USPS-T-22
BEFORE THE
POSTAL RATE COMMISSION
WASHINGTON, D.C. 20268-0001
Postal Rate and Fee Changes,
2000
DIRECT TESTIMONY OF
MICHAEL D. BRADLEY
ON BEHALF OF
UNITED STATES POSTAL SERVICE
Docket No. R2000-1
TABLE OF CONTENTS
AUTOBIOGRAPHICAL
PURPOSE
I.
II.
SKETCH
ii
AND SCOPE
iv
INCREMENTAL
COSTS ARE ESSENTIAL FOR GUARDING AGAINST
CROSS SUBSIDY. THE NEW POSTAL SERVICE METHOD IS
ACCURATE, FLEXIBLE, AND CONSISTENT WITH ESTABLISHED
COMMISSIONCOSTINGMETHODS
._.............___.._.___.
THE CURRENT METHOD FOR ESTIMATING TEST-YEAR
ATTRIBUTABLE
COSTS.
The Method Used for Calculating Attributable
A.
Cost is Known as “Calibration
The Steps Through Which Test-Year Attributable Costs are
B.
Estimated . . . . . . . . . . . . . . ..___.__...............___._.
1
5
5
9
III.
THE NEW METHOD FOR CALCULATING INCREMENTAL COSTS.
14
The Steps Through Which Test-Year Incremental Costs are
A.
Estimated. . . . . . . . . . . . . .._............_..............
15
The
Relationship
Among
Incremental
Cost,
Volume
Variable
Cost
B.
and Attributable Cost..
18
Comparing the Old and New Methods of Calculating Test-Year
C.
Incremental Costs.
.
24
IV,
THE ANALYTICAL STRUCTURE OF INCREMENTAL
Calculating Base Year Costs.
A.
The Role of Product Specific Costs
B.
Calculating Test Year Costs.
C.
V.
HOW THE NEW METHOD OF INCREMENTAL COST CALCULATION
ADDRESSES THE CONCERNS RAISED BY THE COMMISSION IN
DOCKETR97-1.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...42
A.
B.
COSTS
A Discussion of the Three Deficiencies In the Calculation of
Incremental Costs Cited by the Commission.
A Discussion of the Three Additional Concerns about the
Incremental Cost Calculation Cited by the Commission..
I
26
27
33
38
42
44
AUTOBIOGRAPHICAL
1
My name is Michael D. Bradley and I am Professor of Economics
2
3
George Washington
4
have published
5
Postal economics
6
research at various professional
conferences
7
both universities
agencies.
8
extensive experience
9
served as a consultant
10
_-
SKETCH
associations,
University.
at
I have taught economics there since 1982 and I
many articles using both economic theory and econometrics.
is one of my major areas of research.
and government
investigating
my
and I have given invited lectures at
Beyond my academic work, I have
real-world economic problems, as I have
to financial and manufacturing
and government
I have presented
corporations,
trade
agencies.
I received a B.S. in economics with honors from the University of
11
12
Delaware
13
Omicron Delta Epsilon for academic achievement
14
earned a Ph.D. in economics
15
graduate
16
have won both academic and nonacademic
17
Irwin Distinguished
Paper Award, the American Gear Manufacturers
18
Award, a Banneker
Award and the Tractenberg
and as an undergraduate
was awarded both Phi Beta Kappa and
in the field of economics.
I
from the University of North Carolina and as a
student I was an Alumni Graduate
Fellow. While being a professor,
I
awards including the Richard D.
ADEC
Prize.
I have been studying postal economics for about fifteen years, and I have
19
20
participated
in many Postal Rate Commission
21
R84-I,
22
.and in Docket No, R87-1, I testified on behalf of the Postal Service concerning
I helped in the preparation
proceedings.
In Docket No.
of testimony about purchased
ii
transportation
1
the costs of purchased
2
testimony
3
remand, I presented
5
presented
6
costs.
7
econometric
9
10
11
In Docket No. R90-1, I presented
in the area of city carrier load time costs.
testimony concerning
I returned to transportation
4
8
transportation.
testimony
the methods of city carrier costing.
There, I
of a distance taper in postal transportation
In Docket No. R94-1, I presented
both direct and rebuttal testimony
on an
model of access costs.
More recently, in Docket R97-1,
presented
In the Docket No. R90-1
costing in Docket No. MC91-3.
on the existence
rebuttal
I presented three pieces of testimony.
both direct and rebuttal testimony
I also presented
in the area of mail processing
testimony on the costs of purchased
I
costs.
highway transportation
Beside my work with the U.S. Postal Service, I have served as a expert on
12
postal economics
to postal administrations
13
Of particular relevance to this testimony,
14
decade on their incremental
15
for their incremental
16
them with methodological
17
serve as Canada Posts
in North America,
Europe, and Asia.
I have worked with Canada Post for a
cost system.
I provided the original analytical basis
cost model when it was first constructed
and have provided
advice as the model has been refined.
External Methodological
III
Advisor.
I currently
-
PURPOSE
1
2
is to present and explain the Postal
3
Service’s new method for calculating
4
method improves upon the previous method and I demonstrate
5
consistent
with the established
6
estimating
test-year attributable
7
the calculations.
8
9
F.
The purpose of my testimony
AND SCOPE
It is my goal to encourage
place of attributable
incremental
costs.
Postal Rate Commission
costs.
I describe how the new
that it is
methodology
I also provide the mathematical
the Commission
costs in its costing analysis.
to adopt incremental
Incremental
for
basis for
costs in
cost is a more
10
accurate measure of the total cost caused by a product and in the postal context
11
incremental
12
analyzing
13
cross subsidy.
14
cost will exceed attributable
cost. It is thus a better basis for
if a product’s revenue is sufficient to cover its cost when testing for
There are no library references
15
testimony.
16
by witness Kay, USPS-T-23.
Application
or workpapers
of the methods described
iv
directly associated
in this testimony
with this
is presented
1
2
3
4
I.
INCREMENTAL
COSTS
CROSS SUBSIDY. THE
ACCURATE, FLEXIBLE,
COMMISSION COSTING
5
ARE ESSENTIAL FOR GUARDING AGAINST
NEW POSTAL SERVICE METHOD IS
AND CONSISTENT WITH ESTABLISHED
METHODS.
In Docket No. R97-1, the Postal Service presented
6
known as incremental
7
concept of incremental
8
cases, Docket No. R97-1 was the first time actual incremental
9
calculated.*
10
cost, for the Commission’s
a new cost measure,
consideration.’
Although the
cost had been presented to the Commission
The Postal Service introduced
incremental
in previous
costs were
costs in Docket No. R97-1,
11
because of their essential role within the regulatory framework
12
firm. As is well known, incremental
13
product.
14
ensuring that a products
15
calculated
for a multi-product
cost measures the total cost caused by a
It is therefore the ideal cost measure for testing for cross-subsidy
or for
revenue covers its cost.3 Because there is no properly
total product cost measure that can exceed a products
incremental
1
a,
Direct Testimony of William M. Takis on Behalf of the United
State Postal Service, Docket No. R97-1, USPS-T-41 and Direct Testimony of
John C. Panzar on Behalf of the United States Postal Service, Docket No.
R97-1, USPS-T-l 1,
2
For an early discussion of the concept of incremental cost and its
role in the regulatory framework, see Direct Testimony of William J. Baumol on
Behalf of the United States Postal Service, Docket No. R87-I.
3
The incremental cost of a product is the total additional cost caused
by adding that product to the existing product mix. For example, suppose that a
firm produces two products, X and Y. The incremental cost of Y is the total cost
of increasing the output of Y from zero to its current level, Y’, while holding the
level of X constant. Note that the incremental cost of Y depends upon both any
fixed cost devoted to producing Y and the current level of production of X.
2
1
cost, any test of cross-subsidy
2
subject to error,
3
“attributable
4
below its incremental
5
that does not make use of incremental
For example, it is possible for a products
cost” as measured
revenue to cover its
by the Postal Rate Commission,
but still be
cost.
In the last rate case, the Commission
6
incremental
7
of certain perceived deficiencies
a
Commission
9
of the Postal Service’s incremental
endorsed the effort to calculate
cost but did not accept the Postal Service’s measurements
in the method of calculation.
made clear that is was interested
because
Nevertheless,
the
in receiving an improved version
cost calculation:4
Witness Takis’ attempt to develop the incremental
costs of postal services directly responds to
Commission interest expressed in Docket No. R94-1,
PRC Op. R94-1, Appendix F, paras. 167 and 170. It
clearly represents a serious effort to examine an
extraordinarily complex and difficult problem. In
reviewing this testimony, the Commission has had to
bear in mind how the line of inquiry represented by
witness Panzar’s theories and witness Takis’
applications might develop into a useful tool for
identifying cross-subsidy in future proceedings.
