EPA-600/5-74-033
November 1974
Socioeconomic Environmental Studies Series
The Economic and Environmenta
Benefits from Improving Electrical
Rate Structures
£
LU
(3
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development,
Environmental Protection Agency, have been grouped into five
series. These five broad categories were established to
facilitate further development and application of environmental
technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface
in related fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the SOCIOECONOMIC ENVIRONMENTAL STUDIES
series. This series describes research on the socioeconomic impact of
environmental problems. This covers recycling and other recovery
operations with emphasis on monetary incentives. The non-scientific
realms of legal systems, cultural values, and business systems are
also involved. Because of their interdisciplinary scope, system
evaluations and environmental management reports are included in this
series.
This report has been reviewed by the Office of Research and
Development. Approval does not signify that the contents
necessarily reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for use.
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EPA-600/5-7^-033
November 197^
THE ECONOMIC AND ENVIRONMENTAL BENEFITS FROM
IMPROVING ELECTRICAL RATE STRUCTURES
By
Mark Sharefkin
Contract No. 68-01-1850
Program Element 1HA093
ROAPNo. 21-AQL/03
Project Officer
Roger Don Shull
Washington Environmental Research Center
U.S. Environmental Protection Agency
Washington, D.C. 20460
Prepared for
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price $2.65
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ABSTRACT
Quantitative estimates of the internal cost savings to be
derived from changes in the pricing of electric power are
devised and evaluated. The econometric literature on elec-
tricity demand is surveyed, and elasticity values are selec-
ted which are parameters for the overall benefit measures.
A method for using reported utility data to estimate the
cost of delivered power--at the system peak and off the sys-
tem peak, and for each customer class- is devised. Data on
five electric utilities is used to make estimates of the
potential benefits from improvements in the pricing of elec
trie power, for each customer class in each system. The
estimated potential benefits are sufficiently large to
merit load curve studies by block for residential customers,
Such studies are necessary preliminaries to a definitive
assessment of the proposals for so called rate inversion.
11
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CONTENTS
Abstract
List of Figures
List of Tables
Acknowledgements
Executive Summary
Sections
I Conclusions, Recommendations, and
Introduction 1
Conclusions 1
Recommendations 3
Introduction 4
Selection of Sample Companies 7
II The Demand for Electric Power 10
The Econometric Evidence . 11
Econometric Estimation of Elec-
tricity Demand: General
Problems 11
Residential Demand Estimates 26
Industrial Demand Estimates 40
III Some Relevant Features of the Internal
Cost Structure of the Electric Power
Industry 47
A Typology of Customers Based
Upon "Information" Costs 47
The Uses of the Typology: A Pre-
liminary Overview of Indicators
to be Estimated, and Cost Analy-
sis Required 52
The Reconstruction of Internal
Cost Functions: Short Run Mar-
ginal Costs 55
Offpeak Versus Peak Costs: An
Explicit Allocation of Capacity
Costs 67
Estimates of Peak Responsibility
Capacity Cost Recovery 82
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CONTENTS (Continued)
Section
IV The Pricing of Electricity: Indicators
of Potential Improvement 98
The Variety of Tariffs 100
Category I Indicators of Poten-
tial Pricing Improvement 107
Category II Indicators of
Potential Pricing Improvement 113
Category III Indicators of
Potential Pricing Improvement 144
Category IV Indicators of
Potential Pricing Improvement 146
V References 157
IV
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LIST OF FIGURES
No. Page
1 Short Run Marginal Costs, Potomac Electric
Power Company, 1972 58
2 Sample System Load Curves, Potomac Electric
Power Company, 1972 59
3 Welfare Gains from Peak Load Pricing 116
v
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LIST OF TABLES
No.
1 An Overview of the Central Economic Papers
on Electricity Demand 12
2 Variables* Units, and Notations Employed In
Econometric Studies of the Residential
Demand for Electricity l3
3 Selected Regression Results, Residential
Demand Equations 19
4 Residential Elasticity Estimates 32
5 Industry Regressions: Two Digit Industries,
1956 45
6 "Commercial and Industrial Elasticity Esti-
mates 46
7 A Typology of Electricity Customers 48
8 Short Run Marginal Costs of Generation,
Potomac Electric Power Company, 1972 57
9 Efficiency (in Fuel Terms) by Unit, Potomac
Electric Power Company, 1972 60
10 Monthly Peaks; Trial Repair Schedule 1,
Potomac Electric Power Coirtpany, 1972 63
11 System Load Peak by Month 66
12 SRMC(2), Trial Repair Schedule 1, Repair
Period I - January-February 67
13 Income Statement Data, Potomac Electric
Power Company, 1972 70
14 Functionalization of Operating and Mainten-
ance Costs, Potomac Electric Power
Company, 1972 71
15 Generation and Transmission Nonfuel Operd-
tion and Maintenance, Patomac Electric
Power Company, 1972 74
16 Cost of Capital: Rate of Return on Ratet
Base and Depreciation, Potomac Electric
Power Company, 1972 75
VI
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LIST OF TABLES (Continue^
No, Page
17 Electric Plant in Service, Potomac Electric
Power Company, 1972 77
18 Taxes Other Than Federal Income Taxes,
Potomac Electric Power Company, 1972 79
19 Summary of Functionalized Capacity Costs,
Potomac Electric Power Company, 1972 79
20 Crude Estimates of Allocation of Capacity
Costs Among Customer Classes, Potomac
Electric Power Company, 1972 81
21 Number of Hours in Peak Under Various
Periodizations 84
22A Initial Cost Recovery Cpmparisons: Genera-
tion Only, Potomac Electric Power
Company, 1972 86
22B Range of Total Peak Hours, and Corresponding
Approximate Total KWH Sales, Potomac
Electric Power Company, 1972 87
23 Transmission Capacity Cost Allocation,
Potomac Electric Power Company, 1972 89
24 Distribution Cost Allocation, Potomac
Electric Power Company, 1972 92
25 Summary of Allocation of Capacity Costs,
Potomac Electric Power Company, 1972 93
26 Imputation of Customer Class Load Curves,
Potomac Electric Power Company, 1972 96
27 Tariff Types and Cost Recovery Strategies 101
28 Deviation and Elasticity Ratios, Potomac
'Electric Power Company, 1972 110
29 Policy Implications of Table 28 111
30 Bands of Suggested Prices for Peak Season,
Potomac Electric Power Company, 1972 115
31 Illustrative Indicators of Potential Pricing
Improvement, Potomac Electric Power
Company, 1972 117
vii
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LIST OF TABLES (Continued)
No. Page
32 Bands of Suggested Prices by Season: Potomac
Electric Power Company, 1972 122
33 Bands of Suggested Prices by Season: Common-
wealth Edison Company, 1972 123
34 Bands of Suggested Prices by Season: Duke
Power Company, 1972 125
35 Bands of Suggested Prices by Season: New
York State Electric and Gas Corp., 1972 128
36 Bands of Suggested Prices by Season: Penn-
sylvania Power § Light, 1972 130
37 Peak Benefits by Season: Average Prices
Compared With Peak Prices Which Decrease
Peak KWH Ten Percent and With LRMC,
Potomac Electric Power Company, 1972 135
38 Peak Benefits by Season: Average Prices
Compared With Peak Prices Which Decrease
Peak KWH Ten Percent and With LRMC,
Commonwealth Edison Company, 1972 136
39 Peak Benefits by Season: Average Prices
Compared With Peak Prices Which Decrease
Peak KWH Ten Percent and With LRMC, Duke:
Power Company, 1972 137
40 Peak Benefits by Season: Average Prices
Compared With Peak Prices Which Decrease
Peak KWH Ten Percent and With LRMC, New
York State Electric and Gas,, 1972 138
41 Peak Benefits by Season: Average Prices
Compared With Peak Prices Which Decrease
Peak KWH Ten Percent and With LRMC,
Pennsylvania Power § Light Company, 1972 139
42 Net Peak Period Residential, Schedule Indi-
cators of Improved Pricing 143
43 Category III Indicators of Potential Pricing
Improvement 147
44 Potomac Electric Power Company, Demand Billed
Accounts for District of Columbia, Select-
ed Months of 1972 150
Vlll
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LIST OF TABLES (Continued)
No. Pag<
45 Load .Curve for a Single Industrial Customer,
Commonwealth Edison Company, 1972 151
46 Indicators of Potential Pricing Improvement,
Demand-Billed Schedules 154
IX
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ACKNOWLEDGEMENTS
The assistance of Mr. Joseph Kowalski in the empiri-
cal work on this project was invaluable. Mark Seidel
and Jon Goldstein, project officers at the Environ-
mental Protection Agency, contributed above and beyond
the call of duty. Seidel, the original project officer,
helped shape the study with his probing questions; and
Goldstein's careful reading of the draft final report
immeasurably improved the end product. Thanks are
also due to Lee Matthews, Katleen Weiss and Sylvie
Durand-Jansiac for the painstaking typing of the manu-
script and tables.
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EXECUTIVE SUMMARY
This is a study of the pricing practices of the electric
power industry, motivated by the importance of this industry
to any overall program of environmental management. The
generation of electricity is a major source of air and thermal
pollution; the siting of new electric power plants has been
a major focus of the preservation versus development contro-
versy, and a harbinger of the growing importance of the
land use issue. Both the level and pattern of utilization
of existing capacity, and the rate and composition of addi-
tional capacity, are therefore critical to environmental
policy.
Our laws and institutions are built around the presumption
that, unless there is good reason to believe otherwise,
markets and market-determined prices are the best arbiters
of both output and investment decisions. The rationale for
that presumption is very simple: under certain conditions,
market prices equal "social costs". Under these conditions
each consumer, in deciding whether or not to take an addi-
tional unit of the good in question, knows that he must pay
tjie full costs that society will incur in producing that
additional unit of the commodity. Markets and prices then
guide us to a situation in which each consumer (and there-
fore society) takes only as much of the commodity as he
(and therefore we) are willing to pay for.
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Two kinds of "conditions" are necessary to this result.
First, economies of scale must be exhausted with firm sizes
much smaller than market demand: otherwise one firm will
grow to dominate the entire market, and there will not be
any competition between firms. Second, there must be no
externalities, so that the costs to the firm of producing a
unit of the commodity reflect the full costs thereby imposed
upon society.
Both of these conditions are violated in the case of electric
power. This simultaneous violation has brought the issue
of electricity rates to the forefront of environmental con-
troversy. The first condition is violated by economies of
scale in the generation and distribtuion of electric power:
it is cheaper per KWH to supply more KWHs up to and beyond
the number of KWHs taken in large markets. Consequently, we
have devised the social institution of regulated monopoly:
electric power companies are given a monopoly of their ser-
vice areas, so that society may reap the benefits of scale
economies. And they are regulated--their pricing and invest-
ment deicions are subject to the approval of public authori-
ties --in order to spare us the potential dangers of. monopoly
power.
The second condition is violated by the familiar "external
diseconomies" of power generation--air and thermal pollution.
Some associated costs, for example the health costs of air
pollution, are not seen as costs by power companies, and
therefore do not enter into the determination of prices.
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The well-known solution to this second problem is to
"internalize" external costs: in the last example, this
requires adding the health costs of air pollution to the
internal production costs of the polluting firm. Health
costs will then be reflected in prices, thereby restoring
a rough equality between price and social costs.
The implementation of this simple prescription faces severe
difficulties of practice. For, as we have emphasized above,
electric power prices are regulated monopoly prices, set in
order to guarantee a "fair" return on capital. Consequently
it cannot be assumed that some simple adjustment of existing
prices will equate price and social cost. And there is a
further serious difficulty: the internal costs of power
production are rather complex.
A major source of that complexity is associated with the
"peak load" problem. In the early hours of the day much
system capacity is sitting idle, so that the costs which
an additional user imposes upon society are essentially
only the cost of the fuel required to generate enough
electricity to meet that user's demand. But at some hour
of the day the demands of residential, commercial and
industrial electricity customers will inevitably approach
system capacity. All customers taking power at those peak
%»
hours will, collectively, be imposing upon society the full
capital costs of system capacity. The costs of serving
these users therefore include both fuel (or operating) costs
and capital costs. .
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Our purpose in this study is to take two essential steps in
the direction of a rationalization of the pricing of elec-
tricity: first, an examination of the relationship between
existing prices and internal costs, and second, a quantifi-
cation of the potential benefits to be derived from the
redesign of rate structures. In this Executive Summary
we will begin with a highly simplified conceptualization of
the problem. Then, bit by bit, we will introduce the
complexities and data difficulties which have forced us to
imputation, approximation, or estimation. Finally, we
shall discuss the results of our empirical work, and the
policy implications of those results.
CONCEPTUALIZATION OF THE PROBLEM
Consider Figure 3 of the report text, reproduced below.
That figure illustrates the distortions which arise from
failing to charge different offpeak and peak prices for a
commodity subject to a peak load problem. A peak load prob-
lem arises whenever demand fluctuates much more rapidly than
the time in which capacity can be adjusted to demand. (In
the case of electric power, demand varies sharply over the
working day, while capacity takes years to plan and build.)
At the single price P, offpeak customers take KWHQ£^ v
and peak customers take KWHp , , with these quantities de-
fined by the intersections of the P line and the offpeak and
peak demand curves.
the problem with this method of pricing electricity is that
it is inefficient. Economic efficiency requires that every
customer pay the full incremental resource costs his consump-
tion imposes upon society, no more and no less. Depreciation
ES-4
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Peak Demand
Peak
Offpeak
sQffpeak Demand
KWH
Offpeak
ItWH
Peak
Figure 3. Welfare Gains from Peak Load Pricing
is a resource cost, and the peak load pricing problem is
essentially a problem in assigning responsibility for de-
preciation or the maintenance of capacity* A priori) it
may appear that because there is excess capacity during
offpeak hours, offpeak users impose no incremental capac-
ity gosts upon society. More generating capacity need not
be built in order to serve these users: in fact, equip-
ment could be allowed to deteriorate slightly, capacity
could be reduced, and offpeak demand could still be met.
Thus, it may appear that because capacity is not scarce
during offpeak hours, the price paid by offpeak users
should not include a charge for depreciation. Further,
it may also appear that since capacity must be maintained
in order to meet the demands of peak hour users, it is they
who must pay a charge sufficient to cover depreciation.
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This solution is not entirely correct. Depreciation takes
two forms: that associated with use and that which is in-
dependent of use. Any depreciation resulting from use
constitutes a resource cost imposed upon society by that
user. In the case of an electrical utility capacity is
scarce during peak hours, and if depreciation occurs when
electricity is supplied to offpeak users, then a scarce
resource has been used up, a resource cost has been imposed
upon society, and the price charged to offpeak users should
legitimately include a charge for this depreciation.
Obviously the same holds for any depreciation associated
with use by peak hour users.
The situtation is quite different for depreciation which
cannot be attributed to use. Since offpeak users are neither
contributing to such depreciation nor demanding that capacity
be maintained, they are not imposing a resource cost on
society, and the price which they pay should not reflect this
type of depreciation. However, if peak hour demands for
power are to be met, capacity must be maintained. Although
peak hour users cannot be said to be causing non-use depre-
ciation, their demand for electricity implies the need to
maintain capacity and imposes a resource cost on society-
Hence the price charged these peak users must be sufficient
to cover both use and non-use depreciation, normal return
on investment, and incremental operating costs.
Since most depreciation in the electrical utility industry
is not attributable to use, the efficient prices are
P0ffpeak to o£fPealc users, where PQffpeak is ectual to the
incremental operating costs of serving these users, and
Pp , to on peak users, where ?pea^ is the sum of incremental
operating costs and incremental capacity cost.
ES-6
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The shaded areas in Figure 3 represent the losses to society
from incorrectly pricing the commodity at P. At price P,
offpeak users are being denied consumption which they value
more than the resource costs (poffpeak) that consumption
would impose upon society, and AWQp is the magnitude o£ those
losses. Similarly, at price P peak users are being charged
less than the resource costs (Ppeak) they impose upon society
by their consumption, and the area AWp represents the social
gain available if current price P is raised to Pp^^* thereby
eliminating inefficient consumption. Correct pricing will
give net social benefits equal to AW^p + AWp.
DIFFICULTIES OF IMPLEMENTATION
«.
Implementation of this scheme runs up against many practi-
cal difficulties, and here we set out the most prominent,
together with some comments on their resolution.
Demand
In Figure 3, we have drawn two demand curves, one for the
offpeak hours of the day and one for the peak hours of the
day. The demand for electric power fluctuates over the 24
hour daily cycle, and we have taken as "the" peak period of
every 24 hour day that eight hour period in which the larg-
est KWH total is generated. (Electricity demand also ex-
hibits a seasonal peak, with average daily consumption
peaking in some month of the year. This seasonal peaking
problem will concern us later; our focus here is on the
daily peak.)
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In order to compute the potential welfare gains AWQp and
AWp, we need to know how much offpeak and peak demands
change as offpeak and peak prices change. The technical
term for the required measure of price sensitivity is price
elasticity: the information we require is offpeak and peak
price elasticities. But existing studies of the price elas-
ticity of the demand for electricity generally estimate the
price elasticity of total demand--offpeak plus peak demand--
and do not try to estimate the price elasticities of off-
peak and peak demand separately. We were therefore forced
to use the best of recent studies of overall demand elas-
ticity, and to assume that peak demand is independent of
offpeak price--atid vice versa. The latter assumption is
uncomfortable, especially in the long run, since there
would almost certainly be some shifting in temporal .pat-
terns of electricity consumption in response to relative
price changes. ^Moreover, it is the long runthe time span
in which capacity can be adjusted--that interests us most.
The welfare gain AWD in Figure 3 arises in part because
i * *
society is spared the incurrence of the costs of provision
of some inefficient capacity, and that capacity adjustment
can only be made in the long run. Note that were prices
off peak lowered so as to capture the welfare gain AWQp,
electricity constimptiSn offpeak would be increased--as
would be environmental degradation, the costs of which are
not counted in AW~p. For these reasons, we have, in 6ur
welfare gain estimates, used AWp, which can be Used without
reservation as a lower bound -welfare gain estimate* After
a survey of available econometric elasticity estiffiates we
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adopted those of Chapman, et. al., because of the exceptional
quality of their econometric work and their estimation, on a
comparable basis, of elasticities by customer class (residen-
tial, commercial, and industrial) and by state. Their long
run elasticity estimates are roughly equal to one.
Cost
In figure 3 we have drawn two horizontal lines at poffpeak
and Ppeaj,» and these represent the incremental cost of serv-
ing offpeak and peak users respectively. That simple repre-
sentation covers a multitude of conceptual and empirical
difficulties in the estimation of these incremental costs.
The offpeak incremental costs of delivering an additional
KWH to a customer are relatively easy to estimate, since they
are essentially the fuel cost of generating an additional KWH.
Strictly speaking, that cost is different from hour to hour,
for every electric utility has a stock of generating units of
various ages and sizes. Typically, the older and smaller
units are less efficient, and in order to minimize operating
cost, the units are brought on line in ascending cost order.
At any moment, the offpeak incremental cost of delivering an
additional KWH is therefore approximately equal to the genera-
tion costs of the least efficient unit operating at that
moment. Further, it costs more to deliver a KWH to a residen-
tial customer than to an industrial customer, since there are
energy losses in the low voltage distribution system serving
residential customers. But these differences are relatively
small, and we have taken average fuel cost as an approximate
measure of the offpeak cost of delivering a KWH.
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The peak incremental costs of delivering an additional KWH
to a customer are much more difficult to estimate, since
that requires the allocation of capacity costs among cus-
tomer classes. There is inevitably some arbitrariness in
these allocations, but our exploration of a range of reason-
able procedures led to little quantitative variation in re-
sults.
Pricing
Our purposes in making estimates of the costs incurred in
serving offpeak and peak customers of various types (residen-
tial, commercial and industrial) are two: first, to allow
us to compare present prices charged for each of these kinds
of service with the costs incurred in providing that service;
and, second, given that comparison, to suggest improvements
in rates--methods of pricing electricity- -rwhich will better
approximate price cost. We therefore turn to a summary of
our treatment of the pricing problem.
In Figure 3, a single horizontal line P represents the pres-
ent price of electricity. The reality is more complex; elec-
tricity is generally priced at a quantity discount, in so-
called declining block rates. Any customer taking a specified
amount of energy under a schedule is paying some definite mar-
ginal price and some definite average price, but he is not
paying any single price. In order to quantify his sensitivity
to price changes, we need to know what kind of changes he is
sensitive to --marginal, average, or both.
There is no firm basis for asserting that, e.g., residential
customers are responsive only to average prices o'r that indus-
trial customers will shift their time profile of electricity
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consumption in response to price differentials between peak
and offpeak. But a reasonable argument can be made for such
a typology of customers.
Assume that every consumer reacts optimally to the options
open to him. Then any consumer of electricity will allocate
time to the electricity consumption decision to the point
where marginal benefits of such time--the reduction in elec-
tric bill resulting from the incremental minute spent in
making the electricity consumption decision--just equal the
incremental costs involved (in this, case, the value of the
incremental minute in its next most valuable use). The out-
comes of this allocation decision process will be classified
in two dimensions: time differentiating versus time-undif-
ferentiating consumption decisions, and average price respon-
sive versus marginal price responsive consumption decisions.
Table 7 of the text sets out this typology, and is reproduced
below.
Table 7. A TYPOLOGY OF ELECTRICITY CUSTOMERS
Time
Undifferentiating
Time
Differentiating
Average Price Responsive
Marginal Price Responsive
I
III
II
IV
Customers in Category I have found it optimal not to distin-
guish between average and marginal prices in their electric-
ity consumption decisions. For these customers, the existence
of block rates is irrelevant, since they would make the same
^
consumption^decision at a flat price equal to the average
revenue they are currently paying. Customers in Category II
ES-11
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elect to pay the cost of differentiating between their con-
sumption on and offpeak by paying the additional costs of
metering peak and offpeak consumption separately. By assump-
tion, they are insensitive to any differential between aver-
age and marginal prices on peak, and to any differential be-
tween average and marginal prices off peak. They do distin-
guish between average peak period price and average offpeak
price.
Customers in Category III do not find it optimal to distin-
guish between peak and offpeak consumption, but they find it
optimal to distinguish between marginal and average price.
Finally, customers in Category IV find it optimal to distin-
guish between consumption in both dimensions: between power
taken off peak and at peak, and between average and marginal
prices paid for electricity.
So much for typology: which kinds of customers belong where?
There are no unambiguous guidelines. Thus, it is not entirely
clear that all customers on a given rate schedule belong in a
single category. Large residential users, for example, may
have some marginal price sensitivity and may therefore belong
in Category III, whereas very small residential users almost
certainly belong in Category I.
Our identifications of rate schedules with categories of the
above typology are as follows.
Category I
This category is the domain of small residential and commer-
i
cial users. The relevant question regarding possible improve-
ment in rate structures is then restricted by the'.assumptions
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that consumers in this category do not, for information cost
reasons, distinguish either marginal and average price or off-
peak and peak consumption. The only remaining policy question
is then as follows: how much "better" can we do by changing
the average KWH prices paid by customers on individual rate
schedules? For example, how much better can we do, in terms
of our welfare measures, by slightly raising the average price
per KWH paid by commercial customers, and by simultaneously
slightly lowering the average price per KWH paid by industrial
customers? To the extent that the derived quantitative mea-
sures are reliable, they indicate that available gains are neg-
ligibly small.
Category II
We will compute net benefit measures for all rate schedules of
the sample companies as if it were the case that customers are
average-price responsive--that they have found it optimal not
to distringuish between peak and offpeak consumption. For
residential customers, presently metered on. a KWH monthly or
bimonthly basis, this will require netting of the additional
cost of double-rate registers required to charge differential
fates off peak and on peak. A warning regarding the £ull spec-
trum of beiiefits and costs for double rate register metering
is in order: there is a potentially serious drawback to double
ratfe register metering of 6lipeak and peak hours. Should
service to a given area be interrupted and restored in any
time interval not a multiple of 24 hours, the correct setting
of the double rate register shall have been lost. It would
be necessary to meter on a KWH basis, taking the simple sum
of the offpeak and peak registers as the relevant number of
KWH, until the time at which the meter was read; at that time,
the reader could reset the device. The evaluation of this
problem is beyond the scope of this report.
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Category III
The prime candidates for Category III are large residential
users if it is assumed that, for some reason, there is no
possibility of differentiating between offpeak and peak usage
for these customers. Again, recall that all customers on a
given rate schedule need not necessarily fall into the same
category of our typology. Nevertheless, as we will see in
our analysis of Category I, there is little to be gained
from pricing changes which do not discriminate between off-
peak and onpeak consumption. However, there is still the
possibility of "implicitly" differentiating between offpeak
and peak, and our major estimate corresponding to Category
III is the estimation of an upper bound on the gains attain-
able from implicit differentiation. How might this work?
Suppose that some electric utility had a declining block
rate schedule with two blocks, with the tailblock lower than
the first block. Suppose further that tailblock customers
buy all their electricity on peak, while first block cus-
tomers buy all their electricity off peak. Then we can in
some measure simulate peak load pricing by raising the tail-
block and lowering the first block. Advocates of "rate in-
version" often argue for something like this, and we will
calculate a rough upper bound on the potential welfare gains
associated with one kind of rate inversion proposal.
Category IV
In Category IV we place our large commercial and industrial
users. They incur little incremental expense in differen-
.: I :
tiating betwen their consumption off peak and on peak, since
utilities-generally know the instantaneous load being pulled
... *
by their individual large customers, and those customers
ES-14
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generally know the loads they are pulling. Some of these
customers also have that information. Similarly, there is
little incremental expense to be incurred by a "switch" from
average price sensitivity to marginal price sensitivity: so
long as someone is watching the electric bill, the additional
cost of watching it in a slightly different way is negligible.
For these customers, a relevant benefit/cost question is:
what is the magnitude of the gains likely to be had from time-
differentiated pricing, e.g., a better matching of peak period
(perceived) prices and costs? Some technical problems make
this comparison less than straightforward. But we shall see
that it can be made, and that the attainable gains are probably
substantial.
External Costs and Welfare Gain Measures
All of the costs we have described are strictly internal to
the firm. The welfare gain measures depicted as the shaded
areas of Figure 3 are constructed on the assumption that the
horizontal lines PQ££ g^i, and Ppeai, reflect all the incremen-
tal costs of offpeak or peak consumption, and since lowering
the offpeak price will expand offpeak consumption and the
corresponding external costs, we cannot confidently assert
that we gain AWQp by such a change in price. But raising the
price of peak electricity restrains peak consumption, and
spares us both AWp in welfare loss and the associated external
costs. Consequently, the welfare gain measures we report are
our evaluations of AWp alone.
ES-15
-------
WELFARE GAIN ESTIMATES
Category I
The evaluation of several welfare gain measures subject to
the stringent assumptions defining this category--that cus-
tomers are average price responsive and do not distinguish
between offpeak and peak consumption--gave negligible bene-
fit estimates. This line of work was pursued no further.
Category II
Customers in this category were assumed to distinguish be-
tween offpeak and peak consumption, but not between average
and marginal price. In terms of Figure 3, we need PQ££ _ ^
and Ppeaj. for each customer class, and we take for demand
elasticities the average price demand elasticities reported
in econometric studies. For residential customers, we must
remember that additional metering costs will be imposed if
we distinguish off peak and peak, so that for this customer
class these costs must be netted from benefits.
For each electric utility and for each rate schedule, two
kinds1 of AWp were computed. The first of these measures is
the gain to be derived from a peak period price increase
which diminishes peak consumption by 10 percent; the second
is the gain associated with peak prices equal to full peak
costs.
The numerical results obtained are fairly consistent across
our sample of electric utilities. The estimate of AWp based
upon a 10 percent decrease in peak consumption was generally
a small dollar figure, of the order of hundreds of thousands
ES-16
-------
of dollars. The estimate based upon full peak cost was typi-
cally a much larger dollar figure, of the order of millions
or tens of millions of dollars. We believe that a reasonable
interpretation of this divergence is as follows. The analyst's
determination of the "true" figure somehow must attach weights
to these two bounds, and those weights are unavoidably judge-
mental. Our inclination, based upon our experience with the
cost data, is to favor the higher estimate: that expected
social returns to the full cost pricing of peak power are sub-
stantial.
Category III
Customers in Category III are assumed not to distinguish be-
tween offpeak and peak consumption, but to be marginal rather
than average price responsive. Large residential customers
are prototypical of this category. The best hope of simulat-
ing an offpeak versus peak price differential to these cus-
tomers is to exploit whatever correlation there may be between
monthly consumption and load pattern. It is widely suspected
that tailblock customers--customers with high monthly consump-
tion- -take a disproportionate amount of their electricity on
peak. Studies to test this hypothesis are only now being done
by many major systems, and some private communications of pre-
liminary results lend support to the idea.
In order to estimate the potential social gains from a seri-
ous attempt to use the block rate structure to simulate off-
peak-peak differentials, we have made an extreme assumption
and computed benefits on the basis of that assumption. We
assume that all tailblock consumption is on peak, and we esti-
mate the benefits associated with raising the tailblock price
to the level of the first block price. The proposal has been
one frequently advanced by advocates of so called rate inver-
sion.
ES-17
-------
For all electric utilities in the sample, the resulting wel-
fare gain estimates are of the order of millions of dollars.
The policy implications seem clear: the expected social
gains from the use of residential rate block load curve in-
formation to simulate peak period pricing are substantial.
Nevertheless, this method must be inferior to direct peak
period pricing via double register metering.
Category IV
Recall that customers in Category IV are assumed to be both
marginal price responsive and to be able to distinguish be-
tween offpeak and peak consumption. Estimates of the poten-
tial social gain AWp from correct pricing of peak electricity
can then be derived as follows. From the existing rate struc-
tures filed by the individual companies, we can determine what
commercial and industrial customers actually pay for power
taken during peak hours: this corresponds to a determination
of P in Figure 3 above. From our estimates of the cost of
providing peak power to these customers, we- have an estimate
of Pp , in Figure 3. And finally, use of our econometric
estimates of average price demand elasticities together with
the relationship between average and marginal price elastici-
ties gives us an estimate', by state and customer class, of
marginal price elasticities.
