The economic approach to crime: A general analytical framework
This section develops a simple analytical framework for examining some of the economic issues that arise in the analysis of crime and punishment. Suppose that there is some activity, the level of which is denoted by x, which causes uncompensated harm to others. We will refer to x as the 'crime rate', although the analysis can be applied to any activity which the state deems illegal. Individuals benefit privately from this activity, and this benefit is denoted by B(x) with B'(x) > 0 and B"(x) < 0. We assume that the individual has a privately optimal level of illegal activity, denoted by x°, which is where B'(x°) = 0.
Let H(x) be the aggregate external harm caused by the activity x. We assume that these external costs are increasing and that marginal costs are non-decreasing, so H'(x) > 0 and H"(x) > 0. In the absence of enforcement costs or compliance costs, the efficient level of illegal activity maximises W = B(x) - H(x). We assume that there is a unique efficient level of illegal activity x*, where x* satisfies B'(x*) = H'(x*) .
There are several important points to note here. First, the benefits that accrue to the individual are included in the aggregate measure of welfare. To not include them would risk assuming the economic issue away and would ignore the private incentives of individuals to engage in illegal activity - if individuals do not gain some benefit from committing illegal acts, why do they commit them? Secondly, even if enforcement is not costless, the efficient level of illegal activity is generally not zero, although our specification certainly allows this a possibility (rather than imposing it).
Figure 9.2.1 The efficient level of illegal activity