The enforcement of speeding: should fines be higher for repeated offences?

Speed limits are a well-known instrument to improve traffic safety. However, speed limits alone are not enough; there is need for enforcement of these limits. When one observes fine structures for speed offences one often finds two characteristics. First, the fine increases with the severity of the violation. Secondly, the fine depends on the speeders' offence history. We focus on this last point and confront two fine structures, both increasing with speed: a uniform fine and a differentiated fine, which depends on the offence history. Drivers differ in their propensity to have an accident and hence in their expected accident costs. Literature then prescribes that the fine for bad drivers should be higher than for good drivers. However, the government does not know the type of the driver. We develop a model where the number of previous convictions gives information on the type of the driver. We find that the optimal fine structure depends on the probability of detection and on the strength of the relationship between the type and having a record. We illustrate this by means of a numerical example.