The evaluation of AWp by system, season, and customer class
is then routine, and the results are compiled in Column 9 of
Table 46. The dollar estimates of potential gain are large
for all systems. The policy implication is again clear: there
are large benefits to be expected from movement towards a sys-
tem of peak pricing of large commercial and industrial con-
sumption.
ES-18
-------
We conclude this executive summary with a brief recapitula-
tion of our conclusions and recommendations.
CONCLUSIONS
The major discrepancy between cost to the power company and
price charged the user is associated with the large differ-
ence between the costs of serving offpeak and peak customers
and the failure of existing rate schedules to reflect that
cost differential in different prices. Each customer class
(residential, commercial, industrial) has distinctive charac-
teristics which must be considered in evaluating proposals
for better reflecting the offpeak versus peak cost differen-
tial in prices. For all customer classes, there are probably
large net benefits to be derived from doing so.
For residential and small commercial customers, there are two
ways in which the price differential between offpeak and peak
power can be communicated to the customer. First, by double
register metering, the customer's actual consumption can be
metered separately off peak and on peak.
Second, customer load curve surveys can provide information
on the contribution of customers in the different blocks of
the system's block rate structure, and that information can
be used by the system to approximate an offpeak versus peak
price differential. Estimates of the potential benefits to
'' ' >i s
be derived indicate that both methods would be a substantial
"^
improvement over current pricing practice; direct double reg-
ister metering, a "first-best" peak pricing method, is pref-
erable to "second-best" methods based upon rate block load
curves.
ES-19
-------
For large commercial and industrial customers, the change-
over to a pricing system reflecting the offpeak versus peak
cost differential would not require major changes in utility
practice, since companies generally monitor these customers'
loads individually and on a half hourly or hourly basis.
Estimates of the potential benefits to be derived from such
a changeover indicate that they are substantial.
RECOMMENDATIONS
Two kinds of recommendations follow from our work. First,
there are policy recommendations which can be made based on
what can be learned from existing data. Second, there are
recommendations for improving the data base upon which all
rate making rests.
Residential and small commercial customers can and should be
metered with double rate meters. It is of particular impor-
tance that peak hour prices be brought into closer alignment
with peak hour costs.
Large commercial and industrial customers can and should be
charged rates which distinguish between peak hour and off-
peak hours.
For .all classes of customers, there are relatively simple
ways of quantifying the cost differential between offpeak
and peak power. A quantification of this difference should
be required in rate proceedings before public utility com-
missions, and it should be incumbent upon a system applying
for a rate increase to demonstrate that there is no better
i
way to reflect the offpeak versus peak hour cost'differen-
tial in prices.
ES-20
-------
Public service commissions should require that companies do
the demand elasticity studies that can easily be done with
data every system accumulates in the course of time, i.e.,
customer bill histories.
Public service commissions should require that companies do
customer class load curve studies, in order to establish the
contribution each customer class makes to the system peak in
each season.
Public service commissions should require that, if the block
rate structure based upon monthly consumption is to be re-
tained for residential and small commercial customers, then
the company in question do customer surveys of customers in
individual blocks, so that the contribution of each block to
the system peak can be established.
ES-21
-------
SECTION I
CONCLUSIONS, RECOMMENDATIONS AND INTRODUCTION
CONCLUSIONS
Central to the evaluation of any industry is the relation-
ship between internal production cost and selling price:
price, the amount a potential consumer must sacrifice for
another unit of consumption, must equal the cost that pro-
duction of that last unit imposes upon society, otherwise
resources are being misallocated.
In the case of the electric power industry, there are two
special circumstances which make the comparison of price and
social cost somewhat difficult. First, there are high exter-
nal costs associated with the thermal generation of electric
power: thus air pollutants impose health costs, but those
health costs are borne by individuals and not by the power
company. Second, electric utilities are regulated monopolies
whose price and investment policies are publicly regulated,
so that even the relationship between price and internal cost
is not what it is in competitive sectors of the economy.
This study was motivated by the first of these two special'
circumstances, i.e., high external costs. But our emphasis
is almost entirely upon the second--the fact of regulation--
and our objective is a better understanding of the relation-
ship between price and internal cost. We believe that a clear
understanding of that relationship is an essential step to-
wards the rationalization of pricing and capacity decisions
in the industry.
-------
We find that the major discrepancy between internal cost and
price arises from the sharp cost differences between peak and
offpeak electric power and the failure of most existing elec-
tric rate schedules to reflect that cost differential. Each
customer class--residential, commercial, and industrial--has
distinctive characteristics which must be considered in eva-
luating proposals for reflecting that cost differential in
prices. For all customer classes, however, there are probably
large benefits to be derived from doing so.
For residential and small commercial customers, there are two
ways in which the price differential between offpeak and peak
power can be communicated to the customer. First, by double
register metering in which the customer's actual consumption
is metered separately offpeak and on peak. Second, customer
load curve surveys can provide information on the contribution
of customers in the different blocks of the system's block
rate structure, and that information can be used by the system
to approximate an offpeak versus peak price differential.
Estimates of the potential benefits to be derived indicate
that both methods would be a substantial improvement over
current pricing practice.
For large commercial and industrial customers, the changeover
to a pricing system reflecting the offpeak versus peak cost
differential would not require major changes in utility prac-
tice, since companies generally monitor these customers' loads
individually and on a half hourly or hourly basis. Estimates
of the potential benefits to be derived from such a changeover
indicate that they are substantial.
-------
RECOMMENDATIONS
Two kinds of recommendations follow from our work. First,
there are policy recommendations which can be made based
upon what can be learned from existing data. Second, there
are recommendations for improving the data base upon which
all rate making rests.
Residential and small commercial customers can and should be
metered with double rate meters. It is of particular impor-
tance that peak hour prices be brought into closer alingment
with peak hour costs.
Large commercial and industrial customers can and should be
charged rates which distinguish between peak hour and off
peak hours.
For all classes of customers, there are relatively simple
ways of quantifying the cost differential between off peak
and peak power. A quantification of this difference should
be required in rate proceedings before public utility com-
missions, and it should be incumbent upon a system applying
for a rate increase to demonstrate that there is no better
way to reflect the peak hour cost price differential in
prices.
Public service commissions should require that companies do
the demand elasticity studies that can easily be done with
data every system accumulates in the course of time: custo-
mer bill histories.
Public service commissions should require that companies do
customer class load curve studies, in order to establish the
-------
contribution each customer class makes to the system peak in
each season.
Public service commissions should require that, if the block
rate structure based upon monthly consumption is to be re-
tained for residential and small commercial customers, then
the company in question do customer surveys of customers in
individual blocks, so that the contribution of each block to
the system peak can be established.
INTRODUCTION
The Overall Framework
This study was undertaken in the hope of obtaining a more
dependable and quantitative grasp of a related set of prob-
lems critical to environmental management. At the center of
that set of problems is the pricing "policy" of the electric
power industry. It is no longer necessary to discuss the
importance of energy in general, and electricity in particu-
lar, in environmental management. Our concern is with one
possible dimension of that set of problems: the possibility
that they are either exacerbated or made more intractable or
both because of the way in which electric power is priced.
It is a well-known principle of welfare economics, now wide-
ly absorbed into the conventional wisdom, that perfectly com-
petitive markets guarantee a result--in terms of price, the
level of output, and the level of capacity in the industry--
which in some sense is the best' possible the optimal result.
Crudely, this means that no customer who values the particular
good or service at least as highly as the social opportunity
cost of satisfying his demand is left unsatisfied: that, at
4
-------
the margin, the last customer is paying exactly the costs he
imposes upon society for the incremental unit of output. The
usefulness of the competitive model in public policy analysis
arises because, in those situations requiring measurement of
departures from optimum performance. The model suggests those
policies most likely to nudge an imperfect market towards the
competitive outcome.
Turning to the electric power industry, which departures from
competitive industry structure are most likely to lead to
suboptimal performance? Electric power is a regulated indus-
try, and the conventional rationale for regulation rests upon
a feature of the industry which rules out a competitive indus-
try structure. Usually referred to as long run decreasing
average costs, the essence of this problem is that there are
economies of scale over the whole range of the market--that as
more of the market of the typical electric utility is served
by a single utility, up to the extent of the market, larger
plants with lower unit costs can be used, and the market
served at lower cost. It would impose needlessly .high costs
of power production upon consumers of electricity to allow
more than one producer of electricity to serve the market.
Thus our resort to regulated monopoly in the provision of
electric power. Next, the market failure associated with
external costs is of obvious relevance to the electric power
industry. The best known of these is the emission of parti-
culates and of noxious gases into the ambient air during the
process of combustion. To the extent that final product
price--in this case, the price of electricity to the final
user--does not adequately reflect the full social costs of
production, actual industry output can be expected to be
larger than the social optimum.
-------
The solutions to the departures from competitive optimum
which arise from long run decreasing costs and from external
costs have become almost as well known as the problems them-
selves. For the first, the welfare economist prescribes re-
gulated monopoly, with prices equal to marginal cost and the
resulting deficit covered by a subsidy or, if the enterprise
is constrained to balance its budget, so-called second-best
marginal cost pricing: prices which depart from marginal cost
so as to minimize the resulting distortion of consumption
patterns from optimum. And for external costs, the well-known
prescription is internalization. Through effluent fees or
equivalent devices, producers must be made to feel the full
social costs imposed by their production processes; prices,
communicated to consumers, become correct signals to those
consumers of the resource costs imposed upon society by their
consumption decisions.
It would seem that, in applied work, we need only examine
particular industries with these standards, and shape policy
recommendations in accord with these standardized correctives.
Sadly, things are infinitely more complicated, and especially
so in the case of the electric power industry. As elsewhere,
we do not have an accurate measure of the social costs of"the
environmental impacts associated with the industry as a whole,
let alone with particular companies or with particular plants.
As elsewhere, we do not have certain but rather only hazy know
ledge of demand conditions; worse, demand varies rapidly over
time--there is a "peak load" problem--so that our crude mea-
sures of demand are even further removed than usual from the
underlying reality.
But the applied welfare economist is used to this sort of ad-
versity. There is no excuse for defeatism. There can be no
-------
precise determination of "the" optimum of welfare theory.
But intelligent conceptual and empirical work can guide us
in the identification of inefficient aspects of present
policies, and can establish where the main chances for im-
provement lie.
That conceptual and emprical work proceeds through the body
of the report. In Section II, we review econometric work on
t.
electricity demand, with an eye less on a comprehensive re-
capitulation of this literature than on the selection from
that literature of a set of demand elasticities which, much
later in Section IV, enter directly into welfare estimates.
In Section III, we enter into the cost side of power produc-
tion, again with the same limited objective: the derivation
of cost measures required for those welfare estimates. Fi
nally, in Section IV, come the estimates themselves. The
remainder of this Introduction treats a problem of relevance
to every portion of the report, the selection of a sample of
companies used in the empirical work done in later Sections.
SELECTION OF A SAMPLE OF COMPANIES
Our sample of systems should be representative in at least the
foilowing senses:
Clearly it should be representative of the ownership struc-
ture of the industry. In 1970, the approximately 250 in-
vestor-owned systems generated roughly 80 percent of total
continental United States net generation. There are, of
course, publicly-owned systems with,significant generating
capacity, e.g., the Tennessee Valley Authority. But, our
focus in this study is upon pricing practices common to
public and private sectors of the power industry. We have
-------
therefore restricted our sample to Class A investor-owned
utilities, utilities having annual electric revenues of
$2,500,000 or more.
Further, our sample should be representative of the variation
in cost structure found within the industry. If we are to
measure the success or failure of the industry in tailoring
rates to cost, the full variation in cost conditions should
be represented. Two of many determinants of the cost struc-
ture of electric service are location and load pattern.
There are sharp regional variations in cost structure associ-
ated with the availability or unavailability of cheap hydro-
electric or cheap competitive public power. The nature of
the market--the mix of residential, commercial, and industrial
markets, and the specific time pattern exhibited by each of
these loads--varies between regions. For example, Southern
systems have in recent years typically become summer peak
systems, with maximum system load tied to the growth of the
air conditioning load.
Thus much of the variation across systems is ultimately re-
gional in nature, and our selection process was designed
accordingly. First, all Class A companies were assigned to
Federal Power Commission, in part, in order to divide the con-
tiguous United States into regions of roughly similar cost
and load characteristics. Next, the systems within each
region were cross-classified with respect to capacity, by
timing and size of system peak, and as combination* or non-
combination utilities. From this classification we selected
Combination utilities sett both gas and electricity; non-
combination electric utilities sell only electric energy.
8
-------
38 systems, distributed over the regions in rough conformity
with the distribution of system characteristics within each
region. All of those 38 systems were contacted, and the 10
systems which seemed most disposed towards cooperation with
the study then became the study sample.
In this report, full results are presented for five systems.
Even this small sample embraces considerable geographic di-
versity and therefore considerable variation in cost and
load conditions. This should be kept in mind through all
of what follows. We feel that a good sign that our pro-
cedures are relatively robust against many of the inevitable
arbitrary assumptions and imputations employed along the way
is the uniformity--in order of magnitude terms--of results
across the sample.
-------
SECTION II
THE DEMAND FOR ELECTRIC POWER
Any comparison or ranking of rate structures depends, ulti-
mately, upon knowledge of cost structure and of demand.
Implicit in every argument over rates is some disagreement
over either cost or demand or both. We would suggest that
the electric utility industry has, on the whole, better
explored the cost side than the demand side, and for obvious
reasons: utility expenses are registered as tangible dollar
outflows, while the economically relevant measure of demand
must be reconstructed from a quantity measure, instantaneous
system load.
In our discussion of rate making, we will necessarily resort
to a hedged dependence upon the results of econometric
studies of demand. The hedging is required, in part, by
Henri Theil's dictum that models are to be used, but not
necessarily believed. More seriously, the elasticities crit-
ical to rate making--the elasticities of (daily) offpeak and
peak demand for electricity--have never been directly esti-
mated. In view of these constraints, our purpose in this
chapter is not a comprehensive view of the econometric demand
literature but rather an assessment of the conceptual differ-
ences underlying the various, estimates, a defensible ration-
ale for our ultimate choice of elasticities, and a working
knowledge of their limitations.
10
-------
THE ECONOMETRIC EVIDENCE
In the course of our discussion of the econometric evidence
we refer to several tables summarizing the scope, method and
empirical results obtained in the major papers. Table 1 is a
cross comparison of markets studied and the nature of the data
base. Table 2 enumerates and defines the relevant variables,
and specifies the units in which they are measured. Table 3
provides a comparison of regression results obtained by the
various authors in estimation of constant-elasticity equa-
tions for residential demand, so that all variables are to
be thought of as natural logarithms: thus KWH (s,b;a) refers
to the natural logarithm of the number of thousands of KWH
sold, in period t, to customers in block b, of rate schedule
s, in region a. We proceed to a general discussion of the
numerous places at which an econometric study of electricity
demand must make essentially judgmental choices. Subsequent-
ly, in our discussion of the individual papers, we will
examine the choices made by some individual investigators.
ECONOMETRIC ESTIMATION OF ELECTRICITY DEMAND: GENERAL
PROBLEMS
To begin at the beginning, the theory of consumer behavior
tells us that demand for any commodity depends upon the
price of that commodity, upon income, and upon the prices of
all other commodities. A glance at that formulation suggests
the difficulties of application to the electric power case.
In order of descending intractability these are:
(a) The definition of price: electricity is charac-
teristically sold at block rates, i.e., at a
quantity discount, so that there is no one "price."
Stated in another way, marginal price and average
price differ, in contrast to the situation, for
11
-------
Table 1. AN OVERVIEW OF THE CENTRAL ECONOMETRIC PAPERS ON ELECTRICITY DEMAND'
to
Paper
(Fisher and Kay sen, 1962)
(Halvorsen, 1971)
(Wilson, 1971)-
(Baxter and Rees, 1968)
(Anderson, 1971)
(Chapman et. al., 1973)
(Smith et. al., 1973)
Model
Residential
Industrial
I;
pp. 11-13
ii;
pp. 13-16
Markets
Studied
Residential
X
X
X
X
X
X
Conraerical
1
X
X
Industrial
X
X
X
X
X
Data Base
a
o
rt
«J
U
M
V)
VI
in
o
M
U
47 State data
48 Contiguous
state data for
all variables
except MJTliMP
77 Cities
83 SMSA's
48 Contiguous
state data for
SIC primary
metals indus-
try
48 Contiguous
state data
7 New York
State utilties
rt
h
&
V
e
M
H
1946-1957
1961-1969,
inclusive, for
each state
1954-1964
Quarterly data
on 16 British
industry groups
31 states in
1958; 29 states
in 1962
1946-1970
inclusive
1951-1970
i«
M
h
«
MJTEMP time series (for
each state) developed as:
average of MJTEMP for
three largest cities in
that state
Utility price, quantity
data based upon utility
service areas
-
A unified energy supply -
demand model
MJTEMP series (for each
state) taken as mean
January temperature for
largest city in each
state
a
References are compiled at the end of the report.
-------
Table 2. VARIABLES, UNITS, AND NOTATIONS EMPLOYED IN ECONOMETRIC STUDIES
OF THE RESIDENTIAL DEMAND FOR ELECTRICITY
Variable
Unit
Definition
Quantity and
Other
Independent
Variables
KWHt[s,b;ot]
KWHt[s;ct]
KWHt[s,b;otl
Bt[s, b;a]
KWH/HHt[s;a]
KWH/Bt[s;a]
PCTAP3[t[ct]
103KWH per
period
KWH sales to customers in
block b of rate schedule s,
in the t^h period, in
region a
KWH sales to customers on
schedule s in period t, in
region a.
KWH sales per customer in
block b of rate schedule s,
in the t period, in rate
schedule a
KWH sales per household on
rate schedule s, in the tHl
period, in region a
KWH sales per customer on.,
rate schedule s, in the t
period, in region a
Percent of homes in service
area (roughly coincident
with region a) with at least
one unit of applicance
installed, in the tth period
-------
Table 2 (continued). VARIABLES, UNITS, AND NOTATIONS EMPLOYED IN ECONOMETRIC
STUDIES OF THE RESIDENTIAL DEMAND FOR ELECTRICITY
Variable
Unit
Definition
Dependent
Variables:
Own-Price
NOMREVt[s,b;a]
NOMREVt[s;a]
NMQREVt[s,b;a]
REREVt[s,b;a]
REREVt[s;a]
; RMQREVt[s,b;a]
FPCt[s,500,a]
Cents per
KWH
Nominal revenue per KWH for
customers in block b of
schedule s, in the till
period, in region a
Nominal revenue per KWH for
customers on schedule s, in
the till period, in region a
Nominal marginal revenue
for customers in block b of
schedule s, in the till
period, in region a
Real revenue per KWH for
customers in block b of
schedule s, in the till
period, in region a
Real revenue per KWH for
customers on schedule s, in
the tth period, in region a
Real marginal revenue for
customers in block b of
schedule s, in the till
period, in region ci
Federal Power Commission
typical bill for, e.g.,
customers on schedule s, in
the till period, in region
a, taking 500 KWH per month
-------
Table 2 (continued). VARIABLES, UNITS, AND NOTATIONS EMPLOYED IN ECONOMETRIC
STUDIES OF THE RESIDENTIAL DEMAND FOR ELECTRICITY
Variable
Unit
Definition
Dependent
Variables:
Prices of Close
Substitutes
Dependent
Variables:
Income
Other
Variables:
Demographic
NOMNGt[r;a]
RENGJr; ]
NOMDISt[a]
CPIEL,
CPING,
cpr
MFYt[o]
MHEMFGt[a]
DPIPCt[a]
POPt[a]
PCTURB [a]
Cents per
Therm
Dollars
per
Barrel
Dollars
per Year
Dollars
per Hour
Dollars
per Year
per Capita
Thousands
Nominal revenue per therm for
natural gas customers,on rate
schedule r, in the t
period, in region a
\
Real revenue per therm for
natural gas customers
Nominal price of distillate
oil, in the till period, in
region a
Consumer price index for
electricity in the t^- period
Consumer price index for
natural gas in the tth period
General consumer price index
in the t period
Median family income, in the
tM. period, in region a
Average hourly earnings in
manufacturing
Disposable personal income
per capita
Population of region a in the
ttn period
Percent of alll region living in
in urban areas in the t*h
period
-------
Table 2 (continued). VARIABLES, UNITS, AND NOTATIONS EMPLOYED IN ECONOMETRIC
STUDIES OF THE RESIDENTIAL DEMAND FOR^ELECTRICITY
Variable
Unit
Definition
Other
Variables:
Demographic
(continued)
Other
Variables:
Market
Characteristic
Variables
HS/HHt[a]
BPCt[s;a]
R/HSEt[a]
Bt[s,b;a]
Bt[s;ct]
PCTPVTt[a]
FUELSGt[a]
R/ISt[a]
Rooms per
House
Cents per
106 BTU
Number of houses per house-
hold, in the tlE period, in
region a
Number of customers per
capita on rate schedule s,
in the tM. period, in
region a
Average size of housing
units
Number of bills in block b
of schedule s, in the t£h
period, in region a
Number of bills in rate
schedule s, in the t
period, in region a
Percent of total region a
generation by investor-
owned electric utilities
Cost of fuel consumed, in
cents per 10s BTU, times the
percent of total net genera-
tion (in the tth. period) by
thermal plants
Ratio of total residential
KWH sales to total indust-
trial KWH sales
-------
Table 2 (continued). VARIABLES, UNITS, AND NOTATIONS EMPLOYED IN ECONOMETRIC
STUDIES OF THE RESIDENTIAL DEMAND FOR ELECTRICITY
Variable
Unit
Definition
Other Variables: TIME
Market Charac-
tertic
Variables (continued)
Other
Variables:
Climate
Elasticities
JATEMPt
JUTEMPt
DDAYSt[a]
S[s;P]
e[s,a;P]
Z[s;Y]
Z[s,a;Y]
Degrees F
Degrees. F
Time trend
Mean January temperature,
in the t period, in region
a
Mean July temperature
Degree Days
Elasticity of demand with
respect to average price for
customers on rate schedule s
Elasticity of demand with
respect to average price for
customers on rate schedule s
in region a (relevant where
the specification includes
shift variables distinguish-
ing states)
Elasticity of demand with
respect to income for cus-
tomers on rate schedule s
Elasticity of demand with
respect to income for cus-
tomers on rate schedule s in
region a (relevant where the
specification includes shift
variables distinguishing
states)
-------
Table 2 (continued). VARIABLES, UNITS, AND NOTATIONS EMPLOYED IN ECONOMETRIC
STUDIES OF THE RESIDENTIAL DEMAND FOR ELECTRICITY
Elasticities
(continued)
oo
Variable
e[s;NG]
e[s,ot;NG]
Unit
Definition
Cross elasticity of elec-
tricity demand with respect
to (average) price of
natural gas for customers on
(electricity)
Cross elasticity of elec-
tricity demand with respect
to (average) price of
natural gas for customers in
region a on rate schedule s
Lag parameter linking short
run and long run elasti-
cities
-------
Table 3. SELECTED REGRESSION RESULTS,
RESIDENTIAL DEMAND EQUATIONS
HALVORSEN
/KWH [s;a]\
An P rc-rvl = -1-238 - 1.138 AnREREV. [s;a]
\ t * ' J /
+ .0355 &nRENGt[s;a] + .6113
- .3474 JlnPCTURB [a] = .9245 AnJUTEMP [a]
I* L-
- .0151 AnTIME(t)
R = .9031
WILSON
KWH [s;a]
^ 1 = 10.25 - 1.33 £nFPC500^ [s ;a]
rurit L15 > UJ / t
+ .31 £nNOMNGt[s;a] - .46
+ .49 AnR/HSE [a] - .04 £nDDAYS [a]
L* L>
2
R = .566
19
-------
most consumption goods, of equality between mar-
ginal and average price. Which "price" is appro-
priate for the specification of an econometric
model of electricity,demand?
(b) The appropriate approximation to the universe of
all other goods: obviously all other goods cannot
be considered, and so it is necessary to limit the
goods considered to all other relevant goods, goods
which are either close complements of or close sub-
stitutes for electricity. This in turn devolves
into the examination of the disaggregated compo-
nents of residential consumption.
We turn to a discussion of these and related difficulties.
The Relevant Price Variable
Which price is appropriate to the specification of an econo-
metric model of residential electricity demand? The obvious
answer is: whatever price consumers respond to in making
consumption decisions. In asking what that price is, we
must be mindful that information is costly--that time spent
in the careful examination of a rate schedule has an oppor-
tunity cost. Casual empiricism suggests that few residential
consumers know the difference between the steps of their rate
schedules, and it has been suggested that utilities be com-
pelled to mail a copy of their rate schedules to residential
customers at least once annually, as some phone companies
are required to do. The situation is unlikely to change with
the advent of electricity-intensive housing styles, since--
as the evidence we shall review below makes clear--residen-
tial electricity demand is income inelastic and thus comes
to occupy a smaller portion of the family budget, while
20
-------
higher real incomes increase the opportunity cost of time
spent in making consumption decisions.
Average real residential price thus appears to be the appro-
priate price variable in the specification of the residential
demand for electricity. This is the variable that has been
used in most econometric studies of residential demand, so
that we can simply take over those estimates. Further, there
'is a simple relationship between average and marginal price
elasticities of demand for a commodity sold at a quantity
discount, so that we can construct an estimate of marginal
price elasticity from an estimate of average price elasticity.
A quantity discount relationship can be approximated by
ar(q) = pxq -1<3<0, (1)
where q is KWH purchased per month, ar average revenue, and
p and 3 are constants. Then the relationship between aver-
age and marginal expenditure is derived as follows: equat-
ing two necessarily equal expressions for total expenditure
gives
q ar(q) = / (dqjmr(q) (2)
where mr is marginal revenue. Substituting the above rela-
tionship for average price as a function of quantity, we are
left with
(3)
Differentiating with respect to q we have
(l+3)pq3 = (l+3)ar(q) = mr(q) (4)
21
-------
so that we may solve for marginal revenue in terms of average
revenue, obtaining
Now suppose that we have estimated the coefficients in an
average revenue demand equation by regressing the natural
logarithm of average KWH consumption upon average residential
revenue and other variables. Then the resulting coefficients
in the equation
An qt[s;a] = A + BAn ar [s;a] + . . . (6)
can be related to the estimates which must be appropriate to
the marginal-price demand equation as follows. Since
An ar(q) = An mr(q) An(1+3) (7)
substitution into the average price equation gives
An qt[s;a] = (A.-BAn(l+3)J + B An mr(qt) + -(8)
Thus, if -/B/ is the average price elasticity of residential
electricity demand, the "corresponding" marginal price elas-
ticity is -/B/: the two are equal.
Which Other Goods Must be Included?
Which goods are appropriately-close complements and substi-
tutes and therefore worthy of inclusion in the specification
of the demand function? Consider the spectrum of residential
uses of electricity: lighting, space heating, space cooling,
and water heating. With the exception of lighting, there are
22
-------
non-electric alternatives for the other functional require-
ments, e.g., gas and oil for space and water heating. But
the substitution of gas for electricity requires costly con-
version of consumer durable equipment. Residential demand
for electricity and fuels is ultimately demand for service
flows produced by use of fuels and electricity in conjunction
with "appliances" or "white goods" (broadly defined so as to
include lighting fixtures). This complementarity is the
novelty in the problem of electricity demand estimation, and
is ultimately responsible for the discrepancies between ear-
lier and later elasticity estimates. Consider the complica-
tions introduced into the usual conceptual distinction between
short run and long run demand elasticities. The short run is
that period in which consumer-owner capital, or appliance
stocks, cannot be varied in response to demand, so that short
run changes in demand in response to price changes are wholly
attributable to variations in the intensity of use of fixed
stocks of appliances. The relevant "other goods" for an esti-
mate of short run demand elasticity are, therefore, severely
limited: appliance stocks definitionally are fixed, and fuel/
electricity substitutions cannot proceed without changes in
appliance stocks. The appropriate specification of short run
residential electricity demand would seemingly include only
electricity price, and perhaps income, as independent variables.
The long run is that period in which capital stocks of consu-
mer durables are subject to adjustment in response to relative
price changes. A cost minimizing consumer would, in long
run adjustment, be producing the desired bundle of service
flows with least cost fuel-appliance combinations. An
appropriate specification of independent variables for the
long run demand for electricity would, therefore, necessarily
include measures of relative appliance prices, or, more
23
-------
specifically, the annual price of capital services for
various appliance types.
Short Run Versus Long Run Elasticities
In which elasticities are we interested, short run or long
run? Our interest is in the probable response of demand
patterns to changes in rate levels and structures, and in
valuation of the associated benefits. Short run elastici-
ties are, therefore, appropriate to the question of attain-
able benefits within a period where consumers cannot alter
appliance stocks and utilities cannot alter their capital
structure and the requirement of meeting the fixed costs
of that capital structure. Long run elasticities are rele-
vant to the evaluation of benefits attainable over the
"period" in which both producer and consumer capital struc-
tures can be adjusted. They are the benefits foregone by
inappropriate pricing policies.
Cross Section, Time Series and Pooled Models: Which
Elasticities do They Measure?
%
Demand studies have been don^ in cross section, in time
series, and with pooled time series and cross Section data.
Cross sectional studies employ data from a given year, with
the various data points corresponding to different locations;
time series data build upon the observations, for several
years, of data from one location, and pooling of time series
and cross section data is just what the name implies. Time
series data from many locations are thrown together to give
a larger sample than either pure time series or pure cross
section data alone could provide and, hopefully, improved
estimates of model parameters. Table 1 indicates that only
John Wilson's 1971 paper does an estimate in pure cross
24
-------
section, which lends a special significance to the results
of this paper. All other reported results are based upon
pooled time series and cross section data bases.
To begin, then, with the pure cross section case, the elas-
ticity estimates derived from such a study are properly to
be considered long run. For there is great heterogeneity of
cost conditions among the contiguous states, and state data
for any given year presumably reflect the adjustment to local
conditions which consumers have made over time. Since state
cost differences are persistent--due to factors such as the
presence or absence of cheap hydroelectric and/or public
power--cross section coefficients are, therefore, reason-
ably interpreted as based upon data on consumers in long run
equilibrium. The regional variation in cost is, as we shall
see, fortunate, for it enables us to get a significant esti-
mate of the price coefficient.
