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| Grossman's health investment model has been an important development in health economics. However, the model's derived demand function for medical care predicts the demand for medical care to increase if the individual's health status increases. Yet, empirical studies indicate the opposite relationship. In order to improve the informative value of the health investment model, this study introduces a reworked Grossman model by assuming a more realistic Cobb-Douglas investment function with decreasing returns to scale. The resulting dynamic utility maximization problem is tackled by optimal control theory; with individual's health capital and wealth being the two state variables and the amounts of consumed medical care and non-medical market goods being the two control variables. The optimization problem is solved in a deterministic but also in a more realistic stochastic model setting where uncertainty is introduced surrounding individual's health status. For this purpose, health capital is modelled as a linear generalized Brownian motion with drift. The reworked health investment model generates a demand function for medical care that predicts an increasing demand for medical care if the individual's stock of health capital decreases, a relationship that is substantially supported by empirical results. Finally, our empirical analysis highlights the derived theoretical predictions. |
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