Rational addictive cycles (‘binges’) under a budget constraint

We consider an individual whose utility at any moment depends not only on the current consumption of a good but also on the habit accumulated by past consumption. The rational decision maker maximizes the discounted utility stream over an infinite time horizon subject to a budget which can be replenished by habit‐dependent earnings. Addiction to the good requires that past consumption increases the marginal utility of current consumption. It is shown that strong complementarity might imply persistent oscillations in the optimal consumption pattern. Using Hopf bifurcation theory, we prove the existence of stable limit cycles in a numerical example.