What of estimates based upon pooled data? Clearly there is
the possibility of interpretations of such data which conflict
with the interpretation of cross section results offered above,
Each year's data cannot reflect the long term adjustment of
consumption to price and other determinants, for clearly there
must be some adjustment of consumption to changes in short run
determinants--prices and incomes--in a time span smaller than
that in which complementary consumer durables (stocks and
appliances) can be adjusted. In a reasonably long time se-
ries of cross sections--say ten years, a period in which the
stock of consumer durables is considerably changed by re-
placement and additions--both will be present, with short
run adjustment of consumption to changes in price and in-
come accompanied by long run adjustment of consumer durable
stocks. The pressing problem in the interpretation of the
25
-------
results of cross section studies is therefore the disen-
tanglement of short and, long term effects. This, in general,
requires that some specific assumption regarding the mechan-
ism by which consumers adjust to disequilibrating changes in
independent variables be specified. However unpalatable and
oversimplified the specific models employed seem, it is of
some comfort that the form of the lagged response assumed
usually has little effect upon the relevant paxame^ter esti-
mates. Once a specific adjustment structure is assumed,
short run and long run estimates are functionally related.
Having thus enumerated the problems that beset all of the
efforts to date at econometric estimation, we turn to a dis-
cussion of the individual estimates of the residential demand
for electricity. Industrial demand estimates are often very
different methodologically, and are therefore treated sepa-
rately later.
RESIDENTIAL DEMAND ESTIMATES
Fisher and Kaysen
This study merits attention greater than that usually accord-
ed an econometric study more than ten years old, and for a
very simple reason: as a first and an exhaustive study of
the demand for electric power , it set the agenda for almost
all subsequent work in the field. Indeed, most of the im-
provements of later papers and we believe these have been
substantial--are to be found as throwaways in the Fisher-
Kaysen book, suggested but never pursued.
The hallmark of the Fisher-Kaysen approach is the recognition,
at every turn, that residential electricity is used in the
26
-------
home in conjunction with consumer durables--"white goods," or
appliances, with the definition of appliances stretched to in-
clude lighting fixtures--in order to produce desired service
flows. All behavioral models exploit this dependence in the
specification of the demand for electricity.
Fisher-Kaysen start from the behavioral hypothesis that, in
the short run, price and income are determinants of the level
of utilization of the existing stock of white goods, so that
demand may be written
KWHt[s:a] = C
,H
:t[-i]
REREV1
DPIPC. [a]| ***,?* YW [a] (9)
where we have transcribed the notation used in Fisher-Kaysen
into the unified notation introduced in Table 2; additional
variables required here are W. [a], the average stock of the
1 «-
i-1 white good possessed by the community during time period
t. The "price" variable is what purports to be a real price
variable, i.e., nominal average revenue deflated by the con-
sumer price index.
This is not the equation estimated by Fisher and Kay sen; they
first take (natural) logarithms, obtaining
[s;a] = CT + e[s;pj JlnREREVt [s;a]
e[s;y] AnDPIPCt[a] + Jin J(Wu[a]) (10)
and then take first differences, which gives
27
-------
JlnKWHt[s;a]-«,nKWHt_1[s;a] = C" + e[s;p](&nREREVt[s;a]
- £nREREVt_1[s;a]) + e [s;y] (JlnDPIPCt [a]
- JlnDPIPC , [a]) + white goods term (11)
Assuming that changes in the stock of white goods follow an
exponential growth path at a constant growth rate, first-
differencing "eliminates" the time dependence in the white
goods term, since
Jln(WoJlrt) - £n(WoAr^t"1)) = +r. (12)
Then from (11) and (12) we have
KWHt[s;a]
KWH
t-l[s;0]
= C
REREVt[s;a]
REREVt_1[s;a]
DPIPCt[a]
(13)
Note that this equation could almost have been written down
from scratch: it is a variant of the simplest model of short
run demand adjustment, with demand dependent upon own-price
and income. The growth of white goods is thus subsumed into
the constant term of the model of the above equation.
The short run elasticity estimates are thus estimates of a
fluctuation, assumed due to short run fluctuations in prices
and income, about a trend. The growth trend is deemed exo-
genous. The problem of disentangling long run and short run
elasticities is therefore "solved" in this case by assumption,
for price and income are not determinants of the long run de-
28
-------
demand for electricity. That long run trend is determined
solely by exogenous growth. This procedure makes us wary of
the Fisher-Kaysen short run estimates.
The situation is even more serious for the Fisher-Kaysen long
run elasticity estimates. Given the commitment of these au-
thors to the use of white good stock data--as opposed to some
indirect measure of consumer durable stock decisions, such as
appliance prices--the validity of the final estimate will de-
pend critically upon the quality of the stock data. It is
therefore unfortunate that the time series data on white good
stocks employed in the Fisher-Kaysen study is questionable.
This much they recognize. Worse, further examination of
their stock data indicates that it seems to be wrong in just
such a manner as to bias the price elasticity estimate down-
wards: that is, appliance stocks in states in which electri-
city is expensive seem to be overestimated, and appliance
stocks in states in which electricity is cheap seem to be
underestimated. For this reason it would seem unadvisable
to use Fisher-Kaysen elasticities in our subsequent work.
3
Chapman et. al.
This recent addition to the literature, presented at the
February 1973 NSF-MIT conference and available in preliminary
form from Oak Ridge National Laboratory, has one notable ad-
vantage of conceptual simplicity: the simplicity of the dy-
namic specification leads to a transparent and appealing re-
lationship between short and long run demand elasticity esti-
mates.^ The price paid for that simplicity is the somewhat
obscured relationship between the model specification and
behavioral assumptions. The Chapman et. al. specification
is
29
-------
KWHt[s;a] = (KWI^^ [s;a]) A [tthperiod factors] (14)
where only the time dependence of the multiplicative factors,
and not their precise interpretation, are relevant. Suppose
that there is only one multiplicative factor specified in the
form (F(t))£fs;Fl. Then in logarithms
£nKWHt[s;a] = A£nKWHt_ ^s ;a] + e[s;F] £nF(t) (15)
Suppose that in the first period there is a once and for all
(exogenous) increase in the factor F; serviceable examples
include an increase in the price of a substitute fuel or an
increase in the price of complementary goods, e.g., appli-
ances. Then the specification above tells us that the
corresponding first-period fractional change in consumption
is
= £s;- (16)
But this is the beginning and not the end of the story, since
the sequential adjustment specification leads to changes in
all future periods. Thus second-period consumption is deter-
mined by the two equations
AnKWHitsja] = X£nKWHQ[s;a] + e[s;F]£nF(y) (17)
JtnKWH2[s;a] = AJlnKWH! [s;a] + e [s;F] JlnF(y) (18)
so that the percentage change in second-period consumption
arising from a small change in F(l) is, after using tlie first
equation to eliminate AnKWH^sja] from the second and then
differentiating,
30
-------
3&nKWH2[s;aJ
In general, the percentage change in n period consumption
is
il^ (1 + X + X2 +...+ Xn"1)e[s;F]
if 0 < X < 1. The ultimate consumption change--the change as
n is taken to be very large--is thus
W l^T ^'^ C2l)
The conventional interpretation of the parameters--or, more
precisely, of econometric estimates of these parameters--is
as follows. e[s,f] is taken to be the short run elasticity
of electricity consumption with respect to determinant F, and
*l m^V T-TZ.~. """Jr..
i . \ £[s;F] the long run elasticity of electricity consump-
tion with respect to this same determinant. If annual data
is used in the estimation--and all time series estimates with
which we are familiar use annual data--the "short run" of
reference is the year. The long run is, strictly speaking,
infinity. The fraction of adjustment completed after n
periods is, as computed above,
-k_ -I
-L + A *- ... + A _ fl-A*)fl + X + "* X i
1
i - x
= (1 - X) (V^!!\ = 1 - Xn C22)
31
-------
Thus, for X close to zero, adjustment is rapid, and for X
close to 1, adjustment of consumption to long run equilibrium
values is slow: for X = .1, consumption has reached .99 of
its long run equilibrium value after five years, whereas for
X = .8, consumption has reached only .33 of its long run
equilibrium value after five years. As we shall see, the
estimates of X are all approximately .9, indicating a pro-
tracted period of adjustment.
Because of the plausibility and conceptual appeal of the
Chapman et. al. dynamic specification--and the specificity,
to individual states, of their price elasticity estimates--
their long run elasticity estimates are the ones we have used
in our later numerical evaluations of pricing improvement in-
dicators. We have compiled the Chapman et. al. estimates in
Table 4.
Table 4. RESIDENTIAL ELASTICITY ESTIMATES,
Chapman et. al.
System
State
Long Run (Average)
Price Elasticity
of Demand
Potomac Electric
Power Company
Commonwealth
Edison Company
Duke Power Company
New York State
Electric and Gas
Pennsylvania Power
and Light
District of
Columbia and
Maryland
Illinois
North Carolina
New York
Pennsylvania
-1.22
-1.22
-1.18
-1.24
-1.22
32
-------
These are the numbers which we actually use; accordingly,
our remaining discussion of residential demand estimates fo-
cuses principally upon their conceptual innovations, with
little attention to the numerical estimates they actually
yield.
Wilson8
John Wilson's 1971 paper differs from almost all of the other
econometric demand estimates, and in several important dimen-
sions. The data base is purely cross sectional, so that there
is not question of distinguishing short run and long run ad-
justment of consumers to local conditions; the regression
analysis ideally can isolate the long run effect of each of
the variables upon consumption. How, we may ask, does this
square with the underlying reality assumed in the estimation
of the Chapman et. al. models? Or, put another way, what com-
parability is there between a "long run" elasticity estimated
in pure cross section and the "long run" elasticity estimated
from a pooled sample of time series and cross sections with a
specific dynamic adjustment mechanism assumed? In general,
the question is quite complex. Here, it may help to think
along the following lines for specific equations which we
wish to compare. The pure cross section and time series
studies might be contrasted as based, respectively, on the
following data:
Variables
Dependent _ Independent Data Base
Pooled &nQt[a] ^nQt_1[a], t = 1, 2,.
AnF[t;a] a = 1, 2,.
33
-------
Compare the equations to be estimated.
Pure Cross
Sectional ~^t [a] = C + Y *nFIVaJ + '' « = 1, 2,...
o
Pooled AnQt[a] = 6 + XAnQt_1[a] + wAnF[t;a]...
The comparison indicates that, if we consider only the t = t
cross section from the pooled sample, then the lagged term,
its coefficient and the constant term collapse into one over-
all constant. Estimation of this cross section alone is com-
pletely equivalent to estimation of the pure cross section
model. What then is the relationship--in magnitude and re-
liability- -between estimates of the all-important elasticity
parameters in the two models? Suppose, for the sake of expo-
sition, that the general "causal factor" F(t;a) is taken to
be the average real price of electricity. Then the differ-
ence between the parameter estimates Y and --rrp the respec-
tive "long run" elasticity measures, depends upon the corre-
lations between the lagged consumption variable and the price
variable.. Since consumption has grown almost exponentially
over the postwar period, while average real price has, de-
pending upon the measure used, either declined or remained
constant, the correlation between lagged consumption and
average price variables is probably extremely small. We
therefore might anticipate that price elasticity estimates--
Y and -J-TX" ~~should be of comparable magnitude. However, we
know there are strong correlations between income and con-
sumption measures over the relevant period, so that cross
sectional and pooled estimates' of comparable income elasti-
city parameters might be expected to differ substantially.
To be somewhat more precise about comparability, if consump-
tion were dominated by trend growth at rate r, then the com-
34
-------
parable long run elasticity parameters would be
Y and
A - 1 + r
Note that the latter differs from the Chapman et. al. "long
run elasticity" in that (1 - ^~^) > rather than (1 - A),
alone appears in the denominator. In the section in which
we discuss the empirical estimates obtained by the various
investigators, we shall see that these comments are fairly
well borne out. For present purposes, an idea of the numer-
ical magnitudes may help. Were GO = .2, X = .9, and r = .07,
all of which values are fairly realistic, then the expression
[^j X 1 equals 1.258, which is the value we might reason-
ably expect to emerge from a cross sectional study.
We must return, briefly, to the problem of the choice of
price variable. For any direct comparisons of the Wilson
and Chapman et. al. results must take account of the differ-
ent price variables used in the two studies. Chapman et. al.
use average revenue, as do almost all other investigators.
Wilson, in this as in many other respects the exception, uses
FPC500.(s;a), the Federal Power Commission typical electrical
bill for 500 KWH consumption in region a (i.e., state a).
The typical electric bill is a widely-used construct, and
worth a few definitional and critical comments. The typical
electric bill for a given KWH quantity in a given state is
for a given rate schedule--here, residential--constructed as
follows. From utilities serving the state in question the
Federal Power Commission (FPC) obtains rate schedules. Next,
the FPC computes the bill, under each rate schedule, for a
given consumption--in our case 500 KWH, which is the computed
consumption closest to the national average residential con-
35
-------
sumption for the year studied by Wilson. (Incidentally, that
year is never directly identified.) Since typically only one
utility serves a given city, no further work is required.
For cases where a city or a Standard Metropolitan Statistical
Area (SMSA) is served by two or more utilities, the individ-
ual utility bills are weighted by the numbers of customers
served to give an average typical bill. (Note that, since
Wilson works in cross section, there is no need to worry
about real versus nominal price specifications.)
Which price variable--average price or typical bill is to
be preferred, and why? The defects and virtues are distri-
buted over both candidates. The use of statewide average
revenues as a price variable undoubtedly, as Wilson suggests,
blurs the often substantial variation of average revenue
within a state. Using an example of Wilson's, the city of
Buffalo in New York State, which benefits from cheap Saint
Lawrence River hydropower, is averaged with relatively expen-
sive New York City power. Market and State boundaries simply
do not coincide. Furthermore, the use of the typical elec-
tric bill provides a natural means of circumventing the diffi-
culty of estimation imposed by the declining block rate sche-
dule. For if the estimation is to be a single-equation esti-
mate, then how can we face up to the fact that quantity taken,
our dependent variable in Wilson's first model, is in fact
simultaneously determined with "price" because of the declin-
ing block schedule? Technically, the problem is that of the
identification problem of econometrics. In words the diffi-
culty is that, if we seek information on the relationship
between price and quantity taken from data reflecting con-
sumer purchases under declining block rate schedules--i.e.,
with true quantity discounts--then we cannot be certain of
the interpretation of our result. In some measure it will
reflect the negative relation, arising from the rate schedule
36
-------
alone, between quantity taken and unit price; in some mea-
sure it will also reflect the inverse relationship between
quantity taken and effective price, basic to demand theory.
Wilson's use of the typical electric bill for a given level
of consumption as the price variable is one way around the
difficulty, but its rationale is not easy to state precisely.
For KWH consumption per household is the independent variable
in the Wilson paper (cf. Table 3), so that higher and lower
per household consumption levels have been washed out, and all
are being explained by a "price" variable which corresponds,
and only approximately, to the total bill for a KWH total
(500) approximating average consumption. The possibility of
attributing too much explanatory power to the "price" variable
(i.e., of biasing upwards estimates of "price" elasticity of
demand) thus arises as follows. Since utilities typically
cover average costs of service for customer classes, there
may be considerable variation in the block height assigned
any one block. If for some reason there was a systematic
downward bias of the average consumption block in low consump-
tion areas, and a similar upward bias of 'the average consump-
tion block upwards in high consumption areas, the resulting
price elasticity estimate would be too high. There is, how-
ever, little reason to expect such systematic effects.
Halvorsen
E
The wrinkle in this paper is the effort to improve upon pre-
vious estimates by explicitly modeling both demand and supply
sides of the market. The supply side is specified by an
equation in which average nominal supply price is explained
as a function of variables which may be classified as factor
cost variables, market structure variables, and a time trend
variable. Since this is a supply equation and not a demand
equation, it is the only residential-market equation in the
37
-------
papers discussed in this chapter which is not enetered in
Table 3; we therefore enter it here, with all variables as
defined in Table 2:
KWH. (s ;q )
NOMREVt(s;a) = F(B ^.^ , PCTPVTt ( a ), R/ISt( a ),
PCTURBt( a ); FUELSGt( a ), MHEMFGt(a);
TIME(t))
The dependent variable is the average nominal revenue earned
in residential sales. Demand is taken to be a function of
real price, so that deflation is necessary in order to link
demand and supply parts of the Halvorsen model. Since Hal-
vorsen chooses to deflate by the Consumer Price Index, the
relevant linking equation is
NOMREVt =
Use of the Consumer Price Index as a deflator is common to
several papers, notably Chapman et. al. and Halvorsen, and
we comment below on the implications of this procedure. Re-
turning to the Halvorsen supply equation, the factor cost
variables are (13 the average price of fuel used in steam
generation variable FUELSG.(oO --see Table 2 for the exact
definition--and (23 a labor cost variable MHEMFG.. However,
it is capital costs that bulk largest in the cost structure
of the electric power industry, as we will see, and clearly
these costs must be important in explaining supply price.
Where, then, are these costs in Halvorsen's supply equation?
He suggests that the major determinant of capital cost is
"public versus private ownership," so that the variable
PCTPVT , the percent of total electric utility generation
generated by investor-owned utilities in the state in ques-
tion in year t, is in effect a capital cost variable. But
not the only one, for a major component of the cost of resi-
38
-------
dential service is the distribution cost, which is almost pure
capital cost. Distribution costs are in turn determined by
the density of customers and the intensity of use by those
customers. To the latter factors correspond the variables
PCTURB and KWH /B respectively, the percent of the given
state's population in urban areas and KWH sales per customer.
Thus the all important capital cost determinants of the supply
schedule facing the individual residential customers are
spread over three independent variables. The sole remaining
market structural variable R/IS.(a), the ratio of total resi-
dential to total industrial sales, is included as a measure
of possible cross subsidization of the residential market by
the industrial market. For why, were there no such cross
subsidization, should the supply price of electricity to the
residential consumer depend upon the relative market shares
of residential and industrial customers? Note that the var-
iable in question is a ratio, and thus scale effects cannot
be relevant. Clearly a larger overall market allows the ex-
ploitation of economies of scale, so that both residential
and industrial supply prices may be lower than otherwise,
butwith one small quibble--there should be no dependence of
average supply price on the composition of the market. The
quibble is as follows. If residential sales are more sharply
peaked than industrial loads--this is typically the case--
then markets of equal total consumption will be higher cost
the higher the fraction of residential sales in total sales,
since capacity requirements are correspondingly higher. This
argument would lead us to expect a positive coefficient for
the R/ISt(a) variable; the cross-subsidization argument,
in the form that residential customers, being more numerous
and correspondingly more vocal than large power customers,
are likely to get a subsidy from industrial customers, indi-
cates that a negative coefficient for this variable is prob-
able. Since that latter expectation is borne out in the
39
-------
estimates, the first, contrary argument may be dismissed.
Halvorsen's specification of a supply side--remember this is
not "industry" supply, whatever that might mean in the case
of electric power, but the supply schedule faced by the indi-
vidual consumer--is his means of circumventing the problems
raised by the declining block schedule. Note the difference
between his and Wilson's approach: Wilson chooses as price
variable the typical bill for 500 KWH, hopefully a quantity
independent measure of price within a small quantity range.
Halvorsen, on behavioral grounds, uses an average price var-
iable, with supply to the individual customer then considered
perfectly elastic at that price, so that the various data
points given by the time series of cross sections used in the
estimates trace out the demand curve. Wilson's assumption
can be re-expressed as follows: if most consumption occurs
in a relatively narrow band around residential consumption,
then the cross section used in estimation sketches out the
movement of the particular block in which 500 KWH sits along
the demand curve; if customers are responsive to marginal
price, this traces out a small portion of the demand curve,
providing an estimate of that curve. The resulting estimate
is, of course, not clearly a marginal price elasticity or an
average price elasticity, since different data points differ
in both marginal price and average price: an easy way to
think about the different cross section data points is as
originating from the motion of the intersection of the
marginal price graph and the demand curve as the former is
moved vertically-
INDUSTRIAL DEMAND ESTIMATES
We know less about industrial and commercial demand than
about residential demand. The reasons center upon the
40
-------
different pricing schemes employed for the different rate
schedules. Residential electricity is invariably priced at
some block rate, with block heights and lengths independent
of particular characteristics of the customer's load. But
commercial and industrial schedules characteristically are
"demand billed," i.e. the customer's bill depends upon both
energy consumption and load characteristics, and upon the
latter in a way that can become quite complex. Consequently,
the use of an average revenue figure as a price variable
distorts the actual operation of the rate structure even more
seriously than in the residential case. We know of no study^
wherein this problem is faced even somewhat squarely. What
is known, is summarized briefly below. Brevity is dictated
not by the intrinsic unimportance of the subject--certainly
an allocation of time between residential and commercial and
industrial markets on the basis of any measure of intrinsic
importance would heavily favor the latter two categories--but
by the circumstance that, although the data base for estimation
and, of course, the resultant estimates are different, the
methods either yield little or are suspiciously similar to
those developed for the estimation of residential demand.
Roughly speaking, there are two sorts of estimates of indus-
trial demand: those based upon specific industry data, and
those based upon data on sales to customers served under
industrial rate schedules in the individual states. The
original industrial demand 'estimates of Fisher and Kaysen
and the subsequent work of Baxter and Rees and of Anderson
are in the first category, whereas the industrial estimates
presented by Chapman et. al. are in the second category. For
reasons to be discussed below, the applicability of the Baxter
and Rees and the Anderson papers to a discussion of electricity
r
alone is questionable. The remaining menu of industrial demand
studies is limited, and it is to a comparison of those approaches
41
-------
that we turn. After the completion of that general compari-
son, we return to the individual papers and finally to their
numerical estimates.
Industrial Demand Estimates: Some General Comments
Very crudely, what is likely to be the difference between
econometric estimates of industrial electricity demand based
upon aggregative industry data and estimates based upon state
industrial rate schedule data? In the first category, for
example, we might have electricity consumption by two-digit
Standard Industrial Classification industry group, and value
of purchased electricity at that same level of aggregation.
(Self-generated electricity can, and typically is, adjusted
for in these studies by valuing such an input as the firm
"should," i.e., at the market average revenue "price" for
electricity. The adjustment is added to purchased electric
power to give a market value of electricity used, and it is
this latter market value that enters the industry demand
studies.) Thus there is considerable aggregation over phys-
ical outputs, since the two-digit industry groups are already
aggregates of firms producing closely-related products.
Further, there may be considerable geographic aggregation
since, for example, a two-digit manufacturing industry may
subtend establishments spread over the entire country. What
of the other kind of industrial demand estimate? If we use
state data on sales under industrial rates schedules, then we
disaggregate in one dimension while further aggregating in
another: the aggregation over .products includes everything
produced by firms purchasing electricity under industrial
rates schedules, while spatial aggregation is restrictedcto
areas no larger than the largest state.
To put the matter in this way virtually dictates our choice
* - v- "Zj
of elasticity estimate. Our work is to be based upon the
42
-------
study of individual utility costs and rates, and the customer
classes we study will be the customer classes served by indi-
vidual utilities under individual rate schedules. Ideally,
we should like to have elasticity estimates specific to those
individual rate schedules of individual systems. As a second
best choice, estimates based upon sales by rates schedule and
by state will probably not be too bad, since an individual
utility service area is often a good part of a state, and
there is at least some hope that industry mix is not too
nonhomogeneous across one state. Thus, we must work with the
state-based estimates. To work in the other direction--from
industry-specific estimates through some estimate of industry
mix in individual service areas to an imputed elasticity for
a specific utility service area--would be close to impossible.
Nevertheless, it is instructive to look at the magnitudes of
elasticity estimates obtained on the two types of studies,
and for this purpose we discuss the Fisher and Kaysen esti-
mates. The estimates we actually use in our later work are
those of Chapman et. al. and are made in the same way as the
residential demand estimates given by those authors, so that
our above discussion of their method of estimation need not
be repeated.
Fisher and Kaysen
The industrial demand estimates of Fisher and Kaysen are a
relatively small portion of their book. As in the case on
their residential demand estimates, there is an extensive and
not entirely persuasive effort, based upon the theory of
derived demand, to justify the final specification. We con-
tent ourselves, as Fisher and Kaysen might have done, with the
following observation, which automatically yields the functional
form they finally estimate. For industry j, suppose that
output Y-(t) in period t is produced with electricity in-
43
-------
put E..(t) and other inputs Xk(j,t), k = 1, ...m. Then if
all firms in the industry are identical in size and production
technology, and the technology is Cobb-Douglas, the industry
production function can be written as
= (Constant)x(E..(t))a^ (Xk(j,t))ak
If the price of electricity to the industry in period t is
IQ 1
PJ (t), and the price of each other input in that period p. (t),
then the Cobb-Douglas production function has the pleasant
property of giving inverse demand functions which are them-
selves products of powers of (industry) output and input
prices:
D?(t) = (Constant)x(Y.(t))P(P?(t))a (Prices of other
J J J inputs to differ-
ent powers.)
Because Fisher and Kaysen have no information on other inputs,
they drop all other factors, and proceed with estimation on
the assumption that industry electricity demand may be repre-
sented as the product of industry output to some power and
the price of electricity to some other power, a sort of
truncated Cobb-Douglas derived input demand function:
D*(t) - (Constant)X(Yj(t))3(P^(t))a.
This is the equation Fisher and Kaysen estimate. The data
base for estimation, as indicated in table 1, is derived from
Census of Manufactures 1956 data for selected states. Since
the number of such states differ across two-digit industries,
the degrees of freedom for each industry estimate (See Tables,
Industry Regressions: Two-Digit Industries, 1956, repro-
duced from Fisher and Kaysen) differ between states.
44
-------
Table 5. INDUSTRY REGRESSIONS: TWO-DIGIT INDUSTRIES, 1956
Industry
20 Food and
Kindred
I'roducts
22 Textile
Mill
I'roducts
26 Pulp, Paper,
and
Products
28 Chemicals
and
Products
32 Stone. Clay,
and Glass
Products
33 Primary Met-
al Industries
34 Fabricated
Metal
Products
35 Machinery,
Except
Electrical
36 Electrical
Machinery
37 Transpor-
tation
Equipment
a.
0.7841
(0.4065)
1.6167*"
(0.1117)
0.9747*
(0.2077)
2.5976*»
(0.5234)
1.7386
(1.2231)
1.2829"»
(0.2117)
+ 0.5533
(0.4832)
1.3349"
(0.4286)
1.8209*
(0.4489)
+ 0.6877
(0.6445)
P
+ 0.6591***
(0.1324)
+ I.007IM*
(0.0877)
+ 0.7203
(0.4205)
+ 0.6150"
(0.2167)
+ 1.0273*
(0.3074)
+ 0.4937*"
(0.1188)
+ 1.1094*"
(0.1143)
+ 1.1 009*»»
(0.1175)
+ 0.9043s"
(0.0870)
+ 0.3797
(0.2191)
+ 1 .0526*"
(0.1174)
+ 0.9SD9aaa
(0.1005)
K
12.88
2.84
26.43
22.55
2.44
9.17
0.29
0.39
1.30
76.50
0.61
1.04
£2
.8323***
.9880»a»
.8822*
.6387***
.8429
.7428"*
.9593aaa
.9460s8*
.9742""
.8985*
.9521"*
.9412"*
Degress ot
Freedom
11
6
3
14
3
16
4
5
7
4
5
6
ll
zZ*
IP
ens
-------
Chapman et. al.
We have discussed the method employed in this paper above;
in Table 6 we compile the actual estimates from this paper
which we use in later calculations. Remember that, although
Fisher and Kaysen do not discuss the commercial sector--and
for obvious reasons, since there is no data for the commer-
cial sector which would mesh with their estimation methods--
any unified estimation method constructed so as to mesh with
state data, such as the Chapman et. al. method, can distin-
guish a separate commercial sector. Therefore we employ
this additional level of detail in our later calculations,
and in Table 6 we compile the estimates for the states in
which systems in our sample are located.
This completes our discussion of our selection of demand
elasticities, which enter parametrically into our later indi-
cator estimates. We turn to the cost side of our problem.
Table 6. COMMERCIAL AND INDUSTRIAL ELASTICITY ESTIMATES
Chapman et. al.
System
Potomac Electric
Power Company
Commonwealth
Edison Company
Duke Power
Company
New York State
Electric and
Gas
Pennsylvania
Power and Light
-State
District of
Columbia
and
Maryland
Illinois
North Carolina
New York
Pennsylvania
Long Run (Average) Price
Elasticity of Demand
Commercial
-1.46
-1.48
-1.13
-1.65
-1.46
Industrial
-1.93
-1.87
-1.65
-1.89
-1.93
46
-------
SECTION III
SOME RELEVANT FEATURES OF THE INTERNAL
COST STRUCTURE OF THE ELECTRIC POWER INDUSTRY
A cost-of-service study for an individual utility is likely
to be a one or two year or longer effort, often involving
much of the staff of the rate division. The number of ques-
tions that can be raised is boundless. But by careful selec-
tion of the portion of the cost structure to be explored, we
can guarantee that our analysis of the cost structure is
exactly as detailed, and no more so, than required by our
objectives. We therefore begin this chapter with the intro-
duction of a framework for classifying and identifying those
dimensions of cost structure which we must quantify. In a
sense, this discussion belongs in the discussion of rates in
Section IV; it has been located here because, without it, the
selection of focus in the cost discussion must seem arbitrary,
A TYPOLOGY OF CUSTOMERS BASED UPON "INFORMATION" COSTS
Assume that every consumer reacts optimally to the options
open to him. Then any consumer of electricity will find it
efficient to allocate time to the electricity consumption
decision to the point where marginal benefits of such time--
the reduction in electric bill, for given consumption, for
the incremental minute spent in making the electricity con-
sumption decision--just equal the incremental costs involved,
in this case the value of the incremental minute in its next
most valuable use. The outcomes of this allocation decision
fro
47
-------
process will be classified in two dimensions: time differen-
tiating versus time-undifferentiating consumption decisions,
and average price responsive versus marginal price responsive
consumption decisions.
