Multiple equilibria and indifference-threshold points in a rational addiction model
Caulkins,J.P. Feichtinger,G. Hartl,R.F. Kort,P.M. Novak,A.J. Seidl,A.
Caulkins,J.P.
Feichtinger,G.
Hartl,R.F.
Kort,P.M.
Novak,A.J.
Seidl,A.
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.
Description
Date
2013-09
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
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Journal Issue
Keywords
optimal control, indiffenrence points, history-dependence, rational addiction
Citation
Caulkins, J P, Feichtinger, G, Hartl, R F, Kort, P M, Novak, A J & Seidl, A 2013, 'Multiple equilibria and indifference-threshold points in a rational addiction model', Central European Journal of Operations Research, vol. 21, no. 3, pp. 507-522. https://doi.org/10.1007/s10100-012-0260-9