MANAGERIAL AND DECISION ECONOMICS
Manage. Decis. Econ. 26: 461–473 (2005)
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/mde.1230
Economies of Scale and Market Power in
Policing
Lawrence Southwick Jr.*,y,z
School of Management, University at Buffalo, Buffalo, NY 14260, USA
The objective of this paper is to use a simultaneous equations method for estimating police
production and demand to determine whether or not there are economies of scale in policing.
In addition, the effect of market power on productivity, using the Herfindahl–Hirschmann
Index, is to be measured. The estimation yields the result that there are diseconomies of scale
with respect to the amount of crime beyond about 22 000 people in the policing jurisdiction and
diseconomies of scale in numbers of police beyond about 36 000 people. Efficiency is also
reduced where there is greater market power. This is conjectured to be the public sector
equivalent of taking market power profits. Copyright # 2005 John Wiley & Sons, Ltd.
INTRODUCTION
An important issue in local government services is
their efficiency. It is often argued that larger
governments are needed to ensure that economies
of scale and thus greater efficiency are realized. As
should other enterprises, local governments ought
to be concerned about measuring the efficiency of
their activities. While their major concern is often
with ensuring the provision of some service, the
cost of that service needs to be kept in mind as
well. The local government can usually raise more
money through taxation in order to continue to
provide the desired set of services, but the pot of
money is not unlimited and the overall well-being
of the citizen-taxpayer should more appropriately
be the objective of the elected officials.
*Correspondence to: School of Management, University at
Buffalo, Buffalo, NY 14260, USA. E-mail: ls5@buffalo.edu
y
University Research Scholar, University at Buffalo, and
Comptroller (retired), Town of Amherst, NY (pop. 116,000).
z
I appreciate several useful comments from an anonymous
reviewer. Neither organization nor any reviewer is responsible
for any of the comments expressed herein.
Copyright # 2005 John Wiley & Sons, Ltd.
It is certainly possible to contract out services in
order to achieve economies of scale. For example,
many municipalities contract out their garbage
collection services. A very large supplier can
service several municipalities so, if there are
economies of scale, they may be achieved through
this mechanism. This can be a substitute for
producing the service in-house. An example in
policing is the city of Lakewood, California. As do
several nearby cities, it contracts with the Los
Angeles County police for the various desired
policing services. An alternate contractor for many
cities in that area is the City of Los Angeles. Also
keeping prices in check is the ability of the local
government to choose to produce the service on its
own.1 In addition, it is possible to contract out
parts of the policing activity, particularly support
services (see Chaiken and Chaiken, 1987).
The objective of this paper is to analyze local
governments which choose to produce policing
services on their own. This is true of most local
governments of even modest size. In particular, the
state of New York will be the focus of this study in
order to provide a consistency over the legal
system and laws. Because most produce as well as
462
L. SOUTHWICK JR.
provide policing services, the question of scale
economies is very important. It leads to higher or
lower tax costs, depending on the size of the
municipality.
Frequently, it is suggested that communities, by
merging, would have lower costs for policing. It is
alleged that this would come about through
elimination of duplicate layers of management. If
there are, in fact, economies of scale, savings could
well be the result of such mergers. On the other
hand, suppose (as one example) that the managerial span of control is fixed. Then, the bureaucracy
will be larger as the size of the police force
increases and there are likely to be diseconomies of
scale. The result of mergers then would be an
increase in costs or a reduction in the level of
service. The question of which effect appears to
dominate is a major reason for this paper. It is
desired to know whether there are economies or
diseconomies of scale or whether there is an
optimal size.
In addition, we shall look at the question of
whether market power affects costs. Certainly, in
the private sector, prices tend to be higher in cases
where firms have more market power. Governments, of course, do not make profits. It is more
likely that they would use their market power to
reduce efforts towards efficiency and would thus
increase costs for their constituents. It is also
possible that the market power on the production
side would allow lower prices to be paid to
providers. Again, the dominant effect of these is
to be found empirically. Benson (1998, Chapter 3)
argues that governments which do not face much
competition are likely to raise their constituents’
costs. This is also similar to Niskanen’s (1968,
1971) argument that bureaucracies attempt to
increase their budgets and that competition can
be used to keep them in line. Wyckoff (1988, 1990)
argues that slack, rather than budget size, can be
an objective of the bureaucrat, but either results
in an efficiency reduction. Benson (1995) gives
an excellent review of how bureaucrats may
well pursue objectives other than those desired
by their employers, with the result that inefficiency
increases.
For the police, the usual objective is the
reduction of crime.2 There are traffic control
objectives and service objectives as well, but the
focus here will be on crime as the leading measure
of success or failure by the police. Inasmuch as
there are several different types of crimes, it is
Copyright # 2005 John Wiley & Sons, Ltd.
desirable to create a single measure of crime to be
used for this measurement.3 Further, since prevention of crime is the primary objective rather
than the apprehension of criminals, it will be
desirable to estimate the amount of crime that
there would be absent the police. At the least, we
want to know how the number of police utilized
affects the amount of crime. Of course, the police,
by apprehending criminals, give a disincentive to
commit crimes. Corman et al. (1987) find that
arrests do give this result. Viscusi (1986) also finds
that deterrence is an important effect. There are
many additional studies which also show this
effect.
