The Optimal Consumption and the Quitting of Harmful Addictive Goods

In this paper we study a model of rational consumption and quitting in the context of harmful addictive goods. We assume that a person has imperfect information about his ability to resist and terminate the addiction. We first characterize the optimal consumption path of a non-addicted person, along which his stock of the addictive substance is either always increasing (and thus addiction occurs stochastically), always decreasing, or always unchanged. We then characterize the optimal consumption path of an addicted person, along which he may attempt to quit the addiction for a period of time, and then resume his consumption if the attempt is unsuccessful. Finally, we remark on the issues of regret, multiple attempts to quit, and quitting programs.