1

The Postal Service Variability Ratio and Some Implications 

Robert Cohen and John Waller

This paper first introduces the concept of the variability ratio and why it is being studied. Section 2 

explains the factors that influence the ratio. Section 3 describes the major developments that have 

impacted its behavior from 1980 thru 2013. Section 4 describes the exogenous events that have 

affected the ratio and Section 5 does the same for costing methodology changes. Section 6 examines the 

behavior over time of the infra-marginal and fixed costs that were calculated in Report 2 of this series. 

Finally, Section 7 investigates implications of some findings from Reports 1, 2, and 3 produced under this 

contract with the Commission.

1. Introduction

The variability ratio is the ratio of the Postal Services’ attributable to institutional costs. Changes to the 

ratio can be determined annually when the Postal Service’s cost system produces estimates of these 

costs. Traditionally these changes were important to the PRC because they determined the percentage 

of total costs that the Commission had to assign judgmentally to the classes of mail based on the pricing 

factors in the Postal Reorganization Act. It was also important to Postal management because it 

determined the amount of flexibility it had when proposing pricing changes. Generally speaking, the 

PRC preferred higher levels of attributable costs while Postal management preferred lower levels. This 

resulted in many contentious disputes about costing methodology. Few observers ascribed much 

meaning to the resulting fluctuations in the ratio beyond those conflicts. 

The ratio, however, has had significance beyond those parochial concerns. The direction of the ratio, 

historically, has been an indication of the financial health of the Postal Service. When institutional costs 

were increasing as a percentage of total costs, in general, volume was decreasing or changing to a lower 

cost mail mix. Declining volume perversely means fewer pieces to cover institutional costs (i.e. increased 

unit institutional costs) and a reversal of the Postal Service economies of scale. A lower cost mail mix 

can be accompanied by a lower unit overhead contribution to institutional costs as has been occurring 

during the steady decline in the percentage of First Class and the increase in the percentage of Standard 

in the mail mix over the period being studied (1980 through 2013.). Unless offset by volume increases, a 

lower-cost volume mix has generally meant that Postal finances were deteriorating. This, however, may 

no longer be the case. The new post-PAEA Postal Service has a thriving business in parcels and these 

have much different revenue characteristics than letters and flats. Consequently Postal revenue is 
2

behaving differently and is no longer as directly correlated with volume and volume mix.1 Consequently, 

Postal finances are improving even though institutional costs are a growing percentage of total costs. 

The ratio has appeared stable for more than a third of a century when intuition suggests that it should 

have been less so. Consequently, the PRC has sponsored this study to investigate the apparent stability 

of the variability ratio. The institutional portion of the ratio consists of a both fixed costs and a variable 

portion called infra-marginal (IM).2This paper investigates the extent to which it varies with volume and 

the influence of infra-marginal (IM) cost on institutional and total cost.

2. Factors that influence the Variability Ratio

A. Operational factors 

The ratio measures the relative size of two components; institutional costs on the one hand and 

attributable costs on the other.3If we start at a point in time (period one) with given percentages of 

total costs that are attributable and institutional and we move to a subsequent point in time (period 

two), several factors will simultaneously determine a new ratio. We will consider them individually.

Volume 

Assuming volume grows from period one to period two, ceteris paribus, variable costs will increase. The 

attributable portion of variable costs will increase and the fixed portion of institutional costs will not 

change. Thus, the ratio will increase, because attributable costs will have grown relative to institutional

costs.

Volume mix

The volume mix or composition of the mail reflects the work content of the volume. For our purposes 

“volume mix” Is measured by the average unit attributable cost of the volume at a given point in time. 

Weighted Volume

Weighted Volume is the sum of the volume of the various products weighted by the average unit 

attributable cost of the products. It reflects both mail mix and total volume. An increase in weighted 

 

1

From 2011 through the first three quarters of 2014, volume fell 9.4 percent while revenue fell only 1.1 percent 

excluding estimated revenue from the exigency rate increase.

2

IM costs are variable but do not vary at the margin. Report 1 and Report 2 of this series are in depth discussions 

of IM costs from a theoretical and quantitative viewpoint.

3

The ratio changes when the percentage of total costs that are institutional or attributable changes. Of course, if 

either attributable or institutional cost changes then the other necessarily changes in an equal offsetting amount. 

Thus, to say that the percentages of institutional or attributable costs change, is equivalent to saying that the 

variability ratio changes. 
3

volume means that attributable costs are increasing faster than institutional costs. A decrease in 

weighted volume means that institutional costs are increasing faster than attributable costs.

Productivity

Productivity increases will, in general, decrease attributable costs more than institutional costs since 

attributable costs are those that respond to changes in volume, and productivity is defined as the ratio

of the volume of inputs to the volume of outputs. Changes in productivity can be expected to primarily 

affect mail processing, either in the plant or the delivery unit as in-office time, because mail processing 

is almost entirely volume variable.

4

B. Non-operational factors

Exogenous changes

Changes to the income statement for non-operational reasons will increase or decrease institutional 

cost and so, affect the ratio of attributable to institutional costs. The most frequent changes have been

adjustments for prior- year workers compensation and for the retiree health benefit escrow required by 

the PAEA (and then modified by subsequent Congressional actions).

Cost methodology

Over the years the ratio has been affected by changes to the cost methodology that affect the way in 

which attributable costs are calculated. An example is the PRC first adopting and later dropping the 

single subclass stop methodology.5 Methodological changes have caused notable changes in the ratio 

several times that are explored in Section 5.