Table 7. A TYPOLOGY OF ELECTRICITY CUSTOMERS
Time
Undifferentiating
Time
Differentiating
Average Price Responsive
Marginal Price Responsive
I
III
II
IV
Customers in Category I have found it optimal not to distin-
guish between average and marginal prices in their electri-
city consumption decisions. For these customers, the exis-
tence of block rates is irrelevant, for they would make the
same consumption decision at a flat price equal to the aver-
age revenue they are currently paying. Customers in Category
II by definition find it optimal to pay the cost of differen-
tiating between their consumption on and off peak--either by
paying the additional costs of metering peak and off peak
consumption separately, or by taking a rate schedule option
under which the company (nominally) bears the costs of such
metering, or by accepting such devices as deferable load
water heating. Note that, by definition, these customers
have not found it optimal to distinguish between average and
marginal price so that, once again, the question of block
structure is of no relevance to them, for they would take
exactly as much electricity at a flat average rate equal to
their current average price as they take presently. ..
Customers in Category III by definition do not find it opti-
mal to distinguish between peak and off peak consumption,
48
-------
but they have found it optimal to distinguish between mar-
ginal and average price. Finally, customers in Category IV
have found it optimal to distinguish between consumption in
both dimensions: between power taken off peak and at peak,
and between average and marginal prices paid for electricity.
So much for typology. The really important question is what,
if anything, belongs in the boxes: which customers wind up
where? There are no unambiguous guidelines. First, it is
not entirely clear that all customers on a given rate sche-
dule belong in a single category. Large residential users,
for example, may have some marginal price sensitivity and
therefore belong in Category III, whereas very small residen-
tial users almost certainly belong in Category I.
Our identification of rate schedules with the categories of
the above typology, and the corresponding benefit-cost cal-
culations performed, are as follows.
Category I
This category is the domain of small residential and commer-
cial users. The relevant question regarding possible improve-
ment in rate structures is then restricted by the assumptions
that consumers in this category do not, for information cost
reasons, distinguish either marginal and average price or
offpeak and peak consumption. That relevant question is in
fact restricted to the question of inter customer-class ad-
justments in average price. How large are the efficiency
gains to be expected from improved average pricing? Our
methodology for the derivation of a quantitative measure of
such available gains is based upon the work of Baumol and
Bradford.
49
-------
The method and results are spelled out in Section IV below.
To the extent that the derived quantitative measures are re-
liable, they indicate that available gains are negligibly
small.
Category II
Almost all rate schedules are potentially fair game for this
category, and we will compute net benefit measures for all
rate schedules of the sample companies as if it were the case
that all rate schedules are average-price responsive--that
they have found it optimal not to distinguish between peak
and offpeak consumption. For residential customers presently
metered on a KWH monthly or bimonthly basis, this will re-
quire netting of the additional cost of double-rate registers
required to charge differential rates off peak and on peak.
A warning regarding the full spectrum of benefits and costs
for double rate register metering is in order: there is one
potential serious drawback to double rate register metering
of offpeak and peak hours. Should service to a given area
be interrupted and restored in any time interval not a mul-
tiple of 24 hours, the correct setting of the doube rate
register shall have been lost. It would be necessary to meter
on a KWH basis, taking the simple sum of the offpeak and peak
registers as the relevant number of KWH, until the time at
which the meter was read, at that time the reader could reset
the device. The evaluation of this problem is beyond the
scope of this report.
Category III
The prime candidates for Category III are large residential
users if it is assumed that, for some reason, there is no
possibility of differentiating between offpeak and peak
50
-------
usage for these customers. Again, recall our observation
that all customers on a given rate schedule need not neces-
sarily fall into the same category; for the return to an
additional minute spent in a consumption decision is higher
the higher the range of the contemplated purchase, so that
it may pay a large residential user to become familiar with
his or her rate schedule where it would not so profit a
small residential user. Nevertheless, as we will see in our
analysis of Category I, there is little to be gained from
pricing changes which do not discriminate between offpeak
and onpeak consumption. However, there is still the possi-
bility of "implicitly" differentiating between offpeak and
peak, and our major estimate corresponding to Category III
is the estimation of an upper bound on the gains attainable
from implicit differentiation. How might this work?
Suppose that some system had a declining block rate schedule
with only two blocks, with the tailblock lower than the first
block. Suppose further that tailblock customers buy all
their electricity on peak, while first block customers buy
all their electricity off peak. Then we can in some measure
simulate peak load pricing by raising the tailblock and
lowering the first block. Advocates of "rate inversion"
often argue for something like this, and we will calculate
a rough upper bound on the welfare gains that implementation
of one kind of rate inversion proposal will confer.
Category IV
Finally, in Category IV, we place our large commercial and
industrial users. They incur little incremental expense
in differentiating between their consumption off peak and
on peak, since many utilities know and must know what the
instantaneous load being pulled by their individual large
customers is. Some of these customers also have that infor-
-------
mation. Similarly, there is little incremental expense to be
incurred were such a large customer to "switch" from average
price sensitivity to marginal price sensitivity, since so long
as someone is watching the electric bill, the cost of watching
it in a slightly different way is negligible. For these cus-
tomers, a relevant benefit/cost question is: what is the mag-
nitude of the gains likely to be had from time-differentiated
pricing, e.g. a better matching of peak period (perceived)
prices and costs? Some technical problems--the existence of
demand-billing--make this comparison awkward, but we shall see
that it can be made, and that the attainable gains are probably
substantial.
THE USES OF THE TYPOLOGY: A PRELIMINARY OVERVIEW OF
INDICATORS TO BE ESTIMATED, AND COST ANALYSIS REQUIRED
Our purpose in constructing the above typology is the organi-
zation of our welfare gain calculations, and guidance of the
cost analysis necessary for those calculations. In this
section we spell out the first linkage. The discussion of
cost structure, which completes the work of this section,
follows.
It is simplest to proceed seriatim through the four categories
of the typology. In each case the question is the same: what
welfare gain estimates are apposite to the corresponding
typology category?
Category I
These are customers who find it impossible--extremely costly--
to differentiate between peak and off peak consumption and
similarly costly to distinguish between average and marginal
prices. Where, under these constraining conditions, could
52
-------
improvement reasonably be sought? Only in adjustment of the
relative average prices paid by the various customer classes.
Suppose further that utility management chose to avoid the
problems of offpeak versus peak period cost allocation for
this class of customer, and attempted to follow naive se-
cond-best short run marginal cost pricing rules. (Discussed
in detail below, and mentioned above, these rules suggest
that prices be deviated from short run marginal cost in or-
der to cover costs, with the deviations designed so as to
minimize the resulting distortion of consumption patterns.)
Then we can actually compute the welfare gains associated
with such improved pricing. Obviously we will need for these
purposes a reconstruction of short run marginal costs. That
reconstruction will prove useful in introducing us to the
difficulties inherent in utility cost data, and in the iden-
tification of marginal costs. The indicator associated with
this calculation, call it indicator I, will be evaluated in
Section IV.
Category II
These are customers assumed to differentiate between offpeak
and peak usage, but not between average and marginal price.
The relevant question is: how much is to be gained by charg-
ing differential flat average prices in offpeak and peak
periods? We therefore cross into territory where a knowledge
of the differential costs of providing electric service off-
peak and on peak is necessary. Consequently, we require an
extensive discussion of peak versus offpeak cost structures.
The welfare gain calculation relevant to this customer cate-
gory is, as suggested, efficiency gain available from a bet-
ter matching of price and cost in offpeak and on peak periods
53
-------
Category III
These are customers who, because of their information cost
structure, distinguish between marginal and average price but
not between peak and offpeak periods; large residential users
who cannot be metered in a way that distinguishes between time
periods might reasonably be placed in this category. Then
some leverage over their consumption pattern is available from
changes in tailblock rates, i.e., from a form of what has come
to be known as rate inversion. An upper bound to the efficien-
cy gains from such inversion may then be estimated as follows:
assume all tailblock consumption occurs during the peak, and
assume marginal elasticities are relevant. By a "tailblock
customer" we mean a customer whose monthly consumption of elec-
tricity is sufficiently large to place him in the last block
of the rate structure:, if, for example, all KWHs over 800KWH
per month are billed at 1.0
-------
demand schedules--the difference is explained below--for-
mulation of the corresponding indicator is not as straight-
forward as in the previous cases. But the cost-structural
information required for this evaluation is the same: an
explicit identification of offpeak and peak costs.
We have completed a sketchy survey of the cost information
we shall require, and we turn to the development of that
information.
THE RECONSTRUCTION OF INTERNAL COST FUNCTIONS:
SHORT RUN MARGINAL COSTS
Our objective in this subsection is a reconstruction of the
short run marginal cost of serving each customer class, and
an understanding of the limitations of the measure construc-
ted. The incremental cost of service, at any particular
time, is almost purely generating cost, the cost of the fuel
required to generate an incremental KWH. There are usually
larger line losses involved in "delivering" a KWH to a resi-
dential customer than in delivering the same amount of elec-
trical energy to a large industrial customer, since in the
former case there are additional losses in passage through
the low-voltage distribution system. But the major differ-
ence in incremental cost of serving different customer classes
turns upon the timing of the additional KWH, since the major
cost differential involved in serving various customers at
various times arises from the capacity costs imposed by peak
period users--no such costs are imposed by offpeak users.
Short run marginal cost is, strictly speaking, different at
every moment, as demand fluctuates in relation to capacity.
In this section we shall see that the variation over time in
what can be explicitly identified as marginal generation
cost is not extreme. Later, in Section IV, we will therefore
feel justified in using as an approximation a time-independent
_ " * - ^ "
and constant marginal cost of generation.
55
-------
Any electric utility has in operation, at any given time,
plants of varying vintage and consequently of varing econo-
mic efficiency. The trend to larger capacity units which
exploit economies of scale in generation has left all systems
with a spectrum of plant from oldest and least efficient to
newest and most efficient. A cost-minimizing management will
meet any given load on the system by firing plants in decreas-
ing- efficiency order.* Thus, given a list of all plants owned
by a given system and the unit production costs of boiler-
turbine-generator combination in each plant, we can construct
a first and most naive estimate of marginal generation costs
which we refer to as SRMC(l). This function specifies the
marginal cost of a KWH, given any load, subject to the assump-
tion that all units at all plants are functioning. Table 8
below lists what Federal Power Commission Form I calls "total
production cost per KWH" for individual plants, with those
plants ranked from least efficient to most efficient. The
FPC "total production cost" concept includes some small fixed
costs, such as the salaries of plant personnel. But because
these are negligible in comparison with the fuel cost compo-
nent, "total production cost" per KWH is a reasonable measure
of fuel cost per KWH. And, with some important qualifications
discussed below, fuel cost per KWH is a reasonable measure of
short run marginal cost. Figure 1 depicts SRMC(l). (As the
table and figure captions indicate, 1972 Potomac Electric
Power Company data is used here and elsewhere in the report
in describing methodologies.) Table 9, a compilation of fuel
efficiency by unit, provides the basis for a stricter measure
of marginal cost, given fuel prices. The latter are currently
reported to the Federal Power Commission on a monthly basis.
How useful is SRMC(l)? Consider Figure 2, the system load
curve for three representative days in three representative
*Under many current -interchange and pooling agreements ,* the
pool rather than the utility itself makes the operating de-
cisions.
56 .
-------
Table ,8. SHORT RUN MARGINAL COSTS OF GENERATION
Potomac Electric Power Company, 1972
Pl^nt
Morgantown
Connemaugh
Dickerson
Chalk Point
Potomac River
Benning Station
Connemaugh Diesel
Buzzard Point
Chalk Point GT
Morgantown GT
Buzzard Point GT
Dickerson GT
Total Production
Cost <£/KWHR
.454
.516
.598
.674
.725
.971
1.301
1.3331
1.530
1.679
1.745
2.135
Cumulative
Capability 10*KW
1.114
1.273
1.823
2.533
3.019
3.713
4.019
4.041
4.076
4.344
4.367
57
-------
oo
in
o
U
'g
H
+J
U
O
M
(X.
-I
toriint
! i
Connmauth
la I.I
jj I
Dlckerion
. .*
'
Chilk Point I
M
: J.J !
TT
i-r
. iennlm smion
i I i I
M.U
'
I I L
i
'..«J ft.nl c.l
Chilk Folnt CT
1
Fu::ar« nt
Plant Load (106KW)
Figure 1. Short Run Marginal Costs, Potomac Electric Power Company, 1972
-------
en
August
Monday
April
Monday
December
Monday
12 1234 56789 10 11 12 1234 56789 10 U 12
Time
Figure 2. Sample System Load Curves, .Potomac Electric Power Company, 1972
-------
Table 9. EFFICIENCY (IN FUEL TERMS) BY UNIT
Potomac Electric Power Company, 1972
ON
O
Plant
Potomac River
Dickersoh
Dickerson GT
Chalk Point
Chalk Point GT
Morgantown
Morgantown GT
Unit
No,
1
2
3
4
5
1
2
3
1
2
1
2
Installation
Date
1949
1950
1954
1956
1957
1959
1960
1962
1964
1965
1970
1971
Fuel Type and Rate
Tnal Ct0nS
Coal TrD
38
38
37
37
37
55
55
55
115
115
200
200
Oil(^i\
mm.)
630
630
Net
Continuous
Plant
Capability
486.0
550.5
507.0
710.0
1114
Net
Peak
Demand
On
Plant
478.0
547.0
23. 0
654.0
22.0
1128.0
35.0
Gross
Capacity
103KWH
95
95
108
108
108
190
190
190
16.2
355
355
573
575
Efficiency
103BTU/KWH
11.0
11.0
9.0
9.0
9.0
8.7
M
8.5
- o a
o«O
-------
Table 9 (continued). EFFICIENCY (IN FUEL TERMS) BY UNIT
Potomac Electric Power Company, 1972
Plant
Connemaugh
Benning
Station
Buzzard Point
Buzzard Point
Combustion
Turbines
Unit
No.
10
11
12
13
14
15
16
1
;2
3
4
5
6
(16
Units
Installation
Date
1927
1929
1931
1947
1952
1968
1972
1933
1938
1940
1942
1943
1945
)
Fuel Type and Rate
-0 , (tons
Loal i \
hr.)
30 total
23
31
mm.)
74
100
340
340
58
58
70
70
70
70
500
Net
Continuous
Plant
Capability
1640
712
288
(Not.
applicable
since not
base load
plant)
Not
Peak
Demand
On
Plant
1732.0
720
205
251
Gross
Capacity
10'KWH
total plani
30.0
30.0
30.0
55.0
28.0
289.0
289.0
37.5
37.5
57.5
57.5
57.5
57.5
268.0
Efficiency
103BTU/KWH
WMi
~ combined
«M
11.0
11.0
13.0
13.0
11.0
11.0
11.0
11.0
15.0
-------
How useful is SRMC(l)? Consider Figure 2, the system load
curve for three representative days in three representative
months (August, April, and December). The comparison with
Table 8 reveals that, were all units in the system function-
ing perfectly with no downtime, the system peak load could
be met with ample excess generating capacity in August, the
peak month, and with superabundant excess capacity during
the seasonal winter trough. Somehow this scenario does not
square with the current fears of brownout and blackout, and
the problem is one of equipment availability. Every unit,
boiler and generator, must be periodically taken "down,"
inspected, and perhaps repaired or overhauled. A common
rule of thumb concerning such scheduled outages is: every
boiler must be scheduled for one outage per year, and every
generator for one outage every three years. Unfortunately,
not all outages are scheduled. "Unscheduled outages," as
they are called in the trade--breakdowns or takedowns in an-
ticipation of trouble--are far from infrequent. This supply
side uncertainty is not the only source of uncertainty for an
electric utility: on the demand side the uncertainty is
associated with the unpredictability of load. Trouble can
arise from either side, and the problem may be stated as:
what are we willing to pay for service of a given quality--
one component of that quality index being the guarantee that,
with certain probability, all loads will be served? The
problem of how much of a capacity margin is necessary is
amenable to benefit-cost analysis. We are not aware of any
such analysis in the literature on the electric power indus-
try.
If the utilities have based their capacity requirement poli-
cies upon such analysis, the process has been implicit.
What one finds repeatedly--in the trade- literature and in
62
-------
conversation with engineers in utility generating depart-
ments --is the citation of rules of thumb. Two are cited more
frequently than others: first, that a 20 percent margin of
capacity over expected load must be carried, and second, that
the system must be able to meet loads even if the largest
unit operating at any given point in time should fail.
Such rules of thumb should be replaced by a more explicit
benefit-cost calculus. But our purpose is the reconstruc-
tion of short run cost functions "as they are," not as we
think they should be. We therefore accept the second rule
as binding and proceed with our reconstruction, now with the
knowledge that any such reconstruction turns upon availabili-
ty assumptions. There are two possible sources of informa-
tion on availability: individual company data on scheduled
and non-scheduled outages of individual units, and Edison
Electric Institute (EEI) data. The latter is a compilation,
by unit size, of industry availability data, and is there-
fore closer to what we might call "expected availability"
than any one year record for an individual firm. We there-
fore take the EEI overall availability measure, compute the
corresponding expected downtime, and proceed to a "by sight"
scheduling of downtime over the course of the year. The ca-
pacity margin requirement we impose is, as discussed above,
that in any given month capacity on line to be able to meet
last year's demand during that month even if the largest on
line unit were to fail. The scheduling problem thus defined
is, when formulated as a mathematical programming problem,
of forbidding complexity. We therefore follow utility prac-
g
tice in scheduling "by sight," guided by the rule: repair
your most efficient capacity in the minimum demand months,
the next most efficient capacity in the next highest demand
months, and so on.
63
-------
Table 10 presents the results of this exercise for one system
in one year. By comparing Column 6 of this table, "Margin if
Largest Running Plant Fails," with Table 11, "System Peak
Loads by Month," we can verify that the suggested schedule
satisfies the rule of thumb discussed above. Finally, given
this schedule, the linkage to system short run marginal costs
of generation--call this schedule SRMC(2), an improvement in
realism over SRMC(l) above--is a simple matter of construct-
ing the SRMC schedule in each month, given the capacity
available in that month. Table 12 compiles SRMC(2), for the
above repair schedule, in repair period I. Entries in the
column headed "SRMC of Generation" are fuel costs per KWH
for the least efficient unit that must be operated (in order
to meet system load) when the major unit listed in the left-
hand column is down for repairs.
Thus we have, in any month, a SRMC schedule reflecting ac-
tually available capacity. When placed side by side with the
system load curve for any day of that month, we have the cost
of generating the marginal KWH during any hour that day or,
when averaged over peak hours (respectively Off peak hours),
the marginal generation cost during peak hours (respectively
off peak hours).
SRMC(2) is about the best that can be said about short run
marginal costs from Federal Power Commission "total produc-
tion cost" data. The limitations of this measure have been
sufficiently belabored above. Here we re-emphasize two
points. First, note the comparatively small variation of
SRMC(2) between peak and offpealc periods. From Table 11 note
that the January peak load was 1,975 MW. From Table 12 we
know that, had availability been as assumed in constructing
that table, peak hour short run marginal costs would have
been roughly . 72<£. Suppose that January offpeak hour demand
64
-------
Table 10. MONTHLY PEAKS; TRIAL REPAIR SCHEDULE 1,
Potomac Electric Power Company, 1972
en
Month
January
February
March
April
May
June
July
August
September
October
November
December
System
Peak
Demand
106KW
1.98
1.99
1.87
1.94
2.33
2.73
3.48
3.29
3.03
2.04
2.06
2,11
If Repair
Morgantown
1 § 2
Chalk Point
x Ci £*
Dickerson
3
Dickerson
152
No Scheduled
Outages
No Scheduled
Outages
Benning Stati
15 5 16
Potomac River
3, 4, « 5
Remaining
Capacity
106KW
2.372
2.618
3.138
3.518
on
2.616
Largest
Plant
Running
106KW
.355
.573
.573
.573
.573
Margin if
Largest
Running
Plant Fails
106KW
2.017
2.045
2.565
Need
Peaking
2.945 Capacity
2.043
-------
Table 11. SYSTEM PEAK LOAD BY MONTH
Load Data
Month
January
February
March
April
May
June
July
Augus t
September
October
November
December
Annual Peak
Peak Demand
106KW
1.975
1.990
1.867
1.944
2.331
2.730
3.479
3.288
3.034
2.044
2.061
2.110
3.479
Peak Load
Date
17
7
14
20
31
19
21
25
14
6
30
18
7-21-72
was roughly 1,000 KW: then the corresponding SRMC(2) esti-
mate is approximately . 47<£.
But it would be a mistake to accept even this improved short
run marginal cost measure as a reliable guide to "true" peak
period short run marginal cost. For, at the peak, short run
marginal cost cannot be approximated by incremental fuel
costs for generation from baseline capacity. If capacity
has been appropriately adjusted to peak demand, the short run
cost of serving the marginal peak customer must equal the
(long run) cost of serving that customer by expanding capacity
Thus, system long run marginal cost is a better measure of
66
-------
Table 12. SRMC(2), TRIAL REPAIR SCHEDULE 1
Repair Period I January-February
Plant and
Unit
Morgan town
1
2
Dickerson
1
2
3
Chalk Point
1
2
Potomac River
3
4
5
Potomac River
1
2
Benning Station
15
16
Net Continu-
ous Capabil
ity 106KW
.557
.557
.184
.184
.184
.355
.355
.108
.108
.108
.095
.095
.289
.289
Last
Unit
-------
Electric Utility Costs: Some Nomenclature
Discussions of electric utility costs lean heavily upon four
cost "vocabularies." Each will serve us in what follows.
For purposes of discussion, we distinguish these vocabularies
as the conventional utility, income statement, economic cost,
and functional vocabularies. First, we introduce them seria-
tim; below, we make use of these classifications in apportion-
ing costs between subperiods and between customer classes.
The Conventional Utility Vocabulary--So named (here) because
of its origin in the utility literature, this framework clas-
sifies the cost of service into energy, capacity, customer
and residual costs. Each category specifies one dimension
of service, and the dimensions of service provided are pre-
sumably independent. Thus energy costs are those associated
with the provision of delivered KWHs, all else held fixed.
Capacity costs are, similarly, costs incurred for the pro-
vision of capacity. Customer costs are those which vary when
the number of customers is varied. Among the latter are, un-
ambiguously, the (annualized) installed cost of a meter, and
the cost of meter reading. Less unambiguous--it can make a
great deal of difference in the calculation of the minimum
charge to be recovered from every customer--is the status of
customer-related distribution plant. Clearly the wire run-
ning from a distribution line to an individual house repre-
sents a pure customer cost, a cost incurred in the service
of an identifiable customer. But what of the distribution
lines and poles? Are they to be subsumed under capacity cost
or customer cost? Finally, residual costs are all costs not
subsumed under energy, capacity or customer cost categories:
for example some, but not all, administrative and general ex-
penses, i.e. such regulatory commission expenses as are in-
dependent of the other three "dimensions."
68
-------
There is much imprecision in this cost classification. In
addition to the ambiguities cited above, there is the ob-
viously unsatisfying fiction of independent dimensions of
cost incurrence: for example, the cost of providing an in-
cremental KWH depends upon the level of capacity in the sys-
tem in a complex way. Nevertheless, the persistence of the
conventional utility vocabulary is a tribute to the adequacy
of certain cost-function approximations implicit in that
vocabulary--in the above example, the approximate constancy
of energy costs over wide ranges--and to the format in which
data are collected and reported. Again, in the above example,
production cost is typically reported on a per unit or per
plant basis, whereas there is always some small variation of
unit efficiency between zero load and maximum load.
The Income Statement Vocabulary--The characteristic framework
in which cost data are summarized for the purposes of review
of the financial status of the company is a useful point of
departure in our later cost calculations, precisely because
the income statement categories, aggregative as they are,
have definite economic content suggestive of correct alloca-
tion procedures. Thus, in 1972, the Potomac Electric Power
Company reported summary income statement data as compiled
in Table 13. Of the broad cost categories--Operating Ex-
penses, Maintenance Expenses, Depreciation, Federal Income
Taxes, Taxes Other than Federal Income Taxes, Interest on
Long Term Debt, and Other Interest and Amortization--only
Operating Expenses and Federal Income Taxes require further
scrutiny, the other categories are clearly assignable in
"conventional utility" terms--to non-energy cost categories.
Table 14, obtained from Federal Power Commission Form 1 as
filed by the Potomac Electric Power Company for 1972, sup-
plies the breakdown of electric operation expenses between
energy and non-energy related costs: only the fuel cost of
69
-------
Table 13. INCOME STATEMENT DATA,
POTOMAC ELECTRIC POWER COMPANY, 1972
(thousands of dollars)
Operating Revenues
Operating Expenses
Maintenance Expenses
Total Operating and
Maintenance Expenses
Depreciation
Federal Income Tax
Other Tax
Total Operating Expenses
Operating Income, Gross
Other Income, Net
Income Before Interest
Charges
Interest on Long-Term
Debts
Other Interest and
Amortization
Total Interest Charges
Net Income
272,717
94,493
21,146
115,639
35,516
10,804
31,844
193,888
78,829
449
79,278
32,704
1,714
34,418
44,860
$105,170,553 represents true energy cost, the remainder of
total operations costs of $113,386,960 being incurred in ways
largely independent of the level of output--e.g., supervision
of generation. Depreciation and Texes Other than Federal In-
come Taxes are subsumed as capacity charges: Depreciation
with little further ado, and Tax.es Other than Federal Income
Taxes because property taxes on assessed valuation should be
in rough proportion to value of electric plant in service.
There remain customer costs--reported separately for the
most part and, with qualifications discussed above arising
from ambiguities in the assignment of certain distribution
70
-------
Table 14:
FUNCTIONALIZATION OF OPERATING AND MAINTENANCE COSTS,
Potomac Electric Power Company, 1972
(dollars)
GENERATION
Operation, Supervision and Engineering
Fuel
Steam Expenses
Electric Expenses
Miscellaneous Steam Expenses
Rents
Total Operation
Operation Overhead
Total Maintenance
OTHER POWER GENERATION
Total Power Production Expenses - Other Power
OTHER POWER SUPPLY EXPENSES
Purchased (Sold) Power
System Control and Load Dispatching
Other Expenses
TRANSMISSION
Total Transmission Expenses
DISTRIBUTION
Meter Expenses
Maintenance of Meters
Total Distribution Expenses
Total Nonmetering Distribution Expenses
CUSTOMER ACCOUNT EXPENSES
Meter Reading Expenses
Total Customer Accounts Expenses
Total Metering Expenses
Sales Expenses
ADMINISTRATIVE AND GENERAL EXPENSES
Total A § G Expenses
484,739
105,170,553
3,723,141
1,972,373
2,033,635
2,519
113,386,960
487,258
12,694,220
2,055,885
(56,349,939)
1,194,892
196,788
320,739
765,938
151,815
12,791,639
12,025,701
978,214
5,244,393
1,895,967
2,444,162
21,659,040
TOTAL ELECTRIC 0 § M
115,638,779
71
-------
plant, readily identifiable--and what might be called non-
depreciation cost of capital charges, the latter category
covering Interest, Net Income and Federal Income Taxes. A
simplifying device for treating these cost categories, a de-
vice which does not violence to the facts, is discussed below
in the sample assignment of capacity costs.
The Economic Vocabulary--The distinction between fixed and
variable costs is related to, but less precise and useful
than, what we have called the conventional utility vocabu-
lary. Fixed costs, those not changing with the level of
output, embrace capacity, customer and residual expenses.
Variable costs, definitionally those which do vary with out-
put, are closest to energy costs. Why bother to complicate
matters with this additional and extremely thin "vocabulary"?
Only because it is so familiar that we shall probably inad-
vertently use it in what follows.
The Functional Vocabulary--Costs are herein classified by the
stage of the production process in which they are incurred.
In sequence, those stages are generation, transmission and
distribution.
A Classification of Capacity Costs
The key first step is the selection of a workable classifica-
tion of capacity costs. The classification we select, based
upon the discussion above, must be exhaustive of all capacity
costs identified in the income statement framework. Such an
exhaustive classification is as follows:
1. Nonfuel Operation and Maintenance Expenses;
2. Cost of Capital: Rate of Return on Rate Base
and Depreciation; and
3. Taxes Other than Federal Income Taxes.
72
-------
Category 1 has been discussed above, and can be obtained di-
rectly from Federal Power Commission Form 1 by subtracting
Fuel Cost from Total Operation Cost to give the Total Non-
fuel Operation Cost. To these must be added System Control,
Load Dispatching Expenses, and Other (nonfuel) Expenses; the
result, Total Nonfuel Operation and Maintenance Expenses, is
as compiled in the final column of Table 15. The same pro-
cedure is applicable to transmission operation and mainte-
nance costs, which are almost wholly "fixed" costs of oper-
ating and maintaining the transmission system. Distribution
nonfuel operation and maintenance expenses are given directly
in Form l--note the last line of the operation and maintenance
distribution category in Table 14--and therefore need not be
adjusted a la Table 15. Note that in terms of our cost vo-
cabularies, Table 15 covers one component of capacity cost,
and decomposes that component by function.
Consider next Table 16, Cost of Capital: Rate of Return on
Rate Base and Depreciation. The title of this table includes
some utility jargon, and an explanation may be helpful. Econ-
omists customarily define the net cost of capital as equal to
the gross cost of capital minus depreciation. When economists
study regulated utilities, they are often asked whether a
company is earning a "fair (net) return on capital." In
practice, a fair return generally means a rate of return
sufficient to attract capital into the industry. And in
practice, the net return on capital is computed as the prod-
uct of a "rate of return" times a "rate base." This proce-
dure could not be faulted if the "rate of return" figure used
were the opportunity cost of capital, and if the "rate base"
figure used were the company's net worth. But how can a reg-
ulatory commission determine the opportunity cost of capital?
What usually happens is that some very rough approximation
to net worth (such as original cost of physical plant) is
73
-------
Table 15.