Would a future Commission wish to be alerted to the
possibility of a cross-subsidy as identified by a more
acceptable and applicable successor to witness
Takis’ incremental cost test? Clearly, the answer is
“yes.”
10
11
12
13
14
15
16
17
ia
19
20
21
22
23
24
25
26
cost is
The Postal Service has produced such an improved version in this case
27
The Commission
28
method of calculation.
This clarity permitted the Postal Service to modify its
methods of calculation
so that the new methods are consistent
4
was very clear in describing
See PRC Op., R97-1, at 246.
the concerns it had with the old
with established
3
1
Commission
methods of product cost measurement.
2
concern that the Commission
3
was that it would have been forced to use incremental
4
dependent
voiced about the Postal Service’s previous effort
costs that were critically
upon untested (and ultimately rejected) costing studies?
5
6
7
a
9
10
11
12
13
14
15
16
17
ia
For example, the primary
In witness Takis’ own words, “it is imperative that any
approach to estimating incremental costs starts with,
and ultimately is consistent with, the analyses that
determine volume variable cost in BY 1996.” Id. at 8.
Since the Commission has rejected the model
proposed by witness Baron with respect to load time
cost variability, and that of witness Bradley with
respect to mail processing cost variability, it would be
inconsistent for the Commission to depend upon
evidence supplied by witness Takis that rests upon
these rejected models.
While I concur with witness Takis’ admonition
19
volume variable costs and incremental
20
consistency
21
new method of calculating
22
of attributable
23
the cost studies themselves.
24
method it will be quite easy for the Commission
25
any set of variabilities/cost
26
costs are predicated
27
the Commission’s
about the consistency
costs, I would point out that such
does not require reliance upon untested cost studies.
incremental
of
costs, like the Commission’s
costs, relies upon only the variabilities
Thus, as I demonstrate
studies it chooses.
In fact, the
calculation
from such cost studies, not
below, under the new
to calculate incremental
costs for
The objection that incremental
upon a specific set of cost studies is no longer a barrier to
use of incremental
costs.
?,
4
The Commission
1
2
97-1 because the calculated
3
Service’s proposed
incremental
cost in Docket No.
costs were related to the Postal
rates, not the rates the Commission
ultimately chose?
Also, the Commission’s recommended rates differ
from those requested by the Postal Service in this
proceeding. Consequently, the Commission makes
no use of witness Takis’ estimates of incremental cost
and relies instead on attributable costs, as it has in
past proceedings, to demonstrate that its
recommended rates are free of cross-subsidies.
4
5
6
7
a
9
IO
.-
also rejected the use of incremental
11
This concern is also alleviated by the new method of calculation.
12
Because the new method requires the same information to calculate test-year
13
incremental
costs that are required to calculate test year attributable
14
incremental
cost test can now be performed on any after-rates
15
volumes.
16
attributable
costs in the past, it now can check its after-rates
17
incremental
costs.
Just as the Commission
has checked its after-rates
test-year
revenues against
revenues against
In sum, the new method of calculating test-year incremental
ia
19
flexible and entirely consistent
20
same information
21
the concerns the Commission
requirements
To understand
22
23
understand,
24
works.
with established
costs, the
costs is
costing methodology.
as test-year attributable
It has the
costs and it addresses
raised in the last case.
the new method and how it works, we must first
from a macro perspective,
That is accomplished
how the current costing methodology
in the next section of my testimony.
The
5
1
subsequent
section explains and discusses the new method for calculating
2
year incremental
3
presented
4
about how incremental
5
discussion
costs. The analytical structure of the cost calculations
and the testimony
ends with a review of the Commission’s
costs were calculated
test
is then
concerns
in Docket No. R97-1 and a
of how the current method addresses
those concerns.
6
7
a
9
10
11
12
13
II.
THE CURRENT
ATTRIBUTABLE
A.
METHOD FOR ESTIMATING
COSTS.
The Method
“Calibration.”
The current method of calculating
14
“calibrated”
15
model has its parameters
16
calibrated
17
some estimated
ia
and some established
19
Use for Calculating
Attributable
attributable
estimated econometrically
econometrically,
In the calibration
determined
cost model.’
as
upon a
An estimated
?
from a single set of data. A
from a variety of sources, with
some determined
from engineering
studies,
by judgment.
approach,
the structure of the model is first determined
20
and then the models is “calibrated;”
21
populated with chosen values for the parameters.
22
can than be solved (or simulated) for the desired variables.
7
Cost Is Known
costs depends
cost model as opposed to an “estimated”
model has its parameters
TEST- YEAR
that is, the structure of the model is
After calibration,
the model
In the case of the
For some introductory discussions of calibration,
Pagan, “Calibration and Econometric Research: An Overview,”
Applied Econometrics, Dec. 1994 or Danny T. Quah, Business
Calibration and Estimation: An Introduction, Economic Journal,
p 1594-l 596.
see, Adrian
Journal of
Cycle Empirics:
November 1995,
-
6
-~
1
attributable
2
keys from a variety of sources and is then “solved” to calculate both base-year
3
and test-year
attributable
The calibration
4
and distribution
costs.
methodology
can be illustrated through a simple example.
5
Suppose that the postal costing structure had three products: Class A, Class B
6
and Class C and four cost pools: Pool l(Retail),
7
(Mail Processing),
a
in this simple case can be envisioned
9
representing
10
,-.
cost model, the model is populated with variabilities
and Pool 4 (Delivery).
Pool 2 (Transportation),
The structure of the product cost model
as a 4 X 3 matrix with the rows
the cost pools and the columns representing
matrix can be represented
Pool 3
the classes.
Such a
as:
11
Product A
12
13
Retail
cost
14
15
Transportation
cost
16
17
Mail Processing
cost
:i
Delivery
cost
WC,
Product B
VVCRB
Product C
WC,,
20
For each cell, the volume variable cost for the individual class is given by the
21
product of the cells accrued cost, (C), its variability (E) and the class’ share of the
22
distribution
23
by the product of accrued cost for retail, (C,), the variability for retail (&s) and
key (8). For example, Class A’s volume variable retail cost is given
7
1
Class A’s share of the retail distribution
2
variable retail cost for Class A is given by:
vvc,
=
key (8,).
Mathematically,
the volume
CREReRA
3
The product cost model, in this case, can be represented
4
for each of the cost pools. The first equation
5
second the transportation
6
the fourth represents
by four equations,
one
represents the retail cost pool, the
cost pool, the third the mail processing
cost pool and
the delivery cost pool.
(4
7
The structure of the model is determined
a
definitions.
9
pools but the model must be calibrated
by selecting the values for the
variabilities
keys (the 8ij).*
10
11
by the cost pool breakout and product
The Postal Service accounting
(the &j) and the distribution
system typically provides the cost
The above model provides volume variable cost, but can be easily
8
There are instances in which the cost pool definition depends upon
systems other than the pure accounting system. For example, in mail
processing, cost pools may in part be defined by MODS data or IOCS data.
--
a
1
augmented
2
costs for Class B in transportation
3
attributable
to provide attributable
cost. Suppose that there are specific fixed
and for Class C in delivery.
The analogous
cost model is given by:
(3)
/-
4
In this set of equations
5
transportation
6
F,, represents the specific fixed cost for Class B in
and F,, represents the specific fixed cost for Class C in delivery.
To be more precise, we will review the current method for calculating
7
attributable
a
calibration exercise.
9
addressed.
10
calibration
11
structure of that model.
That is, there is general agreement
12
of the cost components
and there is a common overall method for calculating
13
base-year
costs.
14
costs and then consider those methods though the lens of a
Before pursuing that detail, however, a final issue must be
Although
the Commission
and Postal Serve have differed on the
of the cost model, there is generally little disagreement
and test-year
The differences
between the Commission
about the
about the structure
and the Postal Service have
15
typically arisen because of divergent views over the choice of the variabilities
16
and distribution
keys required to calibrate the model.
Once those choices are
made, however, a common method is used to calculate test year costs.
that the Postal Service calculates
calculates
“attributable”
“volume variable” costs and the Commission
costs. The difference
between these cost measures is
only specific fixed costs, so there is no fundamental
Commission
It is true
conflict in methodology;
the
simply takes volume variable costs and adds specific fixed costs to
them to calculate attributable
costs.g In what follows, therefore,
I can safely refer
only to “the” cost model without reference to whether it is “the Commission’s
model” or “the Postal Service’s model.”