Police departments can allocate their resources
devoted to preventing crime in a number of ways.
However, we would infer from the choices made
that the allocation equates the ratio of the
marginal disutility of each crime to the marginal
crime prevention effect of the resources devoted to
preventing that crime. This is an optimal allocation procedure. It takes into account the effectiveness in preventing each crime as well as the dislike
the community has for or harm the community
receives or perceives it receives from that type of
crime.
Generally, we would expect that communities
would decide that the more serious crimes provide
greater disutility. However, the relative levels of
disutility may well vary across communities. The
result is that one community may spend more
effort on preventing robberies while another
spends more effort on preventing aggravated
assaults. Presumably, the marginal effort in preventing one robbery is about equal to the marginal
effort in preventing two aggravated assaults, based
on the numbers actually occurring, at least if the
average cost of prevention equals the marginal
value of a crime prevented.4
PRIOR RESEARCH
A number of papers have been written which are
germane to the topic of economies of scale. They
have been done from a number of methodological
points of view, but their general conclusion tends
to be that there are diseconomies of scale.5 As
an example, Beaton (1974) finds economies of
scale only for cities below 2000 population and
diseconomies above that. Ostrom and Parks (1973)
summarize a number of earlier studies, all of which
Manage. Decis. Econ. 26: 461–473 (2005)
463
ECONOMIES OF SCALE IN POLICING
show positive relationships between per capita
costs and community size. They went on to study
how citizens felt about their police services and
found that smaller departments resulted in more
public satisfaction with the police. Walzer (1972)
found that per capita expenditures were strongly
positively correlated with city size. Gyimah-Brempong (1987) found diseconomies in cities larger
than 25 000–50 000 population. In another paper
(Gyimah-Brempong, 1989), he found no economies of scale. Davis and Hayes (1993) also found
diseconomies of scale. Drake and Simper (2002)
claim economies of scale. However, their results
seem to suggest economies for smaller cities and
diseconomies for larger cities. These studies
typically use cost as their measure and do not
consider the effects on crime.
At first look, a counter to that generalization is
by Hirsch et al. (1975, 1976). They find that the
elasticity of crime with respect to population is
about 1.01, not significantly different from one.
They also find, without using simultaneous equations, that having more police results in reduced
crime. Inasmuch as larger cities tend to have more
police per capita, this would imply that there are
increasing costs to crime prevention for larger cities.
Ostrom and Whitaker (1973) looked at the effect
of the size of the community on crime and found
that smaller communities immediately outside and
adjacent to very similar communities within a large
city experienced less crime and that the residents
felt safer in the smaller communities. Glaeser and
Sacerdote (1999) argue that cities provide better
pecuniary returns for criminals due to greater
density and more potential victims. Further, they
note that cities are less likely to apprehend
criminals. They find the elasticity of crime rates
with respect to city size to be about 0.12. An earlier
study, by Christianson and Sachs (1980), used
survey data to argue that larger governments are
better. Of course, an objective measure like crime
is a better measure.
A review article by Brynes and Dollery (2002),
primarily interested in Australia and general government expenditures, but also reviewing other papers,
found that, out of six papers on police economies,
two found U-shaped curves, one found no scale
effect, and three found diseconomies of scale.
In these studies, it was typically the case that
costs were computed as dependent on size. In this
study, a simultaneous equations approach, incorporating both demand and production equations
Copyright # 2005 John Wiley & Sons, Ltd.
will be utilized. There have been no studies of
which I am aware that have used the market power
question in analyzing police efficiency.
MODEL
The usual method of determining economies of
scale in the public sector makes the implicit or
explicit assumption that a homogeneous output is
to be produced. Further, this output is to be
produced in the same amount across communities.
This is at variance with the true state of affairs
where communities deliberately choose different
levels of service in accord with their choice of the
market segment to be served. It can readily be
observed that the ratio of police to population,
even of similarly sized communities, varies substantially.
In addition to choice, there are a number of
factors which change the propensity of the people
in a community to commit crimes. For example,
poverty, broken homes, density, and racial characteristics are often cited indicators. A number of
these factors are correlated, so only a few need to
be included in an empirical model, but any
appropriate method needs to include some such
effects. The variables chosen will also proxy for the
others not included due to their high correlations.
The model will incorporate two simultaneous
equations, production and demand. The former is
the production of safety while the latter is the
demand for policing services. As a result of these
equations, both crime and police are endogenous.
Each of these variables is dependent on other
exogenous variables as well. Exogenous variables
which appear in both equations will include
population and a measure of market power.
Market power is included to measure the potential
profit or waste due to a lack of competition. While
private sector firms can use market power to gain
profits, not for profit organizations can only use
their market power for inefficiency. Azzam and
Rosenbaum (2001) find, using the cement industry,
that, while greater efficiency affects price, market
power is actually a greater factor.
