Extending the Grossman (J Polit Econ 80:223-255, 1972) model of health capital into a stochastic one, we analyze how the presence of Knightian uncertainty about the efficacy of health care affects the optimal health investment behavior of individuals. Using Gilboa and Schmeidler's (J Math Econ 18:141-153, 1989) model of max/min expected utility (MMEU) with multiple priors, we show that an agent retains the initial level of health capital if the price of health care lies within a certain range. We also show that the no-investment range expands as the degree of Knightian uncertainty rises.
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