Rational Addiction Under Uncertainty

Abstract

We develop a new model of addictive behavior that takes as a starting point the classic rational addiction model of Becker and Murphy, but incorporates uncertainty. We model uncertainty through the Brownian motion process. This process is used to capture both random events such as exposure to harmful substances, anxiety, tensions and environmental cues which can precipitate and exacerbate addictions, and those sober and thought-provoking episodes that discourage addictions. We derive closed-form formulas for optimal addictive consumption and capital trajectories and examine their global and local properties. Our theory provides plausible explanations of several typical patterns of addictive behavior and has also novel policy implications.