9
10
B.
11
The established
12
The Steps Through
Estimated.
can be described
13
14
15
16
methodology
Which Test-Year
for estimating
Attributable
Costs are
test year attributable
costs
in five steps
Step 1:
Data collection
The process starts with the collection data by the Postal Service.
17
In some cases, this is an ongoing process in which the same systems are
ia
used to collect product and cost data on an annual basis.
19
instances,
20
parameters.
21
example of a special data set is HCSS.
9
In other
special data sets are collected and used to estimate
new
Examples of ongoing systems are IOCS and TRACS.
The term “specific
confusion in the past as it may
fixed. As I explain below, there
variable but should be included
An
fixed” cost may have been the source of some
have been applied to some costs that were not
are some cost that are neither fixed nor volume
in a products incremental cost.
IO
1
Special studies to update
model’s parameters.
and improve
2
3
Step 2:
4
Postal Service analysts, intervenor analysts,
the
and Commission
staff
5
produce special studies based upon the data the Postal Service collects
6
These studies typically produce either estimates of variabilities
7
estimates of distribution
a
9
Step 3:
keys for the various components.
Commission
selection
the parameters.
During the ten-month
10
or
of its preferred
values for
period of the rate case, the Commission
11
select specific values for the parameters
12
It will chose its preferred values for specific fixed costs, variabilities
13
distribution
keys from the studies presented
14
intervenors,
or it will rely upon parameters
15
consultants.‘0
16
parameters.
17
ia
Finally, the Commission
will
required to calibrate the model.
and
by the Postal Service or
produced
by its own staff or
may choose to retain the old
It is important to note that this process does not require including
the new studies in the cost model
10
-
it only requires including the values
For examples of the Commission choosing a set of parameters
produced by the Postal Service see the adoption of TRACS distribution keys in
Docket No. R90-1 (a
PRC Op., R90-1 at 154). or the adoption of new
variabilities for purchased highway transportation in Docket No. R97-1 (a
PRC
Op., R97-1 at 205). For examples of the Commission choosing parameters
estimated by its own staff or consultants see the adoption of purchased highway
transportation variabilities in Docket No. R87-1 (a
PRC Op., R67-1 at 314) or
the choice of city carrier load time variabilities in Docket No. R90-1 (See PRC
Op., R90-1 at 111-85).
for the parameters
(and analytical
that have been produced.
structures)
underlying
explicitly used in the calculation
calculation
of attributable
from an engineering
This means that the studies
the chosen parameters
of attributable
costs.
cost whether the estimated
study, from judgment,
are not
It matters not in the
parameters
came
or from an econometric
study
using a linear function, a quadratic function, or a translog function.
Step 4: Calculate
7
a
9
base- year attributable
costs
Once the model’s structure has been populated
with the chosen
10
parameters,
the model is used to calculate base year attributable
11
The first step is to calculate base-year volume variable costs. This
12
requires combining
13
elasticity to determine the pool of volume variable costs. These costs
14
then are distributed
15
Total volume variable cost for a particular subclass is found by summing
16
the component
with the relevant
to products based upon the chosen distribution
-
keys
specific volume variable costs for that subclass.
A products
17
the accrued cost in each component
costs,
total base-year
attributable
cost is calculated
by first
ia
identifying
any specific fixed costs for that product and then adding them
19
to the products total volume variable cost. Unit base-year
attributable
20
(volume variable) cost is found by dividing total base-year
attributable
21
(volume variable) cost by base-year
RPW volume.”
11
A review of these steps may leave one with the question of how the
Postal Service could calculate volume variable costs before culmination of a rate
case. Yet, the Postal Service requires these costs before proposing new rates.
-
12
~~-
Calculate
test- year attributable
costs.
1
Step 5:
2
The cost model estimates or forecasts the test-year attributable
3
costs by a process known as “rolling-forward”
the base-year
attributable
4
costs. To calculate the test-year costs, the base year costs are adjusted
5
for anticipated
6
and the test year. These anticipated
changes include volume changes,
7
input price changes and productivity
changes.
a
the base-year
9
effects, non-volume
changes expected to take effect between the base year
In roll-forward
terminology,
costs are adjusted by applying volume effects, cost level
workload
effects, and special program effects.
10
adjustments
11
base year volume variable costs are adjusted upward or downward,
12
multiplicative
13
are applied in a specific manner.
manner, for the anticipated
For example,
in a component
In most components,
These
the
in a
change.
that gets a volume effect, each
14
products
volume variable (and thus the volume variable portion of
15
attributable)
16
product.
17
base year and test year, this calculation would produce test year volume
cost is multiplied by the expected volume growth rate for that
If this were the only change in cost circumstances
between the
The Postal Service’s proposed volume variable costs differ from the volume
variable costs calculated by the Commission solely in the choice of the
parameters used to calibrate the model. Thus, if one replaces “the Commission
chooses” with “the Postal Service chooses” in Step 3, the same process applies.
In this way, the Postal Service determines its proposed rates before the case is
filed. As the Postal Service does not calculate attributable costs, it is my goal to
compare the Commission’s calculation of attributable costs with the Postal
Service’s new method of calculation of incremental costs.
13
-
variable cost. This also means that the ratio of test-year to base-year
attributable
cost would be equal to the growth rate in volume.
of the parameters
test-year
of the model are held constant during the calculation
calculated
however, whose test year costs are
externally to the cost model. I am informed, for example, that
test year workman’s
compensation
costs are not determined
roll forward process but are determined
The established
methodology
costs using parameters
through the
outside the model.
is thus based upon constructing
a model of
IO
attributable
11
Commission’s
12
Once that structure is put into place, it is used to calculate both base-year
13
test-year costs without reference to the special studies.
14
costs are consistent
15
costs are just transformations
16
changes
17
projects.
ia
of
costs.
There are some components,
9
Note that all
from special studies to embody the
beliefs about the relationships
with the base-year
between products and their costs.
Moreover, the test-year
of the base-year
costs based upon anticipated
workload,
and special programs or
As we will see in the next section, the new method of calculating
incremental
20
therefore
21
by the Commission
22
incremental
costs directly replicates this established
methodology
test-year
and is
entirely consistent with it. In this way, it mitigates the concerns
costs.
and
costs, in the sense that the test-year
in volumes, input costs, non-volume
19
4
Docket No. R97-1 about the old method of calculating
raised
-
14
1
2
Ill.
THE NEW METHOD FOR CALCULATING
To ensure that the calculation
of incremental
3
information
4
method of calculating
5
methodology,
6
identical to the first three steps in the attributable
7
I begin the discussion
a
9
10
beyond that required for the calculation
incremental
cost does not require any
of attributable
In fact, the first three steps of the incremental
of incremental
method, and attributable
COSTS.
cost, the new
cost relies upon and parallels the established
cost calculation
cost calculation
cost calculation.
cost calculation
The similarity between incremental
are
Consequently,
with step 3.
cost calculation,
even under the old
has already been acknowledged
by the
Commission:”
Witness Takis works within the same cost accounting
framework as the Commission.
It is the same
accounting framework that is followed by the Service
in its data collection and cost reporting systems and
that is used by Postal Service witness Degen whose
cost pools and attributions have been largely
accepted by the Commission.
11
12
13
14
15
16
17
ia
19
20
21
22
23
24
25
26
27
28
INCREMENTAL
At the subclass level the approach is identical in
many of its assumptions and calculations to the
Commission’s calculations of attributable cost.
Specific fixed costs are identified and used in the
same way. Other information such as the singlesubclass stop information is also used in the same
way. The approach taken by witness Takis parallels
the Commission’s calculation of attributable cost in
many important respects.
The concordance
12
that the Commission
has already recognized
See PRC Op., R97-1, Vol. 1 at 249
has been
15
maintained
in the new method of incremental
cost calculation.
Postal Service’s
modifications
the consistency
between the methods of incremental
established
A.
to the incremental
cost calculation
9
have increased
cost calculation
and the
methodology.
The Steps Through
Estimated.
Which Test-Year
Incremental
The steps required to calculate test-year incremental
a
Indeed, the
Costs are
cost are described
below:
Data collection
Step 1:
10
11
Same as in the Commission’s
attributable
12
13
14
15
16
Step 2:
17
ia
Step 3:
19
Same as in the Commission’s
attributable
20
Step 4: Calculate
incremental
21
Incremental
Special studies to update
model’s parameters
Same as in the Commission’s
attributable
Commission
selection
the parameters.
base-year
cost calculation.
and improve
the
cost calculation.
of its preferred
values for
cost calculation.
costs.
costs are calculated from the same base-year
22
as attributable
costs. There is an essential difference
23
calculation,
24
last unit produced,
25
of the units produced.
however.
