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 versions of the model are contemplated, one with a fully functioning financial market and the other in its absence. The comparative dynamics of the consumption and health-investment demand functions are studied in both models in a general setting, where it is shown that the key to deriving refutable results is to determine how a parameter or state variable affects the lifetime marginal utilities of health and wealth. To add further bite to the results, a stochastic control problem is solved for its feedback consumption and health-investment demand functions, thereby yielding estimable structural demand functions.