Economics 160
Lecture 7
Professor Votey
Crime Control:
Equity vs. Efficiency
Votey, Lecture 4, Notes, p. 51
Crime Control: Equity vs. Efficiency
The Economic Paradigm
 Recall the 3 steps
 A laudable goal: economic efficiency
 No guidance to so conceptually perfect a distribution
The Search for Equity
 Lester Thurow, “Equity vs. Efficiency in Law Enforcement:”
 Not a primary concern for management
 Equity in law enforcement: making some people better off
by making others worse off
Disparate Crime Levels
 North Dakota vs. California
 Santa Barbara County vs. Isla Vista
Achieving Equity
If Efficiency is easy, why is equity hard ?
Efficiency: The competitive market system
Equity: the people vs. Whom?
The American Revolution
Why did we go to war with England?
 “Taxation


without representation”
Unfair regulation of our trade
No say in the enactment of laws governing
the colonies
Achieving Equity
The
Constitution
 Our
representatives spell out how we shall be
governed
 Our rights and responsibilities are set down
 Equity is served
Achieving Equity
Preamble
to the Constitution
 the
Union was formed:
 “to
. . . establish justice, insure domestic tranquility,
..
 ., . . .promote the general welfare.”
Achieving Equity
Article
 There
IV, Section 4.
is no explicit mention of Congressional power
to deal with domestic crime. The article states:
 states can get help in cases of “domestic violence . . .
on application of the Legislature, or the Executive
(when the Legislature cannot be convened)”.
Achieving Equity
Amendment
 Control
X.
of crime is left to the states
 “STATES RIGHTS
Powers not delegated to the United States by the
Constitution nor prohibited by it to the States, are
reserved to the States respectively, or to the people.”
 Note that criminal cases in court are described as
“The People versus . . .”
Achieving Equity
 Article
 “The
VI, Section 2.
citizens of each State shall be entitled to all
of the Privileges and Immunities of the Citizens
in the several States.”
Achieving Equity
The Declaration of Independence
asserts:
“all men are created equal, that they are endowed
by their Creator with certain, inalienable rights,
that among these are Life, Liberty, and the pursuit
of Happiness.”
Achieving Equity
Politicians
MUST believe in Equity
Achieving Equity
What is the evidence?
 If
Efficiency is easy, why is equity hard ?
Efficiency: The competitive market system
Equity: the people vs. Whom?
Politicians MUST believe in Equity
 Crime Victimization:
Achieving Equity
 If
Efficiency is easy, why is equity hard ?
Efficiency: The competitive market system
Equity: the people vs. Whom?
Politicians MUST believe in Equity
 Crime Victimization: Equity ?
Achieving Equity
Crime Victimization: Equity ?
Youths
the most likely victims of crime
Violence peak: Victim age approx. 20
Theft peak: Victim age approx. 22
Achieving Equity
Crime
Victimization: Equity ?
•Males
•More likely victims of theft
•Much more likely victims of violence
Achieving Equity
Crime
Victimization: Equity ?
 Blacks
 most
likely victims of violence
 approx. equal to whites as victims of theft
Achieving Equity
Crime
 the
Victimization: Equity ?
Poor
 more
likely victims of violence
 for incomes <$3,000, >25,000, equally
high for theft
 Report to the Nation, data from 1980
Back to Economic Theory (Notes, p. 52)
4 Concepts
1. The Expenditure Function (for Law Enforcement)
$wL
E
B
wL1
a
0
w = Wage for Police
i.e., Resource Cost
L = Resource quantity
Note that:
tan a = AB = wL1 = w
0A L1
A
L1
L
Resources
wL is the Expenditure Level
and any point on line 0E
represents the expenditure level
for the corresponding level of L
4 Concepts (-cont.)
2. Isovalue Line
$wL
This is the Budget Constraint
of a Higher Income Community
wL1
*
$M1
$M
Other Goods and Services
* 450 if scale same on both axes
4 Concepts (-cont.)
3. Community Preferences
(Indifference Curves)
U3
$M
Other Goods
and Services
U2
DOF
0
OF1
Public Safety (GOOD)
Curves tend to imply
that as incomes rise,
the community would
U1
pay more to eliminate a
given amount of crime
U3 > U2 > U1
OF
Offenses (a BAD)
4 Concepts (-cont.)
4. Crime Control Technology
OF
If Crime is Controllable
OF1
OF2
0
L1
L2
L
Resources
4 Concepts (-cont.)
4. Crime Control Technology
OF