Attributable
whereas
costs incorporate
incremental
model
in the method of
only the cost of the
costs incorporate
the costs of all
16
To see how this works, consider the purchased
1
highway
2
transportation
cost pool. There are no specific fixed costs in this cost
3
pool, so attributable
4
this cost pool is cubic foot-miles
5
if found by multiplying the variability of the cost driver (CFM) times
6
accrued cost. Mathematically,
7
cost of the last CFM provided times the total number of CFMS.‘~ The
a
attributable
cost is then distributed
9
distribution
key.
Incremental
10
cost equals volume variable cost. The cost driver in
(CFM) of transportation.
cost
this is the same as multiplying the marginal
to products with the TRACS
cost, on the other hand, recognizes
11
CFM cost the same amount to produce.
12
multiplying
13
the last CFM.14 Incremental
14
marginal cost changes over the range of the products
Incremental
the fact that not all
cost is found by
each CFM times its own marginal cost, not the marginal cost of
costs thus allows for the fact that the
In any cost component
15
Attributable
output.
for which the variability is less than one
16
hundred percent, like in purchased
17
cost of the driver (CFM) declines with increases in the driver (CFM).
ia
other words, the cost of obtaining an additional CFM falls as the number
19
of purchased
13
calculations
14
CFMs increases.
highway transportation,
the marginal
This means the cost to the Postal Service
The mathematics of the volume variable and attributable
are provide in the next section.
The mathematics
the next section.
In
of incremental
cost calculation
cost
are also given in
17,
1
of providing the last CFM of transportation
2
previous CFMs of transportation.
3
incremental
4
variable purchased
purchased
It also means that a products
highway transportation
highway transportation
More generally,
5
is below the cost of providing
cost will exceed its volume
cost.
this means that for any cost component
6
variability less than one hundred percent the incremental
7
in that cost component
8
component.
9
percent then the products
10
with a
cost of a product
must exceed its volume variable cost in the
If the variability in a cost component
incremental
equals one hundred
cost equals its volume variable
cost as the driver’s marginal cost is constant.
11
To understand
the calculation
of incremental
12
consider the structure of the product cost model.
13
calibrated
14
product cost model is used to calculate attributable
15
year or the test year, the elasticity parameters
16
example, the same elasticity parameters
17
year and test-year attributable
18
elasticity parameter
15
cost, we must
Formally speaking, the
model has a “constant elasticity” structure.
That is, when the
cost, in either the base
are held constant.
For
are used to calculate both base-
costs.‘5 As was explained
above, when the
is less than one, then the model implies that the
A bit of care in terminology is essential to avoid confusion here.
Typically the terms ‘elasticity” and “variability” are used interchangeably
but in
this instance they should not be treated so. Although the model has a “constant
elasticity” structure as described above, it does not have a constant variability
structure. A component’s overall variability is sometimes calculated as the ratio
of volume variable costs to accrued costs. A divergence between the two
concepts occurs in the roll-forward process, where the variability ratio will change
with volume changes, even within the model’s constant elasticity framework.
_
18
~C
1
marginal cost of producing
2
produced
3
calculate incremental
4
advantage
5
aspect that the attributable
6
the calculations
7
cost.
increases.
another unit declines as the number of units
This characteristic
is exactly what is required to
cost and the incremental
cost calculation
takes
of this aspect of the constant elasticity form of the model, an
cost calculation
that incremental
ignores.
It is at this point in
cost begins to exceed volume variable
8
The calculation
10
-~
Calculate
Step 5:
9
test-year
incremental
of test-year incremental
parallels the calculation
11
test-year attributable
12
effects, non-volume
13
used to roll forward attributable
14
incremental
15
methods used to calculate test-year attributable
16
calculate test-year
17
18
B.
19
costs.
of
cost. The same set of volume effects, cost level
workload
effects, and special program effects that are
costs are also use to roll forward
costs. This means that the same set of assumptions
incremental
and
cost are now used to
costs.
The Relationship
Among Incremental
Cost and Attributable
Cost.
Cost, Volume
In this section, I discuss the relationship
among the three widely
20
used postal cost measures,
volume variable cost, attributable
21
incremental
22
Postal Service and attributable
cost. Volume variable and incremental
cost is calculated
Variable
cost and
costs are calculated
by the Commission.
To
by the
19
1
understand
2
there are eight different types of cost pools in the cost model.
3
pool types are defined by the nature of the cost generating
4
costs to arise. A cost pool can be assigned to one of the eight types by
5
answering
6
decision tree relating the set of questions
7
8
the relationship
a series of questions
I first observe that
The eight cost
process causing
about the nature of the costs in the pool. The
is presented
in Figure 1.
The first question to be asked is whether or not the costs are fixed or
variable.
A fixed cost is one that does not vary with the level of output:‘6
A good example of a fixed cost is the fee a
government charges for a firm to incorporate and
conduct business. Whether the firm produces a lot or
a little, it must pay the fee. Another example is the
monthly rent that a lawyer must pay for an office after
signing a one-year lease. The monthly rent must be
paid regardless of how much business the lawyer
does.
9
10
11
12
13
14
15
16
17
among these cost measurements,
In contrast, a variable
cost is one that does vary with the level of output.
18
If the costs in the cost pool are fixed, then they are clearly not volume related
19
and the volume related causality link can not be applied to calculate incremental
20
cost. Instead, the nature of the costs must be examined to find out if there are
21
any specific-fixed
22
but are associated
23
that product and that product alone; they are thus included in that products
24
incremental
15
Orqanization,
costs.
Specific-fixed
costs do not vary with the level of volume
with only one product.
They are caused by the provision of
cost. Fixed and common costs neither vary with the level of volume
a,
Jeffery M. Perloff and Dennis W. Carlton, Modern Industrial
HarperCollins, 1994, at 51.
20
1
nor are they caused by the provision of single product.
2
the incremental
3
They are not included in
cost of any product.
When a cost pool contains variable costs, the choices, in terms of tracing
4
cost causality, are more extensive.
Consequently,
a series of questions
5
required to determine
6
the series asks whether on not only one product is handled in the cost pool. If
7
so, then the entire cost in the cost pool is incremental
8
handled.
9
only remaining
the correct cost allocation method.
In fact, incremental
are
The first question in
to the product being
cost equals the accrued cost for the cost pool. The
issue is whether or not incremental
cost equals volume variable
10
cost. If the variability in the cost pool is equal to one, the two are equal.
11
variability is less than one, incremental
12
cost pool. There are no specific fixed costs in this cost pool, by definition,
13
attributable
14
than one, then incremental
15
If the
costs exceed volume variable cost in the
so
cost will equal volume variable cost. Thus, if the variability is less
cost will exceed attributable
cost.
For many cost pools, there is more than one product handled, so cost
16
attribution
17
answered to determine
18
not there are any intrinsic costs. An intrinsic
19
sense that it varies with the level of output, but it does not vary at the margin.”
20
By that, I mean that these costs are not increased
21
product.
17
associated
is not so straightforward.
Nevertheless,
In these cost pools, two questions
proper cost attribution.
must be
The first question is whether or
cost is a variable cost, in the
by additional volume of the
the are caused by the provision of the entire volume of
Intrinsic costs would include things like the premium costs
with an expedited air transportation network.
21
1
the product and are thus incremental
2
costs in a cost pool, then both the volume-related
3
are attributed to the product that caused them to arise. Other products in the
4
cost pool will cause volume-related
5
intrinsic costs.
6
to that product.
incremental
When there are intrinsic
costs and the intrinsic costs
costs but will not generate
An example of this type of cost pool is given by the manual Priority Mail
7
cost pool. All costs are labor costs and are variable costs. However, the cost
8
pool arises because of the intrinsic characteristics
9
exist but for that product.
of Priority Mail and would not
If there were no Priority Mail, this cost pool would
10
disappear.
The volume variable costs for non-Priority
11
disappear,
but both the Priority Mail’s volume variable cost and all of the
12
institutional
13
Mail so the incremental
14
Mail’s volume variable cost and all of the institutional
15
institutional
16
cost would disappear.
Mail products
would not
This latter set of costs are intrinsic to Priority
cost for Priority Mail in this cost pool is the sum of Priority
cost. In this instance, the
costs are intrinsic costs.