GENERATION AND TRANSMISSION NONFUEL OPERATION AND MAINTENANCE
Potomac Electric Power Company, 1972
(dollars)
Functional Component
of Plant in Service
GENERATION
Total Steam
Production
Plant
Total Other
Production
Plant
Total Production
Plant
TRANSMISSION
Total
Operation
113386960
1718671
155975
Fuel
.105170553
1714086
Total
Nonfuel
Operation
8216407
4585
Total
Maintenance
12694220
2055885
164764
System
Control
and Load
Dispatching"
1194892
Other
Expenses0
196788
Total
Nonfuel
0$M Plus
20910627
2060470
24362777
320729
In principle some of these expenses are allooable between modes of generation. But there is no
data available with which to make the allocation, so that we must attribute these expenses to
overall generation. '
-------
--J
1/1
Table 16. COST OF CAPITAL: RATE OF RETURN ON RATE BASE AND DEPRECIATION,
Potomac Electric Power Company, 1972
(dollars)
Functional Component
of Plant in Service
GENERATION
Total Steam
Production Plant
Total Other
Production Plant
Total Production
Plant
TRANSMISSION
Total Transmission
Plant
Plant in
Service :
Balance, at
End of Year
558,409,172
30,203,993
588,636,054
200,706,727
Cost of Capital
at 8 Percent
of Original
Cost
44,672,734
2,418,151
47,090,884
16,056,538
Depreciation
at Composite
Rate12
16,417,230
888,670
17,305,900
5,900,778
Gross Cost
of Capital
61,089,964
3,306,821,
64,396,785
21,957,316
-------
taken as the "rate base," and some rough estimate of the
opportunity cost of capital is taken as the "rate of return."
All that matters is the product of these two numbers, which
is the "target" net income allowed the company.
The purpose of Table 16 is the compilation, in a form conve-
nient for allocation procedures, of the cost of capital in
terms of the income cost vocabulary. The relevant categories
are (recall the income statement categories in Table 13)
Depreciation, Federal Income Taxes, Interest on Long Term
Debt, Other Interest and Amortization Charges, and Net In-
come. Treating these income statement categories seriatim,
we begin with Depreciation. Conceptually the least ambiguous
of the cost of capital categories, our difficulties in the
treatment of depreciation arise from the wide variations in
economic lifetime of the capital stock held by electric uti-
lities, and the practice of reporting only the total depre-
ciation category found in Form 1. Thus generating plant may
have an economic life of twenty years--many older units are
still in servicewhereas underground distribution plant may
function for fifty or more years. Public Service Commissions
typically will assign allowed rates of depreciation for spe-
cific types of equipment. A composite straight line rate
will then be computed by weighting equipment-specific rates
by some weights related to the division of plant in service
between various equipment types.
Our procedure in assembling depreciation estimates by func-
tion begins by computing an "effective" composite straight
line rate in force, that "effective" rate being defined as
the ratio of total depreciation charges to end-of-year elec-
tric plant in service. (A minor ambiguity surrounds the use
of end-of-year electric plant since, for plant completed
during the year, something less than an annual depreciation
76
-------
charge at the composite straight line rate is appropriate.
The "effective" electric plant in service is somewhere be-
tween beginning-of-year and end-of-year plant in service.)
Table 17, derived from Federal Power Commission Form 1,
assembles electric plant in service by function. Applica-
tion of the imputed composite straight line depreciation
rate to functionally identified plant in service gives the
column of Table 16 headed Depreciation at Composite Rate.
Table 17. ELECTRIC PLANT IN SERVICE,
Potomac Electric Power Company, 1972
(dollars)
Electric Plant in Service
End-of-Year
Total Intangible Plant
Total Steam Production Plant
Total Other Production Plant
Total Production Plant
Total Transmission Plant
Distribution Plant:
Land and Land Rights
Structures and Improvements
Station Equipment
Poles, Towers, Fixtures
Overland Conductors and Devices -
Underground Conduits
Underground Conductors and Devices
Line Transformers
Services
Meters
Installation on Customer Premises
Street Lights and Signals
Total Distribution Plant
Total General Plant
Total Electric Plant in Service
75,578
558,409,172
30,203,993
588,636,054
200,706,721
8,806,101
18,439,647
46,641,883
25,775,660
29,860,660
89,960,956
67,877,917
86,938,999
52,965,185
21,300,501
2,347,571
26,092,906
478,008,178
27,160,981
1,284,587,512
77
-------
Turning next to the net cost of capital concept--the oppor-
tunity cost of capital which is present even in the absence
of economic depreciation--our method is pegged to an eight
percent rate of return on original cost. That computed fig-
ure appears in the column of Table 16 headed Cost of Capital
at 8 Percent of Original Cost. The sum of that pure cost of
capital and of the depreciation estimate leads to a Gross
Cost of Capital estimate. Since electric plant in service is
already broken out by function, the Gross Cost of Capital es-
timate is likewise automatically broken out by function. Fi-
nally, only the third component of our simplified cost of
capital classification remains. Table 18, Taxes Other than
Federal Income Taxes, allocates such taxes among functionally
specified components of electric plant in service in propor-
tion to electric plant in service. The validity of that pro-
ration as a reasonable measure of cost incurrence associated
with various facilities depends upon the assumption that in-
direct business taxes are levied in proportion to assessed
valuation, with the later assessment assumed to reflect the
costs of services provided by state and local governments.
In Table 19, Summary of Functionalized Capacity Costs, the
three simplified capacity cost components--Nonfuel Operation
and Maintenance Expenses, Cost of Capital, and Taxes Other
than Federal Income Taxes--are summed for each function, with
the last column, the sum, giving total capacity cost respon-
sibility by function. Note that this table includes, albeit
somewhat out of sequence, the full results for Nonmeter Dis-
tribution costs. Calculation of those costs requires that
metering costs be deducted from total distribution costs,
and this is done below.
78
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Table 18. TAXES OTHER THAN FEDERAL INCOME TAXES
Potomac Electric Power Company, 1972
(dollars)
Functional Component
of Plant in Service
Total Production
Plant
Total Transmission
Plant
Total Distribution
Plant
Total Electric
Plant in Service
Corresponding
Original Cost
559,288,714
200,706,721
456,707,678
1,294,587,512
Fraction of
Plant in
Service, by
Function
.432
.155
.353
Proration of
Tax Over
Plant
14,507,157
4,941,999
11,255,003
Table 19. SUMMARY OF FUNCTIONALIZED CAPACITY COSTS,
Potomac Electric Power Company, 1972
(dollars)
Function
GENERATION
TRANSMISSION
NONMETER
DISTRIBUTION
Total
Nonfuel
0 $ M
24,352,777
320,729
11,873,886
Cost of
Capital
64,396,785
21,957,316
49,963,820
Taxes Other
Than Federal
Income Taxes
14,507,157
4,941,999
11,255,003
Total
by Function
103,266,719
27,220,044
73,092,709
79
-------
Allocation of Capacity Costs Among Rate Schedules:
A Preliminary Example
!
We repeat what we have said several times above: that we
have neither the time nor the resources for a fine-grained
cost of service study, but that we can tolerate much less.
It will prove sufficient to have a fairly accurate compari-
son of actual versus appropriate patterns of cost recovery-
In moving towards that comparison we first sketch what it
might mean, and then turn to the actual allocation of the
capacity cost components listed in Table 19 among individual
customer classes. By a customer class we mean all those
customers served on a given rate schedule.
For a guide to how fixed costs are actually recovered, the
simplest procedure is to use crude average revenue data.
Consider Table 20, Crude Estimates of the Allocation of
Capacity Costs Among Customer Classes, Potomac Electric Pow-
er Company, 1972; all data derive from Federal Power Commis-
sion Form 1 filed by that company in that year. For present
purposes, it will suffice to take, from our previous work on
short run marginal generation costs, a flat, conservative
estimate, say . 7
-------
Table 20. CRUDE ESTIMATES OF ALLOCATION OF CAPACITY COSTS AMONG CUSTOMER CLASSES,
Potomac Electric Power Company, 1972
oo
Customer Class
Total
Residential
Total Low
Voltiigc
Commercial
Total Large
Power
Interchange
and Resale
KWH Sold
3,128,684,929
6,123,240,159
3,181,396,529
5,803,591,000
Revenue $
77,455,188
133,766,262
45,330,042
56,349,939
Average
Number of
Customers
391,046
47,596
239
--
KWHR Sales
per
Customers
8,001
128,650
194,515
--
Revenue
per
KWHR *
2.476
2.185
1.42S
.971
Marginal
Cost
.7
.7
.7
.7
Capacity
Costs
Recovered
per KWH
1.776
1.485
.725
.271
Capacity
Costs
Recovered
by Custo-
mer Class
55,565,444
90,930,116
23,065,125
15,727,732
Capacity
Costs
Recovered
per
Customer
142.1
1,910.5
189,685.8
--
Total Capacity
Costs Recovered $ 185,288,417
-------
As must be true because of the heavy distribution costs
associated with residential service, the highest capacity
cost per KWH recovery figure is the residential figure, with
remaining rate schedules in the expected sequence: commer-
cial, large power, and interchange and resale. The very low
figure for interchange and resale is remarkable. Remember
that the . 271
-------
definite prices and will change if those prices change, so
the question should be stated: given the load curve obtained
under present prices, what is "the peak"? As in other places
above, we have a problem susceptible of formalization, but
a formalization of such complexity as to be nearly useless.
That formal problem is: given a set of (independent or in-
terdependent) demands in several subperiods of a period over
which demand is periodic, and given the costs of pricing
differentially between periods and of having additional
rates, what optimum switching times and rate levels will be
selected by a seller seeking to maximize the sum of consumer
and producer surpluses? In practice, we might proceed as
follows: from the known form of the system load curve (in
peak season and off peak season months) we select some band
of hours during the peak season as "the peak" hours for the
year. One measure of peak responsibility capacity costs to
be recovered is then obtained by dividing, for each customer
class, fixed costs of generation to be recovered by the num-
ber of hours in the peak under various definitions of the
peak. Table 21, Number of Hours in Peak Under Various
Periodizations, compiles total peak hours (over the year)
under three definitions of the daily peak and two alterna
tive definitions of the division of the year between peak
and offpeak seasons. The plausibility of these definitions
of the peak, has been based upon inspection of the system
load curve, and the location--both seasonal and time of day--
of peak hours will be different for different systems. Nev-
ertheless, the range of "total peak hours" can be taken as
applicable to all systems: for any given system, a reason-
able definition of the peak will fall within this total
hours range. Our initial cost recovery range comparison is
therefore based upon one total peak hours range exhibited
in Table 21, the four month peak season with an eight hour
daily peak period.
83
-------
Table 21. NUMBER OF HOURS IN PEAK UNDER
VARIOUS PERIODIZATIONS
Seasonal Division
Assumption
Daily Division Assumption
a
Peak
lpm-»-9pm
= 8 hrs
Peak
9am-»-9pm
= 12 hrs
Peak
3pm-*-7pm
= 4 hrs
Peak Season
= 4 months
s 96 days
Peak Season
= 6 months
s 180 days
768
1,152
1,152
1,728
384
576
a
Sundays excluded* 4 x 6 = 24 days/months.
Having adopted a preliminary definition of the peak, we turn,
in Tables 22A and 22B, to some initial cost recovery compari-
sons. (Remember that here, in order to have a clear illustra-
tive example, we are looking at generation costs alone.)
Table 22B is a set of calculations of upper bounds on the
number of KWH taken during peak hours for various definitions
of "the peak." In Column 1 of that table we have entered
the number of hours in the peak period under various period-
izations (see Table 21). The first row of Table 22B is com-
puted as follows. In Column 4 of Table 22B we list the peak
season months, June through September, corresponding to the
choice of the four month season. In Column 5 of Table 22B
we enter, for each of those months, the maximum demand upon
the system as reported in Federal Power Commission Form 12.
Assume that monthly maximum demand is approximately equal to
actual system demand during all system peak hours. Then KWH
84
-------
taken during peak hours in any one month is approximately
equal to system peak demand times the number of peak hours
in a month. By summing over months we get the final column of
of Table 22B, Upper Bound on Annual Peak KWH.
That column becomes the third column of Table 22A. But from
Table 19 we have an estimate of total generation capacity
costs to be recovered, i.e. $103,266,719. Column 5 of Table
22A is computed by dividing this figure by each upper bound
figure in Column 4.
Columns 6 through 9 of Table 22A compile the ratios of actual
fixed cost recovery per peak KWH to our Column 5 estimates of
advisable fixed cost recovery. For example, the first row
entry in Column 6, 4.82£, is equal to the first row entry in
Column 5 divided by 1.78<£/KWH. Column 5 is therefore a first,
crude estimate of the capacity costs per KWH that "should"
have been recovered.
The implications of Table 22A should be stated explicitly.
For all definitions of the peak period, presently recovered
fixed costs were far exceeded by peak responsibility assign-
ment of fixed costs.
Again, a reminder that Table 22A is an initial comparison,
since transmission and distribution costs have yet to be in-
cluded. When that reckoning is made, it will be seen that
results for residential service are much closer to those for
commercial and industrial service than presently, so that for
all categories of service the conclusions are the same: the
deviation of present cost recovery from any reasonable patr
tern of cost recovery which acknowledges peak responsibility
is significant. The implication--that there are realizable
gains to be had from peak load pricing--is, in part, the
work of Section IV.
85
-------
Table 22A. INITIAL COST RECOVERY COMPARISONS: GENERATION ONLY,
Potomac Electric Power Company, 1972
Total
Annual
Peak
Hours
384
576
768
1,152
1,152
1,729
Hours
in
Daily
Peak
4
4
8
12
8
12
Months
in
Seasonal
Peak
4
6
4
4
6
6
Upper
Bound
on
Peak
KWH
Sales
103KWH
1,202,976
1,622,976
2,405,952
3,608,928
3,245,952
4,868,928
Correspond-
ing Fixed
Generation
Cost to be
Recovered
per KWH
in {
8.58
6.36
4.29
2.86
3.18
2.12
Actual Recovery of All Fixed Costs per KWH
Actual
Residential
1.78 <£/KWH
Actual
Low Voltage
Commercial
1.49 */KWH
Actual
Large Power
.73 f/KWH
Actual
Interchange
and Resale
.27 */KWH
Ratios of Column 5. to Actual
4.82
3.57
2.41
1.61
1.79
1.19
5.76
4.27
2.88
1.92
2.13
1.42
11.75
8.71
5.88
3.92
4.36
2.90
31.78
23.56
15.89
10.59
11.78
7.85
00
aBaaed upon total fixed generation ooat to be recovered = $103^266^719 (Table 19 above).
Baaed upon Table 20, Crude Estimates of Allocation of Capacity Costa Among Customer Classes.
-------
Table 22B. RANGE OF TOTAL PEAK HOURS, AND CORRESPONDING APPROXIMATE TOTAL KWH SALES,
Potomac Electric Power Company, 1972
(Total)
Annual
Peak
Hours
384
576
768
1,152
1,152
1,728
Hours
in
Daily
Peak
4
4
8
12
8
12
Months
in
Seasonal
Peak
4
6
4
4
6
6
Months
June
July
August
September
May
June
July
August.
September
October
System Peak
Demand in
Those
Months
103KW
2,730
3,479
3,288
3,034
2,331
2,730
3,479
3,288
3,034
2,044
I System
Peak Demands ,
4 Month and
6 Month Cases
103KW
(12,531)
(16,906)
(12,531)
(12,531)
(16,906)
(16,906)
Monthly
Peak
Hours
96
96
192
288
192
288
Upper Bound
on Annual
Peak KWH
1,202,976
1,622,976
2,405,952
3,608,928
3,245,952
4,868,928
00
-------
Extension to Transmission and Distribution Costs
A full comparison of costs and benefits associated with peak
responsibility pricing obviously requires a full reckoning of
all costsnot just the generation costs discussed above of
serving peak and offpeak users. We have used generation
capacity costs in our illustrative example for, with the
obvious qualification regarding losses, every KW of demand
at the system peak is equally responsible for the incurrence
of generation capacity costs, and therefore must share co-
equally in that cost burden. But transmission and distribu-
tion capacity costs are, equally obviously, not so simply
interpretable. Clearly the line of causal responsibility
for the incurrence of these costs is nowhere as simple as in
the case of generation. To take only the most obvious exam-
ple, any reasonable assignment of distribution capacity costs
must show a highly disproportionate assignment of such costs
to residential customers, since there are so many more of
them and since each requires a separate connection. We be-
lieve the crude allocation introduced below is adequate for
our later purposes, and we proceed to illustrate that allo-
cation.
First, an allocation of transmission capacity costs among
rate schedules. Table 23, Transmission Capacity Cost Allo-
cation, begins this process with an apportionment of total
transmission capacity costs between interchange and resale
and all other customer classes--in. the case of our illustra-
tive system, the Potomac Electric Power Company, the other
categories are Residential, Commercial, and Industrial.
Interchange and resale agreements are agreements between com-
panies to "interchange" electric energy under certain speci-
fied conditions and at certain specified times. Such agree-
88
-------
Table 23: TRANSMISSION CAPACITY COST ALLOCATION,
Potomac Electric Power Company, 1972
Total 'Fixed1
Transmission
Cost
$27,220,044
Interchange
and Resale
KWH
5,803,591
Total
Residential
KWH
3,128,685
Total Low
Voltage
Commercial
KWH
6,123,240
Total Large
Power KWH
3,181,397
Total Non-
Interchange
KWH
12,433,322
Interchange
and Non-
Interchange
18,236,913
Inter-
change
KWH as
Fraction
of Total
KWH
.318
Allocation
of Total
Fixed
Transmis-
sion Cost
to Inter-
change
$8,655,974
Non-
inter-
change
KWH as
Fraction
of Total
KWH
.682
Allocation
of Total
Fixed
Transmis-
sion Cost
to Nonin-
terchange
$18,564,070
Total Non-
interchange
'Fixed' Trans-
mission Costs
$18,564,070
Average
Number of
Residential
Customers
391,046
Average
Number
.of Low
Voltage
Commer-
cial
Customers
47,596
Average
Number
of Large
Power
Customers
239
Sum of
Averages
438,881
Residen-
tial
Customers
as
Fraction
.891
Allocation
of Trans-
mission to
Residential
$16,540,586
Commer-
cial
Customers
as
Fraction
.108
Allocation
of Trans-
mission to
Commercial
$2,004,919
Indus-
trial
Customers
as
Fraction
.001
Allocation
of Trans-
mission to
Industrial
$18,564
00
-------
ments can benefit both companies: e.g., by (1) taking advan-
tage of differences in the system load curves so that total
capacity requirements are reduced, or by (2) allowing each
company to expand its capacity at longer intervals and with
larger, more efficient plants.
An interchange or resale customer of an electric utility is
thus another electric utility. We have therefore allocated
transmission capacity costs between interchange and resale
and all other customers on a KWH basis; Table 23 sets out the
numbers.
Our rationale for the above assignment is the obvious inappro-
priateness of a number-of-customers based allocation (as is
employed below for.different purposes) for this first split:
clearly one large interchange connection may account for an
important portion of a system's fixed transmission costs, but
may nevertheless represent a negligible portion of the system's
customers. Then the remaining noninterchange and resale fixed
transmission costs are allocated among the usual customer
classes on a number-of-customers basis, which should be rough-
ly appropriate. For imagine residential, commercial, and in-
dustrial customers to be evenly interspersed over a circular
region surrounding the generation plant a system operates.
Then where individual transmission lines serve individual
squares of a grid covering the service area, the number-of-
customers allocation would be exact.
For the allocation of distribution capacity costs among cus-
tomer classes there is a strong case for allocation on a num-
ber-of-customers basis. The reason is obvious: distribution
costs are most immediately connected with service to individ-
ual customers. Strictly speaking, only the drop wire to the
house from the distribution system--we have isolated metering
90
-------
expenses--is unambiguously identifiable with service to an
individual customer. Nevertheless, the distribution plant
required to serve equal squares of grid with roughly equal
customer density should be roughly equal. Customer densities
do, of course, differ from neighborhood to neighborhood, and
in principle these differences could become the justification
for differences in rates between neighborhoods and, more im-
portant, between localities. But, the American practice
has been overwhelmingly opposed to accurate reflection of
such cost differentials in rates--in part because a sub-
sidy is thus granted rural areas and since our objective
is a careful comparison of each company's rates with their
understanding of costs, we adhere to the number of customers
method of apportioning distribution costs among customer
classes. Table 24, Distribution Cost Allocation, compiles
these results.
The allocations of generation, transmission, and distribution
capacity costs among customer classes, and an estimate of the
cost recovery per KWH that would have reproduced that alloca-
tion, are compiled in Table 25, Summary of Allocation of
Capacity Costs. The elements of this matrix give, for each
rate schedule and each function--generation, transmission,
and distribution--the associated allocation of capacity costs.
The numbers in parentheses below the elements of the matrix,
labelled as "Naive $/KWH Recovery," are obtained by dividing
each matrix element by the number of KWH in "the peak." For
purposes of illustration we have taken, in this case, a 768
hour definition of the peak. By a procedure to be described
momentarily, we estimate (as an upper bound) that our illus-
trative system sold 2,405,000 KWH during these peak hours in
1972. Thus the figures in parentheses have the following in-
terpretation: had all fixed costs been recovered during
these peak hours in 1972, and had the pattern of consumption
91
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Table 24: DISTRIBUTION COST ALLOCATION
Potomac Electric Power Company, 1972
N>
Nonmetering Distribution Operation and Maintenance
Total
Distribution
Operation
Expenses
$
5,690,999
Meter
Expenses
$
765,938
Nonmeter
Distribution
Operation
Expenses
4,925,061
Total
Distribution
Maintenance
Expenses
7,100,640
Meter
Maintenance
Expneses
151,815
Total
Nonmeter
Distribution
Maintenance
Expenses
6,948,825
Total Nonmeter
Distribution
Operation and
Maintenance
Expenses
11,873,886
Total Nonmeter
Distribution
Costs
$ 73,092,709
Fraction of
Residential
Customers
.891
Allocation o£
Nonmeter Dis-
tribution to
Residential
65,125,604
Fraction of
Low Voltage
Commercial
Customers
.108
Allocation of
Nonmeter Dis-
tribution to
Low Voltage
Commercial
7,894,012
Fraction of
Industrial
Customers
.001
Allocation of
Nonmeter Dis-
tribution to
Industrial
73,093
-------
Table 25. SUMMARY OF ALLOCATION OF CAPACITY COSTS,
Potomac Electric Power Company, 1972
Function
GENERATION CAPACITY COSTS
Naive KWH Allocation:
KWHs to Schedules during peak
TRANSMISSION CAPACITY COSTS
Naive $/KWH Recovery:
NONMIiTER DISTRIBUTION CAPACITY
COSTS
Naive $/KWH Recovery:
Customer Class
Residential
647,588 x 103KWH
$16,540,586
(.0255)
65,125,604
(.1006)
Commercial
1,268,353 x 10'KWH
$ 2,004,919
(.0016)
7,894,012
(.0062.)
Industrial
279,009 x lO'KWH
$ 18,564
(.0000)
73,093
(.0000)
Interchange
and Resale
211,002 x 103KWH
$ 8,655,974
(.0410)
Total
$103,266,719
.0429$
KWH
$ 27,220,044
73,092,709
VD
t/J
-------
remained the same even with such cost recovery practice, fixed
costs of generation would have been recovered at the rate of
$.0429/KWH, which figure is obtained as ($103,266,719/2,405,952
x 103)--the ratio of total fixed costs of generation to total
peak KWH. But only the total costs of generation are to be
livided by total peak KWHs, since only generation capacity
costs are commonly incurred. Since we have already apportioned
transmission and distribution costs among customer classes--
the results of that apportionment are summarized in Table 25,
Summary of Allocation of Capacity Costs--those figures must be
divided by the number of KWHs taken on peak by the correspond-
ing customer class. The line of Table 25 labelled KWH to
Schedules During Peak presents our estimate of individual cus-
tomer class consumption on peak, to be explained below; then,
for example, the entry (.0255) below the matrix element for
Transmission/Residential indicates that, had total fixed
transmission costs allocable to residential service--
$15,540,586--been recovered from our estimated number of peak
KWH taken by residential customers, i.e. 647,588 x 103KWH,
recovery per KWH would have been $.0255/KWH. The other
bracketed figures are obtained similarly.
Our description of the procedures whereby Table 25 is obtain-
ed will therefore be complete once we explain our method for
imputing the customer class KWH consumption during peak hours.
In principle, it would, of course, be preferable to work from
directly measured data--from data on customer class load
curves. Some systems do some sampling of some rate classes,
and some have a fairly.accurate knowledge of the load curves
of large individual customers, but very few try seriously to
decompose the system load curve into its individual customer
class constituents. Of the systems in our sample, only
Pennsylvania Power and Light and Commonwealth Edison Company
have a fairly accurate grasp of their customer class load
94
-------
curves. Pennsylvania Power and Light, probably the most so-
phisticated system in the industry in this (and, we suspect,
not only in this) respect, actually decomposes the system
load curve into customer class load curves; Commonwealth
Edison does something similar, but only for the week in which
the system peak day occurs.
How serious a limitation is this? We believe that the answer
is that it is serious for the systems but not so serious for
our purposes. We mean by this peculiar turn of phrase that
intelligent rate making requires greater sensitivity to
changes in customer class load patterns than now exists; but
that for our purposes the construction of indicators of po-
tential pricing improvement--the distortions are sufficiently
large that they survive the crude procedure about to be de-
scribed. That the procedure is not too crude is, we believe,
indicated by our comparison--for Pennsylvania Power and
Light--of actual and imputed customer class load curves:
the two were found to differ by less than 5 percent in KWH
terms.
Table 26, Imputed Customer Class Load Curves, begins this
procedure. Under the assumptions that both interchange and
resale and industrial loads are flat over the year, the con-
tribution of these loads is removed from total peak KWH.
Residential and commercial contributions to the residual
peak KWH are taken in proportion to residential and commer-
cial annual KWH consumption. (A similar calculation gives
customer class contributions to KWH consumption in offpeak
hours during the peak months; those figures will be required
in our indicator estimates and are, therefore, also computed
in Table 26.)
95
-------
Table 26. IMPUTATION OF CUSTOMER CLASS LOAD CURVES
Potomac Electric Power Company, 1972
103KWH
Total Peak
Total Interchange, 1972
Fractioll
768
Peak Interchange = (.0877) (2,405,952) =
Total Peak - Peak Interchange =
Total Industrial, 1972
Peak Industrial = (.0877) (Total Industrial) =
(Total Peak Peak Interchange -\_
I Peak Industrial /"
Total Residential, 1972
Total Low Voltage Commercial, 1972
Sum
Fraction Residential
Fraction Low Voltage Commercial
Peak Residential - (.338) (2,405,952)
Peak Low Voltage Commercial = (.662)(2,405,952)
June
July
August
September
Total Peak Season
Peak Hour in Peak Season
Total Peak Season Offpeak Hour
Fraction of Total Year Hours in Hours
in Peak Season Offpeak Hours
Interchange in Peak Season Offpeak =
(.2466)(5,803,591) =
Industrial Sales in Peak Season Offpeak =
Sum
Total Peak Season Offpeak Hour «
3,291,360 - 2,219,291 =
Fraction Residential
Fraction Low Voltage Commercial
Peak Season Offpeak Hour Residential =
(.338)(1,072,069) =
Peak Season Offpeak Hour Commercial =
(.662)(1,072.069) =
2,405,952
5,803,591
.0877
211,002
2,194,950
3,181,397
279,009
1,915,941
3,128,685
6,123,240
9,251,925
.338
.662
647,588
1,268,353
1,244,243
1,614,291
1,548,762
1,290,016
5,697,312
2,405,952
3,291,360
.2466
1,433,486
785,805
2,219,291
1,072,069
.338
.662
362,359
709,710
96
-------
Return momentarily to Table 25, Summary of Allocation of
Capacity Costs: the above procedure is the one responsible
for the row specifying customer class consumption during
peak hours. Table 25 thus summarizes the capacity cost di-
mensions of cost structure which we require in the construc-
tion of indicators in Section IV. A similar table must be,
and has been, constructed for each system in the sample.
These constructions are, typically, much more tedious and
somewhat more judgmental than the one we have used as an
illustration of the general method, for the simple reason
that most system rate schedules are much more complicated--
there are many more rate classes--than the system used above.
Without further ado, we turn to the work of Section IV.
97
\
-------
SECTION IV
THE PRICING OF ELECTRICITY:
INDICATORS OF POTENTIAL IMPROVEMENT
The purpose of this chapter is to select and estimate quanti-
tative measures of the improvement possible in the pricing of
electricity. Improvement usually can and should be called by
its proper name, welfare gain or gain in net benefit. But
here we will use the term "indicator" for two reasons. First,
our very real ignorance of many crucial features of demand
and cost structure suggests modesty. We believe that the mea-
sures to be discussed are good order of magnitude estimates
and good indicators of where additional demand and cost infor-
mation might usefully be "bought"--where more fine-grained
demand and cost studies could reasonably be expected to pay
for themselves in pricing improvements. Second, there are
large and difficult to measure external effects associated
with the electric power industry. In industries where exter-
nal effects are small, a total surplus measure of welfare is
plausible and acceptable; the difference between what some
customer is willing to pay for a unit of the commodity and
the opportunity cost of the resources used in producing the
commodity is an obviously appropriate measure of the contri-
bution of that unit of the commodity to overall welfare.
The difference between an industry with only minor external
effects and an industry with major external economies is
that in the first case, privately registered costs of pro-
ducing output are a relatively good measure of the social
opportunity costs of producing that output, while in the
case of an industry with large external diseconomies,
98
-------
private costs understate social costs. A proposed change in
pricing practices which in an internal efficiency sense de-
creases output and thereby adds $1 to surplus (as computed
from demand and private costs) is deserving of more careful
attention than a similar proposed change which increases out-
put by enough to add $1 to surplus. In the first case there
are more than the $1 in measureable gains, since the decrease
in external costs imposed by the industry is a net gain. In
the second case, there are less than $1 in gains, since the
external costs imposed by the industry are thereby increased.
