Optimal Consumption Sequence When Habituation Dominates Satiation

In this note, we answer an open problem proposed in Baucells and Sarin (2010, p. 293) to find the optimal consumption sequence when habit formation dominates satiation in an intertemporal choice framework. We find that if consumers do not abstain from consuming goods then, for certain types of S-shaped value functions, consuming the same good in all the periods is optimal. However, if consumers do abstain from consuming goods, that result holds for certain kind of piece-wise linear functions