The final set of cost pools include variable costs, include more than one
17
product, but have no intrinsic costs.
In these cost pools incremental
18
all volume related.
between incremental
19
costs depends
20
equal to one incremental
21
cost as the marginal cost is constant.
22
these cost pools will exceed both volume variable and attributable
23
the same) when the variability is less than one because incremental
The relationship
costs are
costs and attributable
upon the estimated variability for the cost pool. If the variability is
cost will be equal to volume variable and attributable
On the other hand, incremental
costs in
cost (they are
cost will
-_
22
account for the fact that some volume is produced at a higher marginal cost.
Table 1 presents the eight cost pools, the characteristics
relationship
between incremental,
volume variable, and attributable
case. That Table shows that in all instances
incremental
cost equals attributable
10
cost Pool
11
Type 1
12
Type 2
13
14
17
18
in which the variability is one,
cost exceeds attributable
cost.
Table 1
Cost Pools and The Relationship Among Cost Measurements
8
9
16
costs in each
cost and in all instances in which the
variability is less than one, incremental
15
of each and the
Cost Types
Fixed and Common
Cost Relationship
IC=ATRC=WC=O
Fixed and Specific
IC = ATRC > WC
Type3
Variable, One Product,
Variability = 1
IC = ATRC = VVC
Type4
Variable, One Product,
Variability < 1
IC > ATRC = WC
Type5
Variable, More than 1
Product, Intrinsic Costs,
Variability = 1
IC = ATRC > WC
Type 6
Variable, More than 1
Product, Intrinsic Costs,
Variability < 1
IC >ATRC = VVC
Type7
Variable, More than 1
Product, No Intrinsic Costs,
Variability = 1
IC = ATRC = VVC
Type t3
Variable, More than 1
Product, No Intrinsic Costs,
Variability < 1
IC > ATRC = VVC
24
the Old and New Methods
Costs.
C.
3
The old method of calculating
5
functions from the special studies used to estimate the variabilities
6
using the parameters
7
to estimate test-year attributable
8
studies but not the underlying functions.
9
means that the roll-forward
First, the old method used the underlying
from those studies.
inherent in the underlying
To understand
in two ways.
Test-year
cost deviated from the
established
11
methodology
incremental
of Calculating
4
10
instead of just
Recall that the roll-forward
costs applies only the parameters
From a methodological
model used
from the
perspective
this
model does not embody the structural assumptions
studies.
what this means, consider the following example.
12
Suppose that the variability for a particular component
13
a generalized
14
from that special study had been found to be 74 percent.
15
after several years the study was updated, with a new set of data and with a new
16
translog functional form. The new variability was found to be, say, 81 percent.
17
The only change that would be required in the attributable
18
be the substitution
19
functional
20
structure of the model.
21
-.
Comparing
Incremental
1
2
quadratic econometric
had been estimated with
function and that the estimated variability
Then suppose that
cost calculation
would
of the new variability for the old. The fact that a new
form was being used to estimate the variability would not affect the
In contrast, the old method of incremental
22
the underlying
23
that the old incremental
cost calculation
functional form. From a methodological
explicitly used
perspective,
this means
cost model did embody the structural assumptions
25
1
inherent in the underlying
2
model embodied
3
incremental
4
the structure.”
5
by following the established
6
studies.
7
flexible.lg
8
9
10
special studies.
Because the old incremental
this structure, it was difficult for the Commission
cost calculations
methodology
alleviates this potential difficulty
of using only the parameters
In this way it makes the calculation
of incremental
The second deviation from the established
fear incremental
18
to accept the
without accepting the special studies that created
The new method of calculation
old method of calculating
cost
incremental
cost far more
methodology
cost was its technique
cost. The old method first calculated,
from the
contained
for calculating
inf the
test-
for each subclass, the
See PRC Op., R97-1, Vol 1. at 248.
19
Unlike the established methodology, if one would make the
assumption that the true structure of the cost model was described by the
functional forms underlying the special studies, then the new method of
incremental cost calculation would have to be considered an approximation of
the “true” incremental costs. Recent research has shown, however, that for the
Postal Service’s cost model, this approximation is quite close and the increased
ease of calculation would justify it use. (See Michael D. Bradley, Christopher S.
Brehm, Jefferey Colvin and William M. Takis, Empirical Estimation of Incremental
Costs for the US. Postal Service, in Emeraina Competition in Postal and
Deliverv Services, Kluwer Academic Publishers, 1999 at 89, and Michael D.
Bradley, Jeff Colvin and John Panzar, “Issues in Measuring Incremental Cost in
a Multi-function Enterprise, Manaaina Chanae in the Postal and Delivery
Industries, Kluwer Academic Publishers, 1997 at 3.)
More important is the fact that the underlying equations could be used only for
calculating base-vear incremental costs, not test-vear incremental costs. When
the equation-based
approach is used (as in the old method), an approximation
must be applied to transform base-year incremental costs into test-year
incremental costs. There is no basis, therefore, in asserting that the equationbased test-year incremental costs are more accurate than the cost-model-based
test-year incremental cost.
26
1
simple ratio of subclass’
2
variable cost. It then multiplied this aggregate
3
calculated
4
approach
5
changed proportionately
6
avoids this drawback
7
does so by using these same factors, when going from base year to test year,
8
that are used in the test-year
9
IV.
10
base-year
incremental
cost to base-year volume
ratio times the previously
test-year volume variable cost. The Commission
“has the unappealing
noted that this
property that both variable and fixed costs are
from the base year to the test year.“”
The new method
and applies separate factors to variable and fixed costs.
THE ANALYTICAL
attributable
cost calculation
STRUCTURE
OF INCREMENTAL
To promote a better understanding
of how incremental
and to show their correspondence
costs are
calculated
12
I present the analytical structure of the incremental
13
will make more sense, however, if we first describe the analytical structure
14
underlying
15
present the analytical structure of base year volume variable, attributable,
16
incremental
17
the same three cost measurements
volume variable and attributable
costs.
Calculating
19
As discussed
Base-Year
costs, in this section
cost model. That structure
Consequently,
cost. This is followed by a presentation
A.
20
to attributable
COSTS
11
18
It
in this section I
and
of the analytical structure of
for the test year.
Costs
above, variability and distribution
See PRC Op., R97-1, Vol I. at 250,
key studies are used to
27
1
calculate the parameters
2
components,
3
the description
4
permit construction
5
variable costs of component
needed for calibrating the cost model for the cost
but the underlying
of the base-year
studies themselves
calculations,
of the analytical structure.
are not used. To organize
we need some notation that will
Let us start with the volume
j:
vvcj
=
Ej cj,
6
where C, is the accrued cost for the component
7
elasticity.
8
and is not an explicit function of volume.
9
constant with respect to volume changes. *’ At the component
and Ei is the components
Note that once the model is calibrated,
this elasticity is a parameter
That is to say that the variability is
level, the effect of
10
volume changes on cost is captured through the response of a cost driver to
11
those volume changes.
12
volume in broken into its two components,
13
the cost driver and (2) the relationship
14
15
In the cost model, the relationship
between cost and
(1) the relationship
between cost and
between the cost driver and volume.
As a result, the volume variable cost will be distributed
to individual
products based upon the products’ shares of the cost driver in the component,
21
-..
For example, a set of elasticities for purchased highway
transportation were selected by the Commission in Docket No. R87-1. These
elasticities were applied in both Docket No. R90-1 and Docket No. R94-1 despite
the fact that volume changed. It is in this regard that the elasticities are
“constant.” This is not to say the calibration of the model is never changed. In
Docket No, R97-1 the Commission selected a new set of variabilities and the
model was recalibrated.
-4
28
1
D,. A data collection effort or special study is required to determine
2
distribution
3
the product cost model.
4
can thus be expressed
keys and each volume’s distribution
these
share becomes a parameter
in
The volume variable cost for product i in component j
as::
D..
vvc..
=
I’
E.C.A
J
(5)
JD’
i
5
With this notation, we can express both the components
6
cost as well as the products
7
8
-~
9
10
total volume variable
overall volume variable in cost simple formulas:
vvcj
=
2i=l ‘j’jjf’ D..j
vvci
=
E.C.2.
(6)
and,
D..
j=l
J JD
We can be more formal by constructing
embodies the essential characteristic
(7)
i
an explicit cost function that
of the model that the elasticity does not
depend upon the amount of volume or the cost driver. We can also use the
explicit cost function to highlight the difference
defined by the Commission,
Specifically,
between attributable
cost, as
and volume variable cost.
we recognize that the total cost in a component
is the sum of
the variable cost, which is related to the total amount of the driver and any fixed
costs that occur in the component.
