A MEASURE OF SCALE ECONOMIES FOR POSTAL SYSTEMS
ROBERT H. COHEN
U. S. POSTAL RATE COMMISSION
EDWARD H. CHU
U.S. ENVIRONMENTAL PROTECTION AGENCY
PUBLISHED IN MANAGING CHANGE IN THE POSTAL DELIVERY INDUSTRIES,
ED. MICHAEL A. CREW AND PAUL R. KLEINDORFER, KLUWER ACADEMIC
PUBLISHERS, 1997
THE VIEWS EXPRESSED IN THIS PAPER ARE THOSE OF THE AUTHORS AND
DO NOT NECESSARILY REPRESENT THE OPINIONS OF THE POSTAL RATE
COMMISSION OR THE ENVIRONMENTAL PROTECTION AGENCY. MR. CHU WAS A
PROFESSIONAL STAFF MEMBER OF THE POSTAL RATE COMMISSION FROM
1993-1995. A PRELIMINARY VERSION OF THIS PAPER WAS PRESENTED AT
WISSENSCHAFTLICHES INSTITUT FÜR KOMMUNIKATIONSDIENSTE (WIK) GMHH,
3RD KÖNIGSWINTER SEMINAR, COST OF UNIVERSAL SERVICE, NOVEMBER
1995.
Introduction
The delivery function is comparatively new to modern postal
services. Originally the post was simply an inter-city letter
service. One could deposit a letter at the post office in a city
for transportation to the post office in another city where the
recipient would call for it.1 It was not until the mid-nineteenth
century that city delivery began on a regular basis in the U.S. By
the end of the century rural delivery was started on a limited
basis, but it did not become ubiquitous until the early part of the
twentieth century.
Delivery changed the post in many ways. No doubt it has been a
substantial cause of the tremendous growth in volume since its
inception. But delivery also changed the economics of the modern
post because it introduced a large amount of fixed costs.
While the letter mail monopoly preceded the introduction of
delivery service, the fixed costs associated with delivery underlie
the two modern justifications for the letter monopoly. First, it is
argued that a letter mail monopoly is necessary to assure universal
service at a uniform price. Second, it is argued that delivery is a
natural monopoly and that legal protection is necessary to prevent
"cream skimming" and thereby to maximize the benefit of the
universal delivery system.2 The first argument is a political one
which presumes significant urban-rural cross subsidizes in
delivery. The second is an economic argument which presumes that
the Postal Service as a monopolist is an efficient provider of
delivery. The analysis presented here is an attempt to address the
second argument.
1
Campbell, James I., Jr., "An Introduction to the History of the
Postal Monopoly Law in the United States," The Last Monopoly, The
CATO Institute, Washington, D.C., 1996.
2
For purposes of this paper, "cream skimming" refers to
concentration on serving only those markets that exhibit
lower-than-average delivery costs, regardless of the characteristic
that causes those costs to be less than average. Such
characteristics are not confined to network density and could
include favorable geographic, demographic, or operational
characteristics. For example, in the U.S., curb delivery is less
costly than park and loop delivery which is less costly than foot
delivery.
In an unsubsidized postal system as in the United States, the
postal customer bears all costs of the system. The customer
therefore is the beneficiary where return to scale are maximized by
having a single firm (a monopoly) provide delivery. On the other
hand, monopolies can be harmful to consumers when they protect
technically inefficient behavior, and allow economic rents to be
extracted.3 This paper sets up a framework to examine the following
question: Do the economies of scale in the delivery function exceed
the technical inefficiencies and economic rents of the Postal
Service? In short, does the monopoly increase or decrease the price
of postal services to postal customers?4
This paper measures the returns to scale of the U.S. delivery
function. It then compares this benefit with the cost that the
monopoly imposes on the consumer.
Because delivery involves so much fixed cost, it would create a
tremendous barrier to entry even if the legal monopoly were
abolished. Thus, it may be that having once enjoyed a de jure
monopoly, national posts would enjoy a de facto monopoly even if
the legal one were abolished. 5 This paper provides a
quantification of the barrier to entry in the letter mail market in
the United States caused by high fixed costs in the delivery
function.
