A Note on Marginal Deterrence

The theory of deterrence has been concerned primarily with situations in which individuals consider whether to commit a single harmful act. For instance, a person may be deciding whether to discharge a pollutant into a lake. In some contexts, however, a person may be contemplating which of several harmful acts to commitwhether to discharge a pollutant into a lake or instead to discharge it onto the ground (where it might cause a different level of harm). In such contexts, the threat of sanctions plays a role in addition to the usual one of deterring individuals from committing harmful acts: it influences which harmful acts undeterred individuals choose to commit. Notably, undeterred individuals will have a reason to commit less rather than more harmful acts if expected sanctions rise with harm. This tendency is sometimes said to reflect marginal deterrence because an individual will be deterred from committing a more harmful act owing to the difference, or margin, between the expected sanction for it and for a less harmful act. The term “marginal deterrence” seems to be due to Stigler (1970), but the notion has been well known from the time of some of the earliest writing on sanctions. See Beccaria (1770, 32), Montesquieu (1748, Book VI, Ch. 16, 161-62), and Bentham (1789, 171). Bentham, for example, states (citing an essentially identical passage of Montesquieu) that an object of punishment is “to induce a man to choose always the least mischievous of two offenses; therefore where two offenses come in competition, the punishment for the greater offense must be sufficient to induce a man to prefer the less.” A point of the present note, however, is that considerations of marginal deterrence are not a r&on d’e^tre for sanctions to rise with harm. Optimal sanctions rise with harm in models with marginal deterrence only if one makes a particular assumption about enforcement effort-that it is of a general nature (in a sense to be defined). But this assumption also implies that optimal sanctions rise with harm in the usual models without marginal deterrence. Still, as will be noted, marginal deterrence does have a more refined implication for optimal sanctions under the assumption of general enforcement effort. To investigate marginal deterrence, I consider a simple model with monetary sanctions in which each person can do nothing or commit one of two harmful acts: either act 1, a low harm act, or act 2, a high harm act. Because individuals choose between