These fixed costs might be associated
with
individual products or they might be common to all products in the component.
We can express total component
Cj
accrued cost, Cj as their sum:
Fv + cij Djef ,
= z
(8)
i=O
9
where the new notation in this formula includes
F, as the specific fixed cost in
10
the component
for product i, F,as the fixed and common cost in the component,
11
and ai as a measure of the cost of inputs. With this structure,
12
volume variable cost for product i in component j as:
VVC..
‘I
=
D..
e.u.D.‘i’.
I
I
we can define the
J
(9)
,,
i
13
We can also define the attributable
ATRCij
cost for product i in componentj
= Fij +
e. Dij
e.a.D.‘-.
I
I
I
(10)
D
j
-
30
.-~
1
2
3
where F, is the specific fixed cost for product i in this component.
Lastly, we can use this function to define the incremental
cost of product i.
It is the cost that is caused by the inclusion of product i in the output vector.
lCi,
=
Cj - Cj(Dj - DJ
=
Fji + ajDjcj
1
(11)
Fji - Fq + aj(Dj - Dq)ej
-
i=O
4
5
6
A little algebra leads to a simpler expression:
lCii
=
Fii + ajDjej(l
7
where 8, = D, I D,, the product’s proportion
8
the relationship
9
will exceed attributable
between incremental
- (1 - e,)‘i),
(12)
of the driver. We can now examine
cost and attributable
cost. Incremental
cost
cost when?
(l-(l-8JJ)
> 1
EjO,
10
We can see from this expression
22
that the ratio depends
upon only two things, the
This result can be derived by setting the conditional inequality such
that IC > ATRC, subtracting the specific fixed portion from both sides and
dividing through by remaining, volume-related, part of ATRC. Cancelling like
terms yields the above expression.
31
1
elasticity of the cost component
2
product in question,
3
volume in the component
4
make use of the values of the parameters
5
boundaries
6
and the proportion
-,
of the driver caused by the
This means that the ratio depends only upon the mix of
and not the absolute amount.
It also means that if we
from the cost model, can put
on the size of the ratio and understand
what makes it change.
In particular, we know that generally?
0 <
Ej
<
1
($4)
0 < eij 5 1.
I.
7
These limits put bounds on the ratio. 24 For example, it is clear that under these
8
limits, the ratio is never less than one.
9
denominator
IO
Under the conditions
listed above, the
of the ratio can be no larger than one, and will be less than one in
the typical case that either the variability or distribution
key is less than one.
23
The elasticity for a cost component would be greater than one if
there are decreasing returns to scale. However, I am informed that there is only
one such cost pool in the Postal Service version and no such pools in the
Commission version. The cost pool with a variability greater than one is the
RBCS cost pool that has a variability of 100.5%. Because this variability of
100.5% is virtually the same as 1OO%, this de minimis violation of the above
condition has no measurable impact on the relationship between incremental
and attributable cost. The distribution share is always between zero and one by
definition.
24
If the parameters are zero, the ratio is undefined. If either the
elasticity or the distribution key is zero then incremental cost and attributable
cost will only be defined if there are specific fixed cost. If so, the two will be
equal.
32
-~
1
However, the numerator
2
As the distribution
key cannot exceed one, the parenthetical
expression
in
3
the numerator
4
negative, the fraction is raised to a positive power, the outcome of which can not
5
exceed one. Thus the largest possible value for the parenthetical
6
less than one. This means the numerator
7
numerator
a
one, then incremental
9
relationship
10
11
12
13
26
is between zero and one. Morever, as the elasticity is non-
is
is never less than one. If the
is never less than one and the denominator
is never greater than
cost can never be less than attributable
is highlighted
expression
cost. This
in Table 2 which shows the calculation
for the ratio for
the range of values for 8 and & between zero and one.
Ratio of The Volume-Related
Valuesfor
Epsilon
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-
is bounded from below by one.
Table 2
Portion of Incremental
Values for Theta
Cost to Attributable
Cost
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1.05
1.04
1.04
1.03
1.03
1.02
1.02
1 .Ol
1 .Ol
1 .oo
1.10
1.09
1.08
1.07
1.06
1.04
1.03
1.02
1 .Ol
I .oo
1.17
1.15
1.13
1.11
1.09
1.07
1.05
1.03
1.02
1 .oo
1.24
1.21
A.48
1.16
1.13
1.10
1.07
1.05
1.02
1.00
1.34
1.29
1.25
1.21
1.17
1.13
1.10
1.06
1.03
1.00
1.46
1.40
1.34
1.28
1.23
1.17
1.13
1.08
1.04
1.00
1.62
1.53
1.44
1.36
1.29
1.22
1.16
1.10
1.05
1.00
1.86
1.72
1.60
1.48
1.38
1.29
1.21
1.13
1.06
1.00
2.29
2.05
1.85
1.67
1.52
1.39
1.27
1.17
1.08
1.00
10.00
5.00
3.33
2.50
2.00
1.67
1.43
1.25
1.11
1.00
The base year volume variable, attributable
and incremental
27
products is found by simply summing the component
28
the base-year
components:
cost for
specific costs across all of
33
ATRCi
+ c.a.D.‘-.
I I I
=
ICq
=
Fq + tLjDjej(l
D
(15)
iI
1
- (1 - OJef) .
2
B.
3
An important part of the calculation
4
product specific costs. When considering
5
cost can be calculated
6
summing those marginal costs over the range of production
7
measured.
a
augmented.
Product-specific
9
incremental
cost framework,
10
The Role of Product
e. Dii
Specific
Costs.
of incremental
cost is the role of
only volume related costs, incremental
by finding the marginal cost of each unit produced
When there are product-specific
Before discussing
(1’3)
for the product being
costs, this basic procedure
costs are treated in a consistent
but their treatment
and
must be
manner in the
bears further discussion.
their role in the incremental
cost calculation,
we should
11
probably be clear as to what product specific costs are. Product-specific
12
are incurred if any amount of a the product is provided, but they do not increase
13
at the margin with additional
14
15
costs
units of that product.
There are two types of product specific cost in the Postal Service cost
structure:
specific fixed costs and intrinsic costs.
Specific-fixed
costs do not vary
-
34
1
with variations
2
the products
3
just one product and would not exist if the product was not part of the Postal
4
Service’s output vector.25
5
in the products
volume; indeed, they would be incurred even if
volume fell to zero. However, they are caused by the provision of
The other type of product-specific
costs can be called intrinsic costs.
6
These are variable costs that arise because of the particular characteristics
7
product but do not vary at the margin.
a
in the postal cost structure: these instances occur in the Priority Mail distribution
9
operations
and in network air transportation.
10
operations
exist for the purpose of expediting the handling of Priority Mail. They
11
can and do sort other classes of mail, but without Priority Mail, those classes
12
would be sorted in other operations.
13
not to provide Priority Mail, the institutional
14
exist. These costs thus are part of Priority Mail’s incremental
15
Consider two instances of intrinsic costs
The Priority Mail distribution
Consequently,
if the Postal Service decided
costs for these operations
16
expedited
17
exists for the purpose of providing air transportation
18
air transportation
19
additional
25
mail. For example, it is my understanding
is more expensive than commercial
in the case of the Eagle network,
would not
cost.
In similar fashion, the network costs exist for the transportation
expense,
of a
of
that the Eagle Network
for Express Mail. Network
air transportation
and this
is caused by Express Mail.
Note that producing a product at zero volume and eliminating a
product from the output vector are not the same thing. Product-specific
advertising expenses are incurred before the fact and exist even if no units of the
advertised product are sold. On the other hand, if the firm did not plan to sell the
product at all, no advertising would be incurred.
35
Regardless
of what mail is actually carried on the network, the intrinsic costs
exists because of the characteristics
of Express Mail.
The roles of specific fixed costs and intrinsic costs in the incremental
calculation
-
can be illustrated analytically.
cost
The total cost in a cost component
be divided into fixed cost and variable cost.‘”
This is described
can
analytically
cj = Fq+&+vcj.
as:
(17)
i=l
6
Note the two types of fixed cost F, and F,. The former represents
7
common cost, which exist for the provision of all product and are not part of the
a
incremental
9
costing structure,
10
cost of any. The F, represent specific-fixed
fixed and
costs. Within the postal
variable costs are well defined and this equation can be
rewritten as:
+ ajDj ‘j
11
To see the correspondence
with familiar Commission
12
break down these costs into their “institutional”
13
defined by the Commission,
(18)
costing terms, we can
and “attributable”
portions.
