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Vera Institute Calculating Justice System Marginal Costs May 2013

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A Guide to Calculating
Justice-System Marginal Costs

COST-BENEFIT ANALYSIS UNIT

MAY 2013

Christian Henrichson • Sarah Galgano

Bureau of Justice Assistance
U.S. Department of Justice

-

FROM THE PROGRAM DIRECTOR
Why should you read this guide even if you don’t plan to calculate marginal
costs or conduct a cost-benefit analysis?
Because even though this is a technical document, the subject matter is not
esoteric. The costs and benefits of criminal justice policies and activities affect
all of us—taxpayers, politicians, people who work in the justice system, and
society as a whole. That’s why it’s important to understand what goes into the
costs of operating jails, prisons, supervision, courts, law enforcement agencies,
treatment programs, and other criminal justice initiatives.
This document guides both technical users and general readers through the
concepts and calculations behind various types of costs, and the consequences
for policy and practice of focusing on one type of cost over another. For instance, many commentators have likened the annual cost of keeping a person
in prison to the price of tuition, room, and board at Harvard for a year. The
implication: reduce the prison population by one person, and the government
can save more than $50,000. It’s a compelling comparison, but it’s inaccurate,
as this guide explains in more detail.
Simply doing the math is not enough. A better understanding of what we’re
spending our money on—and what we could potentially save if we do things
differently—depends on looking more closely at a justice system’s operations
and budgeting.

I .

....-r-

. .
L.

Tina Chiu
Director, Cost-Benefit Analysis Unit

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A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

Contents
4	Introduction
4	

What Are Marginal Costs?

	

6	

Types of Government Costs

	

6	

Short-run and Long-run Marginal Costs

7	

How to Calculate Marginal Costs

	

8	Methods

	

10	 Data Collection

12	 Examples in the Justice System
	

12	 Prisons and Jails

	

15	 Probation and Parole

	

16	Courts

	

19	 Law Enforcement

	

20	Programs

21	Recommendations
	

21	Analysts

	

22	 Justice Agencies

23	Resources
	

23	Methods

	

23	Data

24	Conclusion

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Introduction

As cost-benefit
analysts and budget
officials know, any
detailed discussion
about government
costs requires an
understanding
of marginal costs
because these are
the costs that policy
changes affect.

In recent years, U.S. government agencies have operated with tight budgets
and limited resources, and criminal justice systems are no exception. As a
result, interest is growing in data-driven strategies to maintain public safety
by maximizing justice investments. Cost-benefit analysis (CBA) is a tool that
weighs an investment’s pros and cons and evaluates a policy’s long-run effects
on government budgets and society at large.
Criminal justice investments include taxpayer costs for law enforcement,
courts, corrections (mainly jail and prison), and community corrections (such
as probation and parole). This guide instructs policy analysts how to calculate
a particular kind of taxpayer costs called marginal costs for use in CBAs of
criminal justice programs and policies. The marginal cost is the amount total
costs change when a unit of output (such as an arrest or court case) changes.
As cost-benefit analysts and budget officials know, any detailed discussion
about government costs requires an understanding of marginal costs because
these are the costs that policy changes affect. Although obtaining government
budget information might be simple, accurately calculating marginal taxpayer
costs is challenging, because the specific type of cost data required for CBA is
sometimes not readily available.
Using marginal costs to measure a program’s impact on taxpayers is important, but it is just one step in a CBA. A cost-benefit analysis aims to measure
the net benefit to society, but this guide covers only costs to taxpayers and not
societal costs of crime, which include fear of crime, avoidance costs, and emotional and physical harm to victims. (For more information on societal costs
and other steps of CBA such as conducting a sensitivity analysis, and reporting
CBA results, go to cbkb.org/toolkit.)
The first section of this guide is an overview of the marginal costs used in
a cost-benefit analysis. Next is a summary of the methods to calculate these
costs. The third section provides guidance on how to calculate marginal costs
in specific segments of the criminal justice system. The guide ends with recommended steps that cost-benefit analysts and justice agencies can take to
improve the quality and relevance of CBAs for policymaking. The glossary on
page 7 includes several important terms that are highlighted in bold throughout the guide.

What Are Marginal Costs?
The marginal cost is the amount the total cost changes when a unit of output
(also referred to as “workload” in this guide) changes. In a CBA, “marginal” does
not mean small or insignificant. It means at the margin of an existing level
of operations and describes the cost or benefit that will be realized because of
changes in units of activity. In the context of the criminal justice system, the

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A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

marginal cost is the amount of change in an agency’s total operating costs
when output (such as arrests, court filings, or jail days) changes because of
changes to policies or programs.
It is impossible to overstate the importance of using marginal costs in a CBA.
One of the fundamental errors an analyst can make is using average costs,
which usually results in overestimating the costs related to the policy change.1
This is because the average cost includes fixed costs—such as administration
and other overhead costs—that policy changes may not affect. (For the purpose of a cost-benefit analysis, in some circumstances the average cost is also
the marginal cost. See “Prisons and Jails,” page 12, and “Programs,” page 20, for
more on these scenarios.)
The average and marginal costs of prison illustrate this important distinction. Nationwide, the average annual per-inmate cost of state prison is about
$30,000.2 A common misconception is that reducing the prison population by
a small amount will translate into $30,000 per inmate in taxpayer savings. But
the average cost includes costs for administration, utilities, and other expenses
that will not change when the prison population is slightly reduced. A small
change affects expenses such as food, clothing, and medical care: these are the
marginal costs associated with a small reduction in the inmate population. The
difference between the average and marginal cost of prison is vast. In Massa­
chusetts, for example, the average annual per-inmate cost of incarceration is
$46,000, whereas the marginal cost is only $9,000 (see Figure 1).3

Figure 1. Annual per-inmate costs of state prison
in Massachusetts
Average cost: $46,000
Marginal cost: $9,000

The term “marginal cost” comes from the field of economics, which defines
it as the change in total cost when the quantity produced changes by one unit.
However, a cost-benefit analysis rarely seeks to measure such a minuscule
policy effect; it usually measures a more sizable impact (for example, a change
in 100 jail beds or 1,000 arrests). Thus, the marginal cost in a CBA is the change
in cost caused by the change in policy.
To assess policies with smaller effects on workload, one must calculate the
marginal cost of a small change in workload; assessing policies with larger effects requires the use of the marginal cost of a larger change in workload. Costbenefit analysts often distinguish between these smaller and larger marginal
costs as short-run and long-run marginal costs, respectively (see page 6).

TAXPAYER BENEFITS
VERSUS TAXPAYER
SAVINGS
Throughout this guide, the economic consequences of a reduction in government workload
are called taxpayer benefits
rather than taxpayer savings.
A decrease in workload—for
example, in a prosecutor’s
caseload—will not necessarily
result in more dollars in taxpayers’ pockets. It might mean that
prosecutors have more time to
devote to their remaining cases,
and the quality of services may
improve—which would be a
benefit.* However, reductions
in workload, particularly if
they are large, may create the
opportunity to reduce staffing
levels, a result that may generate taxpayer savings. A CBA
can assess whether there will be
a taxpayer benefit, but only the
budget process can determine
whether there will be taxpayer
savings.
*Billy L. Wayson and Gail S. Funke,
What Price Justice: A Handbook for
the Analysis of Criminal Justice Costs
(Washington, DC: National Institute of
Justice, 1989), 93.

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TYPES OF GOVERNMENT COSTS

Marginal costs
required to conduct
a cost-benefit
analysis of a justice
policy are rarely
available off
the shelf.

The costs of a government agency—or a private firm, for that matter—are said
to be variable, fixed, or step-fixed.4 (See Figure 2 for examples of each type of
cost.) Identifying these costs is the first step in calculating marginal costs.
Variable costs are those directly related to workload and change immediately
as workload increases or decreases. Examples of variable costs include overtime, supplies, and fuel.
Fixed costs, in contrast, are those that remain fixed over a given period and
are not usually affected even if the workload changes. Examples of fixed costs
include rent, utilities, and central administration.
Step-fixed costs remain constant for a certain range of workload, but can
change if the workload exceeds or falls below that range. The most common
examples of step-fixed costs are staff salaries and benefits. These step-fixed
costs are sometimes said to be lumpy or tiered, because positions are typically added or subtracted only if the workload reaches a certain threshold. For
example, a probation department might not hire a new officer in response to
a small increase in its caseload, but is likely to wait until the caseload reaches
a point at which the work would fully occupy the time of an additional officer.
Similarly, a county corrections department cannot reduce jail staffing if the
inmate population decreases slightly, but if the decline is sufficient to close an
entire housing area, the corrections department could eliminate the positions
related to that unit.