For the production function,
(1) Crime=f (police, density, percent non-white,
population, HH)
where HH refers to the Herfindahl–Hirschmann
Index of market power. The effect of Police on
Manage. Decis. Econ. 26: 461–473 (2005)
464
L. SOUTHWICK JR.
Crime should be negative while Density and
Percent Non-White should have a positive effect.
Density causes more interpersonal interactions
and the percent non-white represents the group
most likely to be victimized by crime. The effects of
Population and HH are to be determined.
For the demand function,
(2) Police=f (crime, assets, unit cost, population, HH)
where assets are the taxable property value and
unit cost is the cost to the community of a unit of
policing (essentially the wage rate). Crime and
assets (wealth) should be expected to positively
affect the number of police. The unit cost (wage)
should have a negative effect. While there is no a
priori reason for them to affect the quantity
demanded, population and HH are included to
see if there is an effect.
MEASURING CRIME
There are a variety of crimes which may be
committed, varying in severity. We will include
here only those which have direct victims. Some
are more common than are others. The Federal
Bureau of Investigation (FBI) keeps track of seven
of these and reports on them annually. As Maltz
(1975) argues, the use of crime as the measure of
(lack of) police success implicitly assumes that the
same proportion of actual crimes is reported in
each community. It seems likely, however, that
those communities which are less successful in
preventing crime, typically the larger communities,
will have a lower proportion reported. This will
tend to produce a spurious economy of scale. Of
course, if the differential effect is small, the bias
will also be small.
The FBI’s Index Crimes include, in decreasing
order of severity, Murder, Rape, Robbery,
Aggravated Assault, Burglary, Larceny, and
Motor Vehicle Theft. The first four involve violent
confrontation between individuals while the latter
three are usually non-confrontational and tend to
be for commercial purposes. Of course, Robbery is
also primarily for commercial purposes, although
it may be committed as part of one of the other
crimes. When a crime falls potentially into more
than one of these categories, the police typically
choose the most serious of the charges as the type
of crime.
Copyright # 2005 John Wiley & Sons, Ltd.
The FBI has published annual reports of the
seven index crimes for each community in New
York State which provides the data to the FBI.
The State of New York is chosen because the laws
under which each community operates with
respect to apprehension and punishment for these
crimes are uniform across the State.6 That does
not necessarily mean that the application of the
laws is uniform but, rather, that it is as uniform as
uniform laws can make them. Judges may vary
and juries obviously do so as well. If one
jurisdiction is more lenient, it may encourage
more crime in that community as compared to
others which treat criminals more severely. In New
York, the court involved in the adjudication of
these crimes usually has jurisdiction over several
counties. The prosecutors are from a single
county. Police in towns, villages, cities, and
counties usually make the arrests, although the
State Police also make some arrests.
In order to estimate the desired functions, it is
necessary to create an index of crimes for each year
for each community. Crime, in this measure, will
be reduced to a single variable from the seven
listed above. In order to create an index across
these crimes, it is necessary to realize that the
numbers of the different types of crimes reported
can be expected to vary by orders of magnitudes.
In 2000, the US had about 15 500 murders, 90 200
rapes, 408 000 robberies, 911 000 aggravated
assaults, 2 050 000 burglaries, 6 966 000 larcenies,
and 1 165 000 motor vehicles stolen.7 If we simply
sum these, as the FBI does, it will effectively
overweight the three non-violent crimes in terms of
their importance.
In the following analysis, an averaging method
will be used which adjusts for the different
numbers. In this, the averages for each year will
be computed of each crime across the municipalities in the study and the percentage each
municipality has of that average will be used as
the measure of the amount of that type of crime
for that locality. Then, the average of each
community’s percentages will be taken across the
index crimes to give a single figure measuring the
relative crime level for that community.8 Implicitly, this rates each crime type as equal in terms
of the relative effect on the overall average. Thus,
for example, a single murder is likely to affect
a community’s average by considerably more than
a single robbery or aggravated assault. It will take
a decrease of several of the less important crimes
Manage. Decis. Econ. 26: 461–473 (2005)
ECONOMIES OF SCALE IN POLICING
to offset an increase of one murder. The effect is to
treat one murder as approximately equal in harm
to 5.8 rapes, 26.3 robberies, 58.8 aggravated
assaults, 132.3 burglaries, 449.4 larcenies, or 75.2
auto thefts.
VARIABLE DEFINITIONS AND MEASURES
The next step is to estimate Equations (1) and (2)
by a two stage least squares process (2SLS). This
will be done using data on New York State Police
departments. A number of these serve more than
one community or only serve part of a community
because another police department serves the rest
of the community. Thus, it is necessary to gather
the data for Population and any population
related variables for only the area covered by the
relevant Police department. Because the census
data are available both for Towns and for Villages,
it is possible to include only those Villages in a
Town Police Department for which policing is
actually done by the Town Department.9 For the
Police departments covered by this study, contracting out is generally a minor factor and will not
affect the data substantially.
