Mitchell_6-17-Mit.txt

Postal Worksharing: Welfare, Technical Efficiency, and Pareto
Optimality
Presented at the Sixth Conference on Postal and Delivery
Economics The Center for Research in Regulated Industries at
Rutgers University Montreux, Switzerland June 17-20, 1998

Robert W. Mitchell
The author is Special Assistant to the Postal Rate Commission,
an independent U. S. Government Agency, separate from the United
States Postal Service. The opinions expressed are those of the
author and do not represent opinions or positions of the Postal
Rate Commission.



Introduction
Competition is generally believed to lead to efficiency, be it
economic or technical. One method of introducing competition into
postal systems, without affecting the universal service obligation,
is through what have been termed "worksharing" discounts. One
begins with the view that the postal system is a vertically
integrated network involving the collection, sorting, transporting,
and final delivery of mail. Under the presumption that the postal
monopoly applies in its clearest form only to the final delivery
process, where scale economies are likely the greatest, the
worksharing notion is that a discount should be offered to mailers
or competitors1 who do portions of the postal work and then turn
the mail over to the postal service for completion of delivery. As
a technical matter, it should be noted up front that there is no
requirement that the mailer or the competitor really perform any
particular piece of work, only that the mail be presented so that
the postal service2 does not have to do that piece of work. In
terms of understanding the functioning and effects of the
worksharing process, this distinction will be shown to be a matter
of some importance.
Because simplicity and ease of administration are usually given
some weight in rate setting, the number of worksharing discounts is
limited. Such a limitation might not exist in the private sector,
where the categories of customers to be served can be prescribed
and contract rates can be tailored to specific customers or
situations, but it is taken as a constraint on broad-based
government organizations.3 Given this limitation, attention focuses
on several obvious questions: (1) Should worksharing discounts be
offered? (2) What are the effects of these discounts on mailers and
on the Nation? (3) How should the size of these discounts be
determined? This paper answers the first primarily in terms of the
second. The framework within which these issues will be considered
is the existing United States postal system, about which the author
knows a little.
1 The term competitors stands for private firms that compete for
portions of postal work, possibly as contractors or agents of
mailers or mailing organizations. 2 The term postal service is a
reference to a country's dominant or government-run postal delivery
system. References to the United States Postal Service will be
capitalized. 3 This paper refers almost interchangeably to rate(s)
and price(s). The former term is more common in postal rate circles
and the latter more common in economics.
Needless to say, these issues involve much more than just the
fringes of postal activity. In the United States, almost half of
the First-Class mailstream is workshared and an even larger portion
of Standard A4 is either workshared or has preparation requirements
that involve work the mailer must do. Accordingly, the number of
dollars involved in worksharing is in the billions and the effects
on mailers and the economy are quite large. Also, considerable sums
are spent by the Postal Service analyzing the costs associated with
worksharing, and mailers/competitors incur considerable expense
litigating their positions on worksharing before the Postal Rate
Commission.
Although competition and efficiency are important, and may be
the bottom line, the movement toward worksharing has been guided by
other justifications as well. Recognizing that these other
justifications overlap and may not all qualify as basic starting
points, it is worthwhile to list them. First, there are those who
argue that worksharing is a kind of deaveraging, which brings
prices closer to costs, and that deaveraging is both economically
efficient and fair. Second, there is the view that worksharing
discounts are needed to make the postal service more competitive,
thus helping to stave off threats from competing carriers and
electronic substitutes. Third, there are arguments that worksharing
discounts are needed to send signals to mailers that allow the
mailers to decide whether they or their agents can do the work for
less than the postal service.5 Fourth, there are those who argue
that worksharing discounts are a natural outcome of traditional
"make or buy" decisions. That is, businesses commonly contract out
any function that can be done by another firm at a lower cost.
Fifth, some parties take the Efficient Component Pricing (ECP) rule
as one that should be applied wherever opportunity presents itself.
Within ECP, there are four possibilities: set the discount equal to
the simple cost difference between the two categories; set the
discount equal to the average incremental savings in
4 Due to a name change which is difficult to explain and is
confusing, Standard A mail is the same mail that was formerly
identified as Third Class. It consists primarily of advertising
mail that is not required to be sent First Class. It also includes
some mail that might be viewed as community newspapers or shoppers
and some that could be viewed as Periodicals. As a formal matter,
Standard A mail in the United States is broken into two subclasses,
one called Regular Standard A and the other called Enhanced Carrier
Route Standard A. This paper will have some implications for this
distinction, but will not focus specifically on it. 5 The
achievement of having the lowest cost person do the work is
sometimes referred to as an outcome of "lowest combined cost."
cost associated with the worksharing program; set the price of
the workshared product equal to its marginal cost plus the unit
opportunity cost of the worksharing program; or set the discount
equal to the savings at the margin.6 Finally, there is the notion
that it is fair to provide nondiscriminatory downstream access to
the delivery network. This notion argues that the postal service
should charge competitors the same amount to use the delivery
system that the postal service charges itself. Since the author has
not been able to figure out how much the postal service charges
itself for delivery, this notion, while sounding meritorious and
politically correct, will not be mentioned again.
These various approaches sometimes lead to different discount
levels and different associated sets of effects. Also, they
sometimes break down in application, when faced with a practical
situation that does not align well with the assumptions of the
approach. Short of that, the information required to apply them can
be subject to wide margins of error and can be costly to
develop.
This paper has four parts. The first part discusses various
kinds of worksharing. The point is that mailers respond to
"worksharing" discounts in a variety of ways and for a range of
reasons, and that these responses need to be understood in order to
understand the effects of the discounts. The second part is
empirical and discusses various welfare aspects of selecting
discount levels for First-Class Mail in the United States. The
entire discussion is based on an econometric model which provides
no-shift elasticities,7 discount elasticities, and, by implication,
own-price elasticities and cross-price elasticities for basic mail
and workshared mail. This model is viewed as good for limited
changes in prices and discount levels. The third part of the paper
takes a broader view and considers welfare, efficiency, and
fairness issues, consistent with the model in part two of the
overall worksharing program for First-Class Mail. Part IV contains
concluding observations. The focus in all three parts is on real
numbers and on how the system is believed by the author to
behave.
6 When the workshare price is equal to the marginal cost plus
the unit opportunity cost, it is often observed that the postal
service is "indifferent" to whether the workshare program is
offered. When the discount is equal to the savings at the margin,
as much work as possible will be transferred to the lower cost
provider.


