# Law and social norms

The coordinating role of speed limits discussed in the previous section is an extreme example of how formal legal rules can interact with more informal standards of individual behaviour. It is important to note that throughout this book, when we refer to 'legal rules' we are not referring exclusively to formal legal rules. Some of the most important legal rules are not formal at all - they take the form of social norms or standards of behaviour which evolve over time. Becker (1974) and Becker and Murphy (2000, chapter 2) show how *strong complementarities* between individual and group behaviour can lead to 'social multipliers' which, in a legal setting, can reinforce (or work against) the individual effects of formal legal rules. We can interpret these situations as occurring when social norms have strong influences on individual behaviour, which may override or reinforce the effects of formal legal rules.

To see how these social norms can operate in a legal setting, suppose that there is a continuum of individuals, and that individual *i* is considering the level of 'illegal activity' in which he will engage. Let this level be denoted by *x**.* The benefit of illegal activity to individual *i* is

dn d2 *B*

B(x,, *X*), with *B _{x} =* — > 0 and

*B*—

_{x x}=*< 0, and where*

_{T}*X*= f

*xdi*is

^{Xi} *dx, ^{XiXi} dx2 ^{J 1}*

the aggregate level of illegal activity. The continuum assumption simply formalises the notion that each individual has a negligible effect on *X*, although acting together individuals have a significant effect. We will assume that *X* affects individual *i*'s benefit negatively (although, as we will see, this assumption is not required for the analysis that follows),

so that *B _{X} = <* 0. If the individual chooses to commit illegal activ-

*dX*

ity of *x**,* we assume that he faces an expected fine of *p**fx**,* where *p* is

the probability of being caught and punished, and *f* is the marginal fine (that is the fine per unit of illegal activity). Thus the individual's expected gain from choosing x, is:

The individual equates marginal benefits with expected marginal costs, so the individually optimal level of illegal activity, denoted by x*, solves:

and we can write:

The presence of *strong complementarities* in this context simply involves an assumption that holding other variables constant, the individual's choice of illegal activity depends positively on the aggregate level of illegal activity *X -* that is, on what all other individuals do. In this sense, *X* can be regarded as a social norm or a standard of behaviour, which influences individual behaviour.^{5} For example, there may be a social norm not to respect private property rights, so that an individual's choice of whether to commit theft depends strongly on his own benefits from theft, as well as the aggregate level of theft - even though a higher aggregate level of theft makes each individuals worse off. Analytically,

strong complementarities depend on the sign of *В _{X} =* , not on

^{i} *dx _{i}dX*

the sign of *B _{X}.* To see this, hold the expected fine constant, and totally differentiate equation (2.1), which yields:

so that:

*dx**

Since *В _{хх}* is assumed to be negative, the sign of L turns on the sign

*dX*

of B_{xX}, which is the effect of *X* on the individual's *marginal* (not total) benefit of illegal activity. If this is positive, then strong complementarities are said to be present.

To see how these strong complementarities or social norms can interact with the formal legal system, suppose that the expected fine is increased, either by increasing p, *f* or both. In the presence of social norms, there are

now two effects that need to be considered. The first is the partial effect of the

Эх*

increased fine on individual behaviour, *i* . Holding *X* fixed, this is nega-

*d(pf*)

tive. The second effect is the reinforcing effect of social norms on individual behaviour.

The change in the expected fine affects all individuals and so affects the aggregate, and this feeds back into individual choices. The effect on the total level of illegal activity is therefore given by:

so that:

The numerator in equation (2.2) is the sum of the partial effects of an increased fine on individual behaviour, holding *X* fixed. The denominator is the 'social multiplier' effect, which boosts the change in aggregate illegal activity above and beyond the effect that would occur in the absence of dx*

any social norms. If 0 < f *—di <* 1, then the increase in the expected fine ^{J} ЭХ

may have a significant effect on aggregate illegal activity, even though

*dx**

the partial effect on individuals ^{!} ?, may be quite small. On the other

d*(Pf*) _{dx}*

hand, if there are no strong complementarities present (so that L < о)

*dX*

then the denominator in equation (2.2) would exceed unity, and the deterrence effect of the increase in the expected fine on individual behaviour would be less than the sum of the partial effects on individual behaviour.