Figure 2. Examples of variable, fixed, and step-fixed costs
VARIABLE
•	 Overtime
•	 Supplies
•	 Contracted services
•	 Client subsidies
•	 Travel
•	 Fuel
•	 Food

FIXED

STEP-FIXED

•	 Rent
•	 Utilities
•	 Central administration
(human resources,
fiscal, legal, etc.)
•	 Debt service
•	 Equipment

•	 Staff salaries
•	 Fringe benefits, such
as health care and
pension contributions
•	 Possibly some fixed
costs when staffing
levels change by a
large amount

Because most government spending is for labor, most of its costs are stepfixed and depend on the level of workload. When studying a policy’s effect on
a government budget, it is important to understand exactly how the policy
would affect staffing levels.

SHORT-RUN AND LONG-RUN MARGINAL COSTS
Marginal costs depend on the size of the change in workload and how the
government adjusts the budget in response to this change. This means that

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A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

more than one marginal cost could potentially be used in justice CBAs. Costs
that change immediately with even a small change in workload are often
called short-run marginal costs (also called variable costs).5 When a policy has
a larger impact on workload, staffing costs need to be considered, yet it may
take time for the government to change these step-fixed costs. Thus, long-run
marginal costs include the short-run marginal cost as well as the staffing costs
that change as governments modify staffing levels in future budget cycles.6
Cost-benefit studies of criminal justice initiatives should use the long-run
marginal cost when the effect of the policy on workload is expected to change
staffing needs. Analysts should use the short-run marginal cost when the
policy impact is not large enough to affect staffing.

How to Calculate Marginal Costs
The marginal costs required to conduct a cost-benefit analysis of a justice
policy are rarely available off the shelf. Therefore, analysts must typically make
these calculations from scratch. Even if another source provides a marginal
cost, analysts must confirm that it is an accurate marginal cost for the policy
being studied. Because the marginal cost is specific to the policy context, it is
important to understand how this cost was calculated.
Moreover, a cost-benefit analysis will likely require marginal costs for
a variety of justice-system resources. For example, if you are studying an
investment shown to reduce burglaries, it would likely lead to fewer arrests,
fewer court cases, and fewer days in jail. To consider the effect this change will
have on justice-system resources requires knowing how many fewer arrests,
cases, and days in jail there will be. Figure 3 provides a list of marginal costs
commonly used in a CBA to measure the impact on taxpayers. The change
in justice-system workload (for example, arrests), is then multiplied by the
marginal cost of that activity or resource. (See Tracking Costs and Savings
through Justice Reinvestment [Urban Institute, 2012] for more information on
how to track policy impacts across the justice system.7)

Figure 3. Commonly measured taxpayer costs
in justice-system cost-benefit analyses

GLOSSARY
MARGINAL COST: The amount
of change in total cost when a
unit of output changes
AVERAGE COST: The total cost
of all output divided by total
output
VARIABLE COST: The cost that
changes directly in proportion
to output; also called short-run
marginal cost
FIXED COST: The cost that
remains constant, even when
the output changes
STEP-FIXED COST: The cost
that remains constant for
a certain range of output
and changes when output
exceeds or falls below a certain
threshold
SHORT-RUN MARGINAL COST:
The cost affected as soon as
the output changes; also called
variable cost
LONG-RUN MARGINAL COST:
Short-run marginal costs, plus
the step-fixed costs that change
in the long run as adjustments
are made to staffing levels in
response to larger changes in
output

•	 Law enforcement (per arrest)
•	 Courts (per case)
•	 Jails and prisons (per inmate)
•	 Probation and parole (per supervisee)
•	 Juvenile detention and commitment (per youth)
•	 Juvenile supervision (per youth)
•	 Criminal justice programs (per participant)

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Once you have determined which justice agencies are affected by the policy
change, two general methods can be used to calculate marginal costs: the topdown or bottom-up approaches.8 The following section describes these methods and provides guidance on how to collect the data necessary to use them.

METHODS

Two general
methods can be
used to calculate
marginal costs:
the top-down
or bottom-up
approaches.

Analysts use either a top-down or bottom-up approach to calculate marginal
costs, and each one has pros and cons. In theory, these approaches should generate similar estimates when conducted properly. The top-down approach is
most commonly used and produces accurate estimates in fields whose budgetary costs can be easily aligned with workload or output (such as corrections).
Regression analysis is sometimes used in justice CBAs and is a type of topdown method that uses aggregate data to measure the marginal cost by examining how changes in workload have influenced changes in cost over time. (See
“Regression Analysis” on page 10.) The bottom-up approach is less frequently
used and more labor-intensive, but is often necessary when it is difficult to link
costs and workload (as is true in courts and law enforcement).
The top-down method. This approach to calculating marginal costs requires
the analyst to divide the change in total cost of a given function by the change
in total output (see formula in Figure 4). This is a top-down approach because
it uses total (aggregate, or top-level) costs and then divides them by the change
in output. When using this approach it is critical to include only the costs related to the change in output.

Figure 4. Top-down formula
Change in total cost ÷ Change in total output = Marginal cost

This approach is recommended when information is available on the total
change in cost related to the change in workload. For example, this method can
calculate the marginal cost of a hypothetical probation case if you have budget
information that provides the cost of expanding capacity in a field office to
supervise more probationers. Using this example, you would divide the annual
costs for new probation officers and their supplies ($550,000) by the average
daily total caseload of adult probationers they will supervise (500). Thus, the
cost per probation case is $1,100 per year ($550,000 ÷ 500 = $1,100). Then divide
this amount by 365 days to calculate the daily cost ($3.01 per probationer, per
day). These calculations are also presented in Figure 5. This is a long-run marginal cost because it includes the step-fixed cost of salaries that will change
only when governments revise their staffing levels.

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A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

Figure 5. Top-down example: hypothetical probation case
Change in total cost ÷ Change in total output = Annual marginal cost
$550,000 ÷ 500 = $1,100
Annual marginal cost ÷ Days per year = Daily marginal cost
$1,100 ÷ 365 = $3.01

When to use the top-down method. Analysts often prefer this method because the calculations are relatively simple if detailed budget data is available.
When the government is delivering only one output (for example, jail beds) the
top-down method is a convenient approach so long as the analyst can identify
which costs the policy will change.9 For example, if a corrections department
reduces the budget by $1 million because it closes one housing unit with 100
beds, the marginal cost—using the top-down method—is $10,000 per bed, per
year ($1 million ÷ 100 beds = $10,000).
Considerations when using the top-down method. Two potential mistakes
can lead to an erroneously high estimation of marginal costs when using
this approach. First, the marginal cost will be overestimated if the total cost
includes costs that do not pertain to the type of output the analyst is measuring. For example, if other expenses were commingled with probation expenses
(such as if juvenile probation costs were included in the above example of
adult probation costs), they would be incorrectly included in the cost of adult
probation. A second possible mistake pertains to the erroneous inclusion of
fixed costs (such as costs of central management), which do not vary as workload changes. When calculating marginal costs in a top-down analysis, fixed
costs must first be removed from the total cost. (The above example includes
salary and supply costs and excludes costs for administration and other fixed
­expenses.)
The bottom-up method. Use the bottom-up approach to investigate all the
costs related to a single unit of output. This typically means identifying all the
employees who are responsible for a unit of output (for example, all the staff
members who work on a court case), identifying how much time each person
spends on that unit of output, and then multiplying this time by the cost of the
employees’ time spent on that activity (see formula in Figure 6).

