1. Estimating Marginal Costs for
Cost-Benefit Analysis in Criminal Justice
February 23, 2011
Christian Henrichson, Senior Policy Analyst, Cost-Benefit Analysis Unit
Valerie Levshin, Policy Analyst, Cost-Benefit Analysis Unit
Slide 1

2. Estimating Marginal Costs for
Cost-Benefit Analysis in Criminal Justice
Christian Henrichson Valerie Levshin
Slide 2

3. The Cost-Benefit Knowledge Bank for Criminal Justice (CBKB) is a
project of the Vera Institute of Justice funded by the U.S.
Department of Justice’s Bureau of Justice Assistance.
• Website (cbkb.org)
• CBA Toolkit
• Snapshots of CBA Literature
• Podcasts, Videocasts, and Webinars
• Roundtable Discussions
• Community of Practice
Slide 3

4. Today’s Agenda
Introduction and Housekeeping 5 minutes
Overview of Cost-Benefit Analysis 10 minutes
Understanding Marginal Costs 15 minutes
Estimating Marginal Costs 25 minutes
Wrap Up 5 minutes
Slide 4

5. Housekeeping items
Questions
 Use the chat feature to send us your
questions at any time during the webinar.
 We will address your questions after
each section of the presentation.
Slide 5

6. Housekeeping items
Webinar support and troubleshooting
 Call: (800) 843-9166
 Email: help@readytalk.com
Handouts
This webinar is being recorded
The recording and all materials will be posted to
cbkb.org
Slide 6

7. Preview of today’s webinar
You will learn:
• The difference between marginal and average
costs.
• An approach to reading CBA reports.
• Questions to ask while reading CBA reports.
Slide 7

8. Overview of
Cost-Benefit Analysis in
Justice Policy
Slide 8

9. What is Cost-Benefit Analysis (CBA)?
• A tool to assess the pros and
cons of policies and programs
• A method for finding out what
will achieve the greatest net
benefit to society
• An approach to policymaking
Slide 9

10. Added Value of CBA
• Monetizes costs and benefits
• Assesses the economic impact over the long term
horizon
• Future costs and benefits are discounted to the present
• Includes both tangible and intangible costs/benefits
Slide 10

11. The CBA Process
• Determine the Impact of the initiative
• Determine whose perspectives matter
• Measure costs and benefits (outcomes)
• Compare costs and benefits
• Test results
Slide 11

12. Measuring Costs and Benefits
• Measure costs
• quantity × unit cost
• e.g.: number of program participants × cost per participant
• Measure benefits (in dollars)
• quantity × unit cost
• e.g.: number of people who will be incarcerated × cost of
incarcerating one person
Slide 12

13. Measuring Costs and Benefits
• Measure costs
• quantity × unit cost
• e.g.: number of program participants × cost per participant
• Measure benefits (in dollars)
• quantity × unit cost
• e.g.: number of people who will be incarceration × cost of
incarcerating one person
The accuracy of the unit costs affects the
accuracy of the cost benefit results.
Slide 13

14. Marginal Costs and Policy Decisions
―There is certain to be some budgetary benefit. It costs $44,563
(the average for the U.S. is $28,817) to incarcerate a prisoner for
a year in California — nearly the same price as a year at Harvard
University with room and board.‖
The Fiscal Times, Runaway Prison Costs Trash State Budgets,
Adam Skolnick, Feb. 9, 2011.
• True: The average cost of incarceration and the average cost of
Harvard are about the same.
• False: The savings that would be generated if the prison
population declined by one inmate would be sufficient to send
one person to Harvard.
Slide 14

15. Marginal Costs and Policy Decisions
―At present, it costs an average of $46,000 per year to house an
inmate in the MA DOC [Massachusetts Department of
Corrections]. But there is more to this figure than one might
realize. This cost changes with the inmate’s security level,
medical needs and other factors. What is less known is that, on
average, the cost associated with one inmate’s specific needs is
about $9K per year – this covers stuff like food, clothing, and
other incidentals that we pay for on an inmate-by-inmate basis.‖
Taunton Daily Gazette, Addressing the prison’s budget and
population. Paul Heroux, Feb. 17, 2011
Slide 15

16. Questions
Slide 16

17. Understanding
Marginal Costs
Slide 17

18. Marginal Costs and CBA
• Programs and policies can create costs or cost-
savings (benefits) to government agencies
• Example: a corrections department decides to expand a
reentry program that decreases recidivism rates. How much
will it cost to serve more people in the program? How much
will the program save by reducing recidivism rates and,
therefore, prison costs?
• To accurately measure the costs or savings from
initiatives, determine the marginal costs of
government operations.
Slide 18

