Optimization of the level of crime is the main task of law enforcement agencies. It is believed that they should eliminate and liquidate the crime rates. However, when considering them in terms of cost-benefit analysis, it is unknown what has biggest loss to society - crime or struggle with the crime.
The more is the protection order, the more pressure is experienced by law-abiding citizens, who are forced not only to hold taxes for provision of army security forces, but also to carry a lot of humiliating bureaucratic procedures to prevent potential socially possible offenses. In principle, it is absolutely all those guilty can be punished if all the resources of society will be thrown exclusively for law enforcement. The practice has proved that, indeed, in totalitarian societies the level of crime is lower than comparable with democratic societies. Moreover, the state can, on the other hand, generally avoid costs on defense, but in such anarchic world the loss from crime will inevitably increase.
Obviously, any extremes in this matter are equally undesirable. The principle of optimizing behavior in this case requires minimizing the total cost of crime, which includes the loss of society from crime, and the costs for the prevention of crime. Criminologists identify four functions of criminal’s sentences: punishment of the guilty, their isolation in order to prevent them from committing new crimes (imprisonment), reeducation of offenders and deterrence of potential criminals. Economists are focusing on the function of deterrence, believing that other functions are purely ethical (punishment), or applicable to a limited number of criminals (isolation), or just questionable (reeducation). One of the most important results of the economic approach to the analysis of crime is the conclusion that punishment in the form of increasing the probability of arrest and the length of sentence is withheld from the crime.
Combined losses of society are minimized only in the case if the probability of the crime and the severity of punishment are such that offenders are only those who are inclined to take risks. If we turn to the equation of the income of the crime, the expected loss from the offense should not exceed the benefit from crime. This equation is fundamental in the development of rational policies of crime deterrence in the form of imprisonment. From this equation it is obvious that the degree of punishment and its severity are the substitutes, that is, they can be interchangeable: the appointment of severe penalties of low crime detection has the same deterrent effect as the assignment of weak of sentences in high crime detection. Empirical studies specify that an increase of 1% probability of sentence deter crime more than the increase of 1% severity of punishment.