Detection avoidance and deterrence: some paradoxical arithmetics

This paper extends Malik's (1990) analysis to the case where criminals' avoidance efforts and public expenditures in the detection of criminals are strategic complements in the aggregate technology of control of illegal behaviours. In this set up, we show that whenever criminals' avoidance efforts are more sensitive to the frequency than to the severity of sanctions, it is always socially efficient to set the fine at the maximal possible level. However, several paradoxical consequences occur: there may exist overdeterrence at optimum; more repressive policies lead to less arrestations of offenders while more crimes may be committed; at the same time, the society may be closer to the first best number of crimes.