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J. P. Caulkins, G. Feichtinger, R.F. Hartl, P.M. Kort, A. Novak, A. Seidl:
"Multiple Equilibria and Indifference-Threshold Points in a Rational Addiction Model";
Central European Journal of Operations Research, (2012), 16 pages.

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 addictionmodels. 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.

Optimal control · Indifference points · History-dependence · Rational addiction

http://dx.doi.org/10.1007/s10100-012-0260-9

http://publik.tuwien.ac.at/files/PubDat_212051.pdf