Impact of nonoperational factors on the ratio

Changes to cost methodology and exogenous changes were frequent throughout the period being 

examined. These caused increases and decreases to attributable and institutional costs that for some of 

the years were not necessarily reflective of the underlying operations of the Postal Service. While the 

values of attributable and institutional costs may not exactly reflect operations of the Postal Service in 

any given year, the overall trends exhibited by the data series are more robust and reliable, and reflect 

underlying operational events that are described below.

 

4

This has been the case since 2000 when productivity began to meaningfully improve.

5

The methodology was adopted in Docket R87-1 and later dropped in Docket R2006-1. It involved attributing 

access and load time of all deliveries that involved only one subclass.
4

3. Major Postal Developments that have affected the Ratio

This section will explain why the Postal Services’ variability ratio has apparently been so stable 

over the period 1980 to

2013 even though

volume doubled and then 

declined by more than 25 

percent. This stability is 

illustrated in Figure 1. 

The ratio deviates from 

the median line of 37.6 

percent by no more than 

4.1 percentage points in 

any year. Many observers 

have not understood how the

ratio could have remained so stable given the volume fluctuations they witnessed. While 

volume was growing during this period, the effect of the increase in total volume on total 

attributable cost was being offset to a large extent by the mix of volume whose average unit 

attributable cost was declining. See Figure 2. This dampened the increase in attributable cost 

that otherwise would have 

occurred with the growth in 

volume. After the year 2000 

when volume growth leveled 

out, attributable costs began to 

decline because of the 

continuing reduction in the unit 

attributable cost of the volume 

mix and because of productivity 

improvements. When volume 
5

began to fall in 2007, the decline in attributable costs accelerated. Since institutional costs have 

a large fixed component, this resulted in an increasing proportion of institutional costs. How 

long this trend can be expected to continue will be discussed at the end of this Section.

The influence of mail mix on the ratio

A casual examination of Figure 1 indicates a static ratio. A closer examination will reveal that 

there are two distinct trends: declining institutional costs from 1980-2000 and increasing 

institutional costs from 2000-2013. This is more easily observed in Figure 3 (where no 

adjustment has been made for retiree health benefits.) The double vertical lines bound the 

beginning of the uptick in institutional costs since, given the imprecision of the data for some 

years, we cannot be certain in which year the inflection took place.

The 20 segments of the 

Postal Services cost system 

are partly variable and 

partly institutional. The 

ones that are more than 

half variable will be called 

“largely variable” and the 

rest will be called “largely 

institutional”. All things 

being equal, growth in 

volume would be expected to increase the largely variable cost segments and decreases in 

volume would be expected to have the opposite effect. The impact of the doubling of volume 

from 1980 to 2000 on attributable cost was greatly mitigated by the introduction of 

worksharing in 1976, which profoundly reduced the work content (or unit attributable cost) of 

the new volume. Lower prices and other advantages of worksharing led to a huge increase in 

third class mail (now called Standard mail), which has the lowest work content of all mail 
6

products.6 Worksharing also greatly reduced the work content of First Class mail.7By 2004, the 

Postal Service was saving over $14 billion annually from worksharing because it reduced

attributable costs by the roughly that amount. Total Postal Service costs were $66 billion in 

2004. They would have been about $80 billion with the same volume without worksharing. 8 

Thus, worksharing greatly reduced the growth in the attributable cost of the mail stream. This,

in turn, reduced the impact of the volume growth on attributable costs.

Weighted volume is of interest because it combines the change in volume and the change in 

mail mix into a single 

variable. Figure 4 displays 

the growth of total volume 

and the highly correlated 

growth in weighted volume 

from 1972 to 2013. In the 

period before about 2000, 

the rate of weighted volume 

growth was much less than 

the rate of volume growth

because of the decline in the 

average unit attributable cost of the mail mix. Weighted volume apparently peaked in the year 

2000 and then declined, as volume growth leveled out in response to increasing use of the 

Internet, the recession of 2001, the anthrax scare, and 9/11. Both volume and weighted volume 

 

6

Third class mail volume tripled from 1980 through 2000, far out pacing the 56 percent growth of all other mail 

categories. Third class was 29 percent of the mail in 1980, but by 2000 it was 44 percent. This was caused by, 

among other factors, a lowering of the sender’s total cost of mailing, an increased ability to target, and the 

development of a third- party mail industry that had an incentive to sell advertising mail to advertisers.

7

In 1980 workshared First Class volume was 11 percent of total First Class letters. By 2000, it was 47 percent.

8

“Worksharing: how much productive efficiency, at what cost and at what price.” Cohen, Robinson, Waller and 

Xenakis; edited by Crew and Kliendorfer; Progress Towards Liberalization of the Postal and Delivery Sector, 2006, 

Springer.
7

turned sharply negative with the great recession of 2007. In 2013, the weighted volume of the 

Postal Service appears to be about at the level of 1985 when total volume was 140 billion.9

1980 to 2000

Figure 5 displays the percentage of total costs that were institutional costs from 1980 to 2000. 

The trend line shows that 

they decreased about 3.5 

percent. The corresponding 

percentage increase in

attributable costs is not 

nearly as much as a 

doubling of volume might 

suggest. The year to year 

fluctuations around the 

trend line, including a big 

dip in the percentage of 

institutional costs between 1986 and 1991, will be examined in Section 5. 