The direction of this line of argument can be dangerous, for
it seems to lead to an argument that computed welfare gains
can be aggregated judgementally when there are unmeasured ex-
ternal effects. We draw the line far short of this in what
follows, but we find the argument persuasive for asking the
usualy questions of welfare economics--how can welfare be in-
creased by changes in pricing--in a somewhat different way,
i.e., how can welfare be increased by selective price in-
creases. Put another way, a naive version of the rules for
a welfare optimum might be stated as: charge no customer
less than the incremental costs of service, nor any customer
more than the incremental costs- of service. Our effective
restatement of that rule is then: in an industry with large
external diseconomies, first insure that no customer is be-
ing charged less than the full incremental costs of service.
The implementation of this rule we leave to later in the
section. We turn to a brief overview of the variety of
electricity tariffs and their traditional rationale. Fol-
lowing that is the construction of the indicators of poten-
tial pricing improvement.
99
-------
THE VARIETY OF TARIFFS
There are probably several dozen electricity tariff types in
use throughout the world, the precise number depending upon
the system of classification. This diversity has its origin
in the great variety of electricity systems throughout the
world and in the way in which rate structures have evolved.
The earliest American electric systems served lighting loads
and often charged a flat subscription fee independent of
actual consumption--actual.consumption was not metered--but
presumably based, in some way, upon expected consumption.
A particular utility's tariff structure is the product of
a long series of incremental changes and therefore reflective
of the distinctive history and policies of that system.
Nevertheless, several distinctive tariff types are identifi-
able, and these have been listed in Table 27. The last
column of that table, headed Cost Recovery Strategy, summar-
izes the cost rationale of the corresponding tariff. Since
it is essential in what follows that we recognize the valid
and invalid content of each tariff rationale, some further
explanation is in order.
The decomposition of costs listed is what we have called the
conventional utility cost vocabulary. Recall from our dis-
cussion of that vocabulary the underlying assumption that
the four dimensions of cost therein identified--energy,
capacity, customer and residual costs are, for purposes of
rate making, roughtly independent dimensions. Suppose we
begin with the two-part tariff entry in Table 27. That
tariff is the simples to explain. A customer whose
monthly bill is computed under such a tariff pays a minimum
bill, or meter rent.M independent of monthly consumption;
that is, the bill even if consumption is zero. The obvious
cost rationale for that meter rent is the necessity of
100
-------
Table 27. TARIFF TYPES AND COST RECOVERY STRATEGIES'*
Tariff Type
Two-Part Tariff
[M;e]
Fixed Energy Block
Rates:
No meter rent and
no seasonal
differential
[B(j), e(j)]
Energy and Demand :
[B(j);e(j)l
[D(j);S(j)]
No meter rent and
no seasonal
differential
Second-Best Marginal
Cost Pricing
Peak Responsibility
[M;P.(D,P(2)]
Bill for ^V of£ Peak» Elasticity o(l)
Consumer * ?n **?' Elasticity a(2)
Talc in* ^ In Toto
laKing ^ Maximum Demand
M +
qe
Zi^BCJDeCj) +
Cq-Z?"1B(j))e(S)
where
2?"1B(j)
-------
covering customer costs--by definition those costs, such as
billing and general and administrative expenses and the an-
nualized cost of the drop line connecting the individual cus-
tomer to the distribution system, independent of consumption.
This is perhaps the least controversial of all features of
utility rate making, for the obvious reason that the cost
incurrence involved is unambiguously identifiable with an
individual customer. Next, the two-part tariff customer
pays an energy charge e per unit of consumption q. And
there, as indicated in the final column of Table 27, the
difficulties and ambiguities begin. For the energy charge
must recover both energy and capacity costs imposed upon the
utility by the two-part tariff customer. Since capacity
charges are being levied at a flat rate independent of the
timing of consumption, and since we have argued that any
reasonable measure of peak versus offpeak costs gives esti-
mates of peak costs many times higher than offpeak costs,
the flat energy charge of the two-part tariff provides
perverse incentives: prices offpeak are too high, discour-
aging consumption unnecessarily, while prices at peak are too
low, inefficiently encouraging consumption. This defect,
among others, has led to pressure for the abandonment of the
two-part tariff, but it should be noted that a two-part tariff
may, under some circumstances, be the best possible tariff.
Suppose, for example, that all consumers take so little elec-
tricity that they will not, within the relevant band of
possible peak versus offpeak prices, distinguish between con-
sumption in those subperiods. Then the question facing a
rational pricing authority would be that of the best single
energy charge.
102
-------
Next, in Table 27, consider the characteristic type of resi-
dential rate, the fixed block rate. In general that tariff
is specified by a block structure {B(jJ} and a structure of
intrablock charges e(j). The first block of KWH is (0,B(1)),
the second block (B(l) ,B(2)) , and so on. Generally, there
will be a minimum bill associated with the first block, so
that the customer must pay e(l)q for consumption q in the
interval 0e(2)>...-- the marginal energy charge is below
the average energy charge. That average charge can be
computed by dividing the total bill by total consumption.
As with the two-part tariff, the interesting question here is
that of cost rationale. And as with the two-part tariff,
the minimum bill can be identified with the customer compo-
nent of cost service. But how can we then rationalize the
differential effective minimum bills paid by customers in
different blocks? For a customer in the second block one
may think of the effective minimum charge as the entire
first block charge 6(1)B(1). But for a customer in the
third block, whose marginal energy charge must be inter-
preted as e(3), that same interpretation of the first block
price as minimum bill and therefore as customer charge will
103
-------
no longer pass master. For that third-block customer is paying
a per unit "excess" of (e(2)-e(3)) above his marginal charge
for each second-block unit he takes. In short, the identi-
fication of customer cost recovery and minimum bill is ob-
scured. The difficulty mentioned above in connection with
the two-part tariff is also present here: the line between
energy and capacity cost recovery is not finely drawn, so
that identical marginal prices obtain off and on peak, with
the corresponding problem of perverse incentives.
Consider next the typical tariff applicable to larger users,
often called a general service tariff, a category is some-
time disaggregated into commercial and industrial rate classes.
(Industrial rates are typically designed for larger users with
higher volumes and better load factors than commercial.rate
users.) This tariff amounts to a doubling of the structure
of the energy-block rate tariff: there are effectively two
block structures, one for the pricing of energy consumption
and one for the pricing of maximum demand. Thus this tariff
requires that total KWH and also maximum demand, or KW, be
metered. As above let {B(j)> be the energy block structure
and let {D(k)} be the demand block structure. Then the
third row third column entry of Table 27 gives an algebraic
expression for the bill paid by a customer who takes energy
q (which puts him in the N energy block) and whose maximum
+ Ti
demand is u, which puts him in the Q demand block. Thus
his first block demand bill is the "length" of that demand
block, D(l), times the charge S(l) per KW in that block.
Summing the contributions to the demand charge from each of
i
the covered blocks and computing the remainder block charge
gives the total demand bill. A similar calculation gives
the energy bill, and the customer's total bill is then the
sum of energy and demand bills.
104
-------
The critique of the cost rationale underlying this tariff
follows the lines of that given above for the energy block
structure alone, but must be extended to the way in which
capacity costs are recovered. For the demand block struc-
ture is an attempt to explicitly price the capacity costs
imposed by the user. Its major difficulty is the non-
coincident demand basis of the capacity charge. User A
and user B may have the same maximum demand, say 1,000 KW.
But if user A's maximum demand comes offpeak, say at 1 a.m.,
there is no reason to bill him at the same rate as user B,
whose maximum demand comes at the instant of the system peak.
User A is imposing no resource cost upon society for the pro-
vision of capacity to meet his demand (He is imposing a
resource cost in the sense of fuel used for generation).
User B is imposing the full costs of providing 1,000 KW of
capacity. Thus the use of noncoincident demand charges can
lead to the same sort of perverse offpeak versus peak incen-
tives as the flat marginal charge tariff.
For completeness, and because several systems in our sample
do employ such tariffs, we what are sometimes called sliding
block tariffs--tariffs with a mixed structure in which the
length of the energy blocks may depend upon maximum demand.
Usually the demand block structure is defined by taking the
lengths of the various blocks to be proportional to maximum
demand u : if the basic demand block structure is {W(l) } then
for a customer with maximum demand ja the first demand block
is of length uW(l), the second of length uW(2), and so on.
The idea is to penalize customers with "poor" load factors--
with maximum demand much higher than average demand -- for
the capacity costs they impose. But note that the scheme is
based upon maximum customer demand, which may or may not be
coincident with the system peak demand. The problem of
perverse incentives remains.
105
-------
The last two row entries of Table 27 are not seen as tariffs
in the United States--there are some attempts to introduce
peak responsibility principles into bulk power pricing, one
of which we refer to below--but are listed as guiding prin-
ciples for rate making, and because of their relevance to
the discussion below. In second-best marginal cost pricing,
each user is charged a price which inevitably must differ
from the short run marginal cost of serving him--because,
since short run marginal cost is below average cost, prices
equal to marginal cost would be insufficient to cover cost.
But the deviation is arranged to cover cost in a way that
least distorts the pattern of consumption that would arise
were prices equal to the short run marginal cost measures
we have discussed in Section III. The appropriate second
best rule is that prices differ from short run marginal
costs of service in inverse proportion to demand price elas-
ticities of demand.
This normative rule for utility pricing has been the subject
of a great deal of theoretical discussion. The correspond-
ing difficulties of interpretation and implementation have
not been so thoroughly treated. Our interpretation and im-
plementation of this rule, which corresponds to Category I
of our customer response typology, may be subject to some
objection.
Our dicussion of Table 27 concludes with some remarks on
the last line of that table. We used the term peak respon-
sibility in the very broad sense'of any tariff which attempts
to restrict recovery of capacity costs to a charge billed at
the system peak; or, in other works, to any tariff the /
demand charge component of which is a strictly coincident
demand charge. The coincidence referred to is coincidence
with the system peak. We have indicated that customer and
106
-------
residual costs can and should be recovered in a minimum bill
or meter rent M under this tariff; and further that there will
be prices per KWH P(l) and P(2) differentiating between off-
peak and peak.
So much for this necessary and preliminary overview of tariff
structure, which has served to introduce the tariffs and to
sketch the structure of the remainder of this Section. For
an overview of that structure we must piece together our
scattered remarks concerning the perverse incentives provided
by the various tariffs with the typology of customer responses
set out above. Indeed, it is only now that the role of that
typology in guiding the construction of potential pricing
gains can be set out.
The remaining four sub-sections of this Section complete
the task of constructing indicators of potential gain, with
each section treating one category of the typology: the
relevant customer classes associated with each category
(this subject has been broached above), the interpretation
of the corresponding indicator, and the evaluation of that
indicator for the companies in the sample.
CATEGORY I INDICATORS OF POTENTIAL PRICING IMPROVEMENT
Category I embraces customers who, for information cost rea-
sons, will not distinguish between peak and offpeak nor be-
tween average and marginal price. Very plausibly, residential
and small commercial customers belong in this category. Under
our assumptions the only signal which registers for these
customers is average price, so that the only relevant poten-
tial pricing change is a change in average price. Thus the
question to pose regarding these customers is as follows:
if the average prices charged the various customer classes
107
-------
are not the prices required by second best short run marginal
cost pricing, how large are the potential gains associated
with realigning these average prices as required by the
second best standard? The answer shall prove to be very
small, so that average price changes are not prime candidates
as instruments of rate structure improvement. A sample cal-
culation for one system should illustrate the orders of
magnitude involved.
First, a formal statement of the second-best efficiency
conditions which have been stated in words above:
P. -
P. B.
- = TT" i, j = all rate classes (26)
Where P. and P. are the average prices charged rate classes
i and j respectively, y. and y. the short run marginal
costs of serving those rate classes, and E. and E. the
elasticities demand of those rate classes. Before launching
into the empirical work, some further discussion of equation
(26) will probably be helpful. Note first that the equations
are necessary conditions for a second best set of (relative)
average prices, but that these equations alone are insuffi-
cient to determine the second best solution- -for that deter-
mination we need another equation, the requirement that
total revenue equal total cost. Next, in what sense is the
solution determined by this set of sufficient conditions
"second best"? Remember that first best always means price
equal to short run marginal cost. Because electric utilities
are required to recover their costs from their customers,
and because short run marginal costs are below short run
108
-------
average costs, first best pricing of electric power would
lead to deficits. It is necessary to price above short
run marginal cost in order to cover costs, and the second
best solution is the least distorting way of doing so: it
leads to the smallest loss in total welfare (the sum of
consumers' plus producer's surpluses). The reader trained
in economics may be troubled because this solution seems
identical with the pricing policy a discriminating monopolist
would pursue. This is true, but there is a crucial difference
The discriminating monopolist is able to capture all of the
surplus, consumers' and producer's*, the public utility
pricing at second best marginal cost leaves consumers with
all realized consumer surpluses.
As a first guide to where pricing improvement of this kind
may be possible, we construct a comparison table, Table 28,
of existing values of "deviation ratios" and "elasticity
ratios". The deviation ratio is the left side of equation
(26) and the elasticity ratio the right side of that same
condition when computed for present values of average price,
marginal cost and elasticity: the equation defines second-
best prices, so that it only holds when prices have been
adjusted to a second-best optimum.
As elsewhere in the report, we use 1972 Potomac Electric
Power Company data for illustrative purposes, and for that
system we treat, initially, the three rate classes--Residen-
tial, Commercial, and Industrial.
For each pairwise combination of customer classes there is a
comparison between deviation and elasticity ratios. Thus,
for our three customer classes case there are three such com-
parisons. Again, the efficiency condition (26) holds only
109
-------
Table 28. DEVIATION AND ELASTICITY RATIOS,
POTOMAC ELECTRIC POWER COMPANY, 1972
^>Henominator
Numerator ^\_
Residential
Commercial
Industrial
Residential
Deviation
.953
.846
Elasticity
.737
.583
Commercial
Deviation
1.049
.888
Elasticity
1.357
.792
Industrial
Deviation
1.182
1.126
Elasticity
1.714
1.263
when prices are optimal, so that present values of deviation
ratios--i.e., values based upon present prices and associated
marginal costs--will not necessarily equal the corresponding
elasticity ratios, and in the case of our trial run utility,
for which deviation ratios have been computed and compiled
in Table 28, they do not. The deviation ratios.computed in
Table 28 are based upon average prices associated with sales
under each rate schedule, and with a marginal cost figure
based upon the marginal unit in use during peak hours in
August (cf. our discussion of marginal costs above). The
elasticity ratios are based upon elasticity estimates by
state and customer class published by Chapman, Tyrell and
Mount and discussed in Section II.
A first question suggested by Table 28 is that of consistency:
are the (pricing) policy implications of the various compari-
sons afforded by Table 28 consistent with one another? Since
the deviation ratiofor example, for the residential-inc^us-
trial comparison--is
110
-------
R
R
(27)
and since the expression - is montonic increasing in p
so long as y>0 , a comparison of deviation and elasticity
ratios suggests the following pricing changes: if the
present deviation ratio is greater than the corresponding
eleasticity ratio, either decrease the "numerator" price
or increase the "denominator" price or do both, in order
to bring the two ratios closer into line. Conversely, if
the present deviation ratio is less than the elasticity
ratio, either increase the numerator price, or decrease
the denominator price, or both.
Carrying through the three possible palrwise comparisons
for the test case summarized in Table 28 leaves us with the
following policy implications, presented in Table 29.
Table 29. POLICY IMPLICATIONS OF TABLE 28
Rate Schedule
Residential
Commercial
Industrial
Direction of Implied Price Chage
111
-------
There is no inconsistency associated with the opposing arrows
in the commercial price column: it simply happens that the
residential-commercial pairing comparison leads to the
policy recommendation raise, or lower, or both; whereas the
commercial-industrial pairing leads to the policy implication
lower or raise or both. We thus may choose residential and
industrial prices as "policy instruments" and proceed to a
determination of the required changes in their magnitudes,
and, following that, of the associated welfare gains.
Now if the revenue constraint is to be continued to be satis-
fied under the new prices (as it presumably has been under
the old) then the changes in residential and industrial prices
are not independent, but must satisfy a condition derivable,
after some manipulation, from the revenue constraint. That
condition is
6Pn qT 1 - ATET
K - __±, * * f?8l
qR 1 - ARER CZ8J
IV Jtx S\.
where AT,AD are the corresponding fractional departures
IK p _p
from marginal cost: A _ is defined as I _ , and similarly
I p -
f or A D *
K..
The efficiency condition requires that changes in residential
and industrial prices be such as to equate deviation and elas
ticity ratios
R
PR + ~^r- - ^ (29)
PI + 5
112
-------
Equations (28) and (29) together determine the required price
changes. Solution of a quadratic equation for pR gives the
numerical value of the required change as roughly + .207
-------
install and operate than a double register meter, so that we
commit no error of overstatement in our final indicator of
feasible benefits for these customers if we assume no change
in metering costs under time differentiated average pricing.
We therefore proceed to the estimation of indicators of po-
tential pricing improvement for all rate classes on a common
basis. When those estimates are completed, we net out the
metering costs for residential customers.
An Overview of the Calculation
It may be helpful to look at a simplified version of the indi-
cator estimate, one which exhibits the essentials of the prob-
lem without the inessential problems associated with the
numerous rate schedules that some systems have. We there-
fore take our Potomac Electric Power Company cost information,
the work of Section III, and construct Table 30, captioned
Bands of Suggested Prices for Peak Months. In the columns
headed Generation, Transmission, and Distribution, we have
entered, from Table 25, our derived costs to be recovered per
KWH figures for the individual functions, cross-classified by
customer class. By summing the functional costs for each
rate schedule we obtain, for each customer class, an "upper
bound" on capacity costs to be recovered during peak season
peak hours from that customer class. By further adding an
estimate of the marginal costs of generation during peak
hours, obtained from our previous analysis of short run mar-
ginal cost, we have what may be considered an upper bound on
total costs to be recovered from each customer class at
peak hours. In Column 3, we record that estimate of marginal
generation costs is $.007/KWH. This is certainly an in prac-
tice lower bound on costs to be recovered. For purposes of
114
-------
Table 30. BANDS OF SUGGESTED PRICES FOR PEAK SEASON,
POTOMAC ELECTRIC POWER COMPANY, 1972
tn
Rate 'Schedule'
Residential
Commercial
Industrial
Interchange
and Resale
Present
Average
Price
IWH
.02476
.02185
.01425
.00971
Lower
Bound
("SRMC")
$
KWH
.007
.007
.007
.007
Generation
$
KWH
.0429
.0429
.0429
.0429
Transmission
$
KM
.0255
.0016
.0000
.0410
Distribution
$
IWH
.1006
.0062
.0000
.0000
Upper Bound
$
OT
.1760
.0577
.0499
.0909
-------
comparison we have tabulated, in Column 1, average revenue
for each customer class. The striking, if unsurprising,
comparison is evident for all rate schedules: marginal cost
is well below average revenue which, in turn, is far below
"peak responsibility" price. Recalling our discussion of
peak responsibility pricing above, there will be substantial
welfare gains from peak responsibility pricing.
Consider next Figure 3, which with Table 31 presents a first
illustrative calculation of the welfare gains available from
improved pricing of electricity sold to the various customer
classes.
Peak Demand
Peak
Offpeak
sOffpeak Demand
KWH
Offpeak
KWH
Peak
Figure 3. Welfare Gains from Peak Load Pricing
116
-------
Table 31. ILLUSTRATIVE INDICATORS OF POTENTIAL PRICING IMPROVEMENT,
POTOMAC ELECTRIC POWER COMPANY, 1972
Rate 'Schedule1
Residential
Commercial
Industrial
Interchange
and Resale
(1).
" /«/
.14
.19
.24
.24
(2)
Present
Average
Price
KwR..
.02476
.02185
.01425
.00971
(3)
'reposed
>{{ Peak
lour, Peak
lonth
Price
S/KKII
.014
.014
.014
.007
(4)
Proposed
Peak Hour
Peak
Month
Price
$/KWII
..088
.029
.025
.045
Off Peak Hour, Peak Season Indicator
(S)
'Pop
2-3
.011
.008
.00025
.0027
(6)
2sa.ca
Pf (T)
.786
.571
.018
.386
(7)
""op
10'KWH
362,359
709,710
785,805
1,433,486
(8)
AWop-
lEApKWHop££
199,370
324,196
424
165,998
Peak Hour, Peak Season Indicator
(9)
*Ppk
4-2
.063
.007
.011
.035
(10)
*Ppk . 9
-PT'T
.716
.241
.440
.778
(")
KKIIpk
10'KIVII
647,588
1,268,353
279,009
211,002
(12)
«pk '
lEipKhHpk^
2,040,161
213,971
159,593
689,470
E 689,988
t 3.103.195
£1 3.793.183
-------
of demand between off peak and peak are taken to be zero.
Finally, note that the calculation refers to only those
months identified as peak season months in the discussion of
Section III. The use of short run elasticities is for illus-
trative purposes, to indicate the orders of magnitude ob-
tained in such estimates.
We turn now to a more realistic indicator estimate in which
some of the restrictive assumptions which make the above
example simple are relaxed.
Indicators of Potential Pricing Improvement:
Seasonally Spread Peak Responsibility Rates
The above calculation is an instructive guide to the source
of the distortions inherent in average cost pricing of elec-
tric power, but is insufficient as a benchmark for further
analysis. As we have argued in our discussion of short run
marginal costs, the notion of "the peak" is complex: at
almost any given time the relationship between capacity and
demand is different, and in order to reduce that relation-
ship to something upon which rate making can be based, con-
siderable "averaging" over random elements in the relation-
ship- -especially the stochastic component of outages--is
necessary. Even where the seasonal load curve of a given
system exhibits a pronounced peak, the month or season of
that peak cannot naively be identified with "the" peak,
since the necessity of scheduling downtime for maintenance
often means that there is no grea£ surfeit of capacity dur-
ing the offpeak seasons. If the point of peak pricing is
to appropriately penalize those casually responsible for the
incurrence of capacity costs, then even peak hour off peak
season customers must be so penalized, since much nominally
"free" capacity is actually in maintenance during that time.
118
-------
Present average price P is too high off peak and too low on
peak, so that there are welfare losses. The off peak wel-
fare losses AW«p arise because off peak customers are being
charged more than the marginal costs of serving them. The
on peak losses AWp arise because on peak customers are being
charged less than the incremental costs of serving them, so
that capacity plus operating costs higher than the value of
the marginal peak KWH are incurred by the utility and imposed
upon society. In terms of Table 30, Figure 3 refers to a
single customer class: the appropriate off peak price Pgp
will be something close to the lower bound for that customer
class compiled in Column 3, and the appropriate peak price
will be something close to the upper bound compiled in Col-
umn 7 of that table. The welfare loss triangles can be com-
puted in terms of e, the elasticity of the relevant demand
p
schedule, Af, the differential between correct and present
average price, and p and q, initial quantities and prices.
Those computations are summarized in Table 31, and the ex-
pressions for the welfare losses are entered at the heads of
Columns 8 and 12 of that table.
In Column 3 of Table 31 we have entered a conservative esti-
mate of proposed offpeak prices, namely twice marginal gene-
ration .cost, and in Column 4 a similarly conservative pro-
posed peak price, half of our Table 30 "upper bound" peak
responsibility price. In Columns 8 and 12 benefits are
tabulated by rate schedule, having been computed with the
formula at the head of each column. Summation of those
benefits gives our estimate of total benefits. The elasti-
cities used in this calculation have been taken as short run
elasticities, and are the short run elasticities estimated
by Chapman et. al. in the paper discussion in Section II.
We have tacitly assumed that these elasticites are identical
on peak and off peak, and that the cross price elasticities
119
-------
and therefore they are imposing capacity costs over and above
those required to meet the demands of off peak hour, off peak
season customers.
But how shall capacity costs be apportioned among seasons?
There is, here as elsewhere, no unambiguous allocation, for
the underlying problem--akin to the scheduling problem men-
tioned in connection with short run marginal costs--is a
difficult one. The use of several reasonable measures of
the relationship of capacity to demand during the three sea-
sons into which we have divided the year--June through Sep-
tember, October through January, and February through May--
gives very comparable results, and we have therefore adopted
the simplest of procedures in this seasonal allocation of
capacity costs, an allocation based upon the seasonal distri-
bution of total 'energy sales. This means that, e.g., depre-
ciation is apportioned among systems as if it were a pure
user cost, incurred only in proportion to output. The ambi-
guities of the allocation of capacity costs among seasons do
not, we feel, blur the basic cost differential, that between
the cost of peak hour and off peak hour power during any day
of any season. Finally, a word on utility practice in doing
what amounts to this allocation. Many summer peak systems
do have some rate seasonal differential, but we have found
it impossible to get, from any one system, a clear statement
of the basis for that differential. We have been told pri-
vately by the officials of several systems that the present
differential is inadequate. A conjecture which seems to fit
the facts is that the interseasonal differential--e.g., the
difference between the heights of the residential tailblocks
in peak and offpeak seasons--is often taken in a rule of
thumb way as the short run marginal cost differential between
the most expensive unit in the system and base load plants.
The latter differential is typically of the order of
120
-------
Given our allocation of capacity costs by system, rate sched-
ule, and season, our steps in deriving upper and lower bounds
for prices can be retraced, and the results are as tabulated
in Tables 32 through 36, Bands of Suggested Prices by Season;
there is one such table for each system in the sample. The
major differential, already evident in our preliminary com-
parison of Table 30, holds: average pricing substantially
underprices peak period power. Also in line with what we
have come to expect is the relative size of the differential
among rate classes. Thus the commercial load is typically
not "as underpriced" as residential and industrial loads.
Two explanations for this seem appropriate. First, the
commercial load is typically right on peak--nowhere near as
flat as the industrial load, and not as spread as the resi-
dential load, since the latter has the lighting component
late into the evening and an early-morning component. Sec-
ond, and not entirely fanciful, since it has been suggested
to us by personnel at several utilities, residential custo-
mers are more numerous, more vocal, and more likely to be
the source of complaints. If not having to deal with irate
customers is a benefit valued by utility personnel, there
should be some bias of rates in favor of residential custo-
mers and against commercial customers.
Having thus spread capacity costs "over seasons," we turn to
the calculation of indicators of potential pricing improve-
ment by rate schedule and season. Recall Figure 3. Both
off peak and peak welfare gains AWQp and AWp are based upon
internal cost measures, since all our cost estimates (which
underlie our peak and off peak price estimates) are based
upon internal cost measures. Further, correct pricing of
off peak power will result in increased off peak consump-
tion- -and increased external cost--while correct pricing of
peak power will result in decreased consumption and decreased
121
-------
Table 32. BANDS OF SUGGESTED PRICES BY SEASON:
Potomac Electric Power Company, 1972
Rate Schedule
by Season
CD
Residential :
June -Sept.
Oct. -January
Feb. -May
Commercial:
June-Sept.
Oct. -January
Feb. -May
Industrial:
June-Sept.
Oct. -January
Feb. -May
Interchange §
Resale:
June-Sept.
Oct. -January
Feb. -May
Lower Bound
"SRMC"
$/KWH
(2)
.007
.007
.007
.007
.007
.007
.007
.007
.007
.007
.007
.007
Generation
$/KWH
(3)
.0171
.0205
.0194
.0171
.0205
.0194
.0171
.0205
.0194
.0171
.0205
.0194
Transmission
$/KWH
(4)
.0125
.0122
.0110
.0008
.0008
.0007
--
""
.0137
.0137
.0137
Distribution
$/KWH
(5)
.0493
.0479
.0433
.0030
' .0030
.0027
--
""
--
Upper Bound
"LRMC"
$/KWH
(6)
.0796
.0813
.0744
.0216
.0250
.0235
.0178
.0212
.0201
.0315
.0349
.0338
Present
Av. Annual
Price
$/KWH
(7)
.02476
.02185
.01425
.00971
ts)
to
SRMC a .Short-Run Marginal Cost.
LRMC » Long-Run Marginal Cost.
-------
Table 33. BANDS OF SUGGESTED PRICES BY SEASON:
Commonwealth Edison Co., 1972
Rate Schedule
by Season
(1)
Small Residential:
June -Sept ember
October- January
February-May
Large Residential:
June-September
October-January
February-May
Residential Space
Heating:
June-September
October- January
February-May
Small Commercial §
Industrial:
June-September
October- January
February-May
Large Commercial §
Industrial :
June-September
October-January
February-May
Lower Bound
"SRMC"
$/KWH
(2)
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
Generation
$/KWH
(3)
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
Transmission
$/KWH
(4)
.0469
.0469
.0469
.0117
.0117
.0117
.0114
.0114
.0114
.0017
.0017
.0017
--
Distribution
$/KWH
(5)
.0933
.0933
.0933
.0233
.0233
.0233
.0028
.0028
.0028
.0035
.0035
.0035
--
Upper Bound
"LRMC"
$/KWH
(6)
.0630
.0630
.0630
.0578
.0578
.0578
.0370
.0370
.0370
.0280
.0280
.0280
.0228
.0228
.0228
Present
Av. Annual
Price
$/KWH
(7)
.0353
.0302
.0170
.0249
.0132
to
Ol
-------
Table 33 (continued). BANDS OF SUGGESTED PRICES BY SEASON:
Commonwealth Edison Co., 1972
Rate Schedule
by Season
'CD
Street Light §
Signal System:
June-September
October- January
February-May
Water § Sewer
Pumping:
June - S ep t emb e r
October -January
February-May
Railroads § Rail-
ways :
June-September
October -January
February-May
Resale, Municipal!
ties:
June- September
October- January
February-May
Lower Bound
"SRMC"
$/KWH.-
-C2)
.0046
.0046
..0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
.0046
Generation
$/KWH
(3)
--
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
.0182
Transmission
$/KWH
(4)
.0001
.0001
.0001
.0094
.0094
.0094
.0067
.0067
.0067
Distribution
$/KWH
(5)
.0435
.0435
.0435
.0002
.0002
.0002
*
w
.*>
Upper Bound
(6)-(2) + (3) + (4)*(5)
"LRMC"
$/KWH
(6)
.0481
.0481
.0481
.0231
.0231
.0231
.0322
.0322
.0322
.0295
.0295
.0295
Present
Av. Annual
Price
$/KWH
(7)
.0209
.0135
.0160
.0112
NJ
-------
Table 34.
