A Theory of Early-Life Parental and Middle- and Late-Life Own Investments in Health

We present an overlapping generations model of early-life parental investment and middle and late-life own investments in health. The parent is motivated by altruism or by an implicit contract with her child to devote time and / or provide financial support to the parent in old age. In contrast to commonly employed overlapping generations models with two or three discrete periods, we allow each distinct period of life (e.g., childhood, young parent and old parent) to consist of an infinite number of periods (i.e., by using continuous time), so that the theory can describe rich lifecycle behavior and inter-temporal trade-offs within and between distinct phases of life and within and between generations. Further, the distinct phases of life of the generations do not need to coincide with one another, that is, for example the death of a grandparent does not need to coincide with the birth of a grandchild. The parent optimizes her own consumption, leisure time, time devoted to work and child investment, health and the duration of her longevity, subject to the constraints she faces in terms of the initial own and child health, cognitive and genetic endowments, the resources at her disposition, the own and child environments, and the nature and efficiency of the own and child health-capital production processes. The theory predicts rich interactions between parental resources, ability, and altruism, economic circumstances, parental and child biology and parental and child economic, social and health outcomes.