How do families behave dynamically? We provide a framework for studying economic problems in which family behavior is essential. Our key innovation is the inclusion of imperfectly altruistic agents in an otherwise standard consumption–savings problem with exogenous income risk. This gives rise to altruistic transfers and strategic behavior in the consumption–savings decision. We study the Markov-perfect equilibrium that arises from the limit of equilibria in a sequence of finite games. The equilibrium's transfer patterns are empirically plausible. Furthermore, agents overconsume relative to the social optimum. In contrast to two-period models, both the richer and the poorer players overconsume long before transfers actually occur. The poorer agent also faces incentives to engage in excessive risk-taking because losses from a gamble are absorbed by both while gains are enjoyed alone.
Altruism inter vivos transfers consumption-savings decision differential games