BANDS OF SUGGESTED PRICES BY SEASON:
Duke Power Company, 1972
Rate Schedule
by Season
CD
Residential (R)
July-October
Nov. -February
March-June
Residential (RA) :
July-October
Nov. -February
March- June
Residential (RW) :
July-October
Nov. -February
March-June
Residential (WGS §
MISC.) :
July-October
Nov. -February
March-June
Commercial § Indus-
trial (G) :
July-October
Nov. -February
March-June
Commercial 5 Indus-
trial (GA):
July-October
Nov. -February
March-June
Lower Bound
"SRMC"
$/KWH
(2)
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
Generation
$/KWH
(3)
.0091
.0091
.0094
.0091
.0090
.0094
.0091
.0090
.0094
.0091
.0090
.0094
.0091
.0090
.0094
.0091
.0090
.0094
Transmission
$/KWH
(4)
.0174
.0169
.0174
.0046
.0045
.0046
.0093
.0090
.0093
.0059
.0058
.0059
.
.0024
.0023
.0024
.0003
.0003
.0003
Distribution
$/KWH
(S)
.0341
.0332
.0341
.0181
.0087
.0090
.0181
.0177
.0182
.0115
.0112
.0116
.0046
.0045
.0046
.0005
.0005
.0005
Upper Bound
"LRMC"
$/KWH
(6)
.0650
.0635
.0653
.0266
.0272
.0409
.0401
.0413
.0309
.0304
.0313
.0205
.0202
.0208
.0143
.0142
.0146
Present
Av. Annual
Price
$/KWH
(7)
.0265
.0167
.0201
.0155
.0168
.0112
N)
Cn
-------
Table 34 (continuedj. BANDS OF SUGGESTED PRICES BY SEASON
Duke Power Company, 1974
Rate Schedule
by Season
(1)
Commercial § Indus-
trial (I)
July-October
Nov. -February
March-June
Commercial § Indus-
trial (IP-IS) :
July-October
Nov. -February
March-June
Commercial § Indus-
trial (All Other) :
July- October
Nov. -February
March-June
Street Lighting §
Signal System:
July-October
Nov. -February
March- June
Other Public
Authorities:
July-October
Nov. -February
March-June
Lower Bound
"SRMC"
$/KWH
(2)
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
.0044
i
.0044
.0044
.0044'
Generation
$/KWH
. (3)
.0091
.0090
.0094
.0091
.0090
.0094
.0091
.0090
.0094
.0091
.0090
.0094
.0091
.0090
.0094
Transmission
$/KWH
(4)
.0001
.0001
.0001
--
.0092
.0092
.0092
.0002
.0002.
.0002
Distribution
$/KWH
(5)
.0001
.0001
.0001
--
.0183
.0183
.0183
»
.0004
.0004
.0004
Upper Bound
(6)-(2) + (3) + (4) + (5)
"LRMC"
$/KWH
(6)
.0137
.0136
.0140
.0135
.0134
.0138
.0410
.0409
.0413
.0135
.0134
.0138
.0141
.0140
.0144
Present
Av. Annual
Price
$/KWH
(7)
.0089
.0079
.0278
.0322
.0105
-------
Table 34 (continued). BANDS OF SUGGESTED PRICES BY SEASON
Duke Power Company, 1974
Rate Schedule
by Season
CD
Sales for Resale:
July-October
Nov. -February
March-June
Interdepartmental :
July-October
Nov. -February
March-June
Lower Bound
"SRMC"
$/KWH
(2)
.0044
.0044
.0044
.0044
.0044
.0044
Generation
$/KWH
(3).
.0091
.0090
.0094
.0091
.0090
.0094
Transmission
$/KWH
(4)
.0061
.0061
.0061
- -
Distribution
$/KWH
(5)
--
"" ""
Upper Bound
(6)-(2) + (3) + (4) + (5)
"LRMC"
$/KWH
(6)
.0196
.0195
.0199
.0135
.0134
. Oloo
Present
Av. Annual
Price
$/KWH
(7)
.0089
.0144
ts)
-------
Table 35. BANDS OF SUGGESTED PRICES BY SEASON:
New York State Electric and Gas Corp., 1972
Rate Schedule
by Season
(1)
Residential:
Nov. -February
March-June
July-Octo'ber
General Service
(SC2 PSC 113):
Nov. -February
March-June
July-October
General Service
(SC2 PSC 108):
Nov. -February
March-June
July-October
Large Light § Power
(SC3 PSC 113) :
Nov. -February
March -June
July- October
Primary Light §
Power (SC3 PSC 108)
Nov. -February
March-June
July -October
Lower Bound
"SRMC"
$/KWH
(2)
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.004.7
.0047
Generation
$/KWH
(3)
.0128
.0131
.0130
.0128
.0131
.0130
.0128
.0131
.0130
.0128
.0131
.0130
.0128
.0131
.0130
Transmission
$/KWH
(4)
.0148
.0146
.0147
.0049
.0048
.0048
.0016
.0016
.0016
.0001
.0001
.0001
::
Distribution
$/KWH
(5)
.0336
.0331
.0331
.0109
.0107
.0108
.0035
.0035
.0036
.0002
.0002
.0002
.0001
.0001
.0001
Upper Bound
C6) = (2) + (3) + (4) + CS)
"LRMC"
$/KWH
(6)
.0659
.0655
.0655
.0333
.0333
.0333
.0227
.0229
.0229
.0178
.0181
.0180
.0176
.0179
.0178
Present
Av. Annual
Price
$/KWH
(7)
.0272
.0273
.0175
.0138
.0103
to
oo
-------
Table 35 (continued). BANDS OF SUGGESTED PRICES BY SEASON:
New York State Electric and Gas Corp., 1972
Rate Schedule
by Season
CD
Other Public
Authority:
Nov. -February
March-June
July-October
Street Lighting §
Signal Systems:
Nov. -February
March-June
July-October
Interchange §
Resale :
Nov. -February
March-June
July-October
Lower Bound
"SRMC"
$/KWH
.(2)
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
Generation
$/KWH
(3)
.0128
.0131
.0130
.0128
.0131
.0130
.0128
.0131
.0130
Transmission
$/KWH
(4)
.0013
.0013
.0013
--
.0115
.0115
.0115
Distribution
$/KWH
(5)
.0031
.0031
.0031
--
_ _
--
Upper Bound
(6) = (2) + (3) + (4) + (5)
"LRMC"
$/KWH
(6)
.0219
.0222
.0221
.0175
.0178
.0177
.0290
.0293
.0292
Present
Av. Annual
Price
$/KWH
(7)
.0169
.0486
.0080
Ni
-------
Table 36. BANDS OF SUGGESTED PRICES BY SEASON:
Pennsylvania Power $ Light, 1972
Rate Schedule
by Season
CD
Residential (RS) :
Nov. -February
March-June
July-October
Residential (RH) :
Nov. -February
March-June
July-October
Residential (SGS,
AL, d, CS) :
Nov. -February
March-June
July-October
Commercial § Indus-
trial (SGS) :
Nov. -February
March- June
July-October
Commercial § Indus-
trial (LP3) :
Nov. -February
March-June
July-October
Lower Bound
"SRMC"
$/KWH
(2)
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
Generation
$/KWH
(3)
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
Transmission
$/KWH
(4)
.0115
.0119
.0115
.0024
.0025
.0019
.0015
.0015
.0011
.0084
.0087
.0066
.0002
.0003
.0002
Distribution
$/KWH
(5)
.0413
.0428
.0323
.0085
.0088
.0067
.0053
.0055
.0041
.0304
.0315
.0237
.0008
.0009
.0007
Upper Bound
(6)-(2) + (3) + (4) + (5)
"LRMC"
$/KWH
(6)
.0741
.0762
.0624
.0318
.0328
.0272
.0277
.0285
.0238
.0597
.0617
.0489
.0219
.0227
.0195
Present
Av. Annual
Price
$/KWH
(7)
.0271
.0171
.0673
.0426
.0231
-------
Table 36 (continued). BANDS OF SUGGESTED PRICES BY SEASON:
Pennsylvania Power § Light, 1972
Rate Schedule
by Season
(1)
Commercial § Indus-
trial (LP4):
Nov. -February
March-June
July-October
Commercial § Indus-
trial (LP5):
Nov. -February
March-June
July-October
Commercial 3 Indus-
trial (LP6):
Nov. -February
March-June
July-October
Commercial § Indus-
trial (LP) :
Nov. -February
March-June
July-October
Commercial § Indus-
trial (HS)
Nov. -February
March-June
July-October
Lower Bound
"SRMC"
$/KWH
(2)
.0047
.0047
.0047
.0047
.0047
,0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
Generation
$/KWH
(3)
.
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
Transmission
$/KWH
(4)
- -
-
.0002
.0002
.0002
.0003
.0003
.0003
Distribution
$/KWH
(5)
.0001
.0001
.0001
.0002
.0002
.0002
- -
"" "
.0008
.0008
.0008
.0010
.0010
.0010
Upper Bound
(6)-(2) + (3) + (4) + (5)
"LRMC"
$/KWH
(6)
.0210
.0216
.0187
.0211
.0217
.0188
.0209
.0215
.0186
.0219
.0225
.0196
.0222
.0228
.0199
Present
Av. Annual
Price
$/KWH
(7)
.0153
.0128
.0096
.0128
.0166
-------
Table 36 (continued). BANDS OF SUGGESTED PRICES BY SEASON:
Pennsylvania Power § Light, 1972
Rate Schedule
by Season
CD
Commercial § Indus-
trial (BST) :
Nov. -February
March-June
July-October
Commercial § Indus-
trial (All Other) :
Nov. -February
March-June
July-October
Street Lighting and
Signal System:
Nov. -February
March- June
July-October
Other Public
Authorities :
Nov. -February
March- June
July-October
Railroads § Rail-
ways :
Nov. -February
March-June
July-October
Lower Bound
"SRMC"
$/KWH
(2)
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
.0047
Generation
$/KWH
(?)
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
.0150
.0156
.0139
Transmission
$/KWH
C4)
--
.0027
.0027
.0027
~ ~
Distribution
$/KWH
(5)
--
.0096
.0096
.0096
.0036
.0036
.0036
- -
_ _
_ «
Upper Bound
"LRMC"
$/KWH
C6)
.0209
.0215
.0186
.0332
.0338
.0309
.0245
.0251
.0222
.0209
.0215
.0186
.0209
.0215
.0186
Present
Av. Annual
Price
$/KWH
(7)
.0092
.0243
.0691
.0223
.0111
Iri
NJ
-------
Table 36 (continued). BANDS OF SUGGESTED PRICES BY SEASON
Pennsylvania Power § Light, 1972
Rate Schedule
by Season
CD
Interdepartmental :
Nov. -February
March- June
July-October
Interchange §
Resale:
Nov. -February
March-June
July-October
Lower Bound
"SRMC"
$/KWH
(2)
.0047
.0047
.0047
.0047
.0047
.0047
Generation
$/KWH
(3)
.0150
.0156
.0139
.0150
.0156
.0139
Transmission
I/KWH
(4)
.0062
.0062
.0062
Distribution
$/KWH
(5)
--
Upper Bound
"LRMC"
$/KWH
(6)
.0209
.0215
.0186
.0271
.0277
.0248
Present
Av. Annual
Price
$/KWH
(7)
.0175
.0110
CM
-------
external cost. In what follows we will therefore take AW
P
alone, or some measure of AW alone, as a conservative esti-
mate of potential pricing improvement.
There is inevitably some element of judgement in the selec-
tion of a procedure for making those conservative estimates.
Peak costs are much higher than average prices, and our econo
metric evidence on demand elasticities is based upon a rela-
tively much smaller variation around average prices. It
therefore would be improper to compute estimates of AW
based upon our full upper bounds--columns 6 of Tables 32
through 36--where those upper bounds are many times higher
than present average prices.
In Tables 37 through 41 we have computed two appropriate
indicators of potential pricing improvement. First, we
have calculated the welfare gain AW-.Q associated with a 10%
decrease in peak consumption. This requires that we calcu-
late the peak price increase AP-.Q over present average price
Po-,r necessary to cut peak consumption by 10%, and then that
av
we compute the corresponding welfare gain. In columns 8 of
Tables 37 through 41, these welfare gain estimates are pre-
sented by system, by season, and by rate schedule. Second,
we have computed an estimate of AW based upon the full
upper bound estimates of peak correct peak prices--columns
6 of Tables 32 through 36. As indicated in columns 9 of
Tables 37 through 41, we have used that full upper bound
directly when it implies less than a doubling of peak price.
When use of the full upper bound'would imply more than a
doubling of present average price, we have taken half the
upper bound as the revised peak price. In this way we have
computed, far each system, season and rate schedule, a sec-
ond estimate AW k of AW . Columns 11 of Tables 37 through
41 summarize the results of this second calculation.
134
-------
Table 37. PEAK BENEFITS BY SEASON: AVERAGE PRICES COMPARED WITH PEAK
PRICES WHICH DECREASE PEAK KWH TEN PERCENT AND WITH LRMC
Potomac Electric Power Company, 1972
. Rate Schedule by Season
Residential
June-September
October -February
February-May
Commercial
Junc-Scptcciber
October -February
February-May
Industrial
June-September
October-February
February-May
Interchange and Resale
June-September
October-February
February-May
Long Run
Average
Price
Elasticity
av
1
1.22
1.22
1.22
1.46
1.46
1.46
1.93
1.93
1.93
1.93
1.93
1.93
Present
Average
Price,
P.v
$/KWH
2
.0248
.0248
.0248
.0219
.0219
.0219
.0143
.0143
.0143
.0097
.0097
.0097
Price
Consls.
with a
10 i
Decrease
in Peak
KKII,
4PM
$/KbH
3
.0020
.0020
.0020
.0015
.0015
.0015
.0007
.0007
.0007
--
LRMC if
|XLRMC 25,367
- 138, 303
- 117,443
- 209,536
- 1S1.3S6
- 192,222
- 233,790
- 220,313
-2,128,700
Percentage
Charge in
1'cak Ki.il
1 2
- SO. 6
- 58.9
- 48.8
* 2.0
- 19.3
- 10.2
- 42.1
- 73.1
- 65.0
- 91.1
-110.8
-104.4
- 38.4
I-1
w
en
"Full upper bound
-------
Table 38. PEAK BENEFITS BY SEASON: AVERAGE PRICES COMPARED WITH PEAK
PRICES WHICH DECREASE PEAK KWH TEN PERCENT AND WITH LRMC
Commonwealth Edison Company, 1972
. Rate Schedule by Season
Snail Residential
June-September
October-January
February -May
Large Residential
June-September
October-January
February-May
Residential Space lleatin
June-September
October-January
February-May
Small Commercial and Ind
June-Scptenber
October-January
February -May
Long Run
Average
Price
Elasticity
>°av'
i
1.22
1.22
1.22
1.22
1.22
1.22
g
1.22
1.22
1.22
Jstrial
1.48
1.48
1.48
'Large Commercial and Industrial
June-September
October- January
February-May
Katcr and Sewer Pumping
June-September
October- January
February-May
Railroads and Railways
June-September
October- January
February-May
Resale, Municipalities
June-September
October-January
February-May
1.87
1.87
1.87
1.87
1.87
1.87
1.87
1.87
1.87
1.87
1.87
1.87
Present
Average
Price,
Pav
j/Ktm
2
. .0353
.0353
.0353
.0302
.0302
.0302
.0170
.0170
.0170
.0249
.0249
.0249
.0132
.0132
.0132
.0231
.0231
.0231
.0160
.0160
.0160
.0112
.0112
.0112
'rice
Change
Consis.
nth a
10 I
iccrcas'e
in Peak
KWII,
APil
J/KKH
3
.0029
.0029
.0029
.0025-
.0025
.0025
.0014
.0014
.0014
.0017
.0017
.0017
.0007
.0007
.0007
.0012
.0012
.0012
.0008
.0008
.0008
.0006
.0006
.0006
LRMC if
|xLRMCkKIVHPK^
pav
1 0
3,558,591
3,473,975
3,218,879
21,217,272
20,332,770
19,191,828
7,427
7,250
6.257
610,972
596,446
552,648
9,520,830
9,297,070
8,614,378
1.413
1.379
1,278
21
:o
19
64,036
88,421
82,746
1100,445,946
Change in
Peak KKH
pk
10'KKH
1 1
256,903
250,799
232,383
- 1,529,569
- 1,465,800
- 1,385,549
9,856
9,622
8,304
393,81:
384,443
356,218
- 1,984,095
- 1,937,453
- 1,795,184
3,136
3,06:
2,837
410
400
371
36,599
35,376
33.105
1-12,113,294
"erccr.taje
:hanj;c in
>cak Xttl
1 2
-6B.8
- 68.8
-66.8
-76.1
-76.1
-76.1
10.2
- 10.2
- 10.2
-17.3
- 17.3
17.3
- 99.7
- 99.7
93.7
- 7.1
- 7.1
- 7.1
- 1.1
1.1
- 1.1
- 50.5
- 50.5
-50.5
-61.1
ON
"full upper bound
-------
OI
Table 39. PEAK BENEFITS BY SEASON: AVERAGE PRICES COMPARED WITH PEAK
PRICES WHICH DECREASE PEAK KWH TEN PERCENT AND WITH LRMC
Duke Power Company, 1972
Rate Schedule by Season
Residential (R)
July-October
Xovenber- February
March-June
Residential (RA)
July-October
Xovunber-Fcbruary
March-June
Residential (RW)
July-October
March-June
Residential (MiS ( Nile
July-October .
March-June
July-October
March-June
Comercial and Industri
July-October
Xoicnber- February
March-June
Coanerclol and Industrl
July-October
March -June
Cooncrcidl and Industrl
July-October
Novcnbor- February
March-June
CoETcrcial and Industrl
July-October
Xoveabcr-Fobruary
March-June
Other Public Authorltie
July-October
Noveaher -February
March-June
Sale! for Resale
Jul) -October
Nnvcnbcr - February
March-June
July-Uctober
Noveaber* February
March-June
"Full ufi'Jf bJund
long Run
Price
Elasticity
/«./
1
1.11
1.11
1.18
l.U
1.11
l.U
1.11
l.U
1.11
....
1.11
1.11
1 '?!
1.13
1.1)
1 (CA)
1.13
1.13
1.13
1 CD
1.6S
1.65
1.65
1 (IRES)
I.6S
1.65
1.65
1 (All Oth
1.6S
1.65
1.6$
1.6S
1.6S
1.6S
1.6S
1.6S
1.6S .
1.6S
1.6S
1.6S
Present
Price,
P.»
J/IKII
2
.0265
.0265
.0265
.0167
.0167
.0167
.0201
.0201
.01111
.0155
.015!
.0155
.0161
.0161
.0169
.0112
.0112
.0112
.0089
.0019
.0049
.0079
.0079
.0079
")
.0271
.0271
.0271
.0105
.0105
.0105
.0019
.0019
.0019
.0144
.0144
.0144
Price
Change
Consist
with a
10 t
Decrease
in Peak
XMI.
4P,,
J/XKII
3
.0022
.0022
.0022
.0014
.0014
.0014
.0017
.0017
.0017
.0013
.0013
.0011
.0015
.0015
.0015
.0010
.0010
.0010
.0005
.0005
.0005
.0005
.0005
.0005
.0017
.0017
.0017
.0006
.0006
.0006
.0005
.0005
.0005
.0009
.0009
.0009
LR.MC if
£xl.KNC«S
146°
137°
136°
140°
135°
134°
131°
410°
409°
413°
141°
140°
144°
191°
>»*
199°
'»S
114°
131°
Peak XKH
in Season,
XMI
P«
10'XHII
S
279,346
270,234
225.059
571,645
559,769
466,193
1,010,01.6
977,911
114,499
13,302
12,161
10,717
191,246
162,173
711,045
541,715
530,116
442,010
1,402,112
1,402,112
1,402,112
73,1154
73,954
73,954
29,512
29,512
29,512
11,347
11,347
11,347
510,130
510,130
510,130
461
461
461
[15,327,744
Efficiency Calm Associated
Kith n Ten Percent Decrease
In I'cak XMI
Frac-
tional.
I'rlce
Change
i|;jj..
av
£"'
6
.0147
.01141
.0147
.0147
.0147
.0147
.0147
.11147
.0147
.0147
.0147
.0147
.0115
.01115
.0115
.0115
.0115
.0115
.0606
.06U6
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
.0606
Efficiency Cains
«K|«
Js^MWIVk^
7
30,711
29,710
24,743
40,413
39,103
30,307
15,116
13,084
69,195
ll>4
136
696
66,147
64,666
53,156
27,437
26,542
22,105
35,051
35,051
31,051
1,149
1,149
1,149
1,509
2,509
2,509
550
550
550
12,769
12,769
12,769
21
21
21
1155,371
Efficiency Gain Associated with
Upper Bound or One-Half Upper Bound
Price Chang*
at Peak, IP ^
LRMC-P., if
jLRHC«P.y.
JlRHC-P.y
Otherwise
8
.0060
.11052
.0062
.0103
.0099
.0105
.0004
00
.0006
.0154
.0149
.0151
.0037
.0034
.0040
.0031
.0030
.0034
.0041
.0047
.0051
.0056
.0055
.0059
.0132
.0131
.0135
,0036
.0035
.0039
.0107
.0106
,0110
.0009
.0010
.0006
Ave age
Fra
lio al
Pri e
Cha ge
9
.203
.179
.209
.471
.457
.471
.020
00
.0:9
.664
.649
.675
.!'.>«
.114
.213
.243
.236
.263
.425
.411
.445
.523
.516
.544
.314
.311
.391
.293
.216
..313
.751
.746
.764
.065
.071
.043
Efficiency Cains
V
a*.^pk""w^t
rav
1 0
201,1:9
125, >67
172,329
1,656,894
1,493,489
1,3»0,33
340, 051
233.190
212,592
223,207
2,359,032
2,273,639
2,625,643
171,702
178,121
195,912
123,493
121,581
128,486
15,917
15,155
11.461
3,386,111
3,332,810
3,542,103
22
27
32
125,456,6.36
Chanue in
Peak XKH
iXHIpk
10'KtVH
1 1
67,043
- 41,372
55,590
- 3J1.72;
- 301,715
- 262,933
24,263
00
27,693
10,4:9
9,144
1,541
10S.747
113,643
1:3,04!)
- 150,197
- 141,721
131,298
- 902,930
967,506
1,029,664
63,122
-. 62.93S
66,411
- 18,711
18,563
19,035
1,143
1,600
9,467
- 632,911
628,832
- 644,157
49
54
32
t-7,:io,ioi
Percentage
Change in
Peak Xiill
1 2
- 24.0
- 21.1
- 24.7
55.6
- 53.9
- 56.4
2.4
0
- 3.4
- 78.4
- 76.5
- 79.7
- 2J.3
2I.J
24.1
- 27.5
- 26.7
- 2S.7
- 70.1
- 69.0
- 73.4
- 86.3
- 15.1
- 19.1
- 63.4
62.9
- 64.5
41. J
- 47.2
51.6
-123.9
-l.'l.l
126.1
- 10.7
11.7
1.1
47.5
-------
Table 40. PEAK BENEFITS BY SEASON: AVERAGE PRICES COMPARED WITH PEAK
PRICES WHICH DECREASE PEAK KWH TEN PERCENT AND WITH LRMC
New York State Electric and Gas, 1972
Rita Schedule by Season
Residential
November-February
March-June
July-October
General Service (SC2 PSC
November- February
Ma rch- June
July-October
General Service ' (SC2 PSC
Novenbe r - February
M.I rch -June
July-October
Large Light and Power (S
November- February
March-June
July-October
Prinary Light and Power
Novcebcr -February
Ma rch -June
July-October
Other Public Authority
Novcnber- February
Ma rch -Juno
July-October
Interchange and Resale
November - February
March-June
July-October
.
Long Run
Average
Price
Elasticity
1
1.Z4
1.24
1.24
113)
1.65
1.65
1.65
108)
1.65
1.6S
1.65
C3 PSC 113)
1.89
1.89
1.89
(SC3 PSC 10
1.89
1.89
1.89
1.89
1.89
1.89
1.89
1.89
1.89
Present
Average
Price,
v.
$/KHH
2
.0272
.0272
.0272
.0273
.0273
.0273
.0175
.0175
.0175
.0138
.0138
.0138
8)
.0103
.0103
.0103
.0169
.0169
.0169
.0080
.0080
.0080
Price
Change
Consls ,
Kith a
10 1
Decrease
in Peak
KKII,
APu
(/KWH
3
.0022
.0022
.0022
.0017
.0017
.0017
.0011
.0011
.0011
.0007
.0007
.0007
.0005
.0005
.0005
.0009
.0009
.0009
.0004
.0004
.0004
LRMC if
2*LRMC
-------
Table 41. PEAK BENEFITS BY SEASON: AVERAGE PRICES COMPARED WITH PEAK
PRICES WHICH DECREASE PEAK KWH TEN PERCENT AND WITH LRMC
Pennsylvania Power and Light Company, 1972
Rite Schedule by Season
Residential (RS)
Novenher- February
March-June
July-October
Rc.'av'
1
1.22
1.22
1.22
1.22
1.22
1.22
d CS)
1,22
1.22
1.22
1 (SCS)
1.46
1.46
1.46
1 (LP3)
1.46
1.46
1.46
1 (LP4)
1.93
1.93
1.93
1 (LP5)
1.93
1.93
1.93
1 (LP6)
1.93
1.93
1.93
1 (LP)
1.93
1.93
1.93
1 (NS)
1.93
1.93
1.93
1 (BST)
1.93
1.93
1.93
Present
Average
Price,
Pav
J/KKH
2
.0271
.0271
.0271
.017!
.0171
.0171
.0673
.0673
.0673
.0426
.0426
.9426
.0231
.0231
.0231
.0153
.0153
.0153
.0128
.0128
.0128
.0128
.0128
.0128
.0128
.0128
.0128
.0166
.0166
.0166
.0166
.0166
.0166
Price
Change
Consis.
with a
10 1
Decrease
in Peak
KIVII,
oPi.
$/KKH
3
.0022
.0022
.0022
.0014
.0014
.0014
.0055
.0055.
.0055
.0029
.0029
.0029
.0016
.0016
.0016
.0008
.0008
.0008
.0007
.0007
.0007
.0007
.0007
.0007
.0007
.0007
.0007
.0009
.0009
.0009
.0009
.0009
.0009
LRMC if
£xLRMCpkKW11PK^
av
1 0
1,348,139
1,285.758
205,405
1,946,389
1,706,773
815,425
43,072
31,958
43,536
486,168
466,667
59,474
20.426
3,527
157,026
277,102
344,669
105,279
321,390
3:6, 909
180,174
684,918
803,541
389,884
203,856
228,079
122,098
109,824
132,530
40,533
40,894
52,627
9,469
Change in
Peak KWH
A1Cpk
'10 'Kim
1 1
- 272,351
- 233,774
- 100,197
- 264,814
- 217,423
- 161,470
* 2.175
» 1.647
» 2,001
56,861
48.865
13,830
* 34,043
« 17,636
» 37. 236
97, 228
- 105,589
61,929
77,468
81.5C-:
60,025
- 175,249
- 184,722
134,442
44,789
47,004
35.9:9
39,222
42,751
24,565
19,022
21,347
9,467
Percentage
Change in
Peak KKH
1 2
- 37.6
- 41.1
- 17.2
- 73.3
- 76.7
- 55.6
1.017
98.8
» 1.165
- 48.8
- 53.4
- 20.1
» 7.7
5.1
:.s
60.6
- 65.8
- 38.6
- 94.6
- 9T.6
73.3
- 9Z.8
- 97.8
- 71.2
- 101.1
-106.1
- 81.1
- 55.8
- 60.8
- 34.9
- 44.2
- 49.6
- 22.0 .
-------
Table 41 (Continued) PEAK BENEFITS BY SEASON: AVERAGE PRICES COMPARED
WITH PEAK PRICES WHICH DECREASE PEAK KWH TEN PERCENT AND WITH LRMC
Pennsylvania Power and Light Company, 1972
Rite Schedule by Season
Commercial and Industrie
November- February
March-June
July-October
Other Public Authorities
Xovenber- February
March-June
July-October
Railroads and Railways
Xovecber -February
March -June
Jilly-October
Intcrdepartnental
Xqvenber- February
March-June
July-October
Interchange and Resale
November -February
March-June
July-October
Long Run
Average
Price
Elasticity
/«'
L (All Otha
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
1.93
Present
Average
Price,
P.v
J/KNH
r)
.0092
.0092
.0092
.0691
.0691
.0691
.0223
.0223
.0223
.0111
.0111
.0111
.0110
.0110
.0110
Price
Change
Cons Is.
with a
10 1
Decrease
in Peak
KKH,
aPit
J/KKI1
.0005
.0005
.0005
.0036
.0036
.0036
.0012
.0012
.0012
.0006 ',
.0006
.0006 ,
.0006
.0006
.0006
LRMC if
|xLRMC
-------
Turning to the task of estimating the incremental cost of
double register metering of residential customers, an ex-
ample will serve to illustrate the procedure. From the
Sangamo Electric Company we have obtained acquisition cost
figures for the ordinary, or single register, KWH meter and
for the double register meter which would be necessary if
residential customers were to be charged different prices
offpeak and on peak. The simpler meter could be acquired
by utilities for $16.00 in 1972, and the double register
meter for $57.58. But it would be incorrect to take these
as capital cost figures, for the capital cost of a meter
which is entered into a utility's rate base is the installed
cost of the meter, and installation cost can be substantial
and varies between companies. From Federal Power Commission
From 1 we can reconstruct each system's installation costs
by the simple expedient of deducting from the reported per
meter increase in the rate base our known acquisition cost
of $16. For example, for the Potomac Electric Power Company,
1972 installation cost computed thus is $56.51. Assuming
that installation costs for the double rate register are no
higher than those for the single rate register, we may add
this installation cost figure to the acquisition cost figure
for the double rate register, $57.58, in order to obtain a
capital cost- figure for double register metering, in this
case $114.09. Of course, the single register figure, ob-
tained directly from Form 1, is $72.51. By annualizing each
of these capital cost figures--as above, we assume an 8 per-
cent rate of return on original cost--we have annual capital
cost figures for single and double rate registers. For oper-
ating and maintenance cost estimates, we have available the
breakdown provided by Form 1 in which operating costs are de-
composed into meter reading costs, meter maintenance costs,
and a miscellaneous meter expenses category. The definition
of meter expenses given in the Federal Power Commission's
141
-------
standard accounts is the obvious one; while meter expenses
"shall include the cost of labor, materials and expenses
used and incurred in the operation of customer meters and
associated equipment," i.e., operating as opposed to main-
tenance expenses associated with metering, exclusive of
meter reading expenses.