Part I: Aspects of Worksharing
In the middle 1970s, the rates for First-Class Mail and
third-class mail in the United States were very simple. First-Class
Mail in 1975 paid 10¢ per piece (plus another 9¢ for each
additional ounce beyond the first), regardless of the piece's shape
or processing characteristics, and regardless of the distance it
needed to be carried. Similarly, third-class mail paid 41¢ per
pound with a minimum charge of 7.9¢ per piece. It could be
letter-sized, flat-sized, or parcel shaped; it could go 3,000 miles
or across the street; it could be mixed in a sack with other pieces
or it could be in a bundle for a specific 5-digit ZIP Code. In all
cases, the rate was the same.
Now, the situation is quite different. The rate for the
First-Class piece depends on whether it is presorted, on whether it
qualifies for an automation category, on whether it is a letter or
a flat within the automation category, on which of 6 presort levels
it achieves within the automation category, and on whether it is
nonstandard in shape. Further, the rate for additional ounces is
considerably less than the rate for the first ounce. The rates for
third class (now Standard A) are similar but even more complex. One
must know whether the piece is a letter or a nonletter, whether it
qualifies for an automation category, whether it qualifies for a
carrier route presorted category, where it is entered in the
system, what its presort level is, what its weight is, and whether
it qualifies as saturation or near saturation. In the latter case,
it must be prepared in what is called the line-of-travel, which is
basically the sequence in which the carrier delivers his or her
route, and there are other requirements as well.
These various price differences, all of which are based to some
degree at least on studies of actual cost differences, send a wide
range of signals to mailers. Some of these signals call for a
decision on whether to workshare and others do little more than
tell the mailer that some pieces cost more to process than others.
But whatever their character or however they are viewed, the
effects on mailers and on the mailstream have been
7 As will be explained further below, a no-shift elasticity is
an own-price elasticity under the constraint either that mailers
may not shift to and from the workshared category or that the size
of the workshare
enormous. Mailers are now presorting their mail, barcoding their
mail, changing flat-size pieces into letter-size pieces,
consolidating their mail, and carrying their mail great distances
in order to enter it at specific locations. Presort firms are
collecting the mail, working with their customers on the quality of
their addresses and on the machinability of their addresses,
sorting the mail, and entering the mail effectively. Private
trucking firms have begun operations to do nothing more than carry
mail across the country.
Viewed simply, four specific discounts are now being offered.
The first is for presorting, the second for putting on barcodes and
assuring machinability, the third for drop shipping, and the fourth
for being letter-sized instead of flat-sized. Potentially more
interesting, however, is to view the discounts in terms of the
responses they receive from mailers and the factors associated with
those responses. For this purpose, a classification of worksharing
types is proposed, with no requirement that the types be mutually
exclusive. This will aid in understanding mailer responses and in
evaluating the benefits of offering the discounts.
Type-1 Worksharing. Type-1 worksharing is the simplest kind and
is most closely aligned with the plain meaning of the term
"workshare." The discount is given when the mailer or competitor
does some of the postal work and does it in essentially the same
way as the postal service would do the work. For example, a
discount could be given for mail presorted into packages, each
package being for one 5-digit ZIP Code area. In a type-1
worksharing situation, the mailer or competitor would sort the mail
in essentially the same way that the postal service would sort the
mail. This means collecting the mail and sorting it either by hand
or on a sorting machine. Such a machine might have an optical
character reader and might put on a barcode.
The purpose here is not to provide reasons or to quantify why
the mailer/competitor might be able to do the work for less than
the postal service, despite the likelihood that the
mailer/competitor's scale of operations will be smaller. Several
possible reasons, however, are clear. The mailer/competitor might
pay lower wages than the postal service, might succeed in managing
and/or scheduling more tightly the sorting operations, might
achieve higher productivity levels, and might be working with a
more
discount does not change.
uniform and more tightly controlled mailstream. The latter
factor exists because postal systems need to be designed to handle
a wide range of mailpieces, generated by a wide range of mailers.
Such operations tend to be higher in cost and may be more difficult
to control.
A drop-ship discount might also evoke type-1 worksharing
activity. A mailer sending a quantity of mail to zone 8 might
achieve a lower rate if he carries the mail to the destination mail
facility. If he can transport the mail for less than the discount,
he will choose to do so. His success in performing the work at a
lower cost might be due to an ability to arrange completely full
trucks or to achieve lower-price contracts with trucking firms. The
latter possibility might exist if the mailer assumed some risk by
placing fewer constraints on the trucking operator.
In pure type-1 worksharing, the analysis of the decision and the
benefits is simple. If the mailer/competitor can do the work at a
lower cost, he will choose to do it. His welfare level will be
increased by the difference between the discount and his cost of
doing the work. The profit position of the postal administration
depends on how the discount level is set, an issue that we need not
specify here.
Type-2 Worksharing. In a type-2 situation, the mailer/competitor
achieves the workshared result but does the work in a different way
from the way the postal service would do it. The best example of
type-2 worksharing involves, again, presort discounts. Either
physically or electronically, the mailer may be able to arrange all
of his addresses in ZIP Code order. This being done, he can then
print together and bundle all of the addresses for one ZIP Code.
After this, the addresses in another ZIP Code would be printed.
When a worksharing situation of this kind is faced, there is the
potential for the mailer to do the work at considerably less cost
than could the postal service. Even if he is sorting the addresses
by hand, he has the option of doing the work in a completely
different way Also, if the same mailing list is used more than
once, or is used again with slight modification, he can sort once
and do many mailings. As a practical matter, mailers are believed
in many cases to be able to do this work for a fraction of the cost
the postal service would face. As a guess, this fraction could
easily be in the neighborhood of onequarter to one-eighth.
Two features of this kind of situation deserve note. First, the
mailer may be able to do in one step what the postal service does
in two or more steps. Such would be the case if the postal service
requires two sortations to get the mail to the 5-digit level while
the computer goes there directly. Second, mailers of some volume
may be in position to take advantage of this discount without the
help of a presort bureau or mailing firm.
From a welfare point of view, a type-2 discount situation is
extremely attractive because the potential gains are large. In
effect, the potential exists to achieve the sortation without doing
the work; but if the discount is not offered, none of the benefit
will be realized.
Type-3 Worksharing. Type-3 worksharing is where the mailer's
decision, whether or not he turns the mail over to a competitor, is
influenced by factors other than the size of the discount and his
cost of doing the work. The primary example of this situation is
one where the mailer is concerned about the level of service
received and finds that taking advantage of the worksharing
discount leads to better service. The most common service
consideration would involve the number of days to delivery, but
mailers can also be interested in achieving delivery on a certain
date or even in reducing the risk that the piece is lost in the
mail.
Two examples of this kind of situation are important. First, a
mailer could find that mail presorted and/or barcoded zips through
the system without delay while other mail, which needs more postal
attention, is either delayed or is unpredictable. In this
situation, the value to the mailer of the improved service would be
considered along with the cost of doing the work.8 Second, a mailer
considering drop shipping could know that mail entered at a
destination facility is always delivered within one or two days
while that entered at a distant location takes much longer and is
less predictable. This mailer would clearly consider the value of
the improved service along with the cost of the drop shipping.
8 Some mailers have found that turning the mail over to a
presort firm, which requires time to do the additional work,
results in a 1-day loss in service. In response, some presort firms
provide same-day entry and some drop ship to nearby locations.
From a welfare point of view, the situation here also has
potential. For example, suppose the discount is 4¢ (per piece) and
the mailer's cost of doing the work is 3.8¢. It would seem on first
glance that the gain from having the mailer do the work is only
0.2¢. But if the value of the improved service is 1 cent per piece,
then the gain from offering the discount is amplified to 1.2¢. If
the discount is not offered, the mailer would clearly not do the
work or receive the improved service. Important also is that if the
improved service is not feasible, the mailer could decide to use an
alternative to the postal system. Conversely, the mailer could
increase his volume if the discount and the associated service are
offered.
Type-4 Worksharing. A type-4 discount situation is where the
mailer reduces the work required by changing his behavior in
efficient ways that were either not predicted or that do not seem
particularly associated with the nature of the discount. Two
examples are offered: The first involves drop-ship discounts and
the second involves the letter/flat differential.
A drop-ship discount can be as simple as a price for nationwide
mail and a price for mail entered at the destination office. A
mailer in New York could be sending mail to Los Angeles. If mailed
from New York, he would pay the nationwide price but if entered in
Los Angeles, he would pay the lower destination price. If the
difference between these two prices is large enough, the mailer
could hire a trucking firm, as discussed above. But there is also
the option of having the mail printed by a firm in Los Angeles,
which would make destination entry quite natural. Without the
drop-ship discount, the mailer will not consider the Los Angeles
printer, even if the printing cost is the same as in New York. With
the drop-ship discount, the mail might be printed in Los Angeles
and the burden of transportation would be avoided entirely.
As a second example, consider the letter/flat differential.9
Under such a rate structure, letter-size pieces have a lower rate
than flat-size pieces. The discount might be justified on the basis
of nothing more than an interest in cost-based rates, and
worksharing might not be an issue. Some mailers, however, will
convert flats into letters. Considering
9 Some readers may not view a letter/flat rate differential as
focused on worksharing. I include it here because it is a discount
and it can lead to a reduction in postal work.
the cost of delivery and the benefits received by the mailer,
the letter-size piece might be a more efficient piece for the
nation as a whole, but the mailer will not make the change unless a
rate differential is offered.
Type-5 Worksharing. A type-5 situation is one that has
worksharing aspects but which is directed primarily at making the
postal system more competitive. The drop-ship discount is, again,
an obvious example. Suppose a mailer in Cleveland has mail that is
to be delivered in Cleveland. If the postal service presents him
with a rate that does not vary with distance, he may, in effect, be
subsidizing other mail. For example, if the average piece of mail
travels 1,000 miles and that is the cost on which the rate is
based, mail going over 1,000 miles gets a relative bargain and mail
staying in the office of entry can be viewed as helping to finance
the long-distance mail.
Now suppose there is a private delivery firm in Cleveland that
is competing with the postal service.10 That private firm will base
its rates on the costs that it incurs, given that it both receives
and delivers the mail in Cleveland-it will not charge a 1,000-mile
rate. If the postal service charges only a 1,000-mile rate, with no
distance differentials and no associated drop-ship discounts, the
postal service will be at a disadvantage and may not be competing
effectively. It could easily lose business, even if it is the
low-cost carrier.
If the postal service offers distance-sensitive rates, it will
be more competitive in Cleveland. This is the case whether or not
any mailers decide on the basis of the price differentials to
engage in drop shipping. In short, the rate structure could be
established in order to be competitive or to base the prices on the
actual costs of the mail, and worksharing activity could occur as a
natural result.
Section Conclusion. Many worksharing discounts evoke responses
based on more than one of the situations described above. For
example, presort discounts have aspects of type 1, type 2, type 3,
and maybe some of type 5. Similarly, drop-ship discounts have
multiple aspects. The reason for delineating these various types is
to emphasize that if the advocacy of offering the discounts is to
be analyzed, all of the dimensions need to be considered.
10 The Private Express Statutes in the United States do not
prevent private firms from delivering parcels, periodicals,
catalogs over 24 pages, or saturation mail. These firms, however,
may not use the mail boxes.