Figure 6. Bottom-up formula
Time spent on output (hours) × Cost per hour = Marginal cost

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REGRESSION ANALYSIS
If you have accurate historical
data for costs and workload
that has been consistently defined over time, you can run a
regression analysis to measure
marginal costs. This is a type
of top-down analysis, because
the calculation begins with the
aggregate costs rather than
individual costs. The regression examines the relationship
between workload (output) and
costs by looking at the relationship between these variables
over time. This analysis measures how the annual change
in cost varies with the change
in workload (say, arrests, court
cases, or jail capacity) while
controlling for factors that have
the effect of changing costs
without affecting workload
(for example, rising salary and
benefit costs). This approach
is useful when only aggregate
data is available and you cannot break down variable, fixed,
and step-fixed costs. There are,
however, a few potential drawbacks to this approach. First,
not many analysts are trained
in this methodology—and even
trained analysts sometimes find
it difficult. Second, some government officials might view the
results with skepticism because
the costs may not align with
actual budget allocations.

This method could also be used to calculate the cost of a hypothetical probation case, as in the previous example: if a probation officer spends 10 minutes
(0.16 hour) on each case in an eight-hour day, the cost per case can be calculated by multiplying the time per case (0.16 hour) by the hourly cost for personnel and supplies ($18.84) to get the result of $3.01 per day (0.16 x $18.84 = $3.01).10
These calculations are also presented in Figure 7. This is the same result calculated using the top-down approach.

Figure 7. Bottom-up example: hypothetical probation case
Time spent on output (hours) × Cost per hour = Marginal cost
0.16 hour × $18.84 = $3.01 per day

When to use the bottom-up method. This is usually the best approach when
measuring the cost of an activity funded by several entities. When an activity
is one of many being undertaken (for example, if probation services include
individual offender management, group work, employment programs, and preventive work) or there are inputs to the activity of interest from other sources
(for example, a court case that involves private attorneys as well employees
from government agencies), then the bottom-up method provides a more accurate estimate of the resources being used.11 The bottom-up method is also
useful when there is a lot of variation in the type of resources each person uses.
For example, the bottom-up method is often used to study drug-court costs because some people use the treatment resources considerably more than others
and it is important to know how costs vary among participants.12
Considerations when using the bottom-up method. This method requires
detailed operational data that is often not readily available and will require
intensive data collection. The calculations are also more complex and this
increases the possibility of error. This method can also yield underestimates of
costs if data collection is not comprehensive for both costs and workload.

DATA COLLECTION
Because detailed data is required to calculate the justice system’s marginal
costs, you may need to collect information through interviews or surveys
­rather than from public data sources. Analysts must address two types of issues when collecting data. The first is ensuring that the data collection instrument captures accurate data. The second is developing a working relationship
with the government official who is sharing the information.
Accuracy. When calculating marginal costs, it is essential that you collect data
from the right sources. Criminal justice systems vary widely, and it is important that costs are specific to the jurisdiction being studied. Moreover, your
data-collection methodology must ensure that costs are both comprehensive

10

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

and comparable. Costs are comprehensive if they capture all relevant expenses.
Costs are comparable if they include all the same components and are adjusted
for differences that result because they are incurred at different times.
Measuring costs comprehensively. The first principle when conducting a cost
analysis is measuring all costs comprehensively. For example, in some jurisdictions, the costs of pensions and other fringe benefits are budgeted in a central
account, and these costs would be erroneously omitted if analysts were to
investigate only agency budgets.13 What’s more, the costs of many justice programs extend beyond the budget of a single department, such as when a probation department makes use of employment or housing services that a different department provides. If the analysis were to focus solely on the probation
department, these employment and housing costs would be overlooked.14
In measuring costs comprehensively, take care not to double-count any costs.
One way to prevent undercounting and double-counting is to confirm which
costs are included in the figures a respondent provides. For example, when
working with a jurisdiction that pays for fringe benefits outside the agency
budget, do not add these costs yourself and assume that the survey respondent
omitted them. (See the survey in the appendix of The Price of Prisons: What
Incarceration Cost Taxpayers [www.vera.org/priceofprisons], which was used to
collect state prison costs; the questions were designed to avoid undercounting
or double-counting any relevant costs.15)

Criminal justice
systems vary widely,
and it is important
that marginal costs
are specific to the
jurisdiction being
studied.

Measuring costs comparably. The second principle of cost analysis is that costs
should be comparable, that is, that analysts liken apples to apples. This is a
particularly challenging issue when aggregating data from multiple jurisdictions, because each one may define or administer justice activities differently.
For example, two jurisdictions might have different names for the same type of
program. One way to address this issue when collecting data is to carefully define all terms clearly and accurately when describing programs and activities.
The principle of comparing apples to apples is also essential when collecting
data over a multiyear period. First, you must adjust for the effects of inflation
when comparing data from the past, and second, you will need to discount
future costs to the current period.16
Communication. Because information about budgets, salaries, and workload
can be sensitive, interview subjects (or survey respondents) may be concerned
about how analysts will use data and the public will interpret it. You can allay
these qualms and earn respondents’ trust by clarifying the goals of the analysis through two important steps.
First, when collecting data, clearly explain why you are doing so (that is, how
costs relate to the cost-benefit analysis), when the analysis will be published,
and which data will be published in the CBA. Providing this kind of context
can increase respondents’ understanding of your methods and goals and help
them prepare for questions that might arise if the costs they share (or those
you calculate) differ from other published costs.

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Second, prior to publication, allow government partners to review any calculations made with their data. This step is useful because it promotes transparency and might uncover potential errors. The government officials who are
responsible for cost data know this information best and can help improve
the calculations’ accuracy. Officials might be reluctant to share data because
of concerns that it could be misreported or misinterpreted. By working closely
with the respondents, you can often assuage these concerns while improving
the quality of data collection.

Examples in the Justice System
Although the guidelines and principles discussed in the section “How to Calculate Marginal Costs” apply to all segments of the justice system, some issues
and challenges in each segment merit further discussion. For example, in some
fields—such as corrections—data on costs are abundant and the challenge is to
obtain the right data. In other segments, such as the courts, the challenge is to
piece together all the costs of a court case because it may involve many people
and be funded through different budgets. This section provides examples of
marginal-cost calculations in each of the criminal justice system’s major segments, as well as guidance specific to each area.

PRISONS AND JAILS

The marginal cost
of incarceration to
use in a CBA depends
on the estimated
change in the
size of the inmate
population.

12

An accurate estimate of the marginal cost of jail or prison is essential to the
study of policies that either reduce the use of incarceration in the near term
(such as through diversion programs or sentencing reform), or in the long term
by means of a reduction in future crime (for example, through a reduction in
recidivism).
Calculating the marginal cost of incarceration is clearest when measuring
the cost to taxpayers of a change in the inmate population that is paid on a perdiem basis through a contract with either a private facility or another state or
local government. For example, if a state corrections department pays $80 per
day to house inmates in a contracted facility, and the new policy or program
causes a change in the use of this contracted capacity, the marginal cost is the
per-diem rate for these inmates ($80 per day). Although the reimbursement
rate may in fact be the average cost from the perspective of the contracted
agency, it is the marginal cost from the perspective of the purchasing agency.
Calculating the marginal cost of incarceration in government-operated facilities is more complicated. The total cost of prisons and jails includes fixed costs
for facility operations and administration; step-fixed costs for security, inmate
rehabilitation, and health care; and variable costs for inmate needs such as
food and clothing. Most corrections agencies publish clear data on their total
costs, populations, and average per-inmate costs. This data represents the cost
of the entire agency; the published per-inmate costs are averages that include
fixed costs that won’t vary as the size of the inmate population changes.

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

The marginal cost of incarceration to use in a CBA depends on the estimated
change in the size of the inmate population. If the population is expected to
change modestly, only variable costs—for things such as food, clothing, and
medical care—will be affected. These are the short-run marginal costs. If the
size of the inmate population is expected to change considerably, analysts
must consider the costs of staffing in addition to the short-run costs. These are
the long-run marginal costs. Figure 8 illustrates the differences among these
costs relative to the average cost of incarceration in Washington State’s prisons
and jails. Note that short-run marginal costs are lower than long-run marginal
costs, which include step-fixed expenses. Long-run marginal costs are lower
than average costs, which include fixed expenses.

