Adjustment Costs in Rational Addiction Health Investment Models

Abstract This paper studies how routine dependence in health investment alters the predictions of rational addiction models used in health economics. We combine a continuous-time health-capital framework with the adjustment-cost formulation of habits developed by Dragone (2009. “A Rational Eating Model of Binges, Diets and Obesity.” Journal of Health Economics 28 (4): 799–804), applying the adjustment cost to healthy behavior: changing the level of healthy consumption is costly, so optimal behavior may adjust gradually rather than immediately. In addition, accumulated health reinforces the marginal utility of healthy behavior, so that persistence arises from two distinct channels. The rational addiction apparatus is used here as a tractable forward-looking habit-formation device in health investment; in this version of the model, the unhealthy good is not assumed to be addictive in the Becker–Murphy sense. We characterize the steady state and derive comparative statics with respect to the prices of healthy and unhealthy goods. The key insight is that reinforcement through the health stock can make healthy and unhealthy behaviors intertemporally linked. As a consequence, price-based interventions that reduce unhealthy consumption may also reduce healthy behavior for some individuals. The results characterize when price instruments shift behaviors and long-run health in non-standard directions, and hence when interventions that facilitate smoother habit transitions operate on margins that prices leave unaffected.