In this article we derive the mix of criminal sanctions—choosing among prison, parole, and probation—that achieves any target level of deterrence at lowest cost. We assume that prison has higher disutility and higher cost per unit of time than parole and probation and that potential offenders discount the future disutility of sanctions at a higher rate than the state discounts the future costs of sanctions. Our primary insight is that there is a front-loading advantage of imprisonment due to these differential discount rates. This advantage implies that whenever a sentence includes both a prison term and a parole term, the prison term should be imposed first, and that it may be optimal to employ a prison term even if prison has a higher cost per unit of disutility than parole and probation and even if prison is not needed to achieve the target level of deterrence.

中文翻译：

---

威慑与监狱，假释和缓刑的最佳使用

在本文中，我们得出了混合的刑事制裁措施（在监狱，假释和缓刑之间进行选择），这些措施可以以最低的成本实现任何威慑目标。我们假设监狱比假释和缓刑具有更高的无用性和每单位时间更高的成本，并且潜在的罪犯以比国家低估未来的制裁成本更高的比率来降低未来对制裁的无用性。我们的主要见解是，由于这些不同的贴现率，监禁具有前期优势。此优势意味着，只要句子同时包含监禁刑期和假释条款，便应首先判处监禁刑期，