Plea bargaining and the costs of trial

In the previous sections we assumed that once offenders were caught, they were automatically convicted. But criminal trials are a costly and uncertain process. In this section we investigate the effects of prosecution and defence costs on illegal activity. Suppose that if an individual is caught (which still happens with some probability p) there is a marginal cost of prosecution that is equal to a > 0. In addition, suppose that there is a marginal cost to the individual of going to trial of b > 0. Once the individual is caught, the outcome of the trial is certain: he will be punished and fined an amount f per unit of illegal activity in which he has engaged. Assume that p is fixed. If the individual commits illegal activity of x, his net expected benefit is:

The individual's optimal level of illegal activity satisfies:

Welfare is now:

where we have omitted the costs of detection and enforcement, which are assumed to be fixed. The efficient level of crime now satisfies:

and the expression for welfare in (9.40) is maximised. To induce the individual to choose this efficient level of illegal activity, we simply set the expected fine in (9.39) to be equal to the marginal cost of illegal activity on the right-hand side of (9.41), which gives:

or:

The enforcement authority should set the fine equal to the costs of prosecution, plus the discounted value of the marginal social harm, where the discount rate is the probability of the individual being caught. Note that at this fine, the level of illegal activity is lower than if prosecution and defence costs were zero, since B'(x*) = p(a + b)+ h > h. However, if p can be varied and fines can be increased without limit, it is again possible to have p ~ 0, in which case we would have p(a + b) = 0 and it would be possible to increase the level of illegal activity, avoid legal costs and increase welfare, so that we again have B'(x*) = h.

However, even if p cannot be reduced to close to zero, there is another way that the costs of going to trial for both the prosecutor and the defendant could be avoided: plea bargaining. Suppose that p is fixed and that setting p(a + b) = 0 is not possible. Under the rule in (9.42) once individuals are caught, they face costs of:

On the other hand, the prosecutor's expected net benefit of going to trial is:

Notice that the incidence of trial costs falls completely on the criminal. At the welfare optimum, the expected trial costs are fully incorporated into the fine, which is paid by the criminal.

Suppose that the prosecutor makes an offer to the individual to accept a fine of F, instead of going to trial. Then for this fine to be acceptable to both parties, it must satisfy:

Such a plea bargain fine always exists, since a + b >0, and the gains from plea bargaining are the total costs of not going to trial. Suppose that the parties split these gains equally. Then the prosecutor receives revenue of:

and the individual faces costs of:

Note that the fine that the criminal accepts could be under a plea bargain could be higher than what he would have to pay in the absence of plea bargaining. Indeed, with the split the surplus rule, this happens if b > a. Intuitively, the criminal is willing to pay a higher monetary fine if the costs of trial that he would otherwise face are sufficiently high.

Are there any social gains from plea bargaining? With plea bargaining, the individual's level of illegal activity now obeys:

which exceeds the level of illegal activity in (9.41). Intuitively, the lower 'price' of committing illegal activity results in an increase in those activities. This higher crime rate is part of the social cost of plea bargaining.

However, plea bargaining also provides a social benefit, since the costs of going to trial by both criminals and prosecutors are now not actually incurred. The 'price' that the criminal faces is now a pure wealth transfer, and this transfer and its receipt by the prosecutor involve no use of real resources. Social welfare is therefore equal to:

where xc obeys the expression in (9.46) above. The difference between the two measures of welfare is:

which is always positive, as shown in Figure 9.4.1. The triangle labelled W* in Figure 9.4.1 is the level of welfare when trials are costly and fines are levied optimally. If plea bargaining occurs, the individual accepts the offer of a fine which reduces his total expected cost of committing

Figure 9.4.1 The costs and benefits of plea bargaining illegal activity, which therefore provides an incentive to increases illegal activity. However, at x*, the marginal social benefit of increasing illegal activity is p(a + b) + h, whereas the marginal social cost in the presence of plea bargaining is only h. Since marginal benefits exceed marginal costs, it is efficient to have the crime rate increase - but only if the costs of trial can be avoided. This is exactly what plea bargaining achieves.