Predicting utility under satiation and habit formation

We introduce a modification of the discounted utility model that accounts for both satiation and habit formation in intertemporal choice. Preferences depend on the satiation level and the habitual consumption level. These two state variables, together with the shape of the value function, drive the properties of the model. One unique feature of our model is that it addresses the trade-off between seeking variety and maintaining acquired habits. We examine several properties of our model, such as the nontrivial patterns of desirability (willingness to pay) for an additional unit of consumption, or the effect of abstaining from consumption (craving). We explore the shape of optimal consumption patterns in discrete and continuous choice settings. If subjects underestimate the changes in satiation and habituation levels, as occurs under projection bias, our model explains why people buy more when hungry, or prefer variety in advance of consumption but stay with the same consumption good in actual use.