2001 to present

After 2000, when total volume began to level off and then decline, First-Class single-piece 

volume decreased the most. 10 This had an effect similar to the increase in worksharing in 

reducing the average unit attributable cost of the mail mix because First-Class single-piece has 

considerably more work content per piece than presort First-Class or Standard mail. 

Coincidently, a marked trend of increasing productivity also began in 2000 and which continues 

to this day. This can be seen in Figure 6. It has served to reduce costs primarily in the largely 

attributable mail processing and in-office delivery cost segments and associated piggyback cost 

 

9

Today the Postal service handles far more parcels than in 1985 and they increase weighted volume more than 

other products. On the other hand, single- piece First- class was a much larger fraction of Postal volume than now.

10 First- Class single- piece volume declined from 52 billion pieces in 2000 to 22 billion in 2013, a 57 percent 

decline, while total volume declined from 208 billion pieces to 158 billion pieces, a 24, percent decline.
8

segments. Productivity has had much less impact on the largely institutional street delivery 

segment. Thus, productivity 

has, on balance, served to 

increase the percentage of 

institutional costs throughout 

the period. Between 1980 and 

2000 productivity growth had 

been negligible and had little 

effect on the ratio.

11

Because volume growth at 

first flattened and then turned 

negative after 2000, it no longer offset the impact of the declining average unit attributable 

cost of the mail. Over this same time, productivity accelerated, which also caused institutional 

costs to increase as a percentage of total costs. This can be seen in Figure 7 where the trend 

line is upward sloping. 

2007 to 2013

In contrast to market 

dominant products which 

have a relatively low unit 

attributable cost, 

competitive products have 

a relatively high unit 

attributable cost. In recent 

years, competitive product 

volumes have expanded. 

Some products were

 

11 The sudden uptick after years of moribund growth suggests that its cause(s) should be the subject of study.

y	=	0.0035x	-	6.7157	

R2	=	0.64433	

36.0%	

37.0%	

38.0%	

39.0%	

40.0%	

41.0%	

42.0%	

43.0%	

2001	 2003	 2005	 2007	 2009	 2011	 2013	

Figure	7:	Percent	Ins tu onal	(No	RHB)	
9

transferred from the market dominant to the competitive category. Competitive products have 

also grown organically at a substantial rate.12 Organic growth of pieces with a relatively high 

level of attributable costs increases the attributable/institutional cost ratio, while the volume 

loss of market dominant products decreases it. This is somewhat like the two regimes observed

prior to, and after, 2000, as seen in Figure 2. The current decline in attributable costs of the 

market dominant products, and of the attributable costs of the Postal Service as a whole,

resembles the post-2000 period. The growth of the total attributable cost of the competitive 

products, on the other hand, resembles the pre-2000 period. Currently, competitive products 

account for about a quarter of total Postal Service attributable costs. As market dominant 

volumes continue to drop and competitive organic volumes continue to grow, the two may

have largely offsetting effects on the Postal Service variability ratio. But for now, the variables 

that negatively affect weighted volume (declining volume, declining attributable-cost volume 

mix, and increasing productivity) are likely to remain in place for the foreseeable future. Thus, 

the ratio can be expected to continue in its current direction of an increasing percentage of 

institutional to total costs. 

It will be seen in the Section 4 that the percentage of total costs that are institutional has 

increased monotonically since 2008. However, this has been a period of improving finances for 

the Postal Service on an operational basis. The reason is that increasing revenues from 

competitive products have more than offset the revenue losses from market dominant

products. There is a large difference between the average unit revenue of the two groups of 

products. This has altered the traditional significance of the variability ratio, which only reflects 

costs.

 

12 By organic growth we mean growth of the products that have been previously designated competitive before 

new products were switched from market dominant to competitive.
10

4. The Impact of Exogenous Events on the Ratio

1980-2006

There have been many exogenous events that have affected the ratio since 1980. They include: 

the Congressional Omnibus Budget Reconciliation Acts (OBRA), restructuring costs, 

recalculating workers compensation liabilities, the PAEA mandate to escrow payments for 

future retiree health benefits (RHB), and accounting rule changes. 

With the 

assistance of PRC 

staff we examined 

the Postal Service 

financial 

statements since 

1980 to find the 

charges made to 

the income 

statement that 

would affect the 

ratio.13 Charges 

that were for 

prior years 

affected only 

institutional costs. 

These were 

examined to see their effect on the ratio. They are displayed in Table 1. The OBRA adjustments 

required the Postal Service to pay prior year costs for Retiree Health Benefits and pension COLAs.14

 

13Charges that failed to materially affect the ratio were ignored. 

14 The legislation required increases in the CSRS liability based on the annuitant COLA’s including interest and the 

premiums for RHB to be paid by the Postal Service from then on. They were a recurring cost from 1989 through 

2003. The retiree health benefits premiums continue to be paid by the Postal Service today. These costs vary with 

all labor and thus do not affect the attributable/institutional ratio.
11

Restructuring costs were primarily for early retirement bonuses. Debt refinancing charges were 

caused by the Postal Service refinancing its debt with the Treasury Refinance Bank. Workers 

compensation adjustments were caused by using new discount rates to calculate the present 

value of the liability and/or to update expected medical and compensation cost inflation. These 

were done on an occasional basis prior to 2008. The Postal Service has been making annual 

adjustments to the workers comp long-term liability since FY 2009 because of a change to an 

accounting rule.

