Harmful addiction

We construct an infinite horizon model of harmful addiction. Consumption is compulsive if it differs from what the individual would have chosen had commitment been available. A good is addictive if its consumption leads to more compulsive consumption of the same good. We analyse the welfare implications of drug policies and find that taxes on drugs decrease welfare while prohibitive policies may increase welfare. We also analyse the agent's demand for voluntary commitment ("rehab"). For appropriate parameters, the model predicts a cycle of addiction where the agent periodically checks into rehab. Between these visits his drug consumption increases each period.