Figure 8. Annual per-inmate costs in Washington State, 2009
AVERAGE COST

LONG-RUN
MARGINAL
COST

SHORT-RUN
MARGINAL
COST

Prison

$31,446

$13,921	

$4,495

Jail

$28,900

$21,469

$3,457

Source: WSIPP’s Benefit-Cost Tool for States: Examining Policy Options in Sentencing and Corrections,
August 2010.

As described earlier, you can accurately calculate the marginal cost of incarceration using either a top-down or bottom-up approach. A 2009 evaluation of an alternative-to-incarceration program in Pierce County, Washington,
determined the marginal cost of jail using both approaches and thoroughly
documented the calculations in a manner that can aid other researchers.17 Using both methods is one way to ensure accuracy and in this study both yielded
similar estimates. The top-down approach resulted in a marginal cost of $56.75
per inmate, per day, and the bottom-up approach resulted in a marginal cost of
$51.51 per inmate, per day. (The average cost is $84.37 per inmate, per day.) These
are long-run marginal costs because they include the step-fixed staffing costs
that change when the size of the inmate population changes substantially.
This section summarizes the top-down and bottom-up methods for calculating
the marginal costs of jail and prison. It also provides a few considerations to
keep in mind when calculating these costs.
The top-down method. For this approach, you must obtain line-item budget
information that is sufficiently detailed to distinguish between the variable,
step-fixed, and fixed costs. From the total cost, subtract the fixed costs—that
is, those costs that will not change when the inmate population increases or
decreases—so that only the variable and step-fixed costs remain. Then divide
that number by the average daily population to estimate the long-run marginal cost per inmate. The short-run marginal cost is calculated by dividing the
variable costs by the average daily population.

Short-run marginal
costs are lower than
long-run marginal
costs, which include
step-fixed expenses.
Long-run marginal
costs are lower
than average costs,
which include fixed
expenses.

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In Pierce County, for example, the total cost of care and custody was $41.5
million, but only $27.9 million was for variable and step-fixed costs. Researchers
calculated this figure by subtracting fixed costs such as facilities, legal research,
administration, and indirect costs from the total annual cost of $41.5 million.18
Only the variable costs, such as food, and step-fixed costs, such as staff for care
and custody, are included in the $27.9 million. The long-run marginal cost of jail
per inmate per day is therefore $56.75 ($27.9 million divided by 1,343 average
daily inmates divided by 365 days).19 The short-run marginal cost is $17.83 per
inmate per day and is calculated by dividing the variable costs by the inmate
population ($8.7 million divided by 1,343 average daily inmates divided by 365
days).20 (See calculations in Figure 9.)21

Figure 9. Marginal costs of jail in Pierce County, Washington:
top-down method
Long-run marginal cost (per day)
Step-fixed costs and Variable costs ÷ Average daily population ÷ 365 days
$27.9 million ÷ 1,343 ÷ 365 days = $56.75
Short-run marginal cost (per day)
Variable costs ÷ Average daily population ÷ 365 days
$8.7 million ÷ 1,343 inmates ÷ 365 days = $17.83
Source: Christopher Murray, Process Evaluation of Breaking the Cycle, Pierce County Performance Audit
Committee, September 24, 2009.

The bottom-up method. This approach requires that you identify the staffing
patterns and compensation levels for corrections officers in order to estimate
the step-fixed costs. You then add the variable costs to estimate the long-run
marginal cost.
In Pierce County, each housing pod accommodates 84 beds. Every day, staff
cover three eight-hour shifts, with 1.75 posts per shift in the general population housing pod, for a total of 5.25 posts in a 24-hour day. Because each post is
covered 24 hours a day, 365 days a year, analysts use a relief factor to convert
a 40-hour-per-week position to a post that is covered 365 days a year.22 More
than one staff member is required per post because employees are entitled to
regular days off. The relief factor in Pierce County is 1.8, meaning that 1.8 fulltime equivalent (FTE) staff are required to fill one post. Therefore, 9.45 FTEs (5.25
posts x 1.8 relief factor) are required to staff one pod that has 84 beds.23
Each FTE costs an average of $101,456 in salary and benefits. Therefore, the
annual personnel cost for the 84-bed pod in Pierce County is $958,759 ($101,456
x 9.45 FTEs), or $31.27 per bed, per day. Adding the direct variable costs of $17.83
per day results in a long-run marginal cost of $49.10.24 (See calculations in Figure 10.) Because each pod in the jail is staffed differently, analysts calculated a
­wei­ghted average of $51.51 per bed, per day.

14

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

Figure 10. Long-run marginal cost of jail in Pierce County,
Washington: bottom-up method
LINE

METRIC/COST

VALUE
	

CALCULATION
84

--

3

--

Posts per shift

1.75

--

d

Posts per day

5.25

bxc

e

Relief factor

1.8

--

f

Full time staff per pod

9.45

dxe

g

Average salary and benefits

$101,456

--

h

Personnel costs, per pod

$958,759

fxg

a

Beds per pod

b

8-hour shifts per day

c

i

Personnel costs, per inmate

$11,414

h÷a

k

Personnel costs, per day

$31.27

i ÷ 365

j

Variable cost, per day

$17.83

--

l

Long-run marginal cost, per day

$49.10

j+k

Source: Christopher Murray, Process Evaluation of Breaking the Cycle, Pierce County Performance Audit
Committee, September 24, 2009.

Keep in mind. When calculating jail and prison costs, analysts must also
consider how the policy will affect certain segments of the inmate population.
For example, if you are studying a policy that affects elderly inmates, you need
to investigate the costs specific to that population.25 Costs also depend on the
security level of the facility. In North Carolina, for example, the average cost of
a maximum-security bed is 45 percent greater than a minimum-security bed
($93.57 per day versus $64.36 per day); in Mississippi, the cost of a maximumsecurity bed is 100 percent greater than a minimum-security bed ($102.27 per
day versus $49.50 per day).26 Similarly, the first few days in jail are the most
expensive of a person’s incarceration because of the cost of intake.27
Finally, it is important to note that although the costs of jails and prisons are
similar in many ways, it may be more difficult for jails to eliminate step-fixed
costs by reducing staffing levels because of the differences between the scale of
a local jail and a state prison system. For example, a 5 percent reduction in the
prison population might present an opportunity to close a small prison, but a
5 percent reduction in a small local jail would likely be insufficient to change
staffing levels.

Although the costs
of jails and prisons
are similar, because
of differences in
scale it may be more
difficult for jails to
eliminate step-fixed
costs by reducing
staffing levels.

PROBATION AND PAROLE
The process of calculating probation and parole costs is similar to the process
for prisons and jails because community corrections and correctional facilities
both have a structured ratio of people under supervision (or incarcerated) to
officers. In probation and parole this ratio is called the caseload, which is the
average number of people an officer supervises at a given time. The average

VERA INSTITUTE OF JUSTICE

15

-

caseload reflects the number of cases a single officer can manage at once.
To measure the long-run marginal costs of probation you can use either the
top-down approach—dividing the variable and step-fixed costs by the average
daily caseload—or the bottom-up approach, multiplying the average salary
and benefits for corrections officers by the ratio of corrections officers to probationers. (See the section “How to Calculate Marginal Costs,” page 7, for detailed
examples of top-down and bottom-up calculations in the field of community
corrections.)
A common approach to calculating marginal costs is to examine changes in
the agency budget that are related to changes in workload. By definition, these
changes are marginal costs. For example, budget documents in New York indicated that the state will save $3.7 million annually because of a projected reduction of 1,500 in the parole population. Therefore, the marginal cost is $2,467 per
parolee, per year ($3.7 million ÷ 1,500 = $2,467).28
But this approach, which calculates the marginal cost of the average
­offender, may potentially be inaccurate if the policy being studied is geared toward people at a particular risk level (high, medium, or low) or a specific population, such as sex offenders. The target population will affect your calculations
because different types of offenders have a different frequency and duration
of contact with their probation or parole officer. For instance, one officer might
be able to supervise 20 high-risk people or 100 low-risk people at the same cost.
Thus, the cost of supervising a medium-risk offender is higher than for a lowrisk offender and less than for a high-risk offender.
Keep in mind that although measuring the marginal cost of incarceration and community corrections are in many ways similar, one distinction is
important: when an inmate population decreases considerably, jurisdictions
may be able to close housing units or facilities to convert the taxpayer benefits
into budget savings. But when an entire population under probation or parole
supervision decreases substantially, jurisdictions might not eliminate officers,
but may use the savings to reduce officers’ individual caseloads. While this is
not a taxpayer savings, it is a taxpayer benefit, because the public will gain
enhanced community corrections services.

