Crime as a Social Cost of Poverty and Inequality: A Review Focusing on Developing Countries

Crime as a Social Cost of Poverty
and Inequality: A Review Focusing
on Developing Countries
E Bourguignon

size, one may thus expect that, other things being equal, the crime rate
increases with the size of the city-.

The probability of crime detection can hardly be taken as given and
independent of the crime rate. What is more likely to be exogenous is the
amount that the urban community’ is spending on crime prevention and
detection, or, roughly speaking, on police. Let P be the corresponding
amount per inhabitant. It is natural to assume that:

q = G (P, c)

(3)

where G( ) is a kind of production function of police activity. It is assumed
to be increasing -at a decreasing rate- with P and decreasing -at an
increasing rate- with c. Substituting in (2) and solving with respect to c
yields a new ’reduced form’ crime function:

Й⁷ F

C = C*(n_p. —.--, P, H)

H' ¼'

(4)

where the argument corresponding to the probability of being caught, q,
has Simplybcen replaced by police expenditures per inhabitant. Therefore,
the statement that the crime rate should increase with city size, at least
in some range, implicitly assumes that police expenditures do not increase
with city size. If it does, this raises the question of what determines the
importance of police expenditures. Wc shall return to that question below;

To complete this simple theoretical framework, we now evaluate the social
loss due to crime. This loss is made of three components: (a) the direct
cost of crime, that is the physical and psychological pain of the victims,
(b) the cost of crime prevention (P) and the cost of the judicial system,
(e) the implicit cost F of sanctions to convicted criminals, typically
foregone earnings, due to imprisonment¹¹. Assuming that the cost of pain
is a proportion s of the economic cost of crime, χ ~bw ∙ the social loss
per capita associated to a crime rate c amounts to:

L = c-m-s- (⅛w) + P + c ■ q ■ [y] ÷ c ■ q ■ F

(5)

** Which would indeed justify F being proportional to w..

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