Part II: A Specific Model
In the Docket No. R97-1 rate case before the Postal Rate
Commission, an econometric model became available for First-Class
Mail with the characteristic that basic mail and workshared mail
are treated separately. The actual model contains a number of
variables.11 For present purposes, however, interest centers only
on the price variables and the discount variables. Holding all
other variables constant, and integrating their effects into the
constant term, the equation for basic mail becomes:
-0.189 D-0.164


Vb = 28.572 Pb (1)
And the equation for workshared mail becomes:
-0.289 D0.227



ws = 51.034 Pws (2)
Where V = volume in billions of pieces, b = basic (referring to
the non-workshared category of First-Class Mail), ws = workshare, P
= price, and D = discount. The volume variables are the number of
pieces in the category and the price variables are fixed-weight
indexes of the range of prices paid by the mailpieces making up the
category. In Fiscal Year 1996, the volume of basic (First-Class)
mail was 54.1 billion pieces and the volume of workshared
(First-Class presorted) mail was 39.1 billion. The workshared mail
consists primarily of mail presorted to the 5-digit level, with a
small proportion of carrier route presorted mail. Some of this mail
is also barcoded. The basic mail consists of all other mail and
therefore includes flat-size pieces as well as letter-size pieces,
and heavy-weight pieces as well as light-weight pieces. Some basic
mail has hand-written addresses but
11 See the Direct Testimony of Thomas E. Thress on Behalf of the
United States Postal Service, USPS-T-7, Docket No. R97-1, U. S.
Postal Rate Commission, pp. 40-41. Mr. Thress' complete model
includes the price of First-Class cards, the price of Standard A,
the workshare discount, three lags on these variables, permanent
income, transitory income, user costs, certain dummy variables, and
seasonal coefficients.
most is machine addressed. Basic mail also includes some parcels
under 11 ounces and some non-standard pieces.
The price index (weighted price) for basic mail in 1996 was
39.2¢ and for workshared mail was 27.6¢.12 The difference between
these two is 11.6¢. This difference, however, reflects much more
than just a weighted average of the discounts available to the
workshared mail. It also includes rate differences due to weight
and to whether the piece is non-standard in shape. The value of D
in 1996 was 6.0¢. This is a weighted average of the various
discounts available for presorting and barcoding.
Compared to the basic category, the qualitative characteristics
of the workshare category are reasonably uniform. In brief, most
workshared pieces are probably paying a rate of about 27.6¢.
Therefore, the similar pieces which are not workshared, and are not
getting the discount of 6.0¢, are paying a price of 6.0¢ + 27.6¢ =
33.6¢. We may think, therefore, of the 39.2¢ price for basic mail
as composed of a group of mailers paying 33.6¢ and another group
paying, maybe, 45.0¢. The pieces paying 33.6¢ may be viewed as
candidates to become workshared, if the discount is increased. If
the prices of all basic mail were increased, say, 20%, the 33.6¢,
the 45.0¢, and the 39.2¢ average would all increase by 20%. At the
new price level, the ratio of the price of the candidate mail to
the average price of basic mail would remain the same. If this
ratio is designated as g, then:
P


candidate
g = Pb (3)
and
D = g P b-Pws (4)
12 The variables in the equations are in dollars and in billions
of pieces. For ease of discussion, they will be referenced in the
text in cents per piece. Also, gains and losses in welfare,
technical efficiency, and profits will be referenced in millions of
dollars, although certain graphs may refer to them in billions.
The value of g in the situation described above is 0.857.
According to the Postal Service's costing systems, the per-piece
cost of basic mail in 1996 was 26.1¢ and the per-piece cost of
workshared mail was 10.6¢.13 The difference between these two costs
is 15.5¢. These costs are developed primarily to be marginal costs
and will be assumed to be marginal costs in this paper. This
difference of 15.5¢ is due to a range of characteristics which
workshared mail exhibits. For example, basic mail has a higher
average weight, with pieces ranging from 1 to 11 ounces, while most
workshared mail weighs in the neighborhood of 1 ounce. Also, most
workshared pieces are letter-size and many basic pieces are flats,
which cost more to process. There are other differences as well.
The addresses on workshared pieces are generally thought to be more
accurate and are almost always machine readable. Some basic pieces
have handwritten addresses, and some basic pieces are parcels.
In order to go much further, we need to know the cost of the
pieces that are candidates for moving from the basic category to
the workshare category. Since, in substantial degree, the rate
setting process in the United States sets discounts equal to
associated cost differences, I am assuming for present purposes
that the current discount equals the current cost difference
between the candidate mail and the workshared mail. Therefore, the
cost of the candidate mail becomes 16.6¢ (10.6¢ + 6.0¢). Also, I
will be assuming that the 6.0¢ cost of the Postal Service to take
the mail from basic to workshared condition is constant as limited
quantities of mail move back and forth between basic and
workshared. This is a simplification of reality, which probably
involves a curve with a slight upward slope. That is, as the
discount is increased in steps, the cost to the Postal Service of
sorting the mail that becomes workshared on step 4 is probably
greater than the cost of sorting the mail that becomes workshared
on step 3. This assumption will be relaxed in Part III below, where
larger discount changes are considered.
Note that since the discount is equal to the savings experienced
at the margin as additional pieces become workshared, the base
(1996) position becomes the efficient component pricing (ECP)
position. In postal parlance, we would say that the discount equals
100 percent of the cost avoidance at the margin, or that the
passthrough of the avoidance is 100 percent.
Now that we know the prices, the quantities, and the costs, the
total revenue is easily calculable as $31.9988 billion, the total
marginal cost as $18.2647 billion, and the contribution to fixed
costs (or to institutional costs) as $13.7341 billion. The
contribution is defined as the difference between total revenue and
total marginal cost. If this initial position is assumed to be a
breakeven position, then any other breakeven position must have
this same contribution.
Note that the demand equations shown above are somewhat
different from those normally encountered. As shown in Equation
(4), the D term in the Vb equation contains Pb, so when Pb changes,
the discount is affected. The exponent of Pb in Equation (1), then,
is not a traditional elasticity; rather, it is an elasticity for
changes in own-price when the discount remains unchanged, referred
to in this paper as a no-shift elasticity. In order for the
discount to remain unchanged when Pb is changed, the price of the
workshare category must be changed in an amount exactly equal to
gDPb, as made clear by Equation (4). Note also that Equations (1)
and (2) have the characteristic that ¶Vb/¶D = -¶Vws/¶D for each
observation point, including 1996.14
As a check, I wanted to have a second model available. The
models presented above can be converted for this purpose into more
traditional models, with ordinary elasticities and cross
elasticities, with the same characteristics at the current
position. Substituting Equation (4) into Equations (1) and (2)
yields:
-0.189 (
Pb - Pws)-0.164
Vb = 28.572 Pb (5)
-0.289 (
Pb - Pws)0.227

