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Rationally risking addiction: a two-stage approach. (English) Zbl 1476.91035

Haunschmied, Josef L. (ed.) et al., Dynamic economic problems with regime switches. Cham: Springer. Dyn. Model. Econom. Econ. Finance 25, 85-110 (2021).
Summary: We extend the Becker-Murphy rational addiction model [G. S. Becker and K. M. Murphy, “A theory of rational addiction”, J. Polit. Econ. 96, No. 4, 675–700 (1988; doi:10.1086/261558)] to account for a period before the onset of addiction. While during the first stage of recreational consumption of the addictive good does not imply negative effects, the second stage is analogous to the classical Becker-Murphy model. In line with neurological research, the onset of addiction is a random event positively related to the past consumption of the addictive good. The resulting multistage optimal control model with random switching time is analyzed by way of a transformation into an age-structured deterministic optimal control model. This enables us to analyze in detail the anticipation of the second stage, including the possible emergence of a Skiba point. A numerical example demonstrates that it is optimal to stop consuming the addictive good in case of an early onset (i.e. at a low level of cumulative consumption) of addiction. A late onset tends to lead into long-run addiction.
For the entire collection see [Zbl 1461.91004].

MSC:

91B05 Risk models (general)
49K20 Optimality conditions for problems involving partial differential equations
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