On Saving and Caring for Dependents

The intergenerational transfer of care is an altruistic but costly behavior. The paper uses a bivariate utility of own wealth and the dependent's health to examine a two-choice problem of saving and care-giving in a two-period prevention framework. A caregiver considers the tradeoff not only between present and future wealth but also between present wealth and the dependent's future health. The paper first studies the optimal levels of saving and of care-giving and the link between them. For a correlation averse caregiver who regards own wealth and the dependent's health as substitutes, it shows that an exogenous decrease in the financial return or an increase in the dependent's healthy status leads to a reduction in saving and a rise in care-giving. In the case of additively separable preferences, the paper then presents necessary and sufficient conditions on preferences for an Nth-order stochastic dominance (NSD) change in financial risk or in health risk about the dependent to have an unambiguous effect on the optimal levels of saving, care-giving, and the sum of risk management expenditure. The analysis generalizes the existing results as well as yields new ones