19. Marginal versus Average Costs
• Marginal costs describe how the cost of an operation
changes when workload changes by a small amount.
• Synonymous with incremental
• Borrowed from economics
• Average costs include both marginal and fixed costs.
• Fixed costs do not change as workload changes.
Slide 19

20. Marginal versus Average Costs
• Example:
• 1,000-bed prison
• Inmate population goes from 900 to 850
• Prison system saves on food, clothing (marginal costs)
• Does not save on electricity, building maintenance, warden
salary (fixed costs)
• The average cost may be $46,000, but this cost
includes both the marginal and the fixed cost
• This small reduction in the inmate population will not
save $46,000
Slide 20

21. Marginal versus Average Costs
When policies have a small effect on agency
operations, using average costs, instead of
marginal costs, will overstate costs/savings.
Slide 21

22. Step-Fixed Costs
• But what if the inmate population decreases from 900
to 700?
• Then add step-fixed costs to marginal costs to
determine the long-term marginal costs.
• Step-fixed costs describe how the cost of an operation
changes with significant changes in activity.
Cost
Quantity
Slide 22

23. Marginal Costs
Inmates Guards Warden
Housing If the inmate
Area 1
population
decreases by 5
people, the prison
system can save on
Housing food and clothing
Area 2
(marginal costs).
Housing
Area 3 Marginal cost:
$5,000
Note: only 3 housing areas are depicted, most prisons have
many more.
Slide 23

24. Long-Term Marginal Costs
Inmates Guards Warden
Housing If the inmate
Area 1
population
decreases by 20
people, the prison
system can save on
Housing food, clothing
Area 2
(marginal costs) and
staff salaries (step-
fixed costs)
Housing
Area 3
Long-term marginal
cost: $20,000
Note: only 3 housing areas are depicted, most prisons have
many more.
Slide 24

25. Average Costs
Inmates Guards Warden
Housing
If the inmate
Area 1 population
decreases by 600
people, the prison
can be closed,
Housing
eliminating all prison
Area 2 expenses.
Average cost:
$60,000*
Housing
Area 3
This cost still
excludes some fixed
costs like the cost of
the central
Note: only 3 housing areas are depicted, most prisons have corrections office.
many more.
Slide 25

26. Which Costs to Use in CBA?
• Magnitude of the costs depends on the policy’s impact
on the system
 Small reduction in the inmate population?
 Prison wings closed? A whole prison closed?
 New reentry program?
• Based on the impact, use marginal, long-term
marginal, or average costs
Slide 26

27. Questions
Slide 27

28. Estimating Marginal Costs
Slide 28

29. Several Approaches
1) Ask government agencies
2) Review budget and workload documents
3) Consider capacity reductions
4) Use estimates from other organizations or states
5) Conduct regression analysis
Slide 29

30. 1. Ask Government Agencies
• How: contact local/state budget
offices and fiscal departments
of criminal justice agencies
• Agency fiscal offices
• Executive budget offices
• Legislative fiscal staff
Ask agencies:
• Do you have marginal or incremental costs?
• How would a change in inmate population (or probation
workload, etc.) affect agency funding?
Slide 30

31. 1. Ask Government Agencies
 Example: a spreadsheet showing marginal cost by levels of
change in the inmate population at a hypothetical jail.
Type of Cost 1-100 101-600 600+
inmates inmates inmates
Corrections personnel n/a $16,700 $52,145
Other personnel n/a $5,575 $15,300
Supplies and materials $1,300 $1,550 $1,550
Total Marginal Cost $1,300 $20,000 $72,000
• Pro: estimates likely reflect actual spending patterns.
• Con: agencies may not have marginal cost estimates.
See Handout for additional detail:
Jail Marginal Cost per Inmate per Year
Slide 31

32. 2. Review budget and workload documents
• How: review budget documents to
identify marginal costs.
• Example:
Marginal Cost of a Prison
Item Estimate Source/Calculation
Inmates per staff 2.5 Budget documents
Staffing ratio (staff per inmates) 0.4 1 / 2.5
Annual Salary $29,000 Sunshinereview.org
Personnel cost per inmate $11,600 $29,000 x 0.4
Supplies & materials per inmate $7,000 Estimate
Marginal Cost $18,600 $11,600 + $7,000
Slide 32

