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Vera Institute Justice System Marginal Costs Factsheet May 2013

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A Guide to Calculating
Justice-System Marginal Costs
Fact Sheet

MAY 2013

of change in total cost when a unit
of output changes
AVERAGE COST: The total cost
of all output divided by total
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
that remains constant for a certain
range of output and changes
when output exceeds or falls
­below a certain threshold
The cost affected as soon as the
output changes; also called variable cost

Justice policies and programs generate taxpayer benefits and
costs. If you want an accurate picture of those costs and benefits,
you need to understand m
­ arginal costs. In cost-benefit analysis
(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 output
or workload.
The costs of a government agency—or a private firm, for that matter—are said
to be variable, fixed, or step-fixed. 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
include overtime, supplies, and fuel. Fixed costs—such as rent, utilities, and
central administration—remain fixed over a given period and are not usually
affected even if the workload changes. Step-fixed costs remain constant for a
certain range of workload, but change if the workload exceeds or falls below
that range. The most common types of step-fixed costs are staff salaries and
benefits, which increase when, for example, a prison population or probation
caseload exceeds a certain threshold and more staff is needed.
The marginal cost is the amount of change in total cost when a unit of output
changes. In the context of the criminal justice system, it is how much the total
operating costs of an agency change when workload (such as arrests, court filings, or jail intakes) changes because of a policy or program.

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

It is critical to use marginal costs in CBA calculations. One fundamental error an
analyst can make is to use average costs rather than marginal costs—a mistake
that usually results in overestimating the costs related to a 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.

Read the complete guide at

The difference between average and marginal costs is often considerable. In
Massachusetts, for example, the average annual per-inmate cost of incarceration
is $46,000, whereas the marginal cost is $9,000.2 The average cost includes costs
for administration, utilities, and other expenses that will not change when the
prison population decreases slightly. A small change in the population affects


For More Information
The Vera Institute of Justice
is an independent nonprofit
organization that combines research,
demonstration projects, and
technical assistance to help leaders
in government and civil society
improve the systems people rely on
for justice and safety.
The Cost-Benefit Knowledge
Bank for Criminal Justice (CBKB)
is a project of Vera’s Cost-Benefit
Analysis Unit and is funded by the
U.S. Department of Justice’s Bureau
of Justice Assistance. 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.
For more information, please visit
the CBKB website at or
contact Tina Chiu at 212-376-3038

This project is supported by Grant No. 2009-MU-BX
K029 awarded by the Bureau of Justice Assistance.

expenses such as food, clothing, and medical care: these are the marginal costs
of a small increase or decrease in the prison population.
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 more
than one marginal cost could potentially be used in justice-system CBAs. Costs
that change immediately with even a small change in workload are often called
short-run marginal costs (or “variable costs”). 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, the long-run marginal
cost includes the short-run marginal cost, as well as the step-fixed staffing costs
that change as governments modify staffing levels in future budget cycles.
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 affect staffing
needs. Analysts should use the short-run marginal cost when the policy impact
anticipated is not large enough to affect staffing.
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 expenses 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—for example,
if the prison could close a housing unit—analysts must consider the step-fixed
costs of staffing in addition to the short-run costs. These are the long-run marginal costs. The following table 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.

The Bureau of Justice Assistance is a component of
the Office of Justice Programs, which also includes

Annual Per-Inmate Costs in Washington State, 20093

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 author and do not necessarily













represent the official position or policies of the
U.S. Department of Justice.

1	 Douglas C. McDonald, “The Cost of Corrections: In Search of the Bottom Line,” Research in Corrections 2,
no. 1 (1989): 1-25.
2	 Paul Heroux, “Addressing the prison’s budget and population,” Taunton Daily Gazette, Feb. 17, 2011.
Bureau of Justice Assistance
U.S. Department of Justice

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3	 Washington State Institute for Public Policy, WSIPP’s Benefit-Cost Tool for States: Examining Policy Options
in Sentencing and Corrections, August 2010.

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