COURTS
It can be difficult to calculate court costs because cases involve many people
and are often funded through a number of agencies. (See Figure 11 for a list of
the personnel in the justice system involved in a court case.)29 But despite the
challenges, both top-down and bottom-up methods can be used to calculate
the marginal cost of a court case.

16

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

Figure 11. Personnel involved in court cases
•	 Judge
•	 Defense attorney
•	 District attorney/Prosecutor
•	 Presentence investigator
•	 Court reporter
•	 Clerk of court

•	 Jury tipstaff (court officer)
•	 Secretary
•	 Law clerk
•	 Courtroom coordinator
•	 Sheriff

The top-down method. One challenge of using this approach is that you need
detailed budget and staffing data to discern which costs are for the various
types of cases (criminal, civil, etc.) and whether the costs are variable, stepfixed, or fixed. If this data is available, you can use a tool developed by the
National Center for State Courts that provides a template to calculate the cost
per case. (See Figure 12 for an excerpt from the tool.)
This tool was designed to measure average costs. However, you can also use
it to calculate long-run marginal costs if you remove the fixed costs from the
total costs. To use the tool, you will need information about the cost of court
operations (excluding fixed costs), the number of dispositions for each type of
case (such as civil, criminal, or traffic), and the number of employees that work
on each type of court case.
For example, if the court spends $23.8 million annually to dispose of 99,519
cases (see Figure 12), the cost per type of case can be calculated by using the
number of personnel who work on each type of case to determine the proportion of court costs incurred for each type of case. In this example, 10.7 percent
of court personnel work on criminal cases and therefore the total cost of all
criminal cases is $2.5 million (10.7 percent x $23.8 million = $2.5 million). Because there were 19,414 criminal dispositions, the cost of a criminal case is $132
($2.5 million ÷ 19,414 = $132). See additional instructions and the Excel template
at courtools.org. 30
The bottom-up method. Although this approach is more time- and laborintensive, it may provide a more accurate picture of court costs when investigating areas that involve wide variation in time spent per case. One benefit of
the bottom-up approach is that it works well when you need to analyze court
activities that involve actors from several agencies.31 This method requires that
you multiply the time spent per case by the hourly cost of labor. You can often
calculate the time spent per case through interviews, published workload studies, or researchers’ observations in the courts. In general, salaries of government employees are publicly available.32
Once you determine the total cost of all the court actors and the average time
spent on case hearings, you can calculate the marginal cost. The Urban Institute, for example, has used this methodology to calculate the marginal cost of
drug-court hearings. Researchers estimated the hourly cost of the ­personnel

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-

Figure 12. National Center for State Courts, CourTool 10, “Cost per Case”
DATA ENTRY

STEP 1

STEP 2

STEP 3

STEP 4

Sort court personnel by case type

Determine total court expenditures
and allocate by case type

Allocate total
costs by case
type

Calculate cost
per case

TOTAL
DISPOSITIONS

COST PER
CASE

1 - - - - - - - - - - - 1 1 1 - 1- - - - - 1 1 1 - 1----111-1----I

CASE TYPES

SINGLE
ASSIGNMENTS

STAFF

JUDICIAL
OFFICER

General Civil

12.0

2.0

Limited Civil

3.5

Criminal

14.0

Dependency

7.0

1.0

Delinquency

6.0

1.0

Probate

14.0

0.5

Traffic

17.0

5.0

Domestic

19.0

2.0

1.0

1.0

Total

MULTIPLE
ASSIGNMENTS

26.5

TOTAL COURT
EXPENDITURES

BY CASE TYPE

PRORATED BY
FTE PERCENT
OF TOTAL

STAFF

JUDICIAL
OFFICER

TOTAL

PERCENT
OF TOTAL

4.0

5.0

23.0

14.9

3,562,969

3,450

1,033

3.5

0.5

7.5

4.9

1,161,838

6,019

193

2.0

0.5

16.5

10.7

2,556,043

19,414

132

8.0

5.2

1,239,294

1,254

988

9.5

6.2

1,471,661

1,624

906

14.5

9.4

2,246,220

1,985

1,132

10.0

47.0

30.5

7,280,850

62,027

117

2.0

23.0

14.9

3,562,969

3,746

951

1.0

5.0

3.2

774,559

19.5

IDI

100.0

2.0

15.0

2.0

IDIIDI
79.5

FTE PERSONNEL

28.5

0.5

154.0

$23,856,402

23,856,402

II

99,519

Source: CourTool Measure 10: “Cost per Case.” Available at http://www.courtools.org/Trial-Court-Performance-Measures.aspx and reprinted with permission
from the National Center for State Courts.

involved in these hearings (judge, clerk, aide, U.S. attorney, defense a
­ ttorney,
and U.S. marshal). This amount totaled $3.50 per minute. Based on direct observation, drug-court hearings averaged 9.7 minutes longer than standard docket
hearings, for a marginal cost of $33.95 per hearing (9.7 x $3.50 = $33.95).33
The bottom-up approach is commonly used to measure marginal costs in
the courts. This is because resources used for court cases vary widely, and the
average may not be representative of the types of cases being studied. Analysts at NPC Research—an organization that has conducted many drug-court
­studies—use a bottom-up method called transaction and institutional cost
analysis (TICA). TICA includes the following steps, which can be used to guide
any bottom-up analysis:

18

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

1.	 Determine the program process and how participants move through the
process.
2.	 Identify where in the case flow client/agency interactions occur.
3.	 Identify the agencies involved in each transaction.
4.	 Determine the resources each agency uses for each transaction.
5.	 Determine the cost of the resources each agency uses for each transaction.
6.	 Calculate the cost results.
For details on the TICA bottom-up method, refer to Enhancing Cost Analysis
of Drug Courts: The Transactional and Institutional Cost Analysis Approach.34
Keep in mind. The benefit of a reduction in court workloads will not translate
into budget savings unless staffing levels are reduced when workload reduces.
Instead, it is common for the courts to use these taxpayer benefits to reduce
caseloads and backlogs. Such benefits are sometimes described as opportunity resources, because these resources are available for other uses.35 This type
of taxpayer benefit will not typically result in a financial savings; it instead
provides the means to benefit the public by lowering caseloads and hastening
case-processing times.

LAW ENFORCEMENT
The cost of law enforcement is an important factor in many justice CBAs
because nearly any effect on crime will have an effect on law enforcement. If
fewer crimes occur in the future, it follows that there should be fewer arrests,
and thus reduced costs.
Because police officers engage in a wide variety of activities, it is usually
difficult to calculate the marginal cost of police work by using a top-down approach without conducting regression analysis (see “The top-down method”
below). In general, it is better to use a bottom-up approach, investigating the
time spent on the activity, and then multiplying that time by the cost of an
­officer’s time.

If fewer crimes
occur in the future,
it follows that
there should be
fewer arrests, and
thus reduced lawenforcement costs.

