School of Mathematical Sciences, DCU

Healthcare and Consumption with Aging

Health-care benefits individuals by slowing the natural growth of mortality, indirectly increasing utility through consumption over a longer lifetime. This paper solves the problem of household dynamic healthcare, consumption, and saving when natural mortality grows exponentially to reflect the Gompertz' law, while both utility and health-care are isoelastic. The optimization problem reduces to a nonlinear ordinary differential equation with a unique solution, which has an explicit expression in the old-age limit. Optimal consumption and health-care spending policies depend on mortality and imply an endogenous curve similar to the Gompertz law. Absolute health expenditure increases with age; relative to consumption, it increase for the typical adult life and slowly declines in the old age.