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.
- optimal control
- indiffenrence points
- rational addiction
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, 21(3), 507-522. https://doi.org/10.1007/s10100-012-0260-9