Phillips/Econ
Winter 2012
Is Criminal Justice Just?-1
There are several aspects of the question, "is criminal justice just?". We examined
one of these in Ch. 5 of Phillips and Votey, when we noted poorer communities consume
less safety, i.e. have more crime, just like they consume less of other goods and services,
compared to more affluent communities.
This was illustrated with a 4-way diagram.
Another aspect of the equity issue is whether sentencing is fair or biased. A controversial
question in this domain is whether sentencing for capital crimes is fairly administered.
Data from the Report to the Nation on Crime and Justice show victimization rates in
1984 and 1985 for seven income classes ranging from less than $7,500 on the low end to
more than $50,000 on the high end. Comparing burglary and robbery, for example, both
victimization rates decline as income increases, as we would expect, but the rate for
robbery falls off more rapidly with income, on a proportional or percentage change basis,
as illustrated in Fig. 1. Why might this be?
--------------------------------------------------------------------5
Logarithm of the Victimization Rate
Ln Robbery
Ln Burglary
4
3
2
1
0
-7500
7500-9999
10000-14999 15000-24999 25000-29999 30000-49999
Income
50000-
Figure 1: Victimization Rate by Income Class
--------------------------------------------------------------------The distribution of the consumption of goods and services is measured
approximately by the distribution of income. Income for families is distributed approximately
log-normally. What this means is that the logarithm of income is distributed normally, or in
a bell-shaped fashion, but that income itself has a fat tail at upper incomes. Consequently,
the median family income, with half of the families above, and half below, was $25,807 in
Phillips/Econ
Winter 2012
Is Criminal Justice Just?-2
1985 while the mean or average family income of $32,944 was above this median since
the average was raised by the relatively small number of fortunate families at high
incomes. The cumulative distribution of family income in 1985, plotting the percentage of
all families below each income level, is illustrated in Fig. 2.
--------------------------------------------------------------------100
Cum. % Families
80
60
40
20
0
0
20000
40000
Income
60000
80000
Figure 2: Cumulativ e Distribution, US Family Income, 1985
--------------------------------------------------------------------A measure of inequality can be illustrated by a Lorenz curve, which plots the
percentage of total family income that is received by a percentage of the families, going
from the poorest to the richest. For example, the poorest 20% of families receive only 5%
of total family income, while the poorest 40% receive only 16% of the total, etc., as
illustrated in Fig. 3. The Lorenz curve can be calculated if the distribution of income is
available. The correspondence between various analytical distributions of income, such as
normal, equally probable (rectangular or uniform) and exponential, with their associated
Lorenz curves, is illustrated in the figure attached to these notes. If total family income was
divided equally among all families with each receiving the same amount, then the Lorenz
curve would be a diagonal. The ratio of the area between the diagonal and the Lorenz
curve to the area in the lower half of the box, as divided by the diagonal, is the Gini
coefficient. If the distribution were perfectly equal, the Gini coefficient would be zero. It is
about 0.36 in the United States compared to 0.31 in Japan, 0.41 in Italy, and 0.57 in India.
Phillips/Econ
Winter 2012
Is Criminal Justice Just?-3
120
Gini Coefficient= Area A/Area (A+B)
Cum. % Income
100
80
60
40
A
20
B
0
0
20
40
60
80
100
120
Cum. % Families
Figure 3: Lorenz Curv e, US Family Income, 1985
--------------------------------------------------------------------The cumulative percentage of families below the upper limit income for each of the
seven income classes suffering robbery or burglary, is listed in Table 1, along with the
(marginal) percentage in each class. The burglary and robbery rates for each class are
also listed (as plotted in Fig. 1). The cumulative percentage of the total number of each
crime's victims accounted for by that income class and lower income groups is also listed
and used to plot Lorenz curves in Fig. 4. Note that since crime is a bad, the Lorenz curve
lies above the diagonal. Note also that, as expected, from the victimization rates, the
incidence of robbery is less fair than burglary. Why is this the case?
Safety is both publicly and privately provided. In the case of burglary, the choice of
location is a big factor in safety. Other privately provided components are locks, alarms,
lighting, etc. A publicly provided service affecting safety is police car patrol and surveillance
and response time. In the case of robbery, private choices, such as avoiding dangerous
areas during leisure time, are a consideration and publicly provided services such as well
lighted streets, police foot patrols, and the like are important. Economists distinguish
between the nature of a good, whether it is public or private, and its provision.
For
example, a university education can be privately provided by Stanford or publicly provided
by UC. A good that is totally private in its economic nature can only be consumed by one
person. A good that is totally public in its economic nature is jointly consumed by all and
Phillips/Econ
Winter 2012
Is Criminal Justice Just?-4
.....................................................................................................................................
