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

Jonathan Caulkins, Gustav Feichtinger, Richard Hartl, Peter Kort, Andreas Novak and Andrea Seidl

Central European Journal of Operations Research, 2013, vol. 21, issue 3, 507-522

Abstract: 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. Copyright Springer-Verlag 2013

Keywords: Optimal control; Indifference points; History-dependence; Rational addiction (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10100-012-0260-9

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