Steven Shavell, A Note on Optimal Deterrence When Individuals Choose Among Harmful Acts (Nat'l Bureau Econ. Res., Working Paper No. w3061, Aug. 1989).
Abstract: The theory of deterrence has been concerned primarily with situations in which individuals consider whether to commit a single harmful act (whether to discharge a pollutant into a lake, whether to steal a car) rather than with situations in which individuals decide which of several harmful acts to commit (whether to discharge one pollutant or another pollutant into a lake, whether to engage in car theft or in burglary). In the latter situations, 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 (it accomplishes "marginal deterrence"). It is shown in the present note that sanctions may increase more with harm when individuals choose among harmful acts than when individuals choose only whether to commit single harmful acts. The reason is that a higher gradation of sanctions encourages the undeterred to commit less harmful acts. The assumption necessary for this conclusion is that probabilities of apprehension for different acts are equal, being determined by a general level of enforcement effort. If enforcement effort is specific to the act, the conclusion does not hold; optimal sanctions for different acts are then equal to each other.