The most recent data available are for the years
1995 through 2000. From the numbers of people in
the 1990 and 2000 census counts in each community, the population figures for each year are
computed by an interpolation process. That is, in
1997, for example, 30 percent weighting is given to
the 1990 figures and 70 percent weighting to the
2000 figures. The percentage non-white is computed analogously; the 1990 and 2000 figures for
whites and non-whites are interpolated as well.
In the data gathered annually by the New York
State Comptroller’s Office,10 there are figures for
the area of the municipality each year as well as
financial figures on spending by various categories.
The former is divided into the population to
compute the density.11 The spending on Police is
used to compute the cost per Police officer or per
Police employee.12 In addition, the full value of
taxable property in the community is used to
compute an Assets or wealth variable. This is, of
course, done on a per capita basis.
In the spending on Police, over the entire data
set used, which does not include New York City,
the spending on personnel averaged 93.4 percent
of all spending on Police. That implies an
extremely low capital/labor ratio and might well
Copyright # 2005 John Wiley & Sons, Ltd.
465
offer some improvements in efficiency with the use
of more capital.13 The analysis of that issue,
however, is beyond the scope of this study. For
our purposes, policing may be thought of as
almost entirely a function of the amount of labor.
The estimation is done with linear functions,
except that population is quadratic so as to
ascertain whether there is an optimal size. Because
the variables are normalized, the additional variable is 1/population. Thus, the equations to be
estimated are
(3) C ¼ a0 þ a1 D þ a2 NW þ a3 P
þa4 POP þ a5 =POP þ a6 HH.
(4) P ¼ b0 þ b1 C þ b2 W þ b3 A
þb4 POP þ b5 =POP þ b6 HH.
The data are for 150 communities and consist of
669 observations over the 6 year time period.
Because some of the communities have incomplete
data on some variables, the actual number of
observations is less than that for particular
estimations.
The definitions of the variables to be used are as
follows:
a. C4 or C7=crime=average of percentage
crime rate is of average for all communities
for that year. Computed respectively for
four violent crimes and for all seven index
crimes.
b. POLPOP or PERPOP=police=number of
police divided by population in thousands.
Alternatively, the number of Police employees divided by population in thousands.
c. DENSITY=population per square mile.
d. NW=non-white=percent of the population
which is non-white in the given year. Keep in
mind that this represents the likelihood of
victimization.
e. W=WPOL or WPER=wage rate=real (inflation adjusted) expenditures for police
personnel, divided by the number of police.
Alternatively, divided by the number of
police personnel as appropriate for the
equation.
f. ASSETS=assets (wealth)=real (inflation
adjusted) full property value divided by the
population.
g. POP=population=total population protected by the particular police department.
h. 1/POP=inverse of population, added to
make the equation quadratic.
Manage. Decis. Econ. 26: 461–473 (2005)
466
L. SOUTHWICK JR.
i. HH=Herfindahl–Hirschman Index=based
on numbers of police hired by all municipalities in a county, even if the municipality
is not in the data set.
The value ranges for these variables are given in
Table 1. The highest crime community has a crime
rate about ten times the lowest, using the seven
index crimes. The violent crimes range upwards
from zero to six times the average. Both the police
per 1000 population and the police personnel
(including non-sworn employees) also have a very
wide range. The population ranges from 6200
(although the FBI wants to collect crime data only
from communities over 10 000, it apparently gets
some from smaller places) to a bit over 300 000.
(New York City is not included because of missing
data as well as because it is so large as to be
substantially different from other municipalities.)
This gives a good range for economies of scale
computation. Non-white percentages range from
0.8 to 74.3.
The HH Index for Counties ranges from 825 to
6969. This is measured over the numbers of Police.
Table 1.
Because there are more than 450 police departments with the numbers of police available, this
gives a more accurate measure of the HH Index.
The average HH value is 2786, well above the level
at which the US Justice Department almost automatically challenges mergers in the private sector.
Table 2 gives the correlations across the variables. The two measures of crime, C4 and C7, are
correlated at the 0.98 level. Other than that, the
highest correlation of crime is with percent nonwhite, at about 0.70. This is because non-whites
are more likely to be crime victims.14 The crime
rate is correlated with population at about the 0.61
level. The two measures of police per 1000
population are also correlated with each other at
the 0.98 level. The only other high correlation of
police is with crime at about the 0.50 level. The
personnel expenditure measures per police officer
or per police employee are correlated at the 0.70
level. Thus, they may represent different philosophies about how to go about performing the
function or may represent a substitution of other
workers for police if police salaries get too high.15
Other than those mentioned, the correlations
Variable Descriptions
Variable
Mean
Std. dev.
Minimum
Maximum
Cases
C4
C7
POLPOP
PERPOP
PCTNW
DENSITY
ASSETS
WPOL
WPER
HH
POP
0.974
0.982
1.966
2.291
0.138
3152
63 232
88 589
75 208
2786
34 965
1.146
0.881
0.757
0.871
0.140
3259
60 217
33 766
18 893
1591
41 907
0.000
0.054
0.049
0.088
0.008
142
14 429
3171
2384
825
6202
6.324
5.253
3.935
4.771
0.743
16 887
517 303
736 362
147 272
6969
310 412
663
663
619
619
663
663
662
618
618
663
663
Table 2.