ws = 51.034 Pws (6)
13 These are the costs as reported by the Postal Service. During
rate cases, the Postal Rate Commission has sometimes made
adjustments to Postal Service costing. It is doubtful that using
adjusted costs would change the nature of the results obtained. 14
This characteristic is a symmetry condition imposed in the
econometrics as the demand equations were developed.
For the own-price elasticities in a traditional model, we need
respectively:

¶ V Pbeb =¶ Pb b Vb (7)
VP

ws ws

ws ¶ P V (8)
ws ws
For the cross elasticities (ce) in a traditional model, we
need:
¶ VP
b ws
ceb = ¶Pws Vb (9)
¶ V Pb
ws
ce ws =¶ PV (10)
b ws
If the partial derivatives of Equations (5) and (6) are
substituted into Equations (7) - (10), we get:
eb =-189.0 +-164.0 gPb =-1.1074
g P -P (11)
b ws
227 . 0 P
ws

ws -= 289 . 0 --= 3328 . 1 (12)
g-P

b ws

P (-) 164 . 0
ws
ceb -= = 7544 . 0 (13)
g-P

b ws
227 . 0 cews = Pb -P = 2707 . 1 (14)
g

b ws
Putting these into a traditional model with a constant
appropriate to the current position yields:
-1.1074 Pws0.7554

Vb = 50.6501 Pb (15)
-1.3328 Pb1.2707



ws = 23.1120 Pws (16)
To those who are conditioned to thinking of the demand for
First-Class Mail as being rather inelastic, the elasticity, for
example, of -1.1074 may seem high. The reason, however, is clear.
If the price of basic mail is incresed and the price of workshared
mail is held constant, the discount will increase automatically and
volume will decline for two reasons: (1) because the price is
higher, some customers will reduce usage and (2) because the
discount is higher, some customers will decide to workshare and
will leave basic.
In Equation (15), an increase in Pws amounts to a decrease in
the discount, causing workshared mail to stop worksharing and shift
to Vb. There is clearly a symmetry between changing Pws in the Vb
equation and changing Pb in the Vws equation. Note, however, that
the cross-elasticities stop short of obeying the Slutsky-Schultz
condition. This is because of Equation (4), which shows that a
change in Pb and a change in Pws do not have the same effect on the
discount.
We now have two models that are equivalent at the current
position. Equations
(1) and (2) are derived from the testimony of witness Thress and
will be referred to as the Thress model or the Thress equations.
Equations (15) and (16) are the more traditional constant
elasticity equations and will be referred to as the eXe (pronounced
e-cross-e) model or the eXe equations. Although built to have the
same characteristics at the current operating point, they
characterize sightly different behavior as we move away from the
current point.
These models represent whatever it is that mailers think about
when they decide how much to mail and whether to presort. The
mailers know their costs, their options, their preferences, and
their other interests, such as service. Note that as the discount
increases, more and more mailers workshare. This provides an upward
sloping supply of workshared mail. In the basic Thress equation,
the discount going from its current level of 6.0¢ up to a level of
7.0¢, with no change in the basic price, causes the basic volume to
go from 54.1 billion down to 52.7495 billion. Thus, a 1-cent
increase in the discount causes about 2.5% of the basic volume to
shift to presort. If anything, at least to the writer, this seems
on the small side.
These models have been constructed to represent the system in
the neighborhood of the current operating point. They should make
good predictions for small or moderate changes about the current
point. Without going too far, the directions of change, the general
magnitudes of changes, and the patterns representing the rates of
change should be meaningful. Two general kinds of changes will be
considered in this part of the paper. The first involves holding
the price of the basic category constant and changing the discount.
The second involves keeping the Postal Service at breakeven while
the discount is changed. In both cases, attention will focus on
welfare levels and technical efficiency. Part III of the paper will
consider changes outside the neighborhood of the current operating
point.
When cross elasticities are weak or non-existent, welfare
changes can be calculated from areas under simple demand curves.
When cross elasticities are strong, however, the demand curves
shift. Since the models being used here are characterized by strong
cross elasticities, it was necessary to develop a method of dealing
with the shifting curves and with mailers that shift toward
worksharing when the discounts increase. The writer explored
several methods of estimating the effects involved. Several
decisions had to be made about how various adjustments would be
handled. In most cases, the results are relatively robust to the
decisions made.
The approach taken is based on the assumption that mailer
decisions on whether to engage in additional worksharing are based
entirely on the absolute level of the discount. Also, the
assumption is made that all new worksharing volume comes from basic
volume. In support of the latter assumption, it seems reasonable to
believe that potential mailers not now sending mail are not likely
well situated to find worksharing attractive at somewhat higher
discount levels than those at the base position. Another assumption
made is that the volume equations are better able to predict market
responses when one variable is changed from the base position than
when both variables are changed.
Within the framework of these assumptions, three steps are
taken. First, the level of the discount is held constant, so that
no mailers will change their decision on whether to workshare, and
estimates are made for the basic market. Second, the level of the
discount is held constant and similar estimates are made for the
workshare market. Third, the discount is allowed to change and
estimates are made for the volume that shifts to or from being
workshared. Note that it is the volume that shifts that can be
processed by a higher or a lower cost provider. Therefore, changes
in technical efficiency are based on the shifting volume. Not
necessarily in this order, these steps are described in the next
two sections.
Behavior of Profits and Welfare with Discount Changes, Basic
Price Held Constant.
If the prices of the basic category were regulated and precluded
from going above a certain level, as might occur under a price cap
arrangement, but the Postal Service were given the freedom to
adjust the discount and therefore the workshare price, a natural
question would concern the extent to which the Postal Service's net
income (hereinafter often called profits) could be changed by
changing the discount, and how this change would compare with the
welfare effects on mailers. Also, a question can be asked about
technical efficiency gains and losses as work is shifted to and
from the mailers.15 These questions can be answered with both the
Thress model and the eXe model. The discount is changed directly in
the former model, and by changing the price of workshared mail in
the latter. Because it is easier to think about, the discussion
will proceed as though the discount were being increased, so that
there is more worksharing. All of the equations, of course, apply
for both discount increases and decreases. Also, the discussion
will focus on the Thress model, with the understanding that similar
calculations can be made with the eXe model. To simplify the
discussion, we will talk about any worksharing as though the mailer
were doing it, even though the mailer might turn the work over to
another firm (a firm that might be viewed as competing with the
Postal Service for portions of the work) or to a
contractor/agent.
The first step is to select a range of discounts from 1¢ to 11¢.
This is a large neighborhood around the current level of 6¢, but
weight need not be given to distant results. With this done, the
workshare prices (Pws) can be calculated immediately as g Pb -D,
where Pb remains at the current level of 39.2¢. Next, using
Equation (1), the volume that leaves the basic category can be
calculated as the initial volume (54.1 billion) less the volume
calculated at the current Pb and the new discount. Graphically, the
leaving shift volume appears as follows:

