Categorization of Threshold Phenomena in Mathematical Models of Demand for Addictive Goods

A lack of mathematical economic demand models for addictive goods that account for nonconvex consumer preferences with thresholds resulting in discontinuous demand curves (frequently with bifurcations) is often attributed to the need that economic variables must be relevant to incentivize behavioral changes in addicts. Once addiction thresholds are reached, and economic variables such as prices or taxes become less efficient or completely inefficient in their corrective role, addressing underlying causal addiction issues becomes maybe the only remedy to the problem. The objective of this paper is to develop a mathematical categorization of threshold phenomena and subsequently suggest a different way to model demand for addictive goods from what has been a standard practice to date. Non-exhaustive set of threshold phenomena including a discontinuous threshold phenomenon (DTP), a singular-point threshold phenomenon (STP), and quasi-threshold phenomenon (QTP) are defined mathematically and presented visually. While economic variables may play a preventative role in addictive goods consumption, prescriptive component in addiction economics research can be accommodated in the models such as these developed here. It is more realistic and useful when coming modeling of addictive behavior comes from positive, rather than normative, framework and analysis. In such cases, the transfer of knowledge acquired through addiction intervention research into clinical settings has great promise as a means of increasing treatment effectiveness and facilitating greater consistency in practice. Indeed, recognizing what are the root causes of observed, actual health behaviors are more likely to lead to more efficient policy interventions. Riches of models in health behaviors research and epidemiology may serve as a good starting point to retooling an economist’s thinking on the subject.