too low.