Figure 8 displays the impact of the workers compensation adjustments in 1980, 1981, and 1982,

and the OBRA 

adjustments in 1991 and 

1993. The two sets of 

adjustments are the 

largest exogenous 

adjustment in the period 

before the year 2000. 

Red represents the data 

as given in the annual 

CRAs. Blue represents 

what the data would 

have looked like if the 

exogenous adjustments had not been made. 

2006-2013

The most significant exogenous effect on the ratio of attributable and institutional costs from 

2006 to 2013 has been the Congressionally-mandated Retiree Health Benefit Fund included in 

the PAEA. The Service was scheduled to pay about $5 billion annually into this 

fund. Subsequent actions by the Congress have altered the amount in the prior fiscal 

years. For example, the FY 2011 RHB was shifted to 2012 by an Act of Congress. These actions 

led to the saw tooth institutional percentage exhibited by the blue line in Figure 9. Subtracting 
12

the RHB effect, which is predominantly institutional, is shown by the red line. The trend line is 

still positive but with a lower slope than when RHB costs is included. For this reason, in all 

subsequent analysis, the RHB payments are subtracted from both the institutional and total 

accrued costs in the CRA. The green line is percent institutional without RHB and without 

Workers Compensation Prior Year Liability Adjustments. The trend lines in both Figure 8 and 9

show that the impact of the exogenous changes do not affect the direction of the longer term 

trends.

5. The Impact of Changes in Costing Methodology on the Ratio

The cost methodology that 

underlies each segment and 

component of the Postal 

Service CRA generally 

generates stable results from 

year to year. However, when a 

change does occur, it can alter 

the ratio of attributable and 

institutional costs for many 

years.

Some of the methodological 

changes affect only the distribution of costs to products, and have little if any effect on the ratio of 

institutional to attributable costs except, possibly, by altering the mail mix. Since 1998 these changes 

were adjudicated in rate and mail classification dockets. Since the adoption of new rules for changing 

cost methodologies in response to the PAEA, the methodology adjustments occur in rulemakings to 

change “Analytical Principles”, commonly called “car washes.” Over time, the methodological changes 

for calculating attributable costs in some cost segments have had small effects on the ratio of 

attributable and institutional costs (i.e., vehicle service drivers and purchased transportation). They 
13

make up 0.8 and 2.4 percent of total accrued FY 2013 costs, which is quite small compared such major 

cost segments as Clerks (19.0 percent) and City Carriers (16.7 percent). 

Adopting a new data source for analysis in 1989 increased Vehicle Service Drivers attributable costs 

from 16.0 percent to 47.3 percent. This contributed to a 0.5 percent increase in total attributable cost 

or, conversely, to a 0.5 percent drop in total institutional cost. The graph of percent institutional costs in 

Figure 8 drops to its lowest point 1989.

The Single Subclass method for attributing City Delivery Carrier Costs was instituted by the Commission 

in 1987 and abandoned in 2005. A new City Carrier methodology was proposed in

Docket R-2005-1 and adopted by the Commission that did not use Single Subclass attribution methods. 

Mail Processing attributable cost methods, which yield variabilities of nearly 100 percent, have changed 

little over the years. In Docket R97-1, the Postal Service proposed a new analysis of Mail Processing 

costs that resulted in an approximate 82 percent variability. The Commission did not adopt the 

proposed change, but the Postal Service continued to use the methodology in its cost estimates until 

2006. A comparison of the Commission’s and Postal Service’s cost estimates during the post 97 era 

provides a good indication of the impact that such an important methodology change would have had 

on the ratio of attributable and 

institutional cost. The actual 

impact of the City Carrier 

methodology changes, and the 

potential impact of the 

proposed Mail Processing 

methodology changes are 

examples of how major 

changes can impact the 

attributable and institutional 

share of costs and helps explain 

the 1997 dip in the percent institutional in Figure 10. 

City Carrier: Impact of Single Subclass Methodology
14

The Single Subclass methodology was adopted by the PRC in Docket R87-1. The data available for this 

study-- Postal Service Costs from 1980 to 2013 and PRC costs from 1997 to 2013-- provides a mechanism 

for exhibiting the impact of the Single Subclass methodology by examining the shift in the share of 

institutional cost between 1996 using Postal Service costs and 1997 using PRC costs. For example, the 

share of institutional costs calculated by the Postal Service (without Single Subclass attributable costs) 

for 1996 is 36.9 percent. The share of institutional costs calculated by the PRC for 1997 (with Single 

Subclass attributable costs) is 35.2 percent. The total difference of 1.7 percentage points in institutional 

share is not entirely due to the Single Subclass methodology since volumes are changing. But it is a good 

proxy. Adding the 1.7 percent to the institutional costs calculated by the PRC for 1997 to 2000, 

provides an indication of what the costs would have been without the Single Subclass methodology after 

1997. Figure 10 displays the effect of the change from 1997 to 2000. It can be seen that the slope of 

the trend line does not change our findings about the downward slope of the trend. Institutional costs 

decreased (and attributable costs increased) by a modest amount.

Of course, it would have been better to have actual costs calculated with the USPS methodology without 

Single Subclass attribution for the period after 1997. The problem is that in 1997, the Postal Service 

began using its mail processing cost methodology in all cost calculations and the impact swamped the 

effect of the Single Subclass methodology. 

