An Extended Theory of Rational Addiction

This study extends the rational addiction theory by introducing an endogenous discounting of future utilities. The discount rate depends on habits accumulating over time because of the repeated consumption of an addictive good. The endogeneity of the discount rate affects consumption decisions via a habit-dependent rate of time preference and discloses a patience-dependence trade-off. The existence of a steady state in which habits do not grow and its optimality are proven. The local stability properties of the steady state reveal that the equilibrium can be a saddle node, implying smooth convergence to the steady state, but also a stable or unstable focus, potentially predicting real-world behaviors such as binge drinking or extreme addiction states that may drive to death. The stability of the steady state mostly depends on the habit formation process, suggesting that heterogeneity in habit formation may be a key component to explain heterogeneity in time preferences.