Economic models of crime have focused primarily on the goal of deterrence; the goal of incapacitation has received much less attention. This paper adapts the standard deterrence model to incorporate incapacitation. When prison only is used, incapacitation can result in a longer or a shorter optimal prison term compared to the deterrence-only model. It is longer if there is underdeterrence, and shorter if there is overdeterrence. In contrast, when a fine is available and it is not constrained by the offender's wealth, the optimal prison term is zero. Since the fine achieves first-best deterrence, only efficient crimes are committed and hence, there is no gain from incapacitation.
Miceli, Thomas J., "Deterrence and Incapacitation: Towards a Unified Theory of Criminal Punishment" (2009). Economics Working Papers. 200911.