Appendix II

Alcohol myopia and present bias

We could model alcohol myopia with the model of present bias used by O'Donoghue and Rabin (2003). Their utility function is given by the following equation:

where u_t is the instantaneous utility of period t, δ is the standard discount factor and β represents the present bias (a preference for immediate gratification).

In order to represent alcohol myopia, we could assume that an individual that has consumed alcohol has a present bias that depends on the amount of alcohol that is accumulated in his/her blood. This term increases the discount of the future as the amount of alcohol in the blood increases. The extended inter-temporal utility function would be given by the following definition.

Definition 5: The perceived utility function for an individual that has alcohol myopia via the present bias is given by the following equation:

where A' is the level of alcohol in the blood in period t and is given by where a_i is the amount of alcohol consumed in period i and w is the number of periods that the alcohol remains in the blood after its consumption. In order to represent that higher consumption of alcohol decreases the attention to the future, we assume that β (A^t) < 0.

Alcohol myopia and exponential discounting

We could also represent alcohol myopia assuming that the consumption of alcohol affects the δ factor of the traditional exponential discounting utility function. In this case, the δ factor would be a decreasing function of the amount of alcohol that is accumulated in the blood. If the alcohol consumption affects the exponential discounting, then the outcomes of lotteries that are paid in the future will be discounted depending on how far they are in the future, as opposed to the case in which alcohol consumption affects the present bias, in which case all future payoffs are discounted equally, independently of how far in the future they are.

The following definition assumes that the exponential discounting is a function of the amount of alcohol that has accumulated in the blood.

Definition 6: The perceived utility function for an individual that has alcohol myopia via the exponential discounting is given by the following equation:

where δ (A^t) < 0.