This paper next estimates the value of scale in delivery
exhibited by 21 national postal systems based on data from an
unpublished paper which was presented at the 1994 Stockholm
conference on Postal and Delivery Services.6 7 Finally, it compares
the estimated value of scale with an estimate of the wage premium
in each country.
3
It is also claimed that monopolies harm consumers with lower
quality of service and by being less innovative than firms which
must compete.
4
It is important to distinguish postal consumers (i.e., paying
customers) from recipients of mail. The latter may derive great
benefits from a monopoly in the form of services that would not be
provided in a competitive postal environment. These might be called
political rents. Consumers, being forced to underwrite the
political rents and any inefficiencies and economic rents in the
system, may be better off in a competitive environment.
5
This may well be the case in Sweden which abolished its monopoly
in 1993. A letter mail competitor began operations in Stockholm
where it captured 20 percent of the market, but, nonetheless,
failed.
6
"An Exploratory Quantitative Comparison of Postal
Administrations in Industrial Countries."
7
The data for each country is from 1988 and is based on UPU
statistics which have been verified and revised as necessary based
on communications with officials in most of the countries.
The Uniqueness of the Delivery Function
We distinguish what is known in the U.S. as the "in-office"
delivery function and the street delivery function. The former is
an extension of mail processing; it is where the mail is sorted
into the delivery sequence. "Delivery function" as used in this
paper refers to street delivery.
Recent empirical research confirms the widely held belief that
economies of scale exist in the delivery of mail.8 Other functional
components of the Postal Service are presumed here not to exhibit
significant scale economies, although this has not been
demonstrated.
John Panzar has characterized street delivery as a bottleneck
function because a single firm can deliver to a recipient at a
lower total cost than multiple firms delivering to the same
customer. He suggests that processing and transportation of mail do
not seem to be characterized by scale economies, and that they
could be provided by competing firms. Under this scenario, he
suggests that rates be set to allow nondiscriminatory access to the
monopoly delivery service by the firms competing in processing and
transportation.9
The Postal Rate Commission and the U.S. Postal Service have
implicitly recognized the absence of significant scale economies in
mail processing and transportation functions in the Postal
Service's rate structure. Postal rates in the
U.S. allow for a substantial degree of competition with the
Postal Service in mailprocessing and transportation. For example,
the U.S. Postal Service gives sorting and barcoding discounts to
about 40 percent of First-Class letter volume. Mailers perform
about 60 percent of this worksharing, while third parties perform
the
8
"Natural Monopoly and Technological Agnosticism: The Case of the
U.S. Postal Service," Michael
D. Bradley and Jeff Colvin, June, 1995.
9
Panzar, John, "Competition, Efficiency, and the Vertical
Structure of Postal Services," Regulation and the Nature of Postal
and Delivery Services, Ed. Michael A. Crew and Paul R. Kleindorfer,
Kluwer Academic Publishers, 1993.
rest.10 11 In some classes, mailers transport much of their mail
to downstream locations to take advantage of zoned rates for
transportation.
Street Delivery Cost
While the Postal Service collects extensive data on the cost
behavior of city delivery carriers, it collects little data on the
cost behavior of rural carriers12 For purposes of this analysis, we
assume throughout that rural delivery cost behavior is similar to
that of city delivery.13 In the U.S., street delivery costs for
rural and city carriers combined comprises 21 percent of total
costs. See Table 1.
Table 1 USPS Operational Costs by Major Function
Note: Nonoperating costs, such as payments made to the Treasury
for retroactive charges are excluded.
10
These third-party sorters collect mail from mailers, sort and
apply barcodes, and deliver the mail to the Postal Service for a
portion of the discount. In addition, discounts encourage bulk
advertising mailers to sort their mail all the way to the carrier's
walk sequence, thereby avoiding the carrier "in-office"
function.