*
Vb Vb
15 In this paper, technical efficiency refers to the absolute
cost of getting a certain quantity of work done. Getting the work
done at a lower cost, regardless of who does the work, is more
efficient. Technical efficiency does not related to consumer
utility or to consumer welfare.
Values at the base (current) position are indicated by an *. The
leaving shift volume
*
equals Vb - Vb. A question needs to be answered about whether
the above curve is really a demand curve, since customary demand
curves hold the prices of substitutes constant and this one holds
the discount constant. Fundamentally, a demand curve shows how a
market responds, given its preferences, to changes in price, when
other factors affecting quantity do not change. I view this demand
curve as showing how the market responds, given its preferences,
when other factors affecting volume do not change, including that
no mailer in the market may consider shifting from basic to
workshared. The curve, therefore, is customarily rich in
information about the utility the mailers in the market gain (or
lose) when the price changes. The constraint relating to shifting
will be relaxed in a separate step.
Using workshare Equation (2), a new workshared volume can be
calculated using the original workshare price and the new
discount.16 Graphically, the estimation appears as follows:


Vws* Vws
16 In the new position in this exercise, Pws will be lower and D
will be higher. Pws is being held constant at this point in order
to focus on the shifting volume.
The difference between Vws and Vws* is one estimate of the
arriving workshare shift volume, i.e., the volume that decided to
workshare under the higher discount, left the basic category, and
arrived at the workshare category. This estimate of the arriving
workshare shift volume turns out to be larger than the leaving
workshare shift volume. Such, of course, would be expected since
the shifting mailers are getting a lower price.
The equation for the basic category has prices in it, with the
understanding that the mailers look at the prices and decide how
much mail to send. As with all demand functions, the mailers are
presumed to understand that they must pay any paper, printing, and
preparation costs associated with their increased use of the mail.
The equation for the workshare category also has prices in it, and
may be presumed to model the decisions made by workshare mailers.
In addition to the costs incurred by basic mailers, however, these
mailers incur what are often referred to as user costs. That is,
they must incur costs to accomplish the worksharing, however they
do it. The mailers who shift from the basic category to the
workshare category face an unbalanced situation with respect to
user cost. Specifically, they go from a price requiring no user
cost to a price with a user cost. Therefore, the gain they
experience by shifting is not equal to the price difference;
rather, it is equal to the price difference less the user cost they
experience. Throughout this paper, I assume that the average user
cost for shifting mail is equal to the original discount (under
which they chose not to workshare) plus ½ of the increase in the
discount.
Comparing this estimate of the arriving shift volume to the
leaving shift volume, and assuming the shifting volume went from
the basic price (which does not change in this exercise) to a
"price" equal to the sum of the new workshare price and the user
cost, I found that the implied elasticity of the growth of the
shifting volume was generally in the neighborhood of -2.5 to -4.0.
Deciding this was unacceptably large (in absolute value), I chose
instead to increase the leaving shift volume with an elasticity of
-0.189, which is the elasticity Thress found for the basic category
when the discount does not change. One could say that we are
growing the shift volume as it moves from its old (higher) price
position to its new (lower) price position. For each discount
level, this provides an alternative estimate of the arriving shift
volumes, based on the leaving shift volume and a reasonable
attendant growth. The situation in which the shifting mailers find
themselves can be graphed as follows:
*
Pb Pws+ user cost
Pws

VL VA
Where VL equals the leaving shift volume and VA equals the
arriving shift volume. Note that the cross-hatched trapezoid area
is the welfare gain of the shifting mailers.17 Note also that there
was no welfare effect on any other basic mailers, because they all
remained
*
at the same Pb , and then the shift volume was allowed to
leave.
The new volume for the workshare category is taken to be the sum
of (a) the calculated workshared volume at the new Pws and the
original discount, and (b) the arriving shift volume. Graphically,
the situation is as follows:
17 The areas of all trapezoid-like figures in this paper are
estimated by assuming that the right-hand sides are straight
lines.

*
Vws VI Vws
Where VI (intermediate) is the volume of workshared mail that
exists at the new workshare price and the original discount, before
the shift volume arrives. The difference between Vws and VI is the
arriving shift volume, VA, discussed above. Note that the
crosshatched trapezoid area is the welfare gain to the workshare
market, given the price decrease they experience, before the shift
volume arrives.
On the question of how much the leaving shift volume might grow,
there is another effect that needs to be mentioned, although it is
not dealt with further in this paper. As worksharing discounts are
given and competitors begin to compete for business and profits, it
is often believed that they might succeed in attracting more
overall volume into the system. This is sometimes called a "beat
the bushes" effect. Such would, of course, affect both postal
service finances and mailer welfare. The basis for believing that
volume growth of this kind might occur is not only that there might
be more sales people and possibly some product differentiation, but
also that these competitors might be able to promote in ways that
the postal service itself cannot. In the United States, for
example, some competitors are convincing customers that delivery
service is good, while the same message coming from a postal
account representative might not be as believable. Also, there are
sometimes restrictions for policy or appearance reasons on the ways
in which government enterprises such as postal services can
advertise and promote.
One more adjustment is needed. The shifting volume that leaves
the basic category is in the lower price range of all the mail in
that category. Therefore, when the shifting volume leaves, the
price index for the basic category increases. Knowing that the
price being paid by the shifting volume just before it shifted was
equal to g times the basic price, a revised price index for the
basic category can be calculated. This revised price index must be
used to calculate the revenue from the basic category after the
shift volume leaves.
For each discount, the revenue and the cost at the new position
can be calculated. The difference between these two is the gain in
profit for the Postal Service. The welfare gain of the mailers is
the sum of the welfare gain of the shifting volume and the gain of
the workshare market before the shift volume arrives. Both of these
areas are cross-hatched above. The technical gain (or loss if
negative) for the new position can be calculated as the leaving
shift volume times the difference between the postal cost of doing
the work and the mailers' user cost of doing the work. Given our
assumption that the Postal Service's cost for doing the work is 6¢,
and knowing that the user cost is above 6¢ for all discount
increases, we can expect the gain to be negative for all discount
increases. If the discount decreases from 6¢, mail which mailers
have been sorting for less than 6¢ will shift to the Postal
Service, and the technical gain will again be negative. These signs
on the technical gain would be expected for movements from an ECP
position.
The two graphs on the next page show the profit results. The top
graph is for the Thress model and the bottom one is for the eXe
model. Several observations may be made. Given a decrease in the
discount, with the basic price held constant, the Postal Service
profit increases in both models and appears in the Thress model to
reach a peak at a discount of about 2¢. Since 2¢ is rather distant
from 6¢, however, this result may not be reliable. At a discount of
4¢, the Thress model shows a profit increase of $563 million and
the eXe model shows $581 million. In these same two cases,
respectively, the technical loss from having the higher-cost person
do the work is $37 million and $29 million. The technical losses,
experienced in some sense by all mailers, are clearly small