Distinguishing the Impact of Applying Single Subclass Attribution Methods from the Impact of Applying 

the Postal Service’s Proposed Mail Processing Attribution Methods

An analysis of FY 1997 segment costs using the PRC and Postal Service cost methodologies can 

separately identify the potential impact of applying the Postal Service’s proposed mail processing 

attribution methods. Had the PRC adopted the Postal Service’s proposed methodology for attributing 

mail processing costs in Docket R-97-1 and had the Postal Service adopted the Commission’s Single 

Subclass attribution method, the ratio of institutional to attributable cost would have been much 

different. Table 2 compares of the total institutional share that using the Postal Service’s proposed 

attribution methods would yield s (with 82 percent Mail Processing variability and no Single Subclass 

attribution method) with the total institutional cost share that using the PRC’s attribution methods 

would yield (with almost 100 percent Mail Processing variability and the Single Subclass method). The 

Postal Service’s method estimates Mail Processing Variability at 82 percent, which increases the percent 

of institutional costs, and the PRC’s methods apply the Singles Subclass attribution methodology, which 
15

increases the attributable costs and reduces intuitional costs. The difference calculated reflects both

the increase in institutional costs using Postal Service methods and decrease when using the PRC’s 

methods. 

To analyze the impact of the difference in 1997, the PRC staff was able to provide a spreadsheet 

comparing the attributable and institutional costs for FY 97 using the PRC’s methods (Single Subclass 

attribution and 100 percent Mail Processing variability) and the Postal Service’s proposed methods (no 

Single Subclass attribution and 82 percent Mail Processing variability.) Applying the Singles Subclass 

attribution primarily affects Segment 7. Other segments are impacted by piggybacking Segment 7 

variabilities (Segments 12, 13, and part of 20.) Similarly, applying the 82 percent Mail Processing 

variability method primarily impacts Segments 3, with Segments 11, 15 and 16 impacted through 

piggybacking Segment 3 variabilities. 

The differences in total institutional costs that result from using Postal Service versus PRC costing are 

given in Table 3. As can be seen in Table 3, of the 8.3 percent difference, 5.2 percent comes from

applying the PRC’s Mail Processing variability assumptions, 1.7 percent is due to applying its Single

Subclass attribution methods, and 1.4 percent is due to other impacts.

The Big Dip in Percent of Institutional Costs from 1987 to 1992

The above discussion does not explain the significant dip in the institutional cost percentage between 

1987 and 1992. The data available for this time period are cost estimates applying the Postal Service’s 

proposed attribution methods and so does not reflect Single Subclass attribution methods. Applying 

Single Subclass methods would cause a dip in institutional cost percentages. A review of adjusted costs 

by segment identifies a big shift of City Carrier costs from institutional to attributable from 1987 to 

1992. Before and after this period, the City Carrier percent attributable is in the low 50’s. During this

period, however, the percent attributable is generally in the high 50’s, reaching 61.1 percent in 1988. 

The percentage of institutional cost is at its second lowest in 1988, and at its lowest in 1989, when the 
16

new Vehicle Service Driver methodology increased attributable costs by another half percent at the 

bottom of the blip. From 1986 to 1987, the City Carrier attributable percent rose from 51.6 percent to 

57.2, precipitating the observed downward blip in the institutional percent of total costs. The slump in 

total institutional percent abruptly ends in 1992 when the City Carrier percent attributable falls back 

towards the low 50’s value. Table 4 presents the actual attributable percentages for City Carrier costs

and total costs for 1986 to 1993, as well as total percent institutional. 
17

A portion of the dip in the share of total institutional costs could be due to changes in mail mix. But the 

increase is so large and so sudden in City Carrier attribution percentages that the drop in percent 

institutional costs appears to be the result of a change of methodology by the Postal Service. Research 

into the nature of the City Carrier attribution methodology changes between 1987 and 1992 found that 

starting in 1987, the Postal Service increased the amount of Elemental Load activity costs by more than 

$300 million. This increase ripples through the other cost segments, producing a total increase in City 

Carrier-related attributable costs t of over $400 million. Because elemental load costs are 100 percent 

variable, total attributable costs are increased by the $400 million transferred to elemental load. Total 

institutional costs are decreased by the same amount. In Figure 11, a $400 addition to institutional costs 

as a percent of total accrued costs for 1987 to 1992 has been added to the institutional costs calculated 

by the Postal Service to demonstrate the impact of this increase in elemental load costs on percent of 

total costs that are institutional. This addition removes a significant portion of the dip in the 

institutional percent.

Segment 18, Total 

Administrative and Regional 

Offices, also contributed to 

the overall dip in the 

institutional percentage with 

an unexplained drop in 

institutional Segment 18 

expenses in 1987 from 56.6 

to 48.9 percent of total costs. 

This impact of the Segment 

18 changes, if added to the 

institutional costs that result from applying Postal Service costing methods, would lift the blue curve in 

Figure 10 even more, but would still maintain its overall downward trend. Accounting for the impact of 

changes in attribution methods over the period 1987 to 1992 does not change our finding that the 

attribution percentage of total costs fell from 1980 to 2000 and rose from 2001 to 2013.