11
Economic rents in the form of a wage premium paid by the U.S.
Postal Service partially explain why mailers and third parties can
sort mail at a lower cost than the Postal Service. When third
parties compete with the Postal Service, however, in highly
automated operations such as applying barcodes with optical
character readers and sorting barcoded mail, a wage premium would
seemingly not be a very significant factor.
12
The U.S. Postal Service has two types of delivery personnel;
city delivery carriers and rural carriers. In 1993, there were 164
thousand city delivery routes with 80 million delivery points and
49 thousand rural routes with 23 million delivery points. Rural
costs were 20 percent of total delivery costs.
13
For example, it is assumed that the ratio of rural carrier
in-office cost to total rural carrier cost is the same as the ratio
of city carrier in-office cost to total city carrier cost.
This paper adopts the analysis of street delivery costs
presented by the U.S. Postal Service in several rate proceedings
over the past 20 years. That analysis disaggregates street delivery
time into three subcomponents: route time, access time, and load
time. "Route time" is the time it would take a carrier to walk or
drive the route, passing, but not accessing, any delivery point.
"Access time" is the time it takes a carrier to deviate from the
route in order to make a delivery. This may mean departing from the
basic line of travel and walking or driving to a delivery point and
returning to the basic line of travel, or it may mean slowing down
from normal driving speed, stopping to make a delivery to a
curbside mail receptacle, and then resuming normal speed. Finally,
"load time" is the time it takes a carrier to place the mail in a
mail receptacle. 14 Table 2 disaggregates street time in the
U.S.
Table 2
Note: For simplicity, coverage-related load time ($1,232
million) is included in access time, and street support is
"piggybacked" on all three functions.
Route time costs are essentially fixed, while access is partly
variable, and
load time is 100 percent variable with volume. The analysis of
variability of access
time involves estimating the number of new accesses that would
be caused by an
increment of volume. In the U.S., approximately 93 percent of
all possible stops
receive mail each delivery day. 15 Consequently, the number of
new accesses
14
Load time is divided into elemental and coverage related load
time. Elemental load time varies with the number of pieces being
loaded. Coverage related load time is the fixed portion of load
time at a stop; it varies with the number of stops. Thus, it is
partly variable and partly fixed.
15
A stop consists of one or more possible deliveries. For example,
a 5 unit apartment house with a cluster of 5 mail boxes would be
one stop and 5 possible deliveries.
caused by an increase in volume would be small. Regression
analysis of carrier street data indicates that at the current
volume, the variability of access cost is about 6 percent. In other
words, a 10 percent increase in volume will yield a
0.6 percent increase in the number of accesses.
The Postal Service regularly collects a representative sample of
street delivery costs, volumes, and delivery point characteristics
for city delivery carriers. The Postal Service's FY 1993 data set
contains observations from about 300 routes.16 Observed every two
weeks over a one year period, data is collected from about 270,000
stops. This data is used to model the behavior of access costs.
The coverage function shown in Figure 1 models the change in the
percentage of possible stops that are accessed on a route as a
result of changes in volume. 17 Marginal access cost can be
estimated from the coverage function. As volume per stop grows and
coverage approaches 100 percent, the volume variability of access
cost approaches zero. As the volume per stop declines, coverage
declines, and the volume variability of access costs rises.
Measure of Scale Economies
Our methodology for measuring scale economies essentially
compares the cost of providing delivery by a single firm with the
cost of providing delivery by two firms.18 We measure the returns
to scale in the U.S. postal delivery function by first determining
the total cost of delivery provided by the Postal Service. Next, we
determine the total cost of delivery performed by the incumbent and
a second firm that is assumed to be equally efficient. We assume
that the two firms share the market equally, each delivering a
random half of the mail. Further, each firm serves
16
See the testimony of U.S. Postal Service witness Bradley in
Docket No. R94-1 (USPS-T-5) at pp. 5-10.
17
The Postal Service developed the coverage function and first
used it in the Docket No. R76-1 rate case. For this paper we have
altered the Service's model slightly. Unlike the Postal Service's
model, all stop types and mail classes are consolidated.