As
the first two terms in the following equation
26
Variable cost is not the same thing as “volume variable cost.” In
fact, volume variable cost is a subset of variable cost found by multiplying the
total variable cost times the relevant “volume variability” or cost elasticity.
-
36
1
represent “institutional”
cost and the sum of the two terms in the parentheses
2
represent “attributable”
costs.
3
Cj
=
Foi + (1 - cj)ajDjei
+
(19)
4
Recall that the incremental
5
that product, and is calculated
6
the total costs of producing
7
“decrementakalculation
a
i, is part of its incremental
9
equation 19, above, one obtains the expression
10
by the difference
between total current costs and
all products but product i. This
highlights the fact F,, the specific-fixed
cost. When the decremental
cost for product
calculation
for incremental
is applied to
cost for product
i:
ICii
11
cost for product i measures the cost caused solely by
=
Fij + ajDjcj (1 - (1 - CI..)‘~)
(20)
The first of our two instances of intrinsic costs arise in the Priority Mail
12
distribution
operations.
As explained above,
13
in these operations,
14
Mail. That is, the operations
15
Mail and would not exist otherwise.
but they are designed
other classes of mail are handled
primarily for the handling of Priority
were created because of the existence
The incremental
cost calculation
of Priority
reflects
37
1
this. From the base-year
2
the individual products
3
identifies the institutional
4
Mail operation
5
institutional
6
one of these operations
handled in a Priority Mail operation.
a
9
cost. The incremental
is thus calculated
costs.
One also then
cost for Priority Mail in a Priority
as its volume variable cost and the total
Mathematically,
IClj
7
cost model, one obtains the volume variable costs of
the incremental
cost of Priority Mail (lC,J in
is given by:”
=
ajDjej(l
+ ~~(0~~ - 1)).
(21)
where 8,j is Priority Mail’s share of the driver.
The other instance of intrinsic cost is for dedicated
transportation.
In these cost components,
the volume variable cost is found by
10
multiplying the amount of the driver (pound-miles)
11
cost of commercial
12
function for the dedicated
air transportation,
air network
times the (constant)
marginal
(pi). In product cost model, the cost
air network is thus given by:
C=
aiDi,
(22)
13
where the bar on the driver indicates that its amount is fixed with respect to small
14
changes
27
in volume and aj represents the cost of a pound mile of dedicated
Note that there are no fixed costs in these components.
-
38
” One can express the volume variable cost for
1
network air transportation.
2
Express Mail as the product of the cost of a pound-mile
3
transportation
times the number of pound-miles
VVClj
4
The incremental
5
to the volume variable cost:
=
Calculating
=
pjD,
pj Dy .
Test-Year
+ (aj-
air
required?
(23)
cost of Express Mail in this component
IClj
of commercial
adds in the intrinsic cost
p,)fij.
(24)
6
C.
Costs
7
When moving from the base year to the test year, the product cost model
a
must forecast the volume variable and attributable
9
with the volumes extant at test year rates.
costs that will be associated
In similar fashion, the incremental
10
cost model must forecast the incremental
costs associated
11
The forecast must take into account four factors:
with those volumes.
28
It is my understanding that the air network is sized for a minium
scale and more capacity exists than is required to handle just the Express Mail.
Thus marginal increase in Express Mail volume do not affect the capacity of
network.
29
The volume variability of commercial
air transportation
is one.
39
6
A.
Changes
in volume
B.
Changes
in cost levels
C.
Changes
in non-volume
D.
Special programs.
The factors are distinguished
7
or they affect a product.
a
accrued cost in a component,
9
In contrast, changes
because they either affect a cost component
For example, changes in cost levels would affect the
based upon the resource mix in that component.
in volume are product specific and the volume growth for
10
each product is the same regardless
11
Depending
12
workload
13
accrued test year in a component
14
methods, or productivity.
15
workload
of which component
on the nature of the activity, some components
is being analyzed.
receive a non-volume
factor while others do not.” Finally, special programs affect the
reflecting a change in technology,
We can examine these factors more closely by considering
production
the formula for
16
test year volume variable cost. Test year volume cost for product i in cost
17
component
78
variable cost, Test year volume variable cost (WC,,)
30
j is found by applying the relevant factors to base year volume
is thus given by:
For example, I am informed that both the Postmasters EAS 23 and
Below Cost pool and the City Carrier Access Cost pool receive a non-volume
workload adjustment
40
vvc.. = [ejajLp,l(l+&)(l
1
where
2
by rrj, non-volume
workload
3
special programs
is captured by @y.
4
5
volume growth is represented
Test year attributable
+ nj)(1+4j)(l+rll).
by gi, cost level changes are represented
changes are represented
by Qj, and the effect of
cost include test year volume variable costs, but
also include test year specific fixed costs:
ATRCij,
= FijT +
+ xjl (l + +i) U + Ilj)’
(26)
6
7
We can now determine the formula for test year incremental
8
calculated
9
methodology.
roll-forward
The test year costs would embody the volume, cost level, non-
10
volume workload
11
which is consistent
12
incremental
31
.-
in a manner that is consistent with the established
cost
and special program effects, but would do so in a manner
with the actual generation
costs would n,&t be calculated
of cost. Specifically,
test year
by applying a simple ratio test year
Special programs are not necessarily implemented in terms of
percentage growth or decline in cost. However, a finite cost change can always
be expressed as a percentage change. That is, the amount of the programinduced cost change can be expressed as a percentage of base year costs. The
same is true for non-volume workload changes.
1
volume variable costs.
Rather, to the level of detail supported
2
cost model, test year incremental
3
component
basis according
%jr =
[ICq - F$(l
costs would be calculated
by the product
on a component
by
to the following formula:
+gi)(l
+ srj)(l
+ qi)(l
+ t$tj) + FiT
(27)
4
where F,, is the test-year
product specific costs for class i in cost componentj.32
5
One obtains the test-year
incremental
cost by adding across the components:
6
IC,*
=
2
[ICY - F$ (1 + gi) (1 + n j) (1 + qi) (1 + 4 ,, + FijT.
(26)
j=l
7
Note that the volume growth rate (gi) is the same for all components,
a
that term can be extracted from the summation,
9
non-zero volume effect) get the same volume growth rate.
as all components
so
(that get a
10
32
Note that in the incremental cost calculation we must allow for both
specific fixed costs and intrinsic costs. Thus, F, in equation 27 refers to product
specific costs. The test year values for product specific costs may be directly
available from the roll forward or may have to be calculated. Either way, they will
not receive a volume adjustment.
42
1
2
3
4
V.
HOW THE NEW METHOD OF INCREMENTAL
COST CALCULATION
ADDRESSES THE CONCERNS RAISED BY THE COMMISSION IN
DOCKET R97-1.
In its Docket No. R97-1 Opinion, the Commission
5
deficiencies
and discussed
6
concerns are each presented
7
new method of incremental
A.
three other concerns.
described
three
Those deficiencies
in this section, followed by a discussion
cost calculation
and
of how the
address them.
A Discussion
of the Three Deficiencies
In the Calculation
Incremental
Costs Cited by the Commission.
of
1
4
The incremental cost calculations were based upon cost
studies that the Commission had reiected:33
1.
2
3
The most important deficiency that the Commission
5
that the Postal Service’s
6
models that the Commission
7
not calculate
a
is flexible enough to allow calculation
9
Service’s choices of variabilities
incremental
incremental
had rejected.
were based upon cost
Consequently,
the Commission
costs. The new method of incremental
10
of variabilities
11
to the calculation
of incremental
12
greatly facilitates
calculating
13
preferred parameters
33
cost calculations
identified was the fact
and distribution
of incremental
or distributions
costs with either the Postal
The new method
costs, as one must only enter the
to calculate the costs.
See PRC Op., R97-I, at 246
choice
is thus no longer a barrier
costs by the Commission.
incremental
cost calculation
keys or the Commission’s
keys. This deficiency
could
43
A “simple ratio method” in which both volume variable and
specific fixed costs were chanaed bv the same orooortion
was used in aoina from base-vear costs to test-vear costs.34
1
2
3
2.
4
The Commission
also cited the deficiency that the calculation
of
5
incremental
costs by the Postal Service in the last case relied upon a “simple
6
ratio” that changed
7
proportions.
a
consistent
9
costs. The incremental
cost calculation
IO
used in the attributable
cost calculation.