The bottom-up method. You can often calculate the marginal cost of policing by multiplying the time an officer spends on an incident by the cost of the
officer’s salary and benefits.36 In Washington State, for example, the Tacoma
Police Department has calculated the marginal cost of arresting a person considered a “chronic minor offender” to be $165.37 Analysts made this calculation
by first estimating that an arrest includes three hours of an officer’s time, and
then multiplying that by an hourly rate of $55 (including wages, benefits, and
­equipment).
Keep in mind that the time it takes to investigate different types of incidents
varies greatly. An analysis by the San Diego Police Department found that an
average arrest keeps an officer out of service for 5.4 hours, but that certain incidents require much more time than others.38 For instance, an arrest for public

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-

KNOW YOUR COSTS
>>DIRECT COSTS
•	 Staff salary
•	 Fringe benefits (such as
health insurance, employer’s
share of Social Security,
workers’ compensation,
unemployment insurance,
pension contribution, and
vacation wages)
•	 Equipment, such as
computers and office supplies
•	 Rent, occupancy, office
maintenance, and other
space-related costs
•	 Training
>>INDIRECT COSTS
•	 Executive staff
•	 Central support (such as
human resources, fiscal
department, and information
technology)
>>START-UP AND ONETIME
COSTS (such as furniture,
equipment, and consultants)
>>FUTURE COSTS
•	 Wage increases, including
anticipated collectivebargaining settlements
•	 Additional pension
contributions
•	 Anticipated escalation of
health-insurance costs
>>CAPITAL EXPENSES
•	 Project planning, design,
development, and
professional services
•	 Real estate, materials, and
construction

20

intoxication keeps an officer out of service for about three hours, whereas
investigating a crime in progress (robbery, burglary, or auto theft) keeps an officer out of service for more than 10 hours.
Additionally, you can use the bottom-up method to calculate the cost of policing activities that do not result in an arrest. Not all incidents result in an arrest, but they all take an officer out of service. One challenge law enforcement
agencies are facing is an increasing number of calls to respond to false burglar
alarms. You can measure the amount of time false alarms keep officers out of
service by calculating the period between officer dispatch and the time the call
is closed. You can then calculate the marginal cost by multiplying the out-ofservice time by the salary and benefits for the officers involved.
It is worth noting that taxpayer benefits resulting from fewer calls for service do not necessarily translate into budget savings. Rather than reduce the
number of officers, jurisdictions might use the taxpayer benefit to increase the
number of officers on patrol.
If the focus of an analysis is the financial savings related to a police department’s change in workload, one approach is to measure the budgetary savings related to a reduction in overtime spending. This was the approach used
to measure the taxpayer benefits to law enforcement in a recent cost-benefit
analysis of a New York City transitional job program for ex-offenders that
reduced recidivism. Rather than look at the total marginal cost of the arrest,
researchers measured only the portion of the marginal cost that required overtime pay ($359).39
The top-down method. Alternatively, some jurisdictions use regression analysis to measure the marginal cost of an arrest by studying the relationship between arrests and total law enforcement costs over a multiyear period. Regression analysis allows you to control for fixed costs and other workload factors
that affect the total cost of policing (such as the number of traffic citations) in
order to estimate the marginal cost of an arrest. (See the sidebar “Regression
Analysis,” page 10). The Washington State Institute for Public Policy has used
this approach to estimate that the marginal cost of an arrest in that state is
$670. The Utah Commission on Criminal and Juvenile Justice (CCJJ) has also
used regression analysis to estimate that the marginal cost of a property arrest is $880 and of a violent arrest is $4,509. These are long-run marginal costs
because they include the cost of changes in staffing. For additional information on using regression analysis to measure the marginal cost of an arrest, see
WSIPP’s Benefit-Cost Tool for States: Examining Policy Options in Sentencing and
Corrections and CCJJ’s white paper Introduction to an Econometric Cost-Benefit
Approach.40

PROGRAMS
The criminal justice system also includes activities that may not be categorized as corrections, community corrections, judicial, or law enforcement.
Best described as programs, these include job training, reentry programs, and

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

­treatment for substance use.
Calculating the marginal cost of these programs is usually straightforward,
because programs, almost by definition, have discrete line-item budgets that
researchers can use to collect costs. But keep in mind this important consideration when calculating the marginal cost of programs: sometimes the average
cost of a program is the correct marginal cost for the purpose of a cost-benefit
analysis.
Because cost-benefit studies sometimes investigate whether it is worthwhile
to begin—or terminate—a specific program, it is appropriate in these cases to
include fixed costs if they are a component of a new investment, or could be
saved if the program were terminated. Thus, the average cost, which includes
the fixed costs, is the appropriate cost for the analysis.
When calculating the cost of programs, look out for a common pitfall:
­although programs are often funded through a single budget, sometimes other
entities bear a portion of the cost. It is often helpful to use a structured template to ensure that you measure costs comprehensively. The Substance Abuse
Services Cost Analysis Program Cost Module, for example, was developed to
measure all costs when researching drug treatment programs.41 This is a useful
tool for estimating costs and can serve as a template for cost-collection instruments for other programs or fields. The sidebar “Know Your Costs” (page 20)
provides a checklist to follow when surveying program costs.
The case of technology investments highlights the potential pitfalls of undercounting program costs. When collecting technology costs, be sure to include
not only the cost of the technology itself, but also those of maintenance, installation, and personnel needed to manage and use the resource, as well as any
additional staff training required.42
Remember that program costs sometimes have offsetting benefits in other
areas of the justice system (for example, an electronic monitoring program
that reduces jail costs). In such cases it is important to clarify whether these
offsetting benefits are included in the calculation of the cost of the program—
that is, whether these savings reduce the cost of the program.

Recommendations
Analysts and justice agencies can take a number of steps to improve the accuracy of marginal costs and the cost-benefit analyses they support. Analysts
should carefully document and explain their calculations and results. Justice
agencies should improve the availability of public data that can be used to
make marginal-cost calculations.

Analysts should
carefully document
and explain their
calculations and
results.

Justice agencies
should improve
the availability of
public data that
can be used to
make marginal-cost
calculations.

ANALYSTS
Because the accuracy of marginal costs is paramount to a rigorous cost-benefit
analysis, report all the marginal costs used in a CBA and document the sources
and methods used to calculate these costs. Detail on these inputs will foster

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-

readers’ trust and improve the policy relevance of the analysis by providing
clarity on how the government costs were measured .
Be sure to refer to taxpayer benefits—that is, the benefits of reduced government workloads—as benefits and not savings. This is a critical distinction:
­although an analysis can determine whether a reduction in workload will
create a taxpayer benefit, only budget and administrative decisions will determine whether these benefits will translate into budget savings. Moreover, to
some people, the term “taxpayer savings” might suggest a reduction in taxes
and revenues. It is more likely that benefits will be used to reduce budget gaps
and fund other needs rather than provide a tangible savings to taxpayers. (See
the sidebar “Taxpayer Benefits Versus Taxpayer Savings,” page 5, for more on
this topic).

JUSTICE AGENCIES
Cost-benefit analysts face two main challenges when investigating justice
system costs: either the available published data is of average costs, rather than
marginal costs, or there is little published data that can be used to calculate
justice agencies’ marginal costs.
When justice agencies calculate marginal costs, they should make these figures available publicly. If agencies do not calculate marginal costs, they should
publish detailed information on spending and workload so that researchers
can use it to make more accurate calculations of marginal costs. Not only do
these steps promote transparency, they also ensure that cost-benefit analysis
conducted by others uses consistent figures.
Corrections agencies already provide clear, accessible information about average costs per inmate, and some also publish the average cost of probation or
parole cases. They should supplement this information with data on the shortrun and long-run marginal costs of both incarceration and supervision. The Illinois Department of Corrections, for example, publishes in its annual report the
short-run marginal cost and average cost for each of its facilities.43 Corrections
agencies could publish data about individual housing units’ staffing ratios that
would allow analysts to calculate long-run marginal costs. This information
would be a tremendous benefit to the field, given the importance of marginal
costs for a credible cost-benefit analysis. It could also potentially have significant impact on policymaking in initiatives such as justice reinvestment.
In other segments of the justice system, such as law enforcement and the
courts, it is not practical for agencies to publish marginal costs regularly, for
the same reason that they don’t publish average costs (such as the average cost
of an arrest or a court case). These are labor-intensive exercises and may not be
worth the investment. Instead, law enforcement agencies and court systems
should report budget and workload data at as detailed a level as possible, so
that researchers can use the information to develop better estimates independently. The New York Police Department, for example, publishes the average
time from arrest to complaint on a yearly basis.44

22

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

Resources
METHODS

Figure 13. Marginal-cost resources
GENERAL SOURCES FOR METHODS

Additional information on marginal
costs is available on the website of
the Cost-Benefit Knowledge Bank for
Criminal Justice (cbkb.org). Figure 13
includes a list of the resources discussed in this guide. Detailed information about the sources and methods used by the Washington State
Institute for Public Policy (WSIPP)—a
leading producer of justice-related
CBAs—is available in the appendices of their cost-benefit reports. (See
Appendix D2 in WSIPP’s Benefit-Cost
Tool for States: Examining Policy Options in Sentencing and Corrections.)