18
Of course, the cost of providing delivery by a single firm could
also be compared with the cost of three or more firms. This would
simply inflate the measure of scale economies.
the entire country each delivery day. Thus, each firm would have
to incur the same route time costs that the incumbent currently
incurs. Since each firm will have only half the volume, the number
of accesses by each firm will be less than the incumbent currently
experiences. The number of total accesses by the two firms will,
however, be greater than the total experienced by the incumbent
alone. This is because some stops receiving multiple pieces will
receive delivery from both firms. We assume here that both firms
provide the same frequency of delivery (daily).19
Since route time is essentially fixed,20 it would double with
two firms providing service, each with half the volume. Conversely,
because load time is 100 percent variable with volume, it would not
change, since total volume is assumed not to change. Access cost
would fall somewhere in between, since it is partly variable and
partly fixed. Access cost variability is estimated from the
coverage function shown in Figure 1. Under the duopoly scenario
described, it would grow by 61 percent. Given these responses to
volume, total street time cost would increase from $10 billion to
$16.1 billion. The difference, $6.1 billion, represents an upper
bound on the benefits from scale economies of delivery.21
Monopoly Rents and Inefficiencies
In 1993, the average U.S. postal worker subject to collective
bargaining received $35,001 in pay and allowances, and an
additional $7,713 in fringe benefits.22 To put these earnings into
perspective, the median annual earnings
19
A niche incumbent might provide delivery less frequently or to a
subset of possible stops. These would be special cases of the more
general case analyzed here.
20
The slight variability the Commission has found in route time is
ignored here for convenience.
21
Ceteris paribus, less efficient postal services do not have
greater scale economies than more efficient ones. Theoretically
scale economies in delivery are not firm specific. They are a
product of the territory served and the current state of technology
which would be employed by an efficient firm. The $6.1 billion
figure is inflated by any inefficiency and/or wage premium which
characterize the
U.S. Postal Service and in that sense it is an upper bound.
22
The fringe benefit figure excludes unfunded civil service
retirement liability, certain annuitant benefits, workers
compensation, unemployment compensation, repriced annual leave,
bonuses and awards.
(without fringe benefits) was $24,076 for full-time U.S. workers
in that year.23 Michael B. Wachter of the University of
Pennsylvania and his colleagues conclude that there is a wage and
fringe benefit premium for the postal bargaining labor force of
29.5 percent with respect to comparable workers in the private
sector.24 Such a wage premium would amount to $9 billion in
monopoly rents for the entire postal system. Wachter's $9 billion
system-wide wage premium exceeds the $6.1 billion delivery scale
economy by $2.9 billion. Wachter's wage premium for the delivery
network alone, however, amounts to only $2.3 billion which is $3.8
billion less than the value of the scale benefit from delivery.
Unlike labor costs, technical inefficiency of the Postal Service
has not been analyzed. There is, however, some indirect evidence of
inefficiencies in the Postal Service. Since 1970, total factor
productivity has increased at an average annual rate of only 0.4
percent. This is in spite of the fact that little mechanization
existed in the Postal Service prior to 1970 and large amounts were
added in the 1970s. Beginning in the early 1980s and continuing to
the present, about $5 billion has been invested to automated mail
processing, including the in-office carrier sequence function and
forwarding for undeliverable-as-addressed mail. Additional billions
have been invested in buildings, in part to house the automation.
In spite of this investment, productivity appears to have increased
only in response to hiring freezes, or reductions in the average
wage and fringe benefit package caused by special circumstances. 25
26
23 Statistical abstracts of the U.S., Table 665, 1994.
24
"The Comparability of U.S. Postal Service Wages and Benefits to
the Private Sector: Evidence from the Total Compensation Premium,
New Hire Increases, Quit Rates and Application Rates," Michael L
Wachter, Barry T. Hirsch, and James W. Gillula, July 10, 1995. Dr.