...
Cumulative
Distribution
of Families
Income Class
-7500
7500-9999
10000-14999
15000-24999
25000-29999
30000-49999
50000-
Income Class
-7500
7500-9999
10000-14999
15000-24999
25000-29999
30000-49999
50000-
.
.
.
.
.
041
092
.223
482
583
824
1.000
Marginal
Distribution
of Families
.041
.051
.131
.259
.101
.241
.176
Cumulative
Distribution of
Robbery Victims
.0790
.1554
.2956
.5727
.6808
.8871
1.000
Robbery Rate
Per 1000
Persons
9
7
5
5
5
4
3
Burglary Rate
Per 1000
Households
86
67
67
59
54
58
56
Cumulative
Distribution of
Burglary Victims
.
.
.
.
0588
1099
2563
5113
.6023
.8355
1.000
Table 1: Distributions of Robbery & Burglary Victims by Income
--------------------------------------------------------------------one person does not consume it or use it up. Education and safety are goods that
have both a private and public nature. Home defense may be largely private, using up
goods and services that could be used to defend other homes. But there is a public
component even to privately provided defense. For example, many of the homes around
mine are protected by private agencies such as WESTEC. I probably benefit without
paying. This is the so-called "free-rider" problem associated with "public" goods. Safety
from robbery, or safe streets, is probably mostly a "public" good. My walking down a safe
street does not consume or use up "safeness". Robbery (or safety from being robbed) is
probably more "public" while burglary is probably more "private".
The "free-rider" problem associated with "public" goods often leads to their underproduction and under-consumption, an inefficiency problem. There is an incentive to let the
other person pay for a "public" good. Consequently, the more "public" in nature the good,
Phillips/Econ
Winter 2012
Is Criminal Justice Just?-5
1.20e+0
Cumulative % Victims
1.00e+0
8.00e-1
Cum Robbery
Cum Burglary
6.00e-1
4.00e-1
2.00e-1
2.71e-20
2.71e-20
2.00e-1
4.00e-1
6.00e-1
8.00e-1
1.00e+0
1.20e+0
Cumulativ e % Families
Figure 4: "Lorenz" Curv es for Robbery & Burglary Victims
................................................................................................................................................
the more imperative that it is publicly provided. The production possibility frontier for
"private" goods and "public" goods in society is illustrated in Fig. 5. The optimal point is A.
The underproduction of "public" goods means we are probably at "B", with too many
"private" goods relative to "public" goods. This was John Kenneth Galbraith's point in The
Affluent Society. If robbery protection is "public" it is probably under-produced, with the
more affluent reluctant to tax themselves to protect the less affluent. This may be why
robbery rates rise so dramatically as income falls. In contrast, burglary protection is
"private" and hence not under-produced, and burglary rates are fairly constant with income
except for the lowest income class, where they rise rapidly probably because this class
cannot afford "private" protection.
Recall that the slope of the production possibility frontier is the ratio of the marginal
costs or social values (prices) of the goods. For example, in Fig. 5, the slope of the
production possibility frontier is the price of the public good relative to the price of the
private good. Note that the slope at B, where the public good is under-produced, is less
than the slope at A, the optimal mix of private and public goods. At B, the public good is
Phillips/Econ
Winter 2012
Is Criminal Justice Just?-6
Private Goods
B - Underproduction of the Public Good
A- Optimal Point
Slope of the PPF is the
Ratio of the Marginal Cost(Price}
of the Public Good to the Marginal
Cost(Price) of the Private Good- Note
that at the Point B, the Public Good is
Undervalued
Production Possibility Frontier(PPF)
Public Goods
Figure 5: The Underproduction of Public Goods(Safety)
.............................................................................................................................................
...............
under-valued relatively, reflecting the "free-rider" problem and the fact that people do not
value public goods which also benefit others as much as they value private goods which
benefit only themselves. This example of the contrast between burglary and robbery
where we compare the variation of victimization rates with income illustrates the point
made in the essay by Thurow that issues of equity and efficiency are often intertwined in
complex ways.
Lastly, with regard to the readings, the RAND study by Klein and all argues that
when all conditioning factors are taken into account, there is no evidence of racial bias in
sentencing in California. In contrast, the study by Myers and Sabol examines the
historical record for the past century and a half and notes that incarceration rates have
been much higher for blacks than for whites in our society, especially in the North. Lastly,
in a book not assigned, Capital Punishment and the American Agenda, by Franklin
Zimring and Gordon Hawkins, in chapter 4 they examine the question of "who should
die?", or perhaps more accurately, who should receive a capital sentence?