Optimal saving and health prevention

This paper examines contemporaneous choices of saving and health prevention under a two-argument utility of wealth and health. Unlike the traditional approach to modelling the cost of prevention as a decline in wealth, health prevention here is assumed to mainly reduce current health level in exchange for a lower probability of contracting a disease in the future. We show that the optimal levels of the two instruments of risk management can move either in the same direction or in opposite directions. One key element in distinguishing these two cases is whether a decision maker is correlation averse or correlation prone. Together with the relative importance of substitution effect over income effect on saving, the sign of correlation attitude is also relevant in determining the reaction of optimal saving and health prevention when the interest rate changes. Lastly, several combinations of preferences in different aspects are provided, which lead to unambiguous effects of a background risk in wealth on the two optimal choices.