History-dependence in a rational addiction model

Defining habitual behavior as a positive relation between past and current consumption and addiction as a strong habit, Becker and Murphy (Journal of Political Economy, 1988) studied a model for rational addiction. They identified multiple steady states as another key feature of addiction. In the present paper it is shown how the interplay of addiction with a budget constraint may generate multiple long-run steady states. In the most interesting case, there exist two boundary saddle-point equilibria, as well as an unstable steady state in-between. The basins of attraction of the upper and the lower equilibria are separated by a threshold. Convergence to the lower long-run steady state may be interpreted as 'cold turkey', i.e., an immediate exit from consumption.