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Steven Shavell, A Simple Model of Optimal Deterrence and Incapacitation, 42 Int'l Rev. L. & Econ. 13 (2015).

Abstract: The deterrence of crime and its reduction through incapacitation are studied in a simple multiperiod model of crime and law enforcement. Optimal imprisonment sanctions and the optimal probability of sanctions are determined. A point of emphasis is that the incapacitation of individuals is often socially desirable even when they are potentially deterrable. The reason is that successful deterrence may require a relatively high probability of sanctions and thus a relatively high enforcement expense. In contrast, incapacitation may yield benefits no matter how low the probability of sanctions is—implying that incapacitation may be superior to deterrence.