Final Conference Copy
Thress Model


eXe Model


relative to the increase in profit. Note also that the slopes of
both graphs decrease in absolute value as the discount
decreases.
Several ceteris-paribus (one-at-a-time) changes were then
investigated. First, the Postal Service's cost of processing
workshared mail was changed from 16.6¢ to 14.6¢.18 Second, the
own-price elasticities in the worksharing equations were made equal
to the corresponding elasticities in the basic equations. This
removed the finding that the noshift elasticity of the workshared
mail is greater than that of basic mail. Third, the discount
elasticity in the Thress model was doubled. When any of these
changes are made, the corresponding elasticities for the eXe model
must be found using Equations
(11) through (14). Fourth, the discount elasticity was set equal
to zero, with corresponding zeros in the eXe model. The findings
are summarized in the following table.
Description (D=4¢ instead of 6¢) Profit Gain (Thress & eXe)
Tech. Gain (Thress & eXe)




Table 1
At the current position, which involves a fixed basic price and
a worksharing discount of 6¢, the following observations may be
made, using figures from the Thress equations.
1. Assuming the Postal Service cost of doing the workshare work
is 6¢, a reduction of 2¢ in the worksharing discount will cause a
profit increase of about $563 million. Due to
18 The implication of this 2¢ reduction in the cost of
processing workshared mail is that the postal service can sort the
mail for 4¢ instead of 6¢.
work being done by a less efficient provider, there would be an
associated technical loss of about $37 million, which is relatively
small.


2.
Under the same conditions, if the Postal Service cost of
doing the workshare work is actually 4¢ instead of 6¢, the profit
gain from reducing the worksharing discount by 2¢ would be notably
greater at $637 million, and there would be a technical gain of $37
million.


3.
For discount decreases, the profits of the Postal Service
increase much more rapidly ifthe discount elasticities (and
associated cross elasticities) are low rather than high.


4.
The profit incentive for the Postal Service to decrease
the discount is less when the no-shift own-price elasticity of the
workshare category is greater than that of the basic
category.


The next two graphs, constituting Figure 2, show Postal Service
profits and mailer welfare gains, as well as the sum of the two.
The two models provide results that are similar in magnitude. The
curvatures are also similar, with small differences at points quite
distant from the current discount of 6¢. The losses in mailer
welfare, which are of course opposite in sign from the profits, are
substantially larger in magnitude than the profits. At a discount
of 4¢ instead of 6¢ in the Thress model, the Postal Service gain in
profit is $562 million and the loss in mailer welfare is $945
million. The lines made up of triangles show the net loss or gain
of the other two curves.

Final Conference Copy
Thress Model

0 0.02 0.04 0.06 0.08 0.1 Discount in Dollars, Current=.06
Profit in Squares, Mailer Welfare in Diamonds, Net in
Triangles
eXe Model

0 0.02 0.04 0.06 0.08 0.1 0.12
Discount in Dollars, Current=.06 Profit in Squares, Mailer
Welfare in Diamonds, Net Gain in Triangles


FIGURE 2
Behavior of Welfare Levels with Discount Changes, Under
Breakeven
The next step is to relax the constraint that the basic price is
fixed and to allow discount changes with the requirement that the
Postal Service remain at breakeven. Due to insoluble algebra, a
simultaneous solution is not possible. Short of that, the
preference would be to select D, express Pb in terms of D and Pws ,
and then express Pws in terms of the desired net revenue (taken to
be the same as the net revenue at the base position- hence
breakeven). This, however, is circular and, although convergence
was sometimes obtained after a number of iterations, the procedure
was found, for the most part, to be unworkable and sometimes
unstable.
In the alternative, the procedure adopted was to select D,
express Pb in terms of D and Pws, and to use the backsolver routine
provided in Lotus 1-2-3 to hunt for the value of Pws that yields
breakeven. Within this approach, a number of steps were needed, as
will be explained.
Given the new discount selected, the leaving shift volume can be
calculated in the same way as in the above example on profits. The
next step is to recognize that since Pb will be changing in this
case, to allow breakeven, there will be a change in welfare in the
basic market. The following graph shows the basic market, before
the shift volume is allowed to leave.

*
Vb Vb
This is a demand curve, conditional on the constraint that the
discount remains the same, under which condition no mailers will
shift to workshared. The crosshatched trapezoid is the welfare loss
to these mailers as a market, given that they cannot shift.
The welfare effects on the mailers who shift are calculated in
the same way as in the above section on profits. The shift volume
is allowed to grow according to an ownprice elasticity of -0.189
and the user costs are estimated in the same way. Also, the welfare
effects in the workshare market are calculated in the same way as
before.
For discount increases (and conversely for discount decreases),
the net welfare is the sum of: (a) the reduction in welfare of the
basic market, before the shift volume leaves, (b) the increase in
welfare of the shifting volume, and (c) the increase in welfare of
the workshare market, before the shift volume arrives. The
technical cost effects, due to the work being done by a party that
may do it at a higher cost, are also calculated in the same way as
before. That is, the leaving shift volume, before it grows, is
multiplied by the difference in the cost of doing the work.
Figure 3 shows the basic results for the two models. The lines
composed of boxes show the welfare level of all mailers combined
and the lines composed of diamonds show the technical losses (if
negative) of shifting the work to another party. Figure 4 shows the
supply curve of workshare services. In traditional form, it has the
discount on the vertical axis.
In the United States, considerable attention is given to setting
the worksharing discounts. Two approaches are often discussed. The
first is the subclass approach and the second is the rate category
approach. In the subclass approach, the basic and the workshare
category are each given a percentage markup over cost, in order to
obtain their average rate. As a simple example, suppose the cost of
worksharing is 10¢ and the cost of basic mail is 16¢. If each is
given a 50% markup, the average rate levels will be 15¢ and 24¢,
respectively. In this case, the rate difference is 9¢, which is
equal to the cost difference of 6¢ inflated by the 50% markup.
Thress Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
eXe Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
FIGURE 3 Change in Discount, Breakeven Maintained
Thress Model

