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SEFΠCMIM DE IW ™ТИ* ЯН
that it is distributed uniformly in the population over the interval [O, H].
In the ease where F is proportional to wealth, it may be seen that very rich
people for whom x is small in proportion to their initial wealth, u,ι, will
never find it attractive to get into crime. To simplify, let us go further and
assume that it is never optimal for individuals in the middle and rich
classes to engage in criminal activities, even if their degree of honesty is
minimum. In other words, condition (1) is never satisfied even with h. = O
for persons in classes m and r. On the contrary, we assume that it is satisfied
for h. = O in class p but not for h. = fl. This means that there always is a
proportion of people in the poor class, p, who will engage in crime. Finally,
we suppose that the crime premium .v is proportional to the mean income
or wealth in the population: .v — bw. This would be the case, for instance,
if crimes consisted of robberies and thefts of which victims would be
randomly taken in the population. When comparing different societies, it
is also a way of representing the fact that, loosely speaking, the crime
premium is related to the average level of affluence of society.
Under these assumptions, it may readily be calculated that the crime rate,
or percentage c of criminals in the whole population is given by10:
n , if Pbw if, + bw <y ρ
----— J=C(n . — .q.H} (2)
W W,, W „ - F wl, W,
According to the canonical model the crime rate thus depends positively
on the extent of poverty and income inequality as measured respectively
by the proportion of poor, rι^ and the ratio w / и,fl, and negatively on ‘crime-
deterrent’ variables, that is the probability of being eaught, q, as well as
the size of the penalty, F, relative to initial income. In addition, it depends
negatively on the cultural or sociological attitude toward crime or the
extent Ofhonestywdthin society, as represented by W.
Although urbanization does not appear anywhere in the preceding
argument, it is implicit in the preceding model. In comparison with small
villages and rural areas, cities guarantee anonymity and therefore diminish
the probability, q, of being caught after a crime. Starting from a small city
U) The following rale is simply the product or the proportion of poor in society times the proportion
of individuals with h satisfying condition (1) among the poor
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