Wachter has published a number of studies on the Postal Service's
labor costs under contract to the USPS. Critics of previous Wachter
studies claim that they ignore the fact that the Postal Service
pays minorities the same as it pays white males. The critics argue
that it is the Postal Service's minority employees (not white male
employees) who earn more than their private sector equivalents, and
this only means that the Postal Service does not discriminate. 25
See "A study of U.S. Postal Service Productivity and Its
Measurement," Staff Study of the Postal Rate Commission, May 9,
1990.
26
Other indications of inefficiency are management claims that
work rules are unnecessarily restrictive and that 73,075 grievances
were filed by employees in FY 1995 and not resolved at the local
level. In addition, the Postal Service has failed to capture a
large market share in two areas of direct competition with the
private sector which are relatively unaffected by the Private
Express Statutes; Parcel Post and Express (overnight) Mail. This
may have been in part caused by either a wage premium or technical
inefficiencies or a combination of both. The Postal Service argues
that a
Figure 2 presents the consumer benefit from delivery scale
economies net of inefficiencies which are expressed as a percentage
of total postal costs. The top curve incorporates any wage premium
the Postal Service may have, the bottom curve nets out Wachter's
29.5 percent wage premium. The top curve shows that if the Postal
Service has 0 percent inefficiencies with its current wage premium,
the measure of scale economies equal $6.1 billion. If the Postal
Service were about 13 percent inefficient, there would be zero net
scale benefit. The bottom curve shows that at 0 percent
inefficiencies, the net scale benefit is -$2.9 billion if the value
of scale is adjusted for Wachter's wage premium. Any inefficiency
would exacerbate the loss. If the wage premium is accurately
calculated by Professor Wachter, it would be difficult to defend
the U.S. postal monopoly on purely economic grounds. Moreover,
understanding the net economic cost of the monopoly allows one to
see how much universal service costs postal customers, at least
under current institutional arrangements.
Figure 3 presents the same information considering the street
function alone. Wachter's wage premium amounts to only $2.3 billion
for the delivery function alone. Thus, the net scale benefit is
initially positive, whether or not we adjust for the wage
premium.
It is far more likely that a monopoly for delivery alone would
produce net benefits for consumers than would a monopoly that
included processing and transportation as well as delivery. This
result lends support to the Panzar's suggestion of opening
processing and transportation to competition while maintaining a
monopoly in delivery.
lack of pricing flexibility has contributed to the Postal
Service's failure. Others argue that the quality of service,
product features, and underlying cost of these Postal Service's
offerings make them uncompetitive.
Barriers to Entry
Because a large proportion of street costs are fixed,27 the unit
(per piece) street cost initially declines rapidly as volume
increases and continues to decline at a decreasing rate. A firm
with a small share of total volume that competes with an incumbent
in delivery only, will find its unit cost high relative to the
incumbent, even if the competitor pays no wage premium and or is
more efficient. A competitor can reduce its fixed costs by reducing
the level of service (i.e., deliver less frequently than the
incumbent). Many First-Class mailers do not require daily delivery
and most advertising mailers do not require daily delivery.
While it may be politically difficult, incumbent postal
administrations have the possibility of reducing delivery
frequency. Table 3 displays the cost savings if the
U.S. Postal Service were to reduce delivery frequency. The
savings are substantial relative to the current $10 billion
delivery costs. They are not so substantial when considered in the
context of the total Postal Service expenditure in 1993 of $48
billion.
Table 3 Cost of Delivery Frequency
Table 4 illustrates how difficult it would be to enter the U.S.
delivery market.28
The table displays the market share that a competitor would have
to capture in order
27
In the U.S., about 71 percent of street cost are fixed.
28
Over and above the problems discussed here, the U.S. mail box
law represents a huge barrier to entry. The law forbids any private
party from placing anything in a receptacle used to deliver mail to
a residence or business.
to have the same unit costs as the U.S. Postal Service. For
example, if a competitor delivered six days a week and its combined
wage and efficiency advantage is 50 percent, the competitor would
have to capture 35 percent of the total market in order to have the
same unit delivery cost as the Postal Service. Even if this
competitor delivered only one day per week, it would have to
capture 15 percent of the total market in order to have the same
unit delivery cost as the Postal Service on a national basis. This
is about 27 billion pieces per year or 519 million pieces per week.