Summary of Sections 2 to 5
18

We have explained that over the period from 1980 to 2013 the variability ratio has been primarily 

influenced first by increasing volume and then declining volume and a decline in the unit attributable 

cost of the that volume due to the effects of worksharing, the growth of Standard Mail, and then the

decline of First Class mail. The post- 2000 growth in institutional cost percentage has gone hand in hand 

with deteriorating finances of the Postal Service. This trend may be arrested by the growth of 

competitive- product volume. We have also shown that neither endogenous changes (e.g., workers 

compensation adjustments and OBRA expenses) nor methodological changes (e.g. single subclass stops 

and elemental load changes) have changed the basic slope of the variability ratio for the two distinct 

periods when weighted volume was growing and then declining (i.e., pre-2000 and post-2000.) 

6. Infra-marginal and Fixed Cost Trends 2007 to 2013

In the Report on Task One of this series, Professor Panzar defines and discusses the concept of inframarginal costs. As he notes “Infra-marginal costs are not a standard economic cost concept. Essentially, 

they are defined by what they are not: i.e., they are variable costs that are not volume variable 

(marginal) costs.15"

Report 2 provides the first calculation of infra-marginal and fixed costs for the fiscal years 2007 to 2013. 

The analysis is with the Retiree Health Benefit (FHB) and Workers Compensation costs removed, since 

they are not under the direct control of the Postal Service. The intent of the analysis is to see how 

operating costs within 

the Postal Service’s 

control are behaving.

16

 

The volume of mail for 

this period was 

monotonically 

decreasing from 212 

billion pieces in 2007 to 

 

15 See page 11 of Report 1 The Role of Costs for Postal Regulation by John C Panzar Definition P2 for a 

mathematical definition. See Figure 1 on page 19 for a graphical representation of infra-marginal costs.

16 Report 2 analyses remove all Workers Compensation, which is reflected in the analysis in this section. The 

analysis in the other parts of Report 3 removes only prior year adjustments of Worker Compensation payments. 

The difference in terms of percent of institutional costs is less than 0.09 percentage points. 
19

158 billion in 2013. Figure 12 portrays the attributable, infra-marginal and fixed nominal costs versus 

volume for these years, as calculated in Case 2 of Report 2. As expected, the attributable costs drop 

monotonically. However, fixed costs rise slightly in 2011 and 2013 and infra-marginal costs rise in 2011. 

This demonstrated that attributable and infra-marginal do not move in the same direction in all years 

and fixed costs can change too. But much of this effect is removed when costs are plotted in real dollars 

as in Figure 13.

The percentage declines observed over this seven-year period are quite dramatic when examined in real 

2007 dollars as shown in Table 5. The drop even in fixed costs is a reflection of the dramatic 

increases in productivity and cost cutting activities of the Postal Service during this post PAEA period. 

See Figure 6 above.

Like many of the deviations from 

static patterns in the variability 

ratio pre 2007 period, the 

increases in fixed costs in 2011 and 

2013 can be traced to some onetime events. In this case, however, 

the events are not exogenous to 

the system, but are of the Postal 

Service’s making. This deviation in 

fixed costs can be traced for the 

most part to an unusually large 

increase in Segment 18 Administrative and Area Operations costs. See Table 6.

Further examination of the components of Segment 18 reveals that the component “Individual Awards”,

which are nearly all fixed costs, is the major source of the increase. In 2010 the individual awards costs 

were $5.9 million versus in 2011 they were $396.2. Also, Segment 16 fixed costs increased by $111 

million between 2010 and 2011. This increase was due overwhelmingly to two cost components-- “ADP 
20

Supplies and Services” and “Product Specific Supplies and Services. The reason for this increase in 

supplies and services is unknown, but may reflect a management decision to replenish after a period of 

financially- enforced frugality. 

The 2013 increases in fixed costs can also be traced to personnel actions. There was a spike of $166.6 in 

Segment 13, Employee Awards, and in Segment 18 $36.5 million in “Individual Awards” and $215.3 

million in “Miscellaneous Personnel Compensation.” These observations are not a criticism of these

personnel rewards. They merely point out that dramatically changing the amount awarded in a given 

year can cause fixed costs to deviate from an overall trend. There may be an incentive to defer awards 

in difficult financial years, and then to meet the deferred demand in a catch-up year to maintain 

employee relations. 

Understanding the reason for the infra-marginal cost changes moving in a different direction from 

volume is a bit subtler. In all years but 2011, total attributable and infra-marginal cost changes dropped 

as volume dropped. But in 2011, infra-marginal costs increased while volume continued to drop. 

The source of the 2011 anomaly is a combination of trends in Segment 3 (Mail Processing Labor) and in 

Segment 7 (City Delivery Carrier Labor) attributable and infra-marginal costs, particularly in the Segment 

7 components “Delivery Activities” and “Support Activities.” Segment 7 attributable and infra-marginal

costs increased in all years (except for infra-marginal costs in 2013). Prior to 2011, the decreases in 

Segment 3 infra-marginal costs offset the Segment 7 infra-marginal cost increases. But Segment 3 Mail 
21

Processing attributable and infra-marginal costs were decreasing each year to the point that in 2011 

they could no longer offset the Segment 7 City Carrier increases. After 2011, decreases in infra-marginal

costs in other segments combined to offset the impact of the increase in Segment 7 infra-marginal costs. 

