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

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

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

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  • Jonathan Caulkins & Gustav Feichtinger & Richard Hartl & Peter Kort & Andreas Novak & Andrea Seidl, 2013. "Multiple equilibria and indifference-threshold points in a rational addiction model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 507-522, September.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:3:p:507-522
    DOI: 10.1007/s10100-012-0260-9
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