marginal costing

1. Slide 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

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

3. Slide 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

4. Slide 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

5. Slide 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.

6. Slide 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

7. Slide 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.

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

9. Slide 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

10. Slide 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

11. Slide 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

12. Slide 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

13. Slide 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.

14. Slide 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.

15. Slide 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

16. Slide 16
Questions

17. Slide 17
Understanding
Marginal Costs

18. Slide 18
• 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.
Marginal Costs and CBA

19. Slide 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.

20. Slide 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

21. Slide 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.

22. Slide 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.
Quantity
Cost

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

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

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

26. Slide 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

27. Slide 27
Questions

28. Slide 28
Estimating Marginal Costs

29. Slide 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

30. Slide 30
• 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?
1. Ask Government Agencies

31. Slide 31
 Example: a spreadsheet showing marginal cost by levels of
change in the inmate population at a hypothetical jail.
• Pro: estimates likely reflect actual spending patterns.
• Con: agencies may not have marginal cost estimates.
1. Ask Government Agencies
Type of Cost 1-100
inmates
101-600
inmates
600+
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
See Handout for additional detail:
Jail Marginal Cost per Inmate per Year

32. Slide 32
• How: review budget documents to
identify marginal costs.
• Example:
2. Review budget and workload documents
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

33. Slide 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

34. Slide 34
• 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
3. Consider Capacity Reductions

35. Slide 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.

36. Slide 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.

37. Slide 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

38. Slide 38
4. Use Estimates From Other States or
Organizations
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%
• Example 2: Calculating North Carolina marginal cost
of law enforcement using data from WSIPP and the
Bureau of Justice Statistics (BJS).

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

40. Slide 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.

41. Slide 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.

42. Slide 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

43. Slide 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.

44. Slide 44
Questions

45. Slide 45
Wrap-Up

46. Slide 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.

47. Slide 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.

48. Slide 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.

49. Slide 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

50. Slide 50
Thank you!