Comparative Dynamics in Health Economics: Some Useful Results

In analysis of atemporal models, comparative statics experiments are typically carried out, often employing envelope properties, such as Roy's identity, Hotelling's lemma and Shephard's lemma, in order to simplify the analysis. In analysis of dynamic models, such experiments are seldom undertaken because of the complexity involved. In this note, we illustrate how to employ dynamic envelope properties in order to arrive at surprisingly simple comparative dynamics results in optimal control theory models. We also extend the envelope theorem to an infinite horizon problem with fundamental time dependency, and apply the result to parametric changes in death risks and health production functions.