Multiple equilibria and indifference-threshold points in a rational addiction model

J.P. Caulkins, G. Feichtinger, R.F. Hartl, P.M. Kort, A.J. Novak, A. Seidl

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


Becker and Murphy (J Polit Econ 96(4):675–700, 1988) have established the existence of unstable steady states leading to threshold behavior for optimal consumption rates in intertemporal rational addiction models. In the present paper a simple linear-quadratic optimal control model is used to illustrate how their approach fits into the framework of multiple equilibria and indifference-threshold points. By changing the degree of addiction and the level of harmfulness we obtain a variety of behavioral patterns. In particular we show that when the good is harmful as well as very addictive, an indifference-threshold point, also known in the literature as a Skiba point, separates patterns converging to either zero or maximal consumption, where the latter occurs in the case of a high level of past consumption. This implicitly shows that an individual needs to be aware in time of these characteristics of the good. Otherwise, he/she may start consuming so much that in the end he/she is totally addicted.
Original languageEnglish
Pages (from-to)507-522
JournalCentral European Journal of Operations Research
Issue number3
Early online date27 Jul 2012
Publication statusPublished - Sept 2013


  • optimal control
  • indiffenrence points
  • history-dependence
  • rational addiction


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