30 354045 Quantity Supplied in Billions
eXe Model

30 354045 Quantity Supplied in Billions
FIGURE 4
In the rate category approach, the difference in the rates for
the two categories is based on the cost difference. Assuming 100%
passthrough of the cost difference, which is 6¢ in this example,
the rate difference would be 6¢. Handled in this way, the rates
might turn out to be 17¢ and 23¢. As discussions concerning rate
setting occur, considerable attention is given to selecting the
passthrough. The (adjustable) assumption of this paper is that the
Postal Service's cost for doing the workshare work is 6¢ and that
100% of this 6¢ is passed through into rates. If the passthrough
were over 100%, a result for which some parties argue, the discount
would be larger and we would say that we are moving from rate
category treatment toward subclass treatment. If the two subclasses
were given different proportionate markups, rather than the 50%
markups in the example just completed, the comparisons would not be
so simple.
In Figure 3, it is clear that as the discount level is
increased, implying a passthrough of over 100%, the general welfare
level increases, but at a declining rate. The curves of both models
appear to reach a maximum at a discount of about 8¢. At the 8¢
level, the Thress model shows a welfare gain of $32 million and the
eXe model of $27 million. At the same time, they show technical
losses, respectively, of $25 million and $29 million.
It is interesting to look at the makeup of these welfare gains.
In the Thress model, at the discount level of 8¢ and the net gain
of $32 million, the basic market incurs a welfare loss of $480
million (0.89¢ per piece), the workshare market realizes a gain of
$487 million (1.23¢ per piece), and the mailers who shift gain $25
million (1.0¢ per piece). The volume of mail shifting is 2.493
billion leaving basic and 2.507 arriving at the workshare category.
This is about 4.6% of the basic volume. At the 8¢ discount level,
the overall volume in the system, basic plus workshared, increases
0.69%.
Peter Bernstein, testifying for the United States Postal Service
in Docket No. R971, prepared estimates of welfare gains under more
efficient worksharing discounts.19 His analysis left some questions
unanswered but pointed to efficient discounts well above the 8¢
level and to gains on the order of several hundred million dollars.
Compared to his
19 Directt Testimony of Peter Bernstein on Behalf of United
States Postal Service, USPS-T-1, Docket No. R97-1, Postal Rate
Commission, p. 93.
estimates, the 8¢ level seems small, as does the gain of $32
million. In fact, the gain of $32 million is small by almost any
standard. Furthermore, achieving it places a burden on basic
mailers of $480 million, which is notably large by almost any
standard. In terms of Pareto optimality, it appears that a change
from the current position imposes large losses on some mailers,
large gains on others, and relatively small net gains.
The supply curves of workshare services, shown in Figure 4, are
less informative. Assuming they are valid around the current
discount level of 6¢, they clearly show a good deal of sensitivity
to the discount. At low discounts, however, they still show more
volume than might be expected; and at high discount levels, they
show supply levels which are not as large as might be expected.
A matter of considerable discussion in the United States
concerns whether the (noshift) own-price elasticity of workshared
volume is greater than that of basic volume, as these two
categories are now constituted. The Thress model suggests that if
the discount remains unchanged, and thus that shifting is not
allowed, the elasticity of basic volume is negative 0.189 and of
workshared volume is negative 0.289. Prior to Thress' work,
information of this kind was not available. A natural question
becomes: how sensitive are the results to differences in the two
elasticities? Figure 5 shows the basic curves for a situation where
both no-shift elasticities are the same at -0.189. It is clear that
the efficient discount moves closer to the cost figure of 6¢ and
that the welfare gains become much smaller. Specifically, in the
Thress model, the peak occurs at a discount of 7¢ and the welfare
gain is only $6 million. The conclusion, then, is influenced
strongly by whether the workshare category is more elastic.
The discussion surrounding rate category versus subclass status
often focuses on the strength of the cross elasticities. In order
to shed some light on this question, three special runs on cross
elasticities were done. Figure 6 shows the curves for a situation
where the discount and cross elasticities are zero, Figure 7 for
when the discount elasticities are doubled, and Figure 8 for when
the discount elasticities are doubled and the two no-shift
elasticities are equal to -0.189. Note that some of the scales on
the vertical axes are different on these plots.
Thress Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
eXe Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
FIGURE 5 No-Shift Easticities of Basic and Workshare equal at
-0.189
The pattern shown by these graphs is clear. When the cross
elasticities are zero, substantial welfare gains are available from
discounts larger than 6¢ and the optimal discount appears to be
well above 8¢. As the cross elasticities become larger, the
efficient discount levels move closer to the ECP level and the
associated welfare gains available become quite small.20 And, when
the no-shift elasticities of the basic and workshared product are
the same, the gains become even smaller and the peak becomes very
pronounced.
These models are good only for small to moderate movements from
the current position. For larger movements, a somewhat different
approach is taken, beginning in the next section.
20 Recall that under the assumptions made in this paper, setting
the discount at 6 cents is the ECP position, where 6 cents is the
cost savings at the margin.
Thress Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
eXe Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
FIGURE 6 Discount and Cross Elasticities are Zero
Thress Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
eXe Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
FIGURE 7 Discount Elasticity is Doubled
Thress Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welf are in boxes, Technical Eff. in diamonds
eXe Model

2 4 6 81012 Discount, Cents/Piece, Current Level = 6.0
Welfare in boxes, Technical Eff. in diamonds


FIGURE 8 Discount Elasticities are Doubled and No-Shift
Easticities are Equal
39



Part III: Some Broader Questions
The advocacy of a worksharing program may be viewed in broader
perspective from a base equilibrium position of no worksharing
program being offered. Then the question becomes: what would happen
if the basic price were held constant and a worksharing program
were begun? The previous section asked only about making changes to
an existing program, and a well developed one at that.
If no worksharing discounts were being offered, it is possible
that some mailers would still workshare. They could feel that the
cost of the worksharing is small and that they receive an
improvement in service. This could happen in presorting. Another
possibility is that they are worksharing without doing anything
extra, such as in achieving drop shipment because they are already
located at the destination.
Consider a program of discounts for presortation. Initially, as
a conservative starting point, suppose the postal service is at
breakeven with no discounts and no presort volume. Since many
mailers have computerized mailing systems in place and have
sufficient volume, they can do presorting work at a very low cost.
Without hard evidence, the author believes that a presort discount
of ¾ of a cent might induce as many as 20 billion presorted pieces.
This is shown in the supply curve in Figure 9.


Beyond ¾ of a cent, one would expect smaller mailers to begin
presorting or that some presort firms would begin to take the mail
of highest quality and presort it with optical character readers,
probably putting on a barcode at the same time. Suggestions have
been offered in the United States that the most attractive
customers of some presort firms are being charged a price in the
neighborhood of one cent per piece. The graph shows supply
increasing up to 30 billion pieces at a discount of 3¢. Beyond 3¢,
less attractive customers and relatively more difficult mail would
begin to convert to presort. In the neighborhood of 6¢, the curve
must align with the supply curve found in the previous part of this
paper. The curve shown above is selected to align (roughly) with
this requirement.
As the discount increases above 6¢, it is clear from Figure 4
that the curve will continue to rise. At some point, however, it is
possible that private industry would rise to the occasion and
collect virtually all of the mail, process it, and give it to the
postal service for delivery. The curve, then, would turn nearly
horizontal and the postal industry, short of delivery, would be
essentially privatized. These are interesting possibilities.
The other curve shown above, in triangles, is a curve of the
cost to the postal service of sorting the mail that begins to
presort. What is shown is that the postal service would spend
approximately 4¢ per piece to sort and barcode the first 20 billion
pieces. The postal service does not have the option of sorting the
mail on a computer before the address is printed. It must read the
mail, look up the ZIP Code for the address, spray on the barcode,
and proceed to do the sorting, probably to the five digit level.
The way to think of the above curves is to begin with a discount,
go over to the supply curve to get a volume, and then go up to the
postal service cost curve to see how much the postal service saved
on the last few pieces that converted to presort. Above the first
20 billion pieces, less attractive mail begins to presort and the
postal service's costs at the margin undoubtedly begin to increase.
They are shown increasing to 5¢ at a presort volume of 30 billion
and then increasing more slowly. At a presort volume of 40 billion
pieces, the postal service's cost curve goes through the current
operating point discussed in the previous part of this paper.
No evidence is available about the slope of the postal service's
cost curve at or above the 40-billion-piece level. For purposes of
small changes, it was assumed to be horizontal in the previous part
of this paper. Almost undoubtedly, however, it has some positive
slope. One reason for it to have a very low slope is the advent in
the United States of what is called Remote Video Encoding. The
mail, which can be anywhere from mildly unattractive to rather
difficult is put through a sorting machine and a picture of it is
taken. The picture appears on a computer screen and an operator
reads it and supplies the address to the computer. The computer
supplies the ZIP Code and the appropriate barcode is sprayed on the
piece. The piece is handled very efficiently from there on. The
cost of this Video operation may function as an upper limit for
most of the mail. If this is the case, the cost curve would turn
almost horizontal at the cost for this operation.
If the above supply and cost curves are accepted, what are the
implications? One can easily increase the discount from zero and,
for each discount level, calculate several figures: (1) the total
revenue lost by the postal service, which is simply equal to the
discount level multiplied by the presort volume; (2) the total cost
incurred by mailers or by mailing organizations, which is the area
under the supply curve; and (3) the total savings of the postal
service because it does not have to do the sorting and processing,
which is the area under the cost curve. The difference between No.
3 and No. 1 is the increase in the profit (net income) of the
postal service. The difference between No. 3 and No. 2 is the
technical gain from have a lower cost provider do the work.
Figure 10 shows the results. The line composed of boxes shows
the profit position of the postal service. As the discount level
(on the horizontal axis) gets up to ¾ of a cent, 20 billion pieces
become presorted. The postal revenue decreases by ¾ of a cent times
the 20 billion pieces, but the postal cost decreases by 4¢ time the
20 billion pieces. Therefore, the profit position of the postal
service increases to the tune of about $650 million and the
technical gain to the Nation goes up to the same $650 million.
Since the basic price (for non-presorted mail) has not increased,
no one has been made worse off. Increasing the discount from zero
to ¾ cent, then, was a Pareto optimal move. The postal service is
better off, no mailers are worse off, and the excess money can be
used to lower prices for all mailers.