C4
C7
POLPOP
PERPOP
PCTNW
DENSITY
ASSETS
WPOL
WPER
HH
POP
Correlation Matrix
C4
C7
POLPOP
PERPOP
PCTNW
Density
Assets
WPOL
WPER
HH
POP
1.00
0.98
0.49
0.50
0.71
0.48
0.28
0.05
0.05
0.04
0.56
0.98
1.00
0.53
0.55
0.70
0.48
0.26
0.06
0.07
0.01
0.62
0.49
0.53
1.00
0.98
0.45
0.43
0.21
0.02
0.18
0.09
0.24
0.50
0.55
0.98
1.00
0.47
0.44
0.22
0.05
0.14
0.05
0.27
0.71
0.70
0.45
0.47
1.00
0.60
0.09
0.16
0.22
0.24
0.44
0.48
0.48
0.43
0.44
0.60
1.00
0.21
0.18
0.31
0.08
0.30
0.28
0.26
0.21
0.22
0.09
0.21
1.00
0.24
0.37
0.03
0.13
0.05
0.06
0.02
0.05
0.16
0.18
0.24
1.00
0.71
0.01
0.03
0.05
0.07
0.18
0.14
0.22
0.31
0.37
0.71
1.00
0.03
0.02
0.04
0.01
0.09
0.05
0.24
0.08
0.03
0.01
0.03
1.00
0.03
0.56
0.62
0.24
0.27
0.44
0.30
0.13
0.03
0.02
0.03
1.00
Copyright # 2005 John Wiley & Sons, Ltd.
Manage. Decis. Econ. 26: 461–473 (2005)
467
ECONOMIES OF SCALE IN POLICING
are low enough to effectively remove the problem
of colinearity. It is interesting that the HH Index
has a near zero correlation with population.
Apparently, as a county’s population increases,
the number of police departments also increases
apace.
ESTIMATION RESULTS
Two stage least squares regressions are next run
using the two equations in four combinations,
C4 or C7 and Police/1000 Population or Police
Personnel/1000 Population. The regression results
are shown in Table 3. The upper half of the table
shows the results for the production equation
while the lower half shows the results for the
demand equation. Each column represents one of
the systems of equations with the production
equation in the top matching the demand equation
below it.
In the four production function estimates, all
the variables are significant at the 5 percent level,
except density in the seven index crimes case where
it is still significant at the 10 percent level. Most of
the coefficients are significant at the one percent
level. In the demand equation estimates, crime and
assets are highly significant. Wages, the HH Index,
and 1/Population are not significant. Population
is significant at the 5 percent level, except in the
4 crimes/personnel case where it is only significant
at the 10 percent level.
These results are much as expected. The
production function has crime positively related
to percent non-white, density, population, population inverse, and the HH Index and negatively
Table 3. Regression Results
Production function
Constant
POP
PCTNW
DENSITY
POLPOP
C4 POL
7.27E-02
(0.31)
1.08E-05
(9.46)
5.9047
(13.69)
4.00E-05
(2.43)
0.5044
(3.76)
C7 POL
9.77E-02
(0.59)
9.62E-06
(11.87)
4.1542
(13.59)
2.28E-05
(1.95)
0.2793
(2.93)
PERPOP
HH
POP1
8.31E-05
(3.45)
7137.13
(4.01)
7.46E-05
(4.37)
5114.87
(4.05)
POLPOP
1.2263
(9.83)
1.87E-06
(2.00)
0.5202
(13.06)
POLPOP
1.0986
(9.02)
3.28E-06
(3.45)
C4 PER
2.79E-02
(0.13)
1.09E-05
(9.64)
5.9384
(13.77)
3.46E-05
(2.22)
C7 PER
4.42E-02
(0.28)
9.60E-06
(12.10)
4.1340
(13.64)
1.86E-05
(1.70)
0.4121
(3.72)
9.42E-05
(3.99)
6670.36
(3.88)
0.2092
(2.68)
8.06E-05
(4.86)
4785.58
(3.96)
PERPOP
1.1959
(7.18)
1.89E-06
(1.79)
0.6106
(13.61)
PERPOP
0.9911
(6.15)
3.53E-06
(3.32)
Demand function
Constant
POP
C4
C7
ASSETS
WPOL
5.33E-06
(11.75)
6.79E-07
(0.91)
0.7157
(13.78)
5.07E-06
(11.90)
3.39E-07
(0.47)
WPER
HH
POP1
2.20E-05
(1.43)
1717.63
(1.47)
Copyright # 2005 John Wiley & Sons, Ltd.