Within Segment 7, the components “Delivery Activities” and “Support Activities” represent around 86 

percent of the total City Carrier Street Time Cost. The constant elasticity method is used to calculate 

attributable and infra-marginal costs of those components. One might expect, ceteris paribus, that 

these attributable and infra-marginal costs would increase and decrease together as volume changes, 

since attributable and infra-marginal costs are proportional for components whose infra-marginal costs 

are assumed to have constant cost elasticity.17 These cost types do move together in the same 

direction, but they move in the opposite direction of volume (except for infra-marginal costs in 2013). 

As shown in Table 7, attributable costs for the Delivery Activities cost increase every year in nominal 

dollars despite a volume drop. Infra-marginal costs also increase for every year except 2013. 

But in real 2007 dollars, the increase in infra-marginal costs is split between increases in three years and 

decreases in three years. 

The cause of the increase in nominal attributable and infra-marginal costs for Segment 7 City Carrier 

Delivery Activities and Support Activities is due to economies of scale lost in these postal operations. In 

2013, the economies of scale in delivery appear to be recaptured, possibly due to management 

efficiency improvements. Two factors that may cause these increases in attributable and infra-marginal

costs are: an increase in the more expensive to deliver competitive products, especially parcels 

requiring retrace, a drop in overall pieces per delivery. It should be noted that a drop in the percent of 

addresses receiving mail on routes, called coverage, could actually reduce fixed and infra-marginal costs 

in the current environment of declining pieces per delivery. Researching these and other possible 

causes is beyond the scope of this project. 

 

17 See Report 2 Section 2.3. Constant Elasticity Cost Function. The proportionality does not extend beyond the 

component or subcomponent level at which the costs are calculated with a constant elasticity function as the costs 

are aggregated across components and subcomponents. The mail mix and various elasticities affect the relationship 

between the cost types. See Report 2, following Table 5 for a discussion of this effect. 
22

The value in finding a deviation from expected changes in fixed or infra-marginal costs is that it indicates 

an unusual cost being incurred possibly due to management decisions concerning personnel payments, 

changes in operating plans, or changes in mail mix resulting in a greater share of pieces that are more 

costly to handle. 

7. Implications of Infra-marginal Cost Calculations on Average Unit Cost

The impact of changes in cost calculations is often judged in terms of the impact on average unit cost. 

For instance average unit cost was the primary measure of impact in the last major study of the quality 

of Postal Service data systems.18 Frequently, all institutional costs are assumed fixed in calculating 

future average unit costs as volume changes. However as just discussed, fixed costs are estimated to be

less than one half of institutional costs. This estimate is likely to improve over time as data limitations 

identified in Report 2 are addressed. 

This section uses an illustrative example to indicate the impact of different estimates of fixed cost on

average unit cost as volume changes. For most small changes in volume, the impact is minimal, but it 

can be large when the declines in volume are as great as those currently being experienced.

When economies of scale are present, average cost per unit decreases as volume, Q, increases. 

Conversely, as volume drops, unit costs will increase. This condition is characterized by a volume 

variability factor, or elasticity, that is less than one. Volume variable costs at volume Q equal total cost 

at Q times marginal cost. 

Two factors drive the changes in unit costs as volume changes: the magnitude of fixed costs and the 

elasticity of variable costs.19 And the results will be different depending on the magnitude of fixed costs. 

Institutional costs are frequently treated as fixed in the estimation of future costs. Report 2, however, 

calculates fixed costs that are considerably less than institutional costs. The following discussion of the 

 

18 See A.T. Kearney, Inc., Data Quality Study (Alexandria, VA April 16, 1999) performed under contract with the 

Postal Service in response to a request from the Congressional Committee on Government Reform and Oversight.

19 This assumes that costs can be represented as a fixed cost plus variable costs. Note that elasticity of variable 

costs and elasticity of total costs are two different things. See Report 1. Elasticity of total costs equal marginal 

costs divided by total average unit costs, which involves the fixed cost element. The elasticity of the variable 

portion of a function does not involve the fixed cost element. The value of the distinction is in creating an 

illustrative example to show the different effect of fixed and variable component which is affected by the elasticity 

of the variable component.
23

difference in unit costs of two postal systems with different volumes but similar cost functions is based 

on an illustrative example developed by Professor Panzar. For convenience of discussion we will treat 

the difference in the Postal Service’s operations at two different volume levels as the two different 

postal operators in Panzar’s initial formulation. Let i = 1,2 where i =1 is the Postal Service at 2013 

volumes Q1and i =2 is the Postal Service at a smaller volume Q2. Focusing on the effects of volume, Q, on 

per unit costs, AC, assume the Postal Service at both volume levels has the same cost function, C(Q). For 

exposition purposes, assume that the costs of the postal operator are given by the function 

C(Qi) = F + zQi

e

, 

where e is the elasticity of variable costs, F are fixed costs and z is a constant chosen to fit the costs20. 

Finally, assume that the volumes are a multiple x < 1 of each other so that Q2 = xQ1. 

This cost function has two sources of economies of scale, each of which may be working without the 

other. That is, there may be substantial economies of scale if fixed costs are large, even if e = 1. 

Similarly, if e <<1, there may be substantial economies of scale even if fixed costs are small (or even 

zero).

Letting AC = average costs gives

 

 

 

 [ 

 

] 

 

 

 

 by substitution and similarly

 

 

 

 

 

 

 

 

 

 

since = x 

and subtracting the two gives

 

 

 

[ 

 

 

] 

 

[ 

 

] by substitution and combining terms in [ ].