FIGURE 10
As the discount is increased beyond ¾ of a cent, the postal
service's profit level declines, but it is still positive. The
losses from giving the higher discount to all of the mailers that
are already presorting are large and the savings from the
additional presorting are small. According to the graph, the postal
service's profit level declines until it is back at breakeven at
discount of about 4.5¢. Additional work, however, has been
transferred to a lower cost provider, causing a technical gain of
about one billion dollars. This is a substantial gain from offering
a presort program, and it accrues entirely to the mailers. Again,
the move from offering no discount to offering a discount of 4.5¢
is a Pareto optimal move-no one is worse off and someone is
substantially better off.
As the discount increases above 4.5¢, the postal service falls
below breakeven and will have to make up the losses with a price
increase for all mailers, both those who are now presorting and
those who have not thus far been affected. A move from offering no
presort program to offering a discount greater than 4.5¢, then, is
not Pareto optimal. Note, however, that up to a discount of 6¢, by
the assumption made in this paper, work continues to be shifted to
a lower cost provider, but the total technical gains beyond a
discount of 2 or 3 cents are very small. This is because we are in
a range where the cost to mailers (or their agents) is
approximately equal to that of the postal service. As shown in the
previous part of this paper, however, the general net welfare level
of the Nation continues to increase to some discount above 6¢. What
is happening to bring about this net increase is that some mailers
are being made better off and some are being made worse off.
Further empirical work along these lines might be difficult.
Data such as those in Figure 9 are not readily available and would
be difficult to develop. It seems clear, however, that substantial
gains are available from presort programs and, by extension, from
other worksharing programs, to a point. Beyond that point, many
considerations need to be balanced in order to decide on the
appropriate discount levels.
Various statements of the ECP rule can now be reviewed. The
first statement suggests that the rate difference be set equal to
the simple cost difference. In the model discussed in Part II
above, the cost of basic mail is 26.1¢ and of workshared mail is
10.6¢. The difference of 15.5¢ is clearly due to much more than
worksharing and is much larger than any savings. A discount of
15.5¢ would not make sense. The second statement is that the rate
difference should be equal to the average incremental savings for
the worksharing program. This would lead to the discount of 4.5¢,
which is where the lines cross in Figure 9. The third statement is
that the workshare price should equal the marginal cost of the
workshared product plus the unit opportunity cost of the program.
The size of this figure would depend on how much the shift volume
grows after it leaves the basic category. No estimate of this is
available but if the growth is high, the postal service loss for
the program could be low, which would yield a discount larger than
4.5¢. The fourth statement is to set the discount equal to the
savings at the margin. This leads to the current discount of 6¢,
which is where the lines in Figure 9 cross.
Although the lines in Figure 9 appear to cross, based on the
models in Part II, it is interesting to consider the possibility
that they may not. Suppose ECP at the margin could be pursued with
full knowledge of the effects. We might increase the discount to 7¢
and find that we saved 7.3¢ on the volume that shifted. Then we
might increase it to 8¢ and find that we saved 8.2¢ on the volume
that shifted. Then we might increase it further. If this process
continued, it might lead to a situation where all of the
collection, sorting, and transporting of the mail is privatized.
The reader is left to consider the desirability of such a
result.


Part IV: Some Concluding Observations


1.
In the sense that the responses drawn from mailers by
worksharing discounts are based on a wide range of factors,
including the consideration of factors that are not tied in any
particular way to the basis for the discount, there are many types
of worksharing. Assessing the advocacy of offering the discounts
should include consideration of these factors. Some of the types of
worksharing situations are discussed in Part I of this
paper.


2.
From the current position, if the price of the basic mail
service is fixed and the discount for presorting can be varied,
there is a powerful profit incentive for the Postal Service in the
United States to reduce the presort discounts. And, importantly,
the associated losses in mailer welfare are on the order of twice
the increase in postal profits (net income).


3.
For small to moderate movements from the current position
in the United States for First-Class Mail, the technical costs
associated with not having the low-cost provider do the work and
the net welfare gains (or losses) appear to be small compared to
the associated welfare effects, plus and minus, on the mailer
groups involved. Specific estimates are provided in Part
II.


4.
When cross elasticities are substantial, the welfare
gains are small for setting worksharing discounts larger than 100%
of the savings at the margin, which is the traditional ECP
position. Further, the maximum welfare position may not involve a
passthrough of much more than 100%.


5.
The "make-or-buy decision" is not a productive way to
look at worksharing discounts. Allowing a discount to be set in
this way would allow it to be based on profit maximization by the
postal service. It is easy to argue that this discount for
First-Class Mail in the United States might be in the neighborhood
of ¾ cent. If large mailers can "presort" the mail for ¾ of a cent
and the Postal Service saves 4¢, there is no profit reason for
offering a larger discount.


6.
Introducing a presort program and increasing the discount
until a Pareto optimal position is reached will result in a much
smaller discount than basing the discount on the savings at the
margin. The Pareto optimal discount may be in the range of 4.5¢,
while the savings at the margin appear to be in the neighborhood of
6¢.


7.
The welfare findings and the advocacy of ECP are affected
strongly by the magnitude of attendant cross elasticities and by
whether the no-shift own-price elasticities of the workshared
product are larger, the same, or smaller than those of the basic
product. It goes without saying that the estimation of these
elasticities is difficult and that the ones we have may not be
highly accurate.




TECHNICAL APPENDIX
The text of this paper is in Microsoft Word 6.0/7.0. With the
graphs, the main file is about 2.4MB. It is most easily supplied in
zipped form, in which it occupies only 0.9MB and will fit on a
1.44MB disk.
The calculations of this paper were done in 5 Lotus files. These
will fit on one disk.
For serious reviewers, the author would be happy to supply the
paper in electronic form and would supply the Lotus files.
Requests and questions may be addressed to:
[email protected] or 1333 H ST NW Suite 300, Washington DC
20268-0001, or 202-789-6871, FAX: [phone].