N. Brooks J. of Economic Behavior Org. 44 2001 249–267 261
Proposition 3. If the average w
i
decreases, ceteris paribus, then the equilibrium percentage of deviant behavior will increase at an increasing rate. If the variance of the returns is
increased holding the average constant, then the equilibrium percentage of deviant behavior will increase at a decreasing rate.
Proof. To hold the variance constant substitute w = ¯ w − variance into the equilibrium
solution of w
∗
as given in footnote 17. The derivative of this with respect to ¯ w is negative
while the second derivative is positive. Similarly, to hold the average return constant substitute w = 2average w
i
− ¯ w into the
equilibrium solution of w
∗
. The derivative of this with respect to ¯ w is positive while the
second derivative is negative. When the average return in the community increases the interior stable equilibrium critical
return w
∗
decreases and thus the equilibrium percentage of deviants also decreases. It is important to note that the equilibrium percentage of deviants decreases non-linearly, thus
there will be a lower overall level of deviance if instead of having one community with a high average return and one community with a low average return there are two communities
with an average return in the middle. If the variance of the returns increases the equilibrium percentage of deviants increases at a decreasing rate.
These comparative static results of the stable interior equilibrium illustrate two points. First, the equilibrium percentage of deviant behavior decreases in response to a increase in
the average return to trade. This is consistent with evidence of the negative effect on behavior of concentrated poverty. Of particular interest is the non-linearity of this relationship, which
implies that the overall level of deviance can be reduced if different neighborhoods have a more equal income distribution. The second result illustrates the increase in the equilibrium
percentage of deviant behavior due to an increase in the mean preserving spread of returns. This implies that the equilibrium level of deviant behavior is a function of income inequality.
5. Discussion of theoretical results
The purpose of this model is to demonstrate the important effect that community economic conditions have on the ability of a community to generate adherence to socially efficient
norms. Individuals who might typically be inclined to follow “mainstream” behavior will not do so given limited returns to cooperating andor a large percentage of fellow deviants who
are costly to ostracize. There are two important externalities. The first is that deviant behavior has a social cost, second the overall cost of sanctioning is a function of the distribution of
statuses in the community.
There are several theoretical results in this paper. If the community is at the stable equi- librium with the lowest percentage of “deviants” then an increase in the average return to
“mainstream” behavior or a decrease in the inequality of returns will non-linearly lower the percentage of “deviants” in the community. This result implies that a lower overall
level of “deviant” behavior can potentially be attained by redistributing income from rich communities to poorer ones in a way that increases the marginal return to cooperative be-
havior. Another result states that if the upper bound on the distribution of returns is below some critical value then there will be only one equilibrium in which all individuals will
262 N. Brooks J. of Economic Behavior Org. 44 2001 249–267
prefer to deviate. This equilibrium is stable so even if the distribution of returns improves, no individual will have an incentive to be cooperative. This results potentially limits the
effectiveness of income redistribution implied by the first two results. This analysis is simplistic in that we are only considering the case of heterogeneous returns
to cooperative behavior w
i
. It may be important to analyze the case of heterogeneous returns to deviant behavior. It may be that some individuals while having a low return to cooperative
behavior may have an even lower return to deviant behavior. Merton 1957 discussed how the “absence of realistic opportunities for advancement
results in a marked tendency toward deviant behavior”.
18
Wilson 1987, 1996 conjectures that a likely cause of the pathological social patterns of the urban poor result in part from
the absence of a middle class or stable working class in the post-industrial inner city. These groups not only reinforced societal norms but they maintained social institutions such as
churches, shops, etc. He also points out that high rates of neighborhood poverty are less likely to create problem of social organization if residents are working in the mainstream
labor market. This model illustrates a mechanism that is consistent with these conjectures and consistent with the observations that increases in deviant behavior have been observed
in areas with increasing concentrated poverty.
6. Empirical issues and estimation