•	 Cost-Benefit Knowledge Bank for Criminal Justice: cbkb.org

DATA

•	 CourTool Measure 10: “Cost per Case.” National Center for State Courts

The most accurate, up-to-date information about justice-system costs
will often be readily available from
justice agencies. When possible, it
makes sense to work directly with
public officials to collect this data. Information on justice-system spending is often available on the websites
of justice agencies and executive
budget offices. These budget documents are often accompanied by information on outputs and workload
that can be useful in analyses. Government agencies sometimes publish
information about public employee
salaries; third-party websites that
promote government transparency,
such as sunshinereview.org, often
aggregate this information.
The federal government collects aggregate data that can be useful when
calculating marginal costs. Information on federal, state, and municipal employee salaries is available

•	 Dave Crumpton, Shannon Carey, and Michael Finigan, Enhancing Cost Analysis

•	 Washington State Institute for Public Policy: wsipp.wa.gov
•	 Greg G. Chen et al., Budget Tools: Financial Methods in the Public Sector
(Washington, DC: CQ Press, 2008).
•	 John K. Roman et al., Cost-Benefit Analysis and Crime Control (Washington, DC:
Urban Institute Press, 2010).
•	 Pamela Lachman and S. Rebecca Neusteter, Tracking Costs and Savings Through
Justice Reinvestment (Washington, DC: Urban Institute, 2012).
CORRECTIONS
Christopher Murray, Process Evaluation of Breaking the Cycle (Pierce County,
WA: Pierce County Performance Audit Committee, September 24, 2009).
COURTS

of Drug Courts: The Transactional and Institutional Cost Analysis Approach
(Portland, OR: NPA Research, October 2004).
LAW ENFORCEMENT
Julius C. Chaidez, “How to Calculate the Cost of a Youth Arrest” (Washington,
DC: National Juvenile Justice Network, November 2012).
PROGRAMS
Substance Abuse Services Cost Analysis Program (SASCAP), (Research Triangle
Park, NC: RTI International).
DATA RESOURCES
•	 U.S. Census Annual Survey of Public Employment & Payroll
•	 U.S. Census Annual Survey of State & Local Government Finances
•	 Bureau of Justice Statistics Expenditure and Employment Data Collections
•	 Sunshine Review (information about public employee salaries)

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-

through the U.S. Census Annual Survey of Public Employment & Payroll. This
survey provides state and local government data on full-time and part-time
employment, part-time hours worked, full-time equivalent employment, and
payroll statistics, by governmental function. Information on aggregate spending for each functional area of government is available through the U.S. Census
Annual Survey of State & Local Government Finances. Additionally, the Expenditure and Employment Data Collections prepared by the Bureau of Justice
Statistics (BJS) uses this Census data to calculate annual expenditures for state
and federal police protection, judicial services, and corrections. BJS also reports
this information for the largest local governments (counties with populations
of 500,000 or more and cities with populations of 300,000 or more).

Conclusion
Governments are increasingly looking to economic analyses to inform their
criminal justice policies and programs. The results will be useful to policymakers only if costs are calculated accurately. As discussed in this guide,
one challenge of collecting marginal costs is that although the process can
seem straightforward, even small errors in calculations can compromise a
­cost-benefit analysis. Practitioners must devote the time and resources necessary to accurately calculate taxpayer costs. This attention to detail will make
cost-benefit studies more valuable and can ultimately help generate justice
programs and policies that are more cost-effective.

24

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

ENDNOTES
1	 Douglas C. McDonald, “The Cost of Corrections: In Search of the
Bottom Line,” Research in Corrections 2, no. 1 (1989): 1-25.
2	 The mean per-capita cost of state corrections institutions was
$28,323 per Tracey Kyckelhahn, State Corrections Expenditures FY
1982-2010 (Bureau of Justice Statistics, December 2012). The mean
per-capita cost of prison—including costs outside the corrections
budget, such as underfunded retirement benefits—was $31,286 in
the 40 states analyzed by Christian Henrichson and Ruth Delaney,
The Price of Prisons: What Incarceration Costs Taxpayers (New York:
Vera Institute of Justice, 2012).
3	 Paul Heroux, “Addressing the prison’s budget and population,”
Taunton Daily Gazette, February 17, 2011. http://www.
tauntongazette.com/opinions/x43522680/GUEST-OPINIONAddressing-the-prison-s-budget-and-population (accessed January
9, 2013).
4	 Greg G. Chen et al. Budget Tools: Financial Methods in the Public
Sector. (Washington, DC: CQ Press, 2009), 13.
5	 Steve Aos and Elizabeth Drake, WSIPP’s Benefit-Cost Tool for
States: Examining Policy Options in Sentencing and Corrections
(Olympia, WA: Washington State Institute for Public Policy, 2010),
28. http://www.wsipp.wa.gov/pub.asp?docid=10-08-1201 (accessed
January 9, 2013).
6	 Ibid., 28.
7	 Pamela Lachman and S. Rebecca Neusteter, Tracking Costs and
Savings through Justice Reinvestment (Washington, DC: Urban
Institute, 2012), http://www.urban.org/publications/412541.html
(accessed January 9, 2013).
8	 Ann Netten, “Identifying Costs and Costing Complex Intervention
Programs,” in Cost-Benefit Analysis and Crime Control, edited by
John K. Roman, Terence Dunworth, and Kevin Marsh (Washington,
DC: Urban Institute Press, 2010), 37.
9	 Ann Netten, University of Kent, “RE: taxonomy of costs,” October
12, 2012, personal e-mail.
10	 The hourly wage in this hypothetical example assumes that the
employee works 365 days per year ($55,000 ÷ 365 days ÷ 8 hours
per day—$18.84 per hour). In practice, employees have days off
and this calculation would require an adjustment that accounts for
the number of days per year that each employee is working. This
adjustment is called a relief factor. See page 14 of this guide for
more information on relief factors.
11	 Ibid.
12	 Cost-Benefit Knowledge Bank for Criminal Justice, “Calculating
Drug-Court Costs: An Interview with Shannon Carey,” September
14, 2011, http://cbkb.org/2011/09/drug-court-costs-shannon-careyinterview/ (accessed January 9, 2013).
13	 Henrichson and Delaney, 2012, 4.
14	 Netten, 2010, 40.
15	 Henrichson and Delaney, 2012, 22-23.
16	 Netten, 2010, 44.
17	 Christopher Murray, Process Evaluation of Breaking the

Cycle (Pierce County, WA: Pierce County Performance Audit
Committee, September 24, 2009). http://www.co.pierce.wa.us/
DocumentCenter/View/1341 (accessed March 8, 2013).
18	 These calculations are on pages 41–42, Murray, 2009.
19	 These calculations are on page 42, Murray, 2009.
20	 These calculations are on page 47, Murray, 2009.
21	 These numbers have been rounded. Actual computations from
Process Evaluation of Breaking the Cycle are as follows: Longrun marginal cost (per day) = 27,892,430 ÷ 1,343 ÷ 366 = $56.75
(see Murray, 2009, page 42). Short-run marginal cost (per day) =
8,739,845 ÷ 1,343 ÷ 365 = $17.83 (see Murray, 2009, page 56).
22	 For more information on relief factors, see Camille Graham Camp,
Prison Staffing Analysis: A Training Manual, (Washington, DC:
National Institute of Corrections, 2008), 39.
23	 These calculations are on pages 43-47, Murray, 2009.
24	 Murray calculates the variable costs using a top-down approach.
The author obtained line-item budgets for the various variable costs
(e.g., medical, food, pharmacy) and divided the annual total by the
average daily population. (See Murray, 2009, 47).
25	  Old Behind Bars: The Aging Prison Population in the US (New
York, NY: Human Rights Watch, 2012), 72. http://www.hrw.org/
reports/2012/01/27/old-behind-bars-0 (accessed January 22, 2013).
26	 North Carolina Department of Public Safety, Cost of Supervision
for fiscal year ending 2011 (Raleigh, NC: 2011). http://www.doc.
state.nc.us/dop/cost/ (accessed January 25, 2013; Mississippi
Legislature’s Joint Legislative Committee on Performance
Evaluation and Expenditure Review, Mississippi Department of
Corrections’ FY 2011 Cost Per Inmate Day (Jackson, MS: 2011).
http://www.peer.state.ms.us/reports/rpt557.pdf (accessed January
25, 2013), 1.
27	 Amanda Petteruti and Nastassia Walsh, Jailing Communities: The
Impact of Jail Expansions and Effective Public Safety Strategies
(Washington, DC: Justice Policy Institute, 2008), 3. http://www.
justicepolicy.org/images/upload/08-04_REP_JailingCommunities_
AC.pdf (accessed January 22, 2013).
28	 State of New York, 2010-11 Executive Budget Agency
Presentations. Available at http://www.budget.ny.gov/pubs/
archive/fy1011archive/eBudget1011/agencyPresentations/pdf/
AgencyPresentations.pdf (accessed January 3, 2013), 387.
29	 Judge Linda Ludgate, The Human Side of Being a Judge: The
People Who Make Courts Work, http://www.americanbar.org/
groups/public_education/resources/law_related_education_
network/how_courts_work/peopleandcourts.html (accessed January
22, 2013).
30	 CourTool Measure 10: “Cost per Case” is available at http://www.
courtools.org/Trial-Court-Performance-Measures.aspx (accessed
April 25, 2013).
31	 Cost-Benefit Knowledge Bank for Criminal Justice, “Calculating
Drug-Court Costs,” 2011.
32	 The salaries for public employees are often available on government
websites. Information for public employee salaries, in many states,