Since we have, for each system, the number of meters, each
of these figures can be put on a per meter basis. For ex-
ample, in 1972 the Potomac Electric Power Company reported
per meter reading expenses of $2.11, per meter maintenance
expenses of $.33, and per meter meter expenses of $1.65, or
total per meter operating and maintenance expenses of $4.09.
In our estimates of the corresponding figures for double
register metering, we have somewhat naively assumed, for
each system, the same numbers. This is certainly defensible
for meter reading: the major expense is the labor and trans-
portation cost involved in moving the reader between meters.
For the remaining components of operating and maintenance
cost, the assumption is not as persuasive, but we have no
alternative. The cost differencial between single register
and double register metering is then equal to the difference
between annualized capital cost figures for the two modes of
monitoring, and it is this differential that is entered as
the column "Incremental Cost of Metering per Customer" in
Table 42, Net Peak Period Residential Schedule Indicators of
Improved Pricing. By multiplying that figure by the average
number of customers served during 1972 under each residential
rate schedule for each of our systems, and deducting the
product from our previous estimates for these schedules in
Tables 37 through 41--remember that there are two such fig-
/
ures, one for a price change which depresses peak consump-
tion by 10 percent, and another for a price change in which
our upper bounds are used as prices--we obtain the net bene-
fit or indicator figures of the final two columns of Table 42.
142
-------
Table 42. NET PEAK PERIOD RESIDENTIAL, SCHEDULE INDICATORS OF IMPROVED PRICING
System Rate Schedule
POTOMAC ELECTRIC POWER
Residential
COMMONWEALTH EDISON COM
Small Residential
Large Residential
Residential Space
Heating
DUKE POWER COMPANY
Residential (R)
Residential (RS)
Residential (RW)
Residential (WGS § MI
NEW YORK ELECTRIC AND G
Residential
PENNSYLVANIA POWER AND
Residential (RS)
Residential (RH)
Residential (SGS,
AL $ CS)
1
Ten
Percent
Peak
Benefits
-Gross
Benefits
(*)
COMPANY
137,610
PANY
156,775
719,558
19,515
85,164
109,953
235,165
SC) 2,396
AS
169,635
LIGHT
206,429
65,457
1,518
2
Peak
Upper
Bound
-Gross
Benefits
(!)
5,548,191
10,251,715
60,741,870
20,934
499,225
4,530,781
13,161
221,115
1,027,309
2,839,302
4,468,587
118,566
3
Average
Number
of
Customers
391,046
1,003,359
1,348,632
62,894
253,559
138,189
488,754
3,657
525,616
674,736
69,486
232
4
Incre-
mental
Metering
Cost
per
Customer
m
4,48
4.84
4.56
4.65
4.59
5
Total
Incremental
Metering
Cost
($)
1,751,886
4,856,257
6,527,379
304,407
1,156,229
630,141
2,228,718
16,676
2,444,114
3,097,038
318,940
1,065
6
Net
Benefits
I
= 1-5
m
-1,614,276
-4,699,482
-5,807,821
- 284,892
-1,071,065
- 520,188
-1,993,553
-2,274,479
-2,890,609
- 253,453
453
7
Net
Benefits
II
= 2-5
m
3,796,305
3,830,542
54,214,491
-9,473
-657,004
-13,906,640
-2,215,557
-1,416,805
-257,736
4,149,647
117,501
-------
CATEGORY III INDICATORS OF POTENTIAL PRICING IMPROVEMENT
Recall that customers in category III are assumed to have
decided, on information cost grounds, to be marginal rather
than average price sensitive; it is further assumed that
they do not, or do not have the opportunity to, distinguish
between offpeak and peak consumption. (The latter constraint
might be assumed to arise institutionally.) This set of as-
sumptions is, as we have argued above, probably most germane
to the situation of large residential users; not because it
is not potentially relevant to large commercial and indus-
trial users, but because these later customers typically know
their load curves, so that the assumption of unwillingness to
differentiate between offpeak and peak consumption seems arti-
ficial.
A major difficulty surrounds the estimates of this section.
For example, no company with which we are familiar knows the
load curve of tailblock residential customers, i.e., those
residential customers whose monthly bills put them in the
final consumption block. Under the curcumstances, we be-
lieve that a sensible estimate of the potential benefits to
be derived from futher investigation of load curves by block
is as follows. Make the somewhat drastic assumption that
all tailblock consumption occurs during peak hours. This,
we hasten to point out, is not much different from what many
utility personnel suspect: that much of peak growth attri-
butable to residential consumption has, in recent years,
been in the tailblock. Then an indicator of potential im-
provement can be computed by estimating the benefits accru-
ing from an upwards adjustment of the tailboock rate towards
the peak prices we have computed (and which are reported in
columns 6 of Tables 32 through 36). For illustrative pur-
poses, we have chosen a variety of "inversion" which many
144
-------
of the advocates of rate inversion have put forward, an in-
version in which the height of the tailblock is raised to be
equal to the height of the first block. Where one half of
the derived upper bound is lower than the first block height,
we use the former figure in this calculation.
Table 43, Category III Indicators of Potential Pricing Im-
provement, presents the results of these estimates. In
column 1 of Table 43, we have entered the fraction of resi-
dential sales assumed to be tailblock sales, .1996. We have
taken the same fraction for all systems only because we were
able to get data for only one system, the Potomac Electric
Power Company. In column 2 of Table 43 we have compiled
estimates of peak KWH sales to residential customers by sys-
tem and by season; these have been computed by the procedure
set out in Table 26. Column 3 of Table 43, an estimate of
peak tailblock sales, is then the product of columns 1 and 2.
In column 4 of Table 43 we have compiled the relevant econo-
metric estimates of price elasticity, the Chapman et. al.
long run elasticity estimates. In column 5 of Table 43, we
have recorded the height of the first block of each residen-
tial rate schedule in 1972, and in column 7 of Table 43 we
have recorded the tailblock rate in effect, by system and
season; in column 6 we have entered our upper bound estimate
of appropriate peak price, from Tables 32 through 36. Gen-
erally, but not always, the tailblock rate is lower than the
upper bound estimate of peak price and the first block rate
lies between the two.
Accordingly, we compute a welfare gain estimate based upon
whichever price is smaller, the difference between tailblock
and first block, or the difference between tailblock and upper
bound prices: that welfare estimate is what we could hope to
gain by raising tailblock price by the smaller differential,
145
-------
assuming all tailblock consumption to be on peak. Column 10
of Table 43 is a compilation of those welfare estimates. A
warning is appropriate in the interpretation of these figures:
the reductions in peak consumption given by the usual elasti-
city formula are very large, sometimes amounting to total
peak consumption. The source of this result is apparent:
the application of our long run elasticity estimates to peak
price changes often amounting to more than 90 percent of in-
itial price. Accordingly, the benefit estimates are to be
taken as order of magnitude estimates.
CATEGORY IV INDICATORS OF POTENTIAL PRICING IMPROVEMENT
Finally, recall that customers in category IV are assumed to
be both marginal price responsive and to be able to distin-
guish, at no additional cost, between offpeak and peak con-
sumption: this certainly would be the case for large commer-
cial and industrial customers who already monitor their load
curves, and of these there are many. Many of these customers
are billed under tariffs which have block structures for
both energy and demand charges, so that the customer's bill
is computed from both energy and maximum demand readings.
Thus, some additional procedures must be devised before pro-
ceeding to the estimation of indicators of potential pricing
gain for this customer category.
Net Benefit Indicators for Demand Billed Accounts
The procedures we have employed above in order to derive in-
dicators of the net benefits available from improved pricing
cannot be directly applied to schedules with a demand charge
component. The reason is somewhat obvious: when the cori-
sumer's bill depends in some complex way upon not only con-
sumption but also upon maximum demand, the relationship be-
146
-------
Table 43. CATEGORY III INDICATORS OF POTENTIAL PRICING IMPROVEMENT
System Rate Schedule. (Season)
POTOMAC ELECTRIC POWER COMPANY
Residential
June-September
October- January
February-May
COMMONWEALTH EDISON COMPANY
Large Residential
June-September
October-January
February-May
DUKE POKER COMPANY
Residential (R)
July-October
November -February
March-June
Residential (RA)
July-October
Novenber- February
March-June
Residential (RW)
July-October
November-February
March-June
Total All Residential
NEK YORK STATE ELECTRIC AND CA
Residential
November -February
March-June
July-October
PENNSYLVANIA POKER AND LIGHT
Residential
Novcobe r - February
July-October
1
Fraction
of Sales
Assumed
in Tail-
Block
.1996
.1996
.1996
.1720
.1720
.1720
.1996
.1996
.1996
.1U96
.1996
.1996
.1996
.1996
.1996
S
.1996
.1996
.1996
.1996
.1996
.1996
2
Peak KWII
in Season
10'KWH
647,588
365,872
362,110
2,383,353
1,290,684
2,155,833
279,346
270,234
225,059
578,645
559,769
466,193
1,010,966
977,988
814,499
574,163
471,407
497,435
724,801
568,600
582,447
3
Peak Tail-
Block
Sales
lO'JCWH
129,258
73,028
72,277
E 274,563
409,937
393,998
370,803
El, 174, 738
55,757
53,939
44,922
E 154,618
115,498
111,730
93,052
E 320,280
201,789
195,206
162,574
E 559,569
El, 034, 467
114,603
94,093
99,288
I 307,984
144,670
113,493
116,256
E 374,419
4
Estimate of
State Average
(and Marginal)
.Price Elasti-
cities
-1.22
-1.22
-1.22
-1.21
-1.21
-1.21
-1.18
-1.18
-1.18
-I'.IB
-1.18
-1.18
-1.18
-1.18
-1.18
-1.24
-1.24
-1.24
-1.22
-1.22
.-1.22
5
1972 First
Block Rate
by Season
KWT
.0375
.0375
.0375
.0386
.0386
.0386
.0390
.0390
.0390
.0400
.0400
.0400
.0390
.0390
.0390
.0501
.0501
.0501
.0500
.0500
.0500
6
Upper
Bound
$
KBR"
.0796
.0796
.0796
.0578
.0578
.0578
.0680
.0635
.0653
.0270
.0266
.0272
.0409
.0401
.0413
.0659
.0655
.0655
.0741
.0762
.0624
77
1972 Tail-
Block Rate
by Seasoa
KWR
.0205
.0135
.0135
.0226
.0226
.0226
.0140
.0140
.0140
.0100
.0100
.0100
.0140
.0140
.0140
.0164
.0164
.0164
.0130
.0130
.0130
8
Difference
Between
Tailblock
Rate and
Smaller of
6 or 7
$
KKH
.0170
.0240
.0240
.0160
.0160
.0160
.0250
.0250
.0250
.0170
.0166
.0172
.0250
.0250
.0250
.0337
.0337
.0337
.0370
.0370
.0370
9
Fractional
Price
Change
-.5862
-.9412
-.9412
-.5230
-.5230
-.5230
-.9434
-.9434
-.9434
-.919
-.907
-.925
-.9434
-.9434
-.9434
-1.0135
-1.0135
-1.0135
-1.175
-1.175
-1.175
10
Upper
Bound on
Efficiency
Gains
*V
T^P^V P
785,755
1,006,265
995,917
E 2,787,926
2,075,320
1,994,628
i,877,:o:
E 5,947,150
775,852
75750,557
625,036
F 2,151,495
1,064,593
992,497
886,534
E 2,943,624
2,306,684
2,715,122
2,261,242
E 7,7S3,048
III, 378,167
2.426,798
1,992,435
2,102,553
E 6,521,841
3,822,236
2,998,523
3,071,526
E 9,892,290
-------
tween perceived price and average price is somewhat more
elusive. For, with few exceptions, demand charges are based
upon noncoincident demand--upon the customer's maximum demand,
whenever that maximum demand may occur, and not upon coinci-
dent demand (the customer's demand at the time of the system
peak). Our route around this dilemma is, and must be, dif-
ferent for the different utilities studies, largely because
the nature of the data we have been able to assemble varies
from company to company; valuable information would be need-
lessly sacrificed with a uniform methodology.
We are encouraged by the comparability of results between
systems. The magnitude of the benefit measure indicator
does not seem to vary widely between systems.
There are three kinds of data upon which an appraisal of the
performance of demand billed rate structures can be based.
(1) From some systems we have been able to obtain data which
summarize, on a monthly basis, total KWH and total KW for
demand billed accounts: for each rate schedule served under
a tariff with both demand and energy charges, we therefore
have, on a monthly basis, total KWH, total KW, and, typically
the number of bills sent. (2) For one system we have been
able to obtain something very unusual: for Commonwealth
Edison of Illinois we have, for a large sample of major in-
dustrial users, individual customer load curves on an hourly
integrated demand basis for the whole of one week in August.
Since industrial loads exhibit relatively little seasonal
variation, this is valuable information. (3) For most sys-
tems, we must work from our rough constructed load curves
by customer class for each season.
148
-------
Such is the variation in data availability across our sample.
We turn to a more explicit description of methodologies em-
ployed in each case, of checks on the adequacy of assumptions
and approximations, and finally to a discussion of the re-
sults. A reminder of our objective: our guiding question is
how well does the existing pattern of demand charges and
energy charges approximate cost at peak? Of interest is not
only the absolute deviation of perceived price from (our
best estimate of) cost at peak, but also the importance of
that derivation--a measure of benefits to be had from nar-
rowing the discrepancy. Because methods for treating the
demand billed accounts must necessarily differ between sys-
tems, whereas the methods for computing indicators of poten-
tial pricing improvement are identical, we reserve our dis-
cussion of those indicators until after the various methodo-
logies have been discussed.
Imputation of a MeanDemand Bill Where Aggregate Demand and
Energy Data are Available--Suppose we have, as we do for the
Potomac Electric Power Company, data on the total KWH, total
KW and number of bills, for each demand billed account, by
month for 1972. Total KWH means the sum of the KWH for which
customers in each demand billed customer class are billed in
each month; total KW means the sum of customer maximum de-
mands for the corresponding customer class and month. These
data are compiled in Table 44. A representative bill may
then be imputed as follows: take the per customer average
KWH and KW, and, using the rate schedule, price out the bill.
Imputation of Mean Demand Bill Where Sample Data on Individ-
ual Demand-Billed Customers is Available--Table 45, Load
Curve for a Single Industrial Customer, Commonwealth Edison
149
-------
Table 44. POTOMAC ELECTRIC POWER COMPANY,
DEMAND BILLED ACCOUNTS FOR DISTRICT OF COLUMBIA,
SELECTED MONTHS OF 1972
Rate Schedule
Commercial
Industrial
Month
January
April
Augus t
January
April
August
Total
KWH
204,825,718
193,396,901
298,741,659
118,316,350
113,582,130
181,845,708
Total
KW
496,079.4
500,531.7
751,304.0
, 280,948.6
280,038.4
395,610.2
Number
of
Bills
5-, 241
5,329
5,391
129
130
131
Company, is included to show the type of data upon which this
section builds, and to emphasize what we have said before--
that it would cost almost nothing for many systems to begin
billing in a time-dependent way, since they necessarily know
the load curves of their major industrial customers. By ex-
amining the hourly-integrated load figures, we can find the
hour and the day, during the week for which we have this in-
formation, of the individual customer's noncoincident peak.
Thus, for the customer occupying premise 47044, the peak
came at 8 p.m. of August 16. We have the size of this cus-
tomer's noncoincident peak--21,816 KW--and, from Table 45,
this customer's energy consumption for the week. By multi-
plying that latter figure by four, we obtain an estimate of
the customer's monthly consumption. Thus we have, for each
individual industrial premise in the sample, an estimate of
energy taken and demand. The calculation of the actual
energy and demand bills paid by the individual customers is
then a simple matter of looking at the relevant rate schedule
and pricing out the particular customer's energy and demand
charges. (This amounts to evaluating the algebraic expres-
sions in the row 4, column 3 entry of Table 27.) In summary,
150
-------
Table 45. LOAD CURVE FOR A SINGLE INDUSTRIAL CUSTOMER,
COMMONWEALTH EDISON COMPANY, 1972
(Hourly Integrated Demand)
Hour
Ending
1 AM
2 AM
3 AM
4 AM
5 AM
6 AM
7 AM
8 AM
9 AM
10 AM
11 AM
12 AM
1 PM
2 PM
3 PM
4 PM
5 PM
6 PM
7 PM
8 PM
9 PM
10 PM
11 PM
12 PM
Total
Aug
13
702
702
756
702
702
702
702
702
756
810
865
756
648
702
702
648
648
648
648
648
702
1,026
1,836
3,240
20,953
Aug
14
14,094
18,090
11,556
9,990
18,684
9,666
10,692
16,686
16,470
8,316
19,872
19,440
13,824
19,278
18,522
9,990
15,822
18,954
12,582
13,338
18,630
17,064
19,656
17,766
368,982
Aug
15
9,882
15,552
16,362
12,042
15,714
16,578
11,826
20,682
16,578
13,878.
13,716
16,794
16,470
17,658
16,632
15,822
13,122
10,692
11,880
14,256
20,250
15,498
20,466
16,200
368,550
Aug
16
9,936
10,962
11,448
5,670
12,690
13,176
11,340
12,312
11,664
18,900
17,496
14,742
19,008
16,254
11,340
12,852
17,334
9,072
16,092
21,816
14,688
18,630
20,358
12,042
339,822
Aug
17
6,426
13,878
9,666
7,992
16,524
12,096
5,076
17,280
21,114
13,176
5,616
5,616
5,022
6,102
6,750
5,238
12,906
19,454
17,766
6,318
5,130
5,022
3,726
3,780
231,714
Aug
18
9,666
18,198
12,420
9,126
17,442
12,744
16,956
12,204
7,506
9,612
7,830
8,262
5,454
9,180
6,048
2,970
2,322
2,538
3,240
3,672
3,240
3,078
2,646
2,322
188,676
Aug
19
2,754
2,430
972
972
864
918
918
1,080
1,026
1,134
1,404
1,134
918
918
918
810
756
702
756
756
810
756
756
702
25,164
151
-------
for this case in which we have obtained individual customer
data, we can compute energy and demand charges for each cus-
tomer.
Imputation of a Mean Demand Bill Where Only Federal Power
Commission Data are Available--Finally, in the case where all
we have to go on are the reports all large systems must file
with the Federal Power Commission (FPC Froms 1 and 12), a
representative bill for demand billed schedules may be con-
structed as follows. First, recall that we have imputed (in
the course of our reconstruction of cost structures) customer
class load curves subject to various assumptions. We may, by
dividing the individual rate schedule contribution to the sys-
tem peak by the average number of customers and by the number
of hours during the system peak, derive an estimate of indi-
vidual customer demand. Similarly, an average energy per cus-
tomer figure can be derived. Taking the resulting energy and
demand combination as our representative bill for each rate
structure, we may price out this mean bill--again, this amounts
to evaluating the algebraic expression in the row 4, column 3
entry of Table 27--and proceed.
These representative bills have .been constructed as guides to
what might be called "perceived" prices at peak. The central
fact about them is that, with few exceptions, all demand
charges are based upon noncoincident demand--upon the cus-
tomer's maximum demand, whenever it occurs. This is in prin-
cipal unrelated to imposed capacity cost, and only makes sense
to the extent that individual customer and system peak demand
coincide. Do they? The question can only be answered by ,
sample data on individual large use load curves. But the only
such sample we have seen, the Commonwealth Edison data in
Table 45 above, is not supportive of this inference. Another
152
-------
rationale for noncoincident demand billing is, of course, that
if industrial demand is approxiamtely flat then it matters not
where billing demand is measured, since maximum noncoincident
and coincident peak demands necessarily coincide.
How then to move from these representative bills to our bene-
fit assessments? The crucial comparison is, of course, be-
tween perceived price at system peak and our reconstruction
of cost at system peak on a rate schedule basis. The cost
estimate has already been done, and amounts to our upper bound
column of Tables 33 through 37. The perceived price estimate
remains to be computed. First, recall that in terms of our
customer typology, customers are here assumed to be both mar-
ginal price responsive and time differentiating, i.e., of
type IV. Thus the price we want is the perceived marginal
price of a peak KWH. Since the rate schedules we are con-
sidering in this section are demand-billed, the marginal
price must be the sum of an energy and a demand component.
For the energy component, the obvious candidate is the actual
marginal energy charge corresponding to the mean bill for
each rate schedule in effect, the height of the energy block
in which the mean bill sits. For the demand charge, things
are. not so clear cut, for here the charge is levied upon a
noncoincident maximum demand basis. We therefore assume, in
constructing a measure of the perceived demand charge, that
customers subject to a noncoincident demand charge spread that
charge evenly over time: they assume that their monthly de-
mand charge is incurred at a constant hourly rate. Summation
of energy and, demand components gives us, at last, the per-
ceived peak period marginal prices compiled, for each system
and each demand billed rate schedule, in column 2 of Table 46.
Given both perceived price and estimated marginal cost, the
construction of new benefit indicators on a rate schedule
153
-------
Table 46. INDICATORS OF POTENTIAL PRICING
IMPROVEMENT, DEMAND-BILLED SCHEDULES
System Rate Schedule (Season)
POTOMAC ELECTRIC POWER COMPANY
General Service (GS)
June-September
October- January
February-May
Large Power Service
June-September
October- January
February -Hay
COMMONWEALTH EDISON COMPANY
Small Commcrical and Industri
June-September
October- January
February 'May
1
10'KWH
1,268,353
716,594
709,222
279,009
279.009
279,009
I 3.531,196
al
2,276,368
2,222,243
2,059,061
Large Commercial and Industrial
June-September*1
October- January^
February-May"
DUKE POWER COMPANY
General Service (G)
July-October
November -February
March-June
General Service (GA)
July-October
November -February
March-June
General Service (I)
July-October
November- February
March-June
1,990,614
1,943,283
1,800,586
£12,292,155
891.246
862.173
718,0.45
548.715
530,816
442,080
1,402,182
1,402,182
1,402,182
£ 8,199,621
2
Perceived
KNH
Marginal .
Price
During
System
Peak
TOT
.0151
.0145
.0145
.00859
.00844
.00844
.0148
.0148
.0148
.0094
.0094
.0094 .
.0121
.0121
.0121
.
.0081
.'0081
.0081
.0061
.0061.
.0061
3
Upper
Bound
$
TGHT
Mlfl
.0216
.0250
.0235
.0178
.0212
.0210
.0280
.0280
.0280
."0228
.0228
.0228
.0205
.0202
.0208
.0143
.0142
.0146
.0135
.0134
.0138
4
%k
.00650
.01050
.00900
.00921
.01276
.01166
.0132
.0132
.0132
.0135
.0135
.0135
.0084
.0081
.0087
.0062
.0061
.0065
.0074.
.0073
.0077
5
3* -4
.354
.532
.474
.698
.861
.817
.617
.617
.617
.841
.841
.841
.515
.502
.529
.554
.547-
.573
.755
.749
.774
6
Estimate of
State Average
(and Marginal)
Price Elasti-
cities
-1.46
-1.46
-1.46
-1.93
-1.93
-1.93
-1.48
-1.48
-1.48
-1.87
-1.87
-1.87
-1.13
-1.13
-1.13
-1.13
-1.13
-1.13
-1.65
-1.65
-1.65
7
Seasonal
Upper
Bound on
Efficiency
Gains -
P*
|eAPKWHpk^
2,131,621
2,919,815
1, 207,172
1,730,847
2,957,993
2,553,178
£14.500.626
13,718,828
13,392,638
12,409,199
21,422,454
20,913,235
19.582,367
£101,239,221
2,178.306
1.980,697
1,867,074
1,064,835
1. 000, 682
930,258
6,462,854
6,324,853
6,894,097
£28,703,656
"circled numbers art aoVumn numbert; unolroled number la the digit Z.
Data are averages from aaleulationa from a eampla of premises.
154
-------
Table 46 (Continued). INDICATORS OF POTENTIAL
PRICING IMPROVEMENT, DEMAND-BILLED SCHEDULES
System Rate Schedule (Season)
NEW YORt STATE ELECTRIC AND GAS
General Service (PSC108SC2)
November-February
March-June
July-October
General Service (PSC113SC2)
November-February
March-June
July-October
1
^k
lO'Klffl
86,342
71,023
74,944
147,458
120,931
127,991
Large Light and Power (PSC113SC3)
November-February
March-June
July-October
191,910
191,910
191.910
Primary Light and Power (PSC108SC3)
November-February
March-June
July-October
33,310
33,310
33,310
I 1.304,349
PENNSYLVANIA POKER AND LIGHT COMPANY
General Service (SGS)
November -February
March-June
July-October
Large General Service (LP-3)
November - February
March-June
July-October
Large General Service (LP)
November-February
March-June
July-October
Primary General Service (LP-4
November - February
March-June
July-October
High-Tension General Service
November - February
March-June
July-October
High-Tension General Service
November-February
March-June
July-October
116,606
91,447
93,709
439,437
345,134
353,557
44,302
44,302
44,502
160,438
160,438
160,438
81,890
81,890
81,890
(LP-6)
188,779
188,779
188,779
E 2,866,077
2
Perceived
KW1!
Marginal
Price
During
System
Peak
J
XHH
.0121
.0121
.0121
.0240
.0240
.0240
.0149
.0149
.0149
.0073
.0073
.0073
.0328
.0328
.0328
.0121
.0121
.0121
.0102
.0102
.0102
.0085
.0085
.0085
.0066
.0066
.0066
.0057
.0057
.0057
3
linn A i*
upper
Bound
VLJU
Ann
.0227
.0229
.0229
.0333
.0333
.0333
.0178
.0181
.0180
.0176
.0179
.0178
.0597
.0617
.0489
.0219
.0227
.0195
.0219
.0225
.0196
.0210
.0216
.0187
.0211
.0217
.0188
.0209
.0215
.0186
4
Ap ,
p*
0106
0108
0106
0093
0093
0093
0029
0032
0031
0103
.0106
.0105
.0269
.0289
.0161
.0098
.0108
.0074
.0117
.0123
.0094
.0125
.0131
.0102
.0145
.0151
.0122
.0152
.0158
.0129
5
*Ppk _ J&,
P zd'
.6092
.6171
.6092
.3246
.3246
.3246
.1774
.1939
.1884
.8273
.8413
.8367
.582
.612
.394
.577
.621
.468
.729
.752
.631
.848
.870
.750
1.047
1.067
.961
1.143
1.162
1.062
6
istimate of
tate Average
and Marginal)
Price Elasti-
cities
-1.65
-1.65
-1.65
-1.65
-1.6S
-r.es
-1.89
-1.89
-1.89
-1.89
-1.89
-1.89
-1.46
-1.46
-1.46
-1.46
-1.46
-1.46
-1.93
-1.93
-1.93
-1.93
-1.93
-1.93
-1.93
-1.93
-1.93
-1.93
-1.93
-1.93
7
Seasonal
Jpper
iound on
Efficiency
Gains
Ah' v "
P*
1 4l>
IeipKWHpk p
459,969
390,497
399,248
367,232
301,167
318,751
93,271
112,491
105,884
268,145
280,625
276,457
I 3,373,737
1,332,126
1,178,758
433,762
1,813,207
1,689,087
893,482
364,635
395,429
253,573
1,641,113
1,764,504
1,184,388
1,199,694
1.273,202
926,486
3.164.962
3.344,583
2,495,703
£25,348.694
155
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basis is straightforward, and is carried out in Table 46,
Indicators of Potential Pricing Improvement, Demand-Billed
Schedules. Again, as in the case of the Category III bene-
fit estimates, a warning is appropriate in the interpretation
of these figures. The reductions in peak consumption given
by the usual elasticity formula are very large, sometimes
amounting to total peak consumption. Here, as before, the
source of this result is apparent: the application of long
run elasticities to peak price changes often amounting to
more than 90 percent of perceived price. Accordingly, the
benefit estimates are to be taken as order of magnitude esti-
mates.
156
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SECTION V
REFERENCES
1. Anderson, K., Industrial Energy Demand (Rand Corporation,
1971).
2. Baumol, W., and Bradford, D., "Optimal Departures from
Marginal Cost Pricing," American Economic Review (June,
1970).
3. Chapman, L.D., et. al., "Electricity Demand in the
United States: An Econometric Analysis," Oak Ridge
National Laboratory, Preliminary, June 1973.
4. Federal Power Commission, The 1970 National Power Survey
(Washington, D.C.: U.S. Government Printing Office,
1971), Volume I, p. 1-1-11.
5. Fisher, P.M., and Kaysen, C., A Study in Econometrics:
The Demand for Electricity in the United States (Am-
sterdam: North-Holland Publishing Company, 1962).
6. Halvorsen, R., "Residential Electricity: Demand and
Supply," Environmental Systems Program, Harvard Univer-
sity, preliminary mimeograph, 1971.
7. Smith, V.K. , et. al. , ".Econometric Estimation of Elec-
tricity Demand," mimeograph, 1973.
8. Wilson, J.W., "Residential Demand for Electricity,"
Quarterly Review of Economics and Business (Spring,
1971) .
157
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BIBLIOGRAPHIC DATA
HEET
1. Report No.
Title and Subtitle
The Economic and Environmental Benefits from
Improving Electrical Rate Structures
3.-Recipient's Accession No.
3. Report Date
November 1971*
6.
Author(s)
Dr. Mark Sharefkin
8. Perfocauix Or*«oiz«iion Kept.