Offense Control Taking into Account Heterogeneity of Age

This paper studies the optimal tradeoff between the benefits and costs of preventing offenses and treating offenders. Based on a flexible age-structured epidemiological framework, a two-state compartment model is analyzed to reduce the prevalence of offending such as illicit drug consumption or violence. It turns out that, even in this highly simplified model, multiple stationary states exist. In particular, three different kinds of equilibria are identified, i.e., law and order, conservative, and liberal. The optimal mix of the control instruments is calculated providing interesting insight into the structure of the paths minimizing the discounted stream of social costs and expenditures for prevention and treatment. It can happen that a Skiba point exists. This implies that, for an initially small number of offenders, saddle-point convergence to a law-and-order equilibrium (boundary solution with no offenders) or to a conservative equilibrium (with few offenders) occurs, while if the number of offenders is large, the effects of prevention and treatment are too low or too expensive so that a liberal equilibrium (with many offenders) occurs.