3.15E-05
(2.15)
1573.50
(1.42)
6.14E-06
(11.40)
0.8383
(14.57)
5.74E-06
(11.47)
1.68E-06
(1.05)
3.94E-06
(0.23)
1341.82
(1.01)
2.92E-06
(1.94)
1.46E-05
(0.88)
1224.85
(0.98)
Manage. Decis. Econ. 26: 461–473 (2005)
468
L. SOUTHWICK JR.
related to police. The demand function has police
increasing with assets and crime and decreasing
with population.
The next step is to use the system of equations to
estimate average elasticities with respect to the
exogenous variables. This is done in Table 4. The
effect on crime of population averages an elasticity
of 0.19 while the effect on police averages an
elasticity of 0.04. From Table 3, the direct effect of
population on police was negative. However,
because crime increases with population, the
indirect effect on police is sufficiently positive to
outweigh the negative direct effect.
Market power also has an effect on both crime
and police, with average elasticities, respectively,
of 0.21 and 0.04. It appears that as citizens have
fewer alternatives, this leads both to more crime
and, as crime increases, to more police. The
increase in market power results not in increased
profits, but rather in more waste.
The average elasticities for percent non-white
for crime and for police are, respectively, 0.57 and
0.17. Again, as crime increases, the number of
police increases due to demand for their services.
Average elasticities for density for crime and for
police are, respectively, 0.08 and 0.02. These are
similar to, although smaller than, the percent nonwhite effects. Assets (property value per capita)
has elasticities of –0.10 and 0.14 on crime and
police. This is due to the causal effect of wealth on
police and the causal effect of police against crime.
Wages (personnel expenditure on police officers or
on police personnel) have little effect, corresponding with the intuition that demand for police is
inelastic and, therefore, there is little effect on
Table 4.
crime. It is possible that higher wages also induce a
higher quality level of police, although we have no
data on this.
Because a formula quadratic in population was
used, it is possible to look at the coefficients to see
if there is an optimal sized community. If we
assume that all the variables other than crime,
police, and population are set to the average
values, we can compute how the levels of police
and crime respond to changes in population. The
results for minima on both crime and police are
shown in Table 5. The averages of these over the
four equations estimated are populations of 22 350
for crime and 35 988 for police.16
At population levels below 22 350, both crime
and police are higher than they could be at a larger
community size. This implies that, unless there are
some additional people nearby who could be
incorporated into the community, consideration
should be given to mergers. Liner and McGregor
(2002) argue for an optimal amount of annexation,
trading off short run savings for longer run
administrative inefficiencies, although not specifically for police. At population levels above about
36 000, both crime and police are also higher than
Table 5.
Population For Minima
C4 POL
C7 POL
C4 PER
C7 PER
Average
Crime
Police
23 097
21 066
22 912
22 328
22 350
38 003
38 133
33 757
34 058
35 988
Average Elasticities
C4 POL
C7 POL
C4 PER
C7 PER
AVERAGE
Of crime WRT
POP
PCTNW
DENSITY
ASSETS
WPOL/WPER
HH
0.1849
0.6554
0.1038
0.1388
0.0248
0.2153
0.1957
0.4800
0.0616
0.0761
0.0071
0.1984
0.1872
0.6648
0.0906
0.1317
0.0429
0.2210
0.1975
0.4876
0.0514
0.0658
0.0399
0.2031
0.1914
0.5720
0.0768
0.1031
0.0127
0.2095
Of police WRT
POP
PCTNW
DENSITY
ASSETS
WPOL/WPER
HH
0.0325
0.1680
0.0266
0.1356
0.0243
0.0240
0.0336
0.1711
0.0220
0.1357
0.0127
0.0260
0.0439
0.1716
0.0234
0.1351
0.0440
0.0522
0.0449
0.1747
0.0184
0.1344
0.0816
0.0550
0.0387
0.1713
0.0226
0.1352
0.0221
0.0393
Copyright # 2005 John Wiley & Sons, Ltd.
Manage. Decis. Econ. 26: 461–473 (2005)
469
ECONOMIES OF SCALE IN POLICING
they could be if the community were smaller.
Consideration should be given in such a case to
lowering the size through splitting the community
into smaller separate communities.
Between the population sizes of 22 350 and
36 000, the community is experiencing a rise in
relative crime rates but a fall in police per capita as
population increases. This implies that there is a
cost to having the greater crime but a savings to
having a relatively smaller police force. This is,
therefore, a range within which it is reasonable to
stay, unlike smaller or larger communities. The
choice with a tradeoff is what makes it rational,
unlike the cases of populations under 22 350 and
over 36 000 where both crime and police and their
associated costs increase.
These results are also shown in Figure 1. There
are two curves. The lower is for the production
function and shows averages for the crime rates,
assuming the demographic characteristics are at
the averages. It reaches a minimum at the
population of about 22 350. The upper line is for
police per 1000 population where, again, the
demographic variables are assumed to be at their
average values. It reaches its minimum at a
population of about 36 000. At the population
Figure 1.
Copyright # 2005 John Wiley & Sons, Ltd.
size for a minimum level of crime, the result of a
doubling of population is an increase of about 15
percent in crime, other things being equal.