VERA INSTITUTE OF JUSTICE

25

-

is available at Sunshine Review, at http://sunshinereview.org
(accessed April 30, 2013). Information on judicial salaries is available
from the National Center of State Courts’ Survey of Judicial
Salaries, at http://www.ncsc.org/salarytracker (accessed April 30,
2013).
33	 Adele Harrell, Shannon Cavanagh, and John Roman, Findings
from the Evaluation of the D.C. Superior Court Drug Intervention
Program (Washington, DC: Urban Institute, 1998), 109. http://www.
urban.org/UploadedPDF/409041_findings.pdf (accessed January 23,
2013).
34	 Dave Crumpton, Shannon Carey, and Michael Finigan, Enhancing
Cost Analysis of Drug Courts: The Transactional and Institutional
Cost Analysis Approach. (Portland, OR: NPC Research, 2004), 1926. http://www1.spa.american.edu/justice/documents/2949.pdf
(accessed January 25, 2013).
35	 Mark Waller and Shannon Carey, Benton County Adult Drug
Treatment Court: Process, Outcome, and Cost Evaluation Final
Report (Portland, OR: NPC Research, 2011), 40. http://www.
npcresearch.com/Files/Benton_County_Adult_Drug_Treatment_
Court_Final_Report_1211.pdf (accessed January 23, 2013).
36	 Julius Chaidez. How to Calculate the Cost of a Youth Arrest
(Washington, DC: National Juvenile Justice Network, 2012). http://
www.njjn.org/uploads/digital-library/NJJN-Arrest-Costing-ToolkitFINAL-Nov12.pdf (accessed November 27, 2012).
37	 Memo from William Vetter, Re: Chronic Minor Offenders in Pierce
County (Pierce County, WA: 2010), 5. http://www.co.pierce.wa.us/
documentcenter/view/1355 (accessed March 8, 2013).
38	 Data provided by Ronald Villa and Sergeant James Keck, San Diego
Police Department, October 15, 2012, personal e-mail.
39	 Cindy Redcross, Megan Millenky, Timothy Rudd, and Valerie
Levshin, More Than a Job: Final Results from the Evaluation of the
Center for Employment Opportunities (CEO) Transitional Jobs
Program (New York, NY: MDRC, 2012), 65. http://www.mdrc.org/
sites/default/files/full_451.pdf (accessed January 23, 2012).
40	 Aos and Drake, 2010, p. 30. http://www.wsipp.wa.gov/pub.
asp?docid=10-08-1201 (accessed November 9, 2012); Richard
Fowles and Sofia Nyström, Introduction to an Econometric CostBenefit Approach (Salt Lake City: Utah Commission on Criminal and
Juvenile Justice, 2012), 5. http://www.justice.utah.gov/Documents/
CCJJ/Cost%20of%20Crime/Utah%20Cost%20of%20Crime%20
2012%20-%20Methods%20Review%20Cost.pdf (accessed January
23, 2013).
41	 RTI International, Substance Abuse Services Cost Analysis Program
(SASCAP), https://www.rti.org/page.cfm/Substance_Abuse_
Economics (accessed November 12, 2012).
42	 Nancy La Vigne, Samantha Lowry, Allison Dwyer, and Joshua
Markman, Using Public Surveillance Systems for Crime Control
and Prevention: A Practical Guide for Law Enforcement and Their
Municipal Partners (Washington, DC: Urban Institute, 2011),
2. http://www.urban.org/UploadedPDF/412402-Using-PublicSurveillance-Systems-for-Crime-Control-and-Prevention-A-PracticalGuide.pdf (accessed December 9, 2012).
43	 Illinois Department of Corrections, Annual Report FY2010, 7. http://
www2.illinois.gov/idoc/reportsandstatistics/Documents/FY10_
DOC_Annual_Rpt.pdf (accessed November 27, 2012).
44	 New York City Mayor’s Management Report, New York City Police
Department, 5. http://www.nyc.gov/html/ops/downloads/pdf/
mmr0912/nypd.pdf. (accessed November 27, 2012).

26

A GUIDE TO CALCULATING JUSTICE-SYSTEM MARGINAL COSTS

Acknowledgments
The authors would like to thank the Bureau of Justice Assistance for providing us with the opportunity to prepare this comprehensive guide on calculating justice-system marginal costs. We
specifically want to thank our program manager, C. Edward Banks, for his support of our work.
Thank you to Steve Aos, director of the Washington State Institute for Public Policy, Michael
Jacobson, president and director of the Vera Institute of Justice, and Michael Wilson, criminal justice and cost-benefit consultant, for their helpful review of earlier drafts of this guide. Thank you
to Ann Netten, professor of social welfare at the University of Kent, for her helpful comments on
the top-down and bottom-up methodologies. Thank you to Tina Chiu and Jules Verdone for their
insight and guidance throughout the drafting process.

About the Cost-Benefit Knowledge Bank
for Criminal Justice
The Cost-Benefit Knowledge Bank for Criminal Justice (CBKB) helps to broaden the knowledge
base of practitioners and policymakers about criminal justice cost-benefit analysis, deepen
the ­knowledge and practice in this area, and support practitioners in building their capacity to
­promote, use, and interpret cost-benefit analysis in criminal justice settings.

About the Cost-Benefit Analysis Unit
Vera’s Cost-Benefit Analysis Unit provides policymakers with clear, accessible information on
the economic pros and cons associated with criminal and juvenile justice investments so that
they can identify effective, affordable interventions for their jurisdictions and allocate resources
­accordingly.

© 2013 Vera Institute of Justice. All rights reserved.
This guide is available on Vera’s website at www.vera.org/marginalcosts.
For more information about this report, contact Christian Henrichson at chenrichson@vera.org.
This project is supported by Grant No. 2009-MU-BX K029 awarded by the Bureau of Justice Assistance. The Bureau of Justice
Assistance is a component of the Office of Justice Programs, which also includes the Bureau of Justice Statistics, the National
Institute of Justice, the Office of Juvenile Justice and Delinquency Prevention, the Office for Victims of Crime, the Community
Capacity Development Office, and the Office of Sex Offender Sentencing, Monitoring, Apprehending, Registering, and Tracking.
Points of view or opinions in this document are those of the authors and do not necessarily represent the official position or policies
of the U.S. Department of Justice.
The Vera Institute of Justice is an independent nonprofit organization that combines expertise in research, demonstration projects,
and technical assistance to help leaders in government and civil society improve the systems people rely on for justice and safety.

Suggested Citation
Christian Henrichson, Sarah Galgano. A Guide to Calculating Justice-System
Marginal Costs. New York: Vera Institute of Justice, 2013.

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