If Crime is not Controllable
the curve would look like this
0
L
Resources
II.
$M
2. Budget Constraint
I.
3.Preferences
Crime-Consumption
Possibility Frontier
MR
0
$wL
N
OFR
OF
wLR
LR
OFR is the Cost Minimizing
level of Offenses with $wLR
expenditures for Crime
Control
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
Suppose there is also
a Poor Community, with
income YPYP
YR
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
YP
0
OFR
OF
$wL
Questions?
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
Suppose there is also
a Poor Community, with
income YPYP
YR
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
YP
0
OFR
OF
$wL
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
Suppose there is also
a Poor Community, with
income YPYP
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
YR
YP
0
OFR
OF
$wL
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
Suppose there is also
a Poor Community, with
income YPYP
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
OFR
OFP
OF
$wL
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
OFR
OFP
OF
$wL
Note that the Poor
community has a higher
level of crime, OFP > OFR
(See Notes, Fig. 4.6)
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
OFR
OFP
OF
$wL
Note that the Poor
community has a higher
level of crime, OFP > OFR
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
OFR
OFP
OF
$wL
Note that the Poor
community has a higher
level of crime, OFP > OFR
Yet the Poor community is
spending a greater share of
its lower income on Crime
Control (See Notes, Fig. 4.7)
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
The implications of this can be seen YR
by closer examination
of the result in Quadrant IV.
YP
Crime-Consumption
Possibility Frontier
N
S
YR
YP
0
OFR
$wL
OFP
OF
P
R
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
The implications of this can be seen YR
by closer examination
of the result in Quadrant IV.
YP
Crime-Consumption
Possibility Frontier
N
S
YR
YP
0
OFR
$wL
OFP
OF
P
R
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
OFR
$wL
OFP
OF
P
R
Points P and R are the
cost minimizing points for
the Poor and Rich
communities
1.Expenditure Function
III.
L
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
$wL
III.
OFP
p
OF
P
p
1.Expenditure Function
OFR
L
R
The Orange (pp) line
reflects the imputed
relative price of resources
to offenses for the Poor
community.
(see Notes, Fig.4.9)
4.Crime Control Technology
IV.
II.
2. Budget Constraint
$M
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
OFR
$wL
OFPrr
P
OF
P
R
P
r
1.Expenditure Function
III.
L
The Red (rr) line reflects the
imputed relative price of
resources to offenses for
the Rich community.
4.Crime Control Technology
IV.
The Implicit Value the Community Places on
Public Safety or Losses to Crime
Economic Theory: 2 Goods
Slope of AB = tan a
Y
0A
0B
= quantity of Y
quantity of X
= pX / pY or
= price of X in terms of Y
A
(Oranges)
Y1
a
0
X1
B
=
Line AB can be thought of as the
budget constraint which can also
X be written as
Income = pX.X1 + pY.Y1
Understanding this allows us to impute the price the community
places on Crime
(Apples)
It helps to rotate the figure (Notes, Fig. 4.6)
in Quadrant IV. 900 to the left
OF
Line pp represents the Social Cost of Crime for
p
r
the Poor community.
How
?
P
R
Crime Control Technology
0
p
r L
At the upper left end we have all offenses, no control costs.
At the lower right end, we have all resource costs, no crime.
At P, we have the attainable mix chosen by society.
The line pp is an isovalue line like the budget constraint, and in this
case is the lowest attainable cost of crime for the Poor community.
Consider what Minimum Social Cost of
Crime means:
The Objective has been written:
Min. SC = VC + CC (victim costs plus control costs)
This is the same as
Min. SC = r . OF + w . L
where r is the loss rate or damages to the
victim, per offense (OF), and
w is the resource price or wage per
resource unit (L).
Just as with the Budget Constraint
Income = pX . X + pY . Y
and as in the theoretical illustration
The Implicit Value the Community Places on
Public Safety or Losses to Crime
Economic Theory: 2 Goods
•
Y
(Oranges)
Slope of AB = tan a
0A
0B
= quantity of Y
quantity of X
= price of X in terms of Y
A
Y1
a
0
X1