It is not always possible to set the size of a
community with precision. People decide to move
in or out according to the mix of taxes paid and
services received, as compared with other alternative communities. However, it is certainly
possible to determine geographic boundaries as
well as setting a maximum density. This can result
in a population upper limit. A lower limit is harder
to create inasmuch as people may choose smaller
or rural communities for other reasons. Of course,
an equivalent to a merger could be an overlay
district with responsibility only for policing in
more than one community.
CONCLUSIONS
There appear to be some economies of scale in
policing, up to a population size of about 22 350.
Beyond that, there are diseconomies of scale.
However, there are reduced numbers of police
per capita up to a population of about 36 000 and
increased numbers thereafter. Thus, the potentially
efficient sizes of communities with respect to crime
and cost may range from about 22 350 – 36 000. In
that range, there is a cost/crime tradeoff which
may be made. As the population is reduced below
22 350, costs and crime both rise and, as the
population increases above 36 000, costs and crime
both rise. Between those sizes, a population
increase results in crime increasing while policing
costs decrease.
Another important result is that increased
market power, as measured by the Herfindahl–
Hirschmann Index, results in increased crime. A
higher degree of market power also increases the
size of the police force. This is the first study of
which I am aware which looks at this factor in
policing. It shows that competition is important
both for the effectiveness of municipalities in
reducing crime and for keeping costs down. As
Crowley (2001) of the Atlantic Institute for
Market Studies said, ‘Public sector competition,
like private sector competition, is not ‘wasteful’,
but is a healthy discipline that promotes efficiency,
accountability and good service. Such competition, where it has been introduced into local
government, has transformed it for the better’.
Frech and Mobley (1995) also find in hospitals
Manage. Decis. Econ. 26: 461–473 (2005)
470
L. SOUTHWICK JR.
that there are both scale and concentration effects,
in that case offsetting. Claggett and Ferrier (1998)
found a similar result that municipalities tended to
overuse inputs relative to cooperatives in electricity distribution. This result is consistent with the
theoretical results found by Niskanen (1968, 1971)
that more competition helps control waste by
bureaucracies.
It may be that the higher concentration gives the
employee unions more power. In New York State,
most police departments are unionized. Contracts
are reached with negotiations which, if agreement
cannot be reached, are concluded in binding
arbitration. Greater concentration may, as Trejo
(1991) argues, give the union more power. This
may result in less efficiency or greater costs. This is
similar to the result found by Captain and Sickles
(1997) where greater union power resulted in
lowered efficiency in airlines.
There is a combination effect of these two
factors. Suppose there is a large population in a
contiguous area. If the communities within that
region are smaller, that will also imply that there
are more communities and a greater competitiveness. The HH Index will decrease and that
will both reduce crime and reduce costs. The
population of the communities will also be smaller
and that will reduce both crime and costs. Of
course, this assumes that the resulting communities are above about 22 350 population.
Let us make up an example to show this
combination of effects. Suppose that there are five
cities within a county, each with 40 000 people and
having the average demographics of all the
Table 6.
communities within the state. This gives an HH
Index of 2000, under the average for New York
State. The two equations estimated for the police
per capita, using respectively the four index crimes
and the seven index crimes, are used and solved for
these cities. The results are shown in Table 6. The
initial crime level is about 0.85 or 0.88 of the state
average and the number of police is about 75 per
city, or 373 overall.
Now, suppose two of these cities merge. The
HH Index increases from 2000 to 2800. Of course,
the new combined city now has a population of
80 000. The result is that crimes in the merged city
increase by over 40 percent while the number of
police per capita increases by about 4.2 percent.
There is an effect on the remaining three cities as
well. They find crime increasing by over 6 percent
with police per capita increasing by less than one
percent. Over the whole county, crime increases by
about 20 percent and police increase by about 2
percent. The merger is thus costly to both the
merging cities and to other cities through the
increase in concentration.17 This suggests that
non-merging cities have an interest in opposing
mergers among their neighbors.
Another conclusion which should be drawn is
that mergers which are intended to save money
should not be done if the resulting community is
larger than about 50 000. This follows from the
decrease in cost from 25 000 to 36 000 and the
increase in cost from 36 000 to 50 000. If the
objective is to have low crime, the merger should
not be done if the resulting community is larger
than about 35 000. This follows from the crime
Five City Examplea Before and After two Cities Merge
4 Crimes
7 Crimes
Police
Crimes
Police
Crimes
Before merger
Each city
Total/average
74.8
373.8
0.8489
0.8489
74.7
373.4
0.8839
0.8839
After merger
New merged city
Other cities
Total/averageb
155.8
75.3
381.8
1.2189
0.9086
1.0327
155.8
74.7
379.8
1.2420
0.9395
1.0605
Percentage change
New merged city
Other cities
Total/average
4.22%
0.72%
2.12%
43.60%
7.03%
21.66%
4.29%
0.00%
1.72%
40.51%
6.29%
19.98%
a
b
Each city 40 000 pop., average demographics.
Weighted average.
Copyright # 2005 John Wiley & Sons, Ltd.
