Consumption and investment demand when health evolves stochastically

Abstract

The health capital model of Grossman (1972) is extended to account for uncertainty in the rate at which a stock of health depreciates. Two general versions of the model are contemplated, one with a fully functioning financial market and the other in its absence. The comparative dynamics of the feedback form of the consumption and health-investment demand functions are studied in these general settings, where it is shown that the key to deriving refutable results is to determine how a parameter or state variable affects the expected lifetime marginal utilities of health and wealth. To add further reach to the results, a simplified stochastic control problem is explicitly solved, yielding estimable structural feedback demand functions.