Assuming a competitor would capture volume slowly and would have to
charge rates no higher than the incumbent, the competitor would
have to be ready to sustain large loses before it could break even.
Thus, the effects of economies of scale in delivery present
significant barriers to entry.
Table 4 Break-Even Market Share for Competitors
Competitor Combined Wage and Efficiency Advantage
An International Comparison of the Values of Scale in Delivery
with Wage Premiums
As mail volume increases in postal systems, variable costs
(processing and transportation) increase and fixed costs decrease
as a percentage of total costs. Therefore, street delivery costs,
which are largely fixed, decrease as a percentage of total costs as
volume increases. Route time cost, which is a fixed cost and the
largest component of street delivery costs, decreases with a rise
in volume. The fixed access cost as a percentage of total cost
would increase with volume until all stops are covered while the
variable access cost percentage decreases as volume increases.
Figure 4 shows these relationships for the U.S. Postal Service
costs.
Conversely as volumes decrease, fixed costs become a higher
percentage of total costs. For example, if the U.S. Postal Service
volume were one third of the 1993 level, then delivery costs as a
percentage of total costs would increase from approximately 21
percent to 36 percent of total costs. In equally efficient but
smaller volume postal systems, street delivery costs should also be
a much greater percentage of total costs than the 21 percent in the
U.S. Postal Service.
Table 5 displays the implied coverage, the percentage of total
cost represented by street delivery cost, and the percentage of
total cost represented by fixed delivery cost for the 21 countries
based on their respective per capita volume in 1988. 29 For
example, Germany had about 230 pieces per capita which yields a
coverage of about 64 percent. Its per capita volume and
corresponding coverage imply that its fixed portion of delivery
equaled about 19 percent of its total costs. The U.S., by
comparison, had about 535 pieces per capita and had 91 percent
coverage for 1988. Thus, the fixed portion of delivery in the U.S.
amounted to about 14 percent of total cost. The implied coverages
range from 16 percent to nearly 100 percent. The implied
proportions of fixed delivery cost tot total cost ranged from 12
percent to 43 percent.
This assumes that the coverage function (Figure 1), developed
from an analysis of delivery routes in the U.S., is valid for the
other countries included in this analysis.
Table 5 Fixed Delivery Costs
Note: Assumes fixed costs are incurred only in the delivery
function. All other functions are assumed to vary with volume.
For each of the 21 countries in the international data set
described above, we calculate the value of scale in the delivery
function using the same approach we used for the U.S. with a slight
modification. For the U.S., we calculate the value of scale by
comparing the cost of a hypothetical duopoly with the cost of a
monopoly. This is calculated using volume per possible stops data
and the coverage function. For the other 20 countries, we use a
slightly different approach because detailed street delivery cost
and point of delivery data are not available. We use volume per
capita as a proxy for pieces per possible stop and assume that the
street delivery cost to total cost relationship of the U.S. is the
same for the other 20 countries. See the Technical Appendix for a
more detailed discussion of the methodology.
Using the 1988 data, we use the per capita volume for each
country to approximate pieces per possible stop. We assume a direct
linear relationship between volume per capita and pieces per
possible stop. Using the estimates of pieces per possible stop for
each country, we then calculate the monopoly and the duopoly costs
based on the U.S. costs. We then take the ratio of the value of
scale to the monopoly cost and multiply that ratio by the actual
total costs for each country to estimate the value of scale for
each country.
