The productivity of health care and health production functions

This paper derives a necessary and sufficient condition under which increased health care productivity must lead to decreased (increased) demand for health care as long as the demand for health care is inelastic (elastic). It is shown that this condition identifies a class of health production functions, which may provide useful guidance to empirical studies that depend wholly or partly on the correct specification of a health production function. As an illustration, it is demonstrated that this class of production functions may be useful for empirical studies that test the hypothesis that schooling, increasing the efficiency of health production, leads to a larger health output from a given set of health inputs. The paper also offers broader classes of production functions that would enable one to test this relationship between the demand elasticity and the effect of health care productivity on health care demand.