Manage. Decis. Econ. 26: 461–473 (2005)
ECONOMIES OF SCALE IN POLICING
decrease from 17 500 to 22 000 and the crime
increase from 22 000 to 35 000 and beyond.
A typical argument for mergers of municipal
police departments is that a layer of management
is duplicative and will be eliminated, saving
money. The above results, however, contradict
this. A more likely result is that increased size
results in more needed management due to
limitations on span of control. For a given span
of control, a larger police department will require
more management positions rather than fewer.
The effect will be that fewer of the police will be
available to directly deal with crime and more will
be absorbed as managers.
This does not necessarily imply that there cannot
be efficiencies through shared services such as
training or laboratories. Potentially, these could be
provided on a contractual basis by private enterprise or by an overlay government or even with
a contract between two or more municipalities.
However, this will work toward efficiency only if
each user is charged a fair cost and if the provider
is able to make a profit with that fair cost below
the cost of individual provision of the service.
A competitive market in such services with free
entry will induce the optimal size organization.18
NOTES
1. Boyne (1998) argues that contracting may result in
greater competition and efficiency as well as scale
effects but reviews a number of papers which he
decides are inconclusive on the issue. Benson (1998,
Chapter 2) gives examples of communities which
have contracted out their policing services to private
firms. He also (Chapter 3) notes several benefits and
costs to contracting out.
2. As Benson et al. (1992) point out, increasing police
resources devoted to enforcement of drug laws
which are not an index crime means frequently that
less effort is devoted to the prevention of the index
crimes. Further, Benson (1995) argues that bureaucrats may want to pursue non-index crimes more
vigorously in order to gain more resources to pursue
the index crimes. See also Benson et al. (1998).
3. There are multi-objective methods available as well.
For example, Data Envelopment Analysis can be
used in such cases.
4. Suppose that the average cost of a crime is equal to
the marginal cost, reasonable because crimes have
individual victims. Suppose further that the number
of crimes of any type is equal to a base number,
multiplied by exp(aiPi) where ai is a constant for
that crime and Pi is the allocation of policing
resources to that crime. Assuming an optimal
allocation of policing resources across crimes, it
Copyright # 2005 John Wiley & Sons, Ltd.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
471
can readily be shown that the ratio of the average
cost of a particular crime to the average cost of
another type of crime is equal to the inverse of the
ratio of the number of crimes of each type. This
method appears superior to that used by Lynch et al.
(2000) and by Lynch et al. (2001) where an attempt
is made to estimate the cost of crime by its effect on
house prices. While their method is potentially
feasible, the actual results are not particularly
encouraging. House prices are subject to wide
variability across communities due to other influences.
Burney (1998) even finds diseconomies of scale in
governmental electricity generation using a time
series.
If a similar analysis is to be performed for a
municipality in some other state, the comparison
should be made across communities in that state.
See Uniform Crime Report 2000, various tables.
This is the same measure used by the firm Morgan
Quitno of Lawrence, Kansas to compare crime rates
across municipalities for the popular media in its
annual report, City Crime Rankings, except that
Morgan Quitno does not include Larceny.
In New York State, Villages may be part of a Town
or may have parts of two or more Towns. Each
municipality may decide to have a Police department or to contract with another municipality for
the service. In many cases, the municipalities are too
small to afford a Police department. Numerous
Towns and Villages choose to have either the
Sheriff’s Department or the State Police provide
policing services.
See New York State, Office of the State Comptroller, Special Report on Municipal Affairs, for each
relevant year.
This does introduce some error where the policing
area is not exactly the same as the area of the
municipality. However, because densities for nearby
areas are typically similar, the error is likely to be
minor.
If there is contracting out for support services,
as indicated by Chaiken and Chaiken (1987),
the cost will still be counted in the cost of police
officers due to this method. However, the number of
police personnel may be affected. Based on typical
police departments in New York State where
contracting out must be negotiated with the police
unions, there seems to be little of this done in those
departments.
Benson (1998) argues that increasing capital results
in decreased effectiveness, so the low capital/labor
ratio may be appropriate, although this is counter to
the effects in other industries.
It is also possible that non-whites are more likely to
be criminals as well. Further, that variable is likely
to be correlated with poverty, lower education, and
other factors leading to the commission of crime. As
noted by an anonymous referee, low job skills are
more likely to exist in the minority community,
leading to a lower opportunity cost of being a
criminal.
Manage. Decis. Econ. 26: 461–473 (2005)
472
L. SOUTHWICK JR.
15. The dispatch function, for example, may be done
either by sworn police officers or by civilians,
depending on management choices made.
16. It is interesting to note that Giordano (1997) found
a similar U-shaped scale function in trucking
through survivor analysis; of course, municipalities
are not subject to a similar competition.
17. The population numbers have been used in this
example to compute the HH Index. However,
earlier, the police numbers were used. This implies
that this example, in fact, underestimates the
adverse effect of the merger.
18. Saal and Parker (2000) found, in another context,
that there are diseconomies of scale in government
services as well as benefits to privatization.
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