11
separates
12
factor for each. It does not apply the same simple ratio to volume variable and
13
fixed costs and this objection is removed.
both volume variable and fixed costs by the same
The new method of calculating
with the established
methodology
16
The Commission
then are
and uses the appropriate
roll-forward
the incremental
cost
observed that although the Postal Service calculated
incremental
costs, it never performed the formal incremental
ia
deficiency was remedied as the incremental
19
testimony
cost test. This
cost test is now presented
of witness Mayes.
See PRC Op., R97-I, Vol. 1 at 250.
u.
test-year attributable
Moreover, the new method explicitly
17
35
for calculating
The Postal Service never performed
tests.35
3.
cost is entirely
uses no more assumptions
volume variable and fixed,costs
14
15
34
incremental
in the
-,
44
B.
A Discussion
of the Three Additional
Concerns about the
Incremental
Cost Calculation
Cited by the Commission.
1.
1
2
Not all DOSSibte combinations
could be tested.36
of oroducts were tested or
3
In writing its Opinion, the Commission
4
the issue of whether or not all possible combinations
5
tested?’
11
of products must be
In principle the approach should consider all possible
combinations of subclasses and services for crosssubsidy as required by the theory. In practice this is
neither necessary nor likely to be entirely feasible.
6
7
a
9
IO
indicated that it has contemplated
Moreover, the Commission
beyond calculation
commended
the Postal Service for going
of only subclass incremental
costs?
In addition to the subclasses taken singly, witness
Takis has actually considered only six combinations
of subclasses and services. This small set was
selected by identifying “groups that share operations”
and “highly competitive groups of products” according
to criteria provided by Postal Service witness Baumol
for Docket No. R90-1. See Tr. REM211 040-2.
Although six combinations fall considerably short of
the theory, and may even be short of all of the
combinations suggested by witness Baumol’s criteria,
it is still a more inclusive application of the
incremental cost test than a simple subclass-bysubclass application.
12
13
14
1.5
16
17
ia
19
20
21
22
23
24
36
37
See PRC Op., R97-I, Vol. 1 at 249
u.
45
1
In this case, the Postal Service extends even further this approach
by calculating
2
the incremental
combinations.
3
These new combinations
4
combinations
calculated
5
combinations
shows the flexibility of the new method of incremental
6
calculations.
7
a
9
10
11
costs for a large vector (twenty-six)
2.
are being calculated
of two-product
in addition to extending
by witness Takis. The calculation
of these addition
cost
When econometric functions were used, the incremental
costs depend uoon the accuracv of the underlvina cost
functions over “considerable ranaes.“3g
Under the old method, incremental
costs were calculated
12
surface of the underlying
13
caused by a particular product and then calculating
14
The Commission
15
calculation
16
forms beyond the ranges of the data use to estimate them.
17
the
along the
cost function by removing the amount of the cost driver
the reduction
in total cost.
raised the concern that there might be cases in which the
of incremental
cost required extension of the underlying
The are two main responses
First, the new method of
ia
incremental
19
cost surface; it just uses the elasticity derived from the function.
20
new method does require assuming constant elasticity over the range of analysis
21
but previous research has shown that incremental
39
cost calculation
to this concern.
functional
does not depend upon moving along the estimated
See PRC Op., R97-I, Vol. 1 at 250.
It is true that the
costs are not sensitive to this
--
46
1
2
Second, it is important to keep in mind that the incremental
cost
3
calculation
4
terms of the amount of the driver analyzed.
5
each product begins at the current level of the driver and then removes only that
6
part of that driver associated
7
cost calculation
a
level of the driver which is up to 50 percent below the current level. This range
9
of variation would typically be within the range of data in the analysis data set.
IO
does not generally require going beyond the range of experience
The incremental
in
cost calculation
for
with the product. This means that the incremental
typically involves recalculating
Table 3 presents the cost components
costs.4’
total cost component
in which equations
cost for a
are used to
It also presents the largest product, as measure
11
calculate incremental
12
by the percentage
of the distribution
13
cost components.
Finally, it presents the share of the cost driver (as represented
14
by the distribution
key) for the largest product.
15
reductions
are typically within the range of data in the data sets used to
16
calculated
the variabilities.
17
MODS all have variations
ia
the mean value.
key generated
by the product, in each of the
Table 3 shows that the volume
In other words, data sets like HCSS, CCS and
in their “volume” variables that exceed 50 percent of
19
40
41
a,
Bradley, Colvin and Panzar at 10-l 3
In other components incremental cost is equal to volume variable
cost or incremental costs are product specific costs.
47
Table 3
A Listing of the Largest Product in Cost Components
Calculate Incremental Cost
Largest % of
Distribution
Key
36.9%
that Use Equations
to
Product With
Largest %
5
6
Cost Component
7
C/S 2.5 HIGHER LEVEL SUPERVISORS
37.4%
First Class
Single
Piece
a
C/S 3.1 MAlL PROCESSING VARIABLE DIRECT LABOR
42.8%
First Class
Single
Piece
9
C/S 3.2 WINDOW SERVICE
53.2%
First Class
Single
Piece
10
C/S 3.3 ADMIN CLERKS - QUALITY CONTROL
42.8%
First Class
Single
Piece
11
C/S 3.3 ADMlN CLERKS - DATA COLLECTION
27.6%
First Class
Single
Piece
12
C/S 4 CLERKS AT CAG K POST OFFICES
58.3%
First Class
Single
Piece
13
C,S 7.3 CITY DELIVERY CARRIERS, LOAD
20.2%
14
C/S 7.2 ACCESS
28.2%
15
C/S 7.1 ROUTE
16.2%
Standard
A ECR
16
C/S 8 VEHICLE SERVICE DRIVERS
16.1%
Standard
A ECR
17
C/S 11.1.1 CLEANING 8 PROTECTION
32.4%
First Class
Single
Piece
18
C/S 11.2 OPERATING EQUIPMENT MAINTENANCE
49.4%
First Class
Single
Piece
19
C/S 11.3 PLANT& BUILDING EQUIP MAINT
32.4%
First Class Single
Piece
20
C/S 14. PURCHASED TRANSPORTATION. HIGHWAY
16.1%
First Class
Piece
21
C/S 14. PURCHASED TRANSPORTATION, RAILROAD
29.3%
Periodicals
C/S 14. PURCHASED TRANSPORTATION. DOMESTIC
WATER
24.4%
Standard
C/S 16.3.2 EQUIPMENT SUPPLIES 8 SERVICES
42.0%
First Class
Single
Piece
25
C,S 20.3 EQUIPMENT DEPRECIATION
47.9%
First Class
Single
Piece
26
C,S 20 EQUIPMENT INTEREST
47.9%
First Class
Single
Piece
%
24
27
C,S 1.1 POSTMASTERS, EAS 23 8 BELOW
First Class Single Piece
Standard
First Class
A ECR
Single
Single
Piece
Regular
A Regular
-
48
1
2
3.
The incremental cost aoproach of allowinq no reconfiauration is
acceptable for small classes but less tenable for larae classes4*
3
The incremental
4
with its incremental
5
produced.
6
the additional
7
already being provided.
8
“decremental”
9
recalculating
In this regard, the incremental
cost for product A is best thought of as
cost of providing product A, given that the firms other products are
Computationally,
costs by “removing”
total costs.
costs of producing
11
A in ways not captured
12
“no reconfiguration
it is much easier to actually calculate
product A from the vector of products and
Implicit in this calculation
is the assumption
in the incremental
assumption”
The Commission
presented
cost calculation.
This is witness Takis’
in the last case.
noted that this assumption
is quite reasonable
classes or groups of classes that do not make up an extremely
15
the driver.
16
single combination
17
large proportion
18
assumption
However, as the Commission
for
large portion of
pointed out, when a single product or
of products that is being “removed” makes up an extremely
of the components
driver, then the “no reconfiguration”
is less palatable.
However, this problem may not be as general as it first seems.
20
3 illustrates there are relatively few instances
21
the driver is caused by a single subclass.
42
that the
the other products are not affected by the addition of product
14
19
revenue
cost, given the existing vector of other products being
IO
13
cost test is designed to compare a products
As Table
in which a very large proportion
Moreover, Table 3 shows
See PRC Op., R97-1, Vol. 1 at 249.
that this
of
49
1
2
issue is confined mainly to First Class.
Finally, one must recognize that the incremental
3
for the Commission
is the examination
of cross-subsidy
4
within the current methods of production.
5
argues for maintaining
6
keeping it in mind when interpreting
cost test that is relevant
among existing products
This use of the incremental
the “no reconfiguration”
assumption
the incremental
cost test
in the calculations
but
cost test for “large” products.
-