For example, for the United Kingdom, the value of scale is about
$4.46 billion using the U.S. model. In 1988, the total cost for the
Postal Service was about $36.5 billion. When we adjust the total
cost for the United Kingdom's coverage level, the total cost would
be about $26.7 billion. If we assume that all cost segments other
than street delivery vary with volume, the value of scale is about
17 percent of the total cost at the United Kingdom's volume and
coverage levels. We then apply the 17 percent estimate to the
United Kingdom's actual total cost for 1988 ($6.58 billion) to
calculate the value of scale.30 The value of scale for the United
Kingdom is about $1.1 billion. Table 6 displays the estimates of
value of scale for the 21 countries in our data set. The value of
scale ranges from $14 million for Luxembourg to $4.5 billion for
the U.S.
A measure of a wage premium can be calculated for each country
by comparing the postal hourly wage with the average manufacturing
wage in that country.31 It should be noted that Belgium, Finland
and Spain have a negative wage premium according to this measure.
The net value of scale is the difference between the value of scale
and the wage premium.
30
The total costs for national postal systems other than the U.S.
are expressed in purchasing power parities.
31
The postal data for calculating the wage premium comes from the
above mentioned paper. The private sector data comes from
International Comparisons of Hourly Compensation Costs for
Production Workers in Manufacturing, 1993, U.S. Department of
Labor, Bureau of Labor Statistics, Report 873, June 1994.
Table 6 Comparison of Value of Scale in Delivery with the Wage
Premium in 21 National Postal Systems ($ millions - 1988)
Note: Expressed in U.S. dollars based on purchasing power
parities.
If the wage premium measure is valid, then seven countries have
a wage premium alone which exceeds the value of scale in the
delivery function; Australia, Austria, France, Japan, Luxembourg,
Switzerland and the United States.
In these countries, it appears that it would be difficult to
justify a postal delivery monopoly based on economic grounds.
Better understanding of inefficiencies in national postal systems
would allow further evaluation of the economic basis for the postal
monopoly in the remaining countries.32
Sweden and Finland do not have legal monopolies.
TECHNICAL APPENDIX
A. Estimating the Coverage Function
1. Data
We use the FY 1993 data from the Postal Service's City Carrier
System (CCS) to model the behavior of access costs. The CCS data
base contains a representative sample of street delivery costs,
volumes, and delivery point characteristics for city delivery
carriers. The CCS FY 1993 data set contains observations from about
300 routes. The Postal Service sampled each route every two weeks
over a one year period resulting in about 8,000 route-level
observations.
2. The Coverage Model
For this paper, we use a nonlinear regression model that
establishes the relationship between volume and coverage. We define
"coverage" as the percentage of stops on a route that receive mail.
It has been well established that route coverages relate directly
to the fixed and variable nature of access cost. The coverage model
specification is as follows:
COVi = 1 - e -b*PPSi (1)
where, COVi = ASi / PSi ASi = Number of actual stops on route i
PSi = Number of possible stops on route i PPSi = Number of pieces
per possible stop on route i
Since coverage cannot exceed 100 percent, we have specified an
exponential function. The regression results from the model are
highly significant. The estimated coefficient, b, is 0.6587.
