The model assumes that the police operate the radar trap at a particular site, or on a stretch of highway where drivers have been warned that a radar trap may be operating, and at certain times so that the probability of its operation can be determined. The model also assumes that a certain proportion of the driver population will comply with the speed limit after the operation of the trap and that on each occasion following nonoperation, the proportion of law-abiding drivers will fall. The model determines the steady-state expected proportion of drivers who cooperate with the law as a function of these variables as well as of the number of epochs necessary to achieve a steady-state. The model may aid in a determination of police patrol effectiveness and in attaining cost-effective patrol levels. Other applications are possible in situations which also have the ingredients of a stable population, repeated exposures to some form of surveillance or other stimulus, significant penalties or rewards, and the inability to discern in advance whether the surveillance is actually operating. In the field of marketing, it may be used to predict the effect of repeated advertising exposure on buyer behavior. The mathematical processes on which the model is based are described, and graphs illustrate their functioning. A reference list is included.