B
X
(Apples)
=
Consider what Minimum Social Cost of
Crime means: (-cont.)
•
Slope of AB = tan a = 0A
0B
= quantity of Y
quantity of X
= pX / pY or
= price of X in terms of Y, similarly
Slope of pp
=
quantity of offenses
quantity of resourses
=
pL / pOF
=
w
r
Finally, since, in absolute value, the slope of pp
is greater than the slope of rr
(look again at the figure from Quadrant IV.)
The figure from Quadrant IV. rotated
900 to the left
OF
p
r
P
R
Crime Control Technology
p
r L
Consider what Minimum Social Cost of
Crime means: (-cont.)
•
Slope of AB = tan a
Slope of pp
0A
0B
= quantity of Y
quantity of X
= pX / pY or
= price of X in terms of Y, similarly
=
=
quantity of offenses
quantity of resourses
=
pL / pOF
=
w
r
Finally, since, in absolute value, the slope of pp is
greater than the slope of rr
,this implies that
(w / r) for the Poor community > (w / r) for the Rich community
Consider what Minimum Social Cost of
Crime means: (-cont.)
•
Slope of AB = tan a
0A
0B
= quantity of Y
quantity of X
= pX / pY or
= price of X in terms of Y, similarly
=
Slope of pp = quantity of offenses = pL / pOF = w
quantity of resourses
r
Finally, since, in absolute value, the slope of pp is greater than tha slope
of rr (look again at the figure from Quadrant IV.), this implies that
(w / r)for the Poor community > (w / r) for the Rich community
Which, in turn, means that the loss rate (r) for the Poor
community is smaller than that for the Rich community.
The logic and the irony:
Efficiency does not lead to Equity
It should not be surprising that damages per offense
are lower in poor communities than in rich ones.
Nor should it be surprising that rich communities are
more willing to pay for defense against crime.
The irony is that, in the face of this, poor
communities will have a tendency to spend a
greater proportion of income on crime control
and yet suffer from higher crime rates.
The logic and the irony:
Efficiency does not lead to Equity
It should not be surprising that damages per offense are lower
in poor communities than in rich ones.
Nor should it be surprising that rich communities are more
willing to pay for defense against crime.
The irony is that, in the face of this, poor communities will
have a tendency to spend a greater proportion of
income on crime control and yet suffer from higher
crime rates.
The theoretical model is supported by empirical evidence.
See references to real world data in this regard in Phillips & Votey, Ch. 5
The Bad News may not be over
So far we have assumed that communities have identical
preferences and identical crime control technologies.
Suppose, however, that the poor community is lacking in
economic opportunities for youth and women, relative to
the rich community.
How would this affect the outcome ?
Consider the Crime Control Technology
Consider the Crime Control Technology
Recall: OF = g( CR, SV, SE, MC)
OF
CR = f( OF, L )
OFP
CCTP|SE2
OFR
CCTR|SE1
L1
L
Resources
II.
2. Budget Constraint
$M
I.
3.Preferences
YR
Crime-Consumption
Possibility Frontier
YP
N
S
YR
YP
0
OFR
OFP
OF
$wL
And an Even greater
proportion of income
spent for crime control
1.Expenditure Function
III.
L
A still higher
Offense Rate
4.Crime Control Technology
IV.
Questions ?

What does it take to achieve equity?
 A tax

Conclusions?
on rich communities
How might we characterize the impact of crime on
the poor communities of our analysis?
 As

a disproportionate tax on the poor
How do we reconcile this with Adam Smith’s
conclusions re “the invisible hand”?
Non-Market Decisionmaking


Is achieved in a democratic society thru the
political process
Adam Smith recognized that the market did not
solve all problems
A competitive market leads to Efficiency
 A concerned citizenry achieves Equity (thru

political processes)
Most political debates deal with equity issues
Next Time
Professor Phillips
I. Strategies to Estimate Deterence / II.
Optimization of the Criminal Justice System
Notes, Phillips Lecture 5
Questions to consider
What is economic efficiency?
 What is equity? Think about how these concepts differ.
 How are rich and poor communities likely
to differ with respect to crime levels?
 Can you explain why?
 Is the resulting difference Equity?
 How might greater equity be achieved?
