# Deterring illegal activity with monetary fines

The basic assumption is that the individual's choice of *x* leads to negative external harm. The economic approach to crime draws on the standard Pigouvian approach to the problem of negative externalities, with some slight modifications. Consider first a legal rule of *strict liability* for illegal acts: the individual is punished for any level of *x* that they choose. An alternative rule (which we examine further below) is one of *fault-based liability**,* where the individual is only punished if the level of activity that they choose exceeds some predetermined level, say X. This is analytically similar to the negligence rules we examined in Chapters 4, 5 and 6, and we examine it further below.

Suppose that there is some probability *p* that the individual will be caught and fined when they commit the illegal activity. Let the resource cost of achieving this probability be C(p), with *C**'(**p**) >* 0 and *C**"(**p**) >* 0. These are *enforcement costs**.* For the moment we assume that the probability of detection is fixed at some level *p* and therefore enforcement costs are fixed at *C **=* C(-). Including enforcement costs, total welfare is now:

Let us consider a system of fines that are designed to deter illegal activity. The analysis again emphasises the importance of marginal incentives, rather than total incentives. Let the size of the *marginal* or per unit fine be equal to *f **>* 0. Thus, if an individual commits a level of criminal activity equal to x, he will face a fine of *fx* >0 with probability p, and no fine with probability 1 *- **p**.*

Note that the marginal fine *f* here does not explicitly include the benefits obtained by the individual. The reason for this assumption is straightforward: for some crimes (such as financial crime) it may be possible to force the criminal to return some or all of the gains that he obtains from crime. But for others (such as murder) this will simply not be possible, since most or all of the criminal's benefit could be non-pecuniary.

Finally, we allow for the possibility that a system of fines may be costly to administer in total (with total costs of *K **>* 0), but that the *marginal* cost of administering fines is zero (this assumption is relaxed later). There are now two questions of interest:

- 1. How does the individual react to different levels of
*f*? (The positive question) - 2. What is the efficient marginal fine? (The normative question).