33. 2. Review budget and workload documents
• Pro: budget documents are usually readily available
• Salaries aren’t secrets!
• Con: can be difficult to determine what is a variable
and what is a fixed cost; estimates may not reflect
actual spending decisions
Salary Data in North Carolina from
sunshinereview.org
Please see Handout #2 Government Employee Salaries:
A Sample Page from Sunshinereview.org
Slide 33

34. 3. Consider Capacity Reductions
• How: review budget documents
and consult with criminal justice
agencies to determine whether
there has been a recent capacity
reduction.
• Example:
From the New York State Budget:
“The parolee population is projected to decline by nearly 1,500;
therefore, fewer parole officers are needed. …Savings are
estimated at $3.7 million.‖ (New York State Budget
Presentations 2010)
Marginal cost = $3.7 million / 1,500 = $2,466 per parolee
Slide 34

35. 3. Consider Capacity Reductions
• Pro: reflects actual savings from past experience.
• Con: previous capacity reductions may represent unique
situations that may not occur in the future, so
marginal cost estimates may not hold in the future.
e.g., if a previous capacity reduction involved a closure of a
outdated facility that was expensive to maintain, these
savings might not be indicative of savings in newer
prisons.
Slide 35

36. 4. Use Estimates From Other States or
Organizations
• How :
• review reports and studies for
marginal cost estimates
• adjust these estimates for
cost-of-living differences
across states and inflation,
if applicable.
• [or] determine the marginal/average cost ratio in another
state, then apply the ratio to determine the marginal cost
in your state.
Slide 36

37. 4. Use Estimates From Other States or
Organizations
• Example 1: unit cost estimates from a WSIPP report:
Please see Handout #3, Marginal Operating Costs, Washington State
Criminal Justice System
Slide 37

38. 4. Use Estimates From Other States or
Organizations
• Example 2: Calculating North Carolina marginal cost
of law enforcement using data from WSIPP and the
Bureau of Justice Statistics (BJS).
Marginal Cost in WA Estimate Source
Average Cost - WA $4,182 WSIPP report
Marginal Cost - WA $670 WSIPP report
Marginal/Average cost 16% $670 / $4,182
Average Cost - NC $3,110 police expenditures / arrests
$1,358,211,000 / 436,676
BJS
Marginal Cost in NC $498 $3,110 x 16%
Slide 38

39. 4. Use Estimates From Other States or
Organizations
• Pro: information is generally available.
• Con: estimates may not accurately reflect local costs.
Slide 39

40. 5. Conduct Regression Analysis
• How: conduct regression
analysis using historical
spending and population data.
• What is regression analysis?
• Technique used to understand how changes in
one or more variables (or factors), affect
changes in a variable of interest.
Slide 40

41. 5. Conduct Regression Analysis
• Example:
Washington State Institute for Public Policy (WSIPP)
uses police expenditures and arrest data to estimate
the marginal cost of policing.
• Pro: reflects changes in actual spending vs. workload.
• Con: spending may change for other reasons; long-
term data on costs and workloads may not be
available.
Slide 41

42. Recap of Estimation Approaches
1) Ask government agencies
2) Review budget and workload documents
3) Consider capacity reductions
4) Use estimates from other organizations or states
5) Conduct regression analysis
Slide 42

43. Key Takeaways
• Marginal costs represent a more accurate measure of
costs and cost-savings associated with new programs
and policies
• There are several ways to estimate marginal costs.
Pick one that is right for you.
• Work with government staff to develop marginal cost
estimates and build relationships.
Slide 43

44. Questions
Slide 44

45. Wrap-Up
Slide 45

46. Recap of Today’s Webinar
You learned:
• The difference between marginal and average
costs.
• Why marginal cost are necessary in a credible
cost-benefit analysis.
• 5 methods to estimate the marginal costs at
criminal justice agencies.
Slide 46

47. Follow-up
Please complete the evaluation form as you leave this
training.
To receive information and notifications about upcoming
webinars and other events
• Visit the Cost-Benefit Knowledge Bank for Criminal Justice at
http://cbkb.org
• Subscribe to receive updates from CBKB.
• Follow us on Twitter at http://www.twitter.com/CBKBank
The next webinar will be on March 24th. Elizabeth
Drake from the Washington State Institute of Public
Policy (WSIPP) will discuss the role of evaluation in
CBA.
Slide 47

48. 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, 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 represent the official position or policies of the United States Department of
Justice.
Slide 48

49. Contact Information
Christian Henrichson
chenrichson@vera.org
(212) 376-3161
Valerie Levshin
vlevshin@vera.org
(212) 376-3062
cbkb@cbkb.org
http://www.cbkb.org
Slide 49

50. Thank you!
Slide 50