Why Should Rational Smokers Find it Hard to Quit? Introducing Uncertainty into the Rational Addiction Model

One problem with the Becker-Murphy model of Rational Addiction, at least in the eyes of many public health specialists, is that it does not explain why so many rational, forward looking, smokers should apparently find it so hard to quit, especially since the terminal conditions are part of an intertemporal optimization problem. In this paper we apply techniques of stochastic control theory to introduce uncertainty into the individual’s perception of how her stock of addiction will accumulate over time as a consequence of her time path of smoking. We assume that addiction capital is basically unobservable, so she cannot adjust her smoking behaviour according to a feedback policy rule but instead builds uncertainty into her consumption plan from the beginning. We discuss the differences between the equation explaining her lifetime smoking trajectory in the deterministic and stochastic cases, and find that the quadratic utility function which underlies the familiar lead-lag consumption form of rational addiction equation is not, in fact, capable of allowing for the type of uncertainty which we consider here.