The unit cost difference between a “large” and “small” post depends upon both the magnitude of fixed 

costs and the elasticity of variable costs.

 

20 Throughout the following example, e does not represent total cost elasticity. It is only the elasticity of the 

variable portion of the cost function. This is consistent with Professor’s Panzar’s presentation in his report on Task 

1. See page 26, equations (27) and (28).
24

Also, let Institutional Costs = I, Volume Variable Costs = VV, Marginal Cost = MC, and Fixed Cost = F.21

Then for this cost function formulation

MC = ezQe - 1 the first derivative of C with respect to Q,

VV = Q * MC = Q * ezQe - 1 = ezQe  

I = C – VV = C – ezQe = C – e(C – F) since C = F + ezQe or C – F = ezQeso, continuing

I - C =– e(C – F) or 

C – I = e(C – F) so

e = (C – I)/(C – F) by rearranging the terms to isolate e. 

22

Benchmark cases can be used to exhibit the influence of these factors as volume drops. If C = I, then e

equals zero, and vice-a-versa. By direct substitution in the cost function with e = 0, gives 

C = F + zQ0 = F + z, and since C = F when Q = 0, F = C and z = 0.

Looking at the ratio of average costs at the two different volumes then gives

 = [ 

 

 

 

] [

 

 

 

 

] = 

 

/ 

 

 = = /x = 1/x since z = 0 and

 = (1/x) . 

Assuming that all costs are fixed is an extreme example since Report 2 shows that F is actually closer to 

20 percent of all costs. As x decreases from one, average unit costs, increases inversely 

proportional to the Postal Service’s unit cost in 2013, . For example, if the average unit cost for 2013 

is 33 cents then the estimated costs would be 41.25 cents if x = 0.8 corresponding to a 20 percent 

decrease in volume. This would be slightly more than a 26 percent increase in average unit costs. 

 

21 These cost elements are all known amounts from annual CRA reports and are all introduced here for the 

purposes of creating the illustrative example.

22 Note that e is the elasticity of the variable portion and not the elasticity of C which is marginal cost of C divided 

by unit average cost.
25

At the other benchmark extreme, assume that F = 0, then substituting in the above general form for e

gives

e = (C – I)/(C – 0) = (C – I)/C = 1 – (1/C) 

 = [ 

 

] [ 

 

] = [ 

 

] [ 

 

] = x

e-1 

= x

(1 - I/C) - 1 = x-I/c or

 = x

e-1 

If the 2013 unit costs are taken as 33 cents then the estimated unit cost at 80 percent of the 2013 

volume is 36 cents a 3 cent or 4.4 percent increase. 

In both benchmark examples, a drop in volume results in an average unit cost increase. For values of 

fixed costs between 0 and total institutional costs, i.e., 0<F< I, an illustrative numerical example provides 

further insight into the respective roles of fixed costs and elasticity on average unit costs.

Consider i = 1 as the Postal Service with the 2013 volume, total costs and institutional costs. Further, 

assume that fixed costs equal institutional costs. Then, using the above equation for e, with I = F, gives 

e = (C-I)/(C-I) = 1 

Fitting the cost equation to these values requires that z = 0.24. 

Then the growth in average unit costs due to a 3, 5, 7 etc. percent loss from 2013 volumes is given in 

Table 8 and Figure 14. The third row reflects the effect of the fixed costs on average unit cost increases 

due to the percent loss in 

volume given in the 

second row. The fourth 

row reflects the effect of 

the elasticity, which in 

this case is absent 
26

because costs are constant. These are total average unit costs so do not reflect attributable or inframarginal costs.

As volume drops by 5 percent, the unit cost increases by 0.87 cents due to the fixed costs. Note that the 

elasticity component does not come into play in this case. Also, the fixed cost component of the 

difference is the same shorthand assumption frequently made in calculating the change in average unit 

costs; i.e. treating all institutional costs as fixed and calculating only the effect of the fixed cost.

Now assume that the fixed costs are one half of the 2013 institutional costs. Continue to use the 2013 

volumes, total costs and institutional costs. Then calculating e with the above formula gives a new 

elasticity of 

e = (C – I)/(C – 1⁄2*I) = 0.74 with 2013 total and Institutional Costs

With a value of z equal to 41.74, the assumed cost function approximates the 2013 Postal Service costs. 

The calculated unit costs for different volume losses are given in Table 9 and Figure 15, which has a 

much smaller slop increase as volume drops. When volume loss is 5 percent of 2013 volume, the unit

cost increases 0.86 cents, with 0.44 cents due to the fixed cost component and 0.43 cents due to the 

elasticity component. This is also the increase when Fixed Cost equals Institutional Cost. But the effect 

is due to the fixed component. 
27

This indicates that, for volumes 

losses less than 10 percent, the 

simplistic assumption of fixed 

costs equal institutional costs 

approximates the more realistic 

calculation of fixed and 

elasticity effects with fixed 

costs at half of institutional 

costs. 

These are modeled costs with 

special assumptions. In reality, 

unit costs can behave quite differently due to changes in mail mixes, productivity and other factors. 

Between 2012 and 2013, volume decreased over SPLY from 2007 to 2013, but average unit costs in 2013 

dollars decreased in 2007 and 2013. The SPLY percent change in average unit costs in the other years 

was positive, but at various rates relative to volume decreases as given in Table 10.