Abstract

Healthcare slows the natural growth of mortality, indirectly increasing utility from consumption through longer lifetimes. This paper solves the problem of optimal dynamic investment, consumption, and healthcare spending with isoelastic utility, when natural mortality grows ex- ponentially to reflect the Gompertz’ law. The stochastic control 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 healthcare strategies imply an endogenous mortality law that is asymptotically exponential in the old-age limit, with lower growth rate than natural mortality. Health spending steadily increases with age, both in absolute terms and relative to total spending. Differential access to healthcare can account for observed longevity gains across different generations.