B. Measure of Scale Economies
1. Scale Economies for the U.S.
We measure the returns to scale in the U.S. postal delivery
function by first determining the total cost of delivery provided
by the Postal Service:
SCm = RCm + ECm + fm * ACm + vm * ACm (2)
where,
SCm = street delivery cost
RCm = route time cost
ECm = elemental load cost
ACm = access cost (also includes coverage-related load cost)
vm = variable portion of access cost = ((e -b*PPS * (b * PPS) /
(1 - e -b*PPS))) fm = fixed portion of access cost = (1 - vm) m =
designates the monopoly case
For the year 1993, street delivery cost totaled about $10.07
billion:
SCm = RCm + ECm + fm * ACm + vm * ACm (2)
= 2.95 + 1.91 + 0.8 (5.20) + 0.2 (5.20)
= 10.07
Next, we determine the total cost of delivery performed by the
Postal Service and a second firm that we assume to be equally
efficient. We calculate the cost for each of the two firms in our
hypothetical duopoly by adjusting equation (2):
SCfirmi = RCm + 0.5 * ECm + ffirmi * ACfirmi + vfirmi * ACfirmi
(3)
where, SCfirmi = street delivery cost for firm i ACfirmi =
access cost for firm i = ACm * NCOV NCOV = new coverage a duopoly
firm i = 1 - (COVm - COVd)
COVm = coverage for a monopoly = 1 - e -b*PPS
COVi = coverage for a duopoly firm i = 1 - e -b*PPS/2
vfirmi = variable portion of access cost = ((e -b*PPS/2 * (b *
PPS/2) / (1 - e -b*PPS/2))) ffirmi = fixed portion of access cost =
(1 - vfirmi)
The total delivery cost for the duopoly market is simply
SCduopoly = 2 SCfirmi (4)
For the year 1993, total street delivery costs for the
hypothetical duopoly in the U.S. are as follows:
SCfirmi = RCm + 0.5 * ECm + f * ACfirmi + v * ACfirmi (3) = 2.95
+ 0.5 (1.91) + 0.52 (4.19) + 0.48 (4.19) = 8.098
SCduopoly = 2 SCfirmi (4) = 2 * 8.098 = 16.2
Value of Scale= SCduopoly - SCm = 16.2 - 10.1 = 6.1
The value of scale in the U.S. is approximately $6.1 billion. In
1993, the total cost for the Postal Service was about $48.2
billion. If we assume that all cost segments other than street
delivery (i.e., in-office delivery, mail processing,
transportation, retail services, and other costs) vary with volume,
the value of scale amounts to about 13 percent of the total
cost.
2. Scale Economies for 21 Postal Systems1
For each of the 20 countries (other than the U.S.) described
above, we use a slightly different approach because detailed street
delivery cost and point of delivery data are not available. We use
volume per capita as a proxy for pieces per possible stop and
assume that the street delivery cost to total cost relationship of
the U.S. is the same for the other 20 countries.
First, we use volume per capita for each country to approximate
pieces per possible stop. We assume a direct linear relationship
between volume per capita and pieces per possible stop:
PPSi = (VCi / VCu.s.) * PPSu.s. (5)
where, PPSi = Average pieces per possible stop for country i
PPSu.s. = Average pieces per possible stop for the U.S. VCi =
Volume per capita for country i VCu.s. = Volume per capita for the
U.S.
For the United Kingdom, for example, we estimate an average of
1.8 pieces per possible stop (with a corresponding coverage of
about 69 percent):
PPSi = (VCi / VCu.s.) * PPSu.s. (5) = (264/536) * 3.66 = 0.49 *
3.66 = 1.8
1In contrast to the previous section, all data in this section
are from the year 1988.
Using the estimates of pieces per possible stop for each
country, we calculate the monopoly cost and the duopoly cost using
equations (2), (3), and (4) based on the U.S. costs. For example,
for the United Kingdom, equations (2), (3), and (4) would result in
the following results:
SCm = RCm + ECm + fm * ACm + vm * ACm (2)
= 2.95 + 0.94 + 0.48 (4.08) + 0.52 (4.08)
= 7.98
SCfirmi = RCm + 0.5 * ECm + f * ACfirmi + v * ACfirmi (3)
= 2.95 + 0.5 (0.94) + 0.27 (2.78) + 0.73 (2.78)
= 6.22
SCduopoly = 2 SCfirmi (4)
= 2 * 6.22
= 12.44
Value of Scale= SCduopoly - SCm
= 12.44 - 7.98
= 4.46
The value of scale is about $4.46 billion using the U.S. model.
In 1988, the total cost for the Postal Service was about $36.5
billion. When we adjust the total cost for the United Kingdom's
coverage level, the total cost would be about $26.7 billion. If we
assume that all cost segments other than street delivery vary with
volume, the value of scale is about 17 percent of the total cost at
the United Kingdom's volume and coverage levels. We then apply the
17 percent estimate to the United Kingdom's actual total cost for
1988 ($6.58 billion) to calculate the value of scale. The value of
scale for the United Kingdom is about $1.1 billion.
