Parental Investments in Child Health – the importance of paternalistic altruism, child egoism and short-sightedness

Parent and child interaction is an important determinant of child health. Typically, parents are more forward-looking than their children and, hence, care about investments in human capital to a larger extent. In this paper we consider the parent-child health-related interaction, when the parent is altruistic and forward-looking and the child is egoistic and short-sighted. The child receives a monetary transfer, from the parent, which is used to finance either health-unrelated consumption or unhealthy behaviour. We apply a simple differential-game approach, assuming linear-state preferences, and study equilibrium time-paths of (a) the parental transfer, (b) the unhealthy behaviour, and (c) the stock of child health capital. We distinguish between the case in which the child is perfectly myopic and the case in which he or she is forward looking.