Rational Addiction

The Becker-Murphy Rational Addiction framework incorporates two important means for describing addictive behavior: reinforcement and tolerance. The current period utility function,

states that well being is determined by consumption of an addictive good, , the capital accumulation of the addictive good, , and a non-addictive good, Reinforcement is imposed on the model if and is consistent in agents with myopic preferences. More clearly stated, reinforcement is observed in a good whose past consumption increases the marginal utility of current consumption. Tolerance requires and describes how past
consumption of an addictive good reduces current utility. In other words, a greater quantity of the addictive substance is required to receive the original euphoric effect.

Presented in this manner, steady state solutions are found and analyzed for the dynamic optimization problem. The model can describe a variety of circumstances, and the existence of unstable steady states illustrate the difference between highly addicted people who continue consuming harmful substances and those who eventually quit entirely. Two other important implications of the model are: First, individuals who heavily discount the future are more likely to become addicted, and second, reinforcement causes addictive goods across time periods to be complements.

Because robust data on illegal drug prices doesn’t exist, the implications for the model are purely hypothetical. However, the model has been empirically tested on cigarette, alcohol, and gambling consumption. From these results a permanent reduction in the price of drugs is expected to increase consumption in the short run. It is likely that addiction would increase in the long run as well. Furthermore, addiction among lower income groups and the young are likely to be affected the most.

The results are certainly not complete and a more thorough study is necessary to evaluate the impact of such a policy. Nevertheless, legalizing drugs like heroin, cocaine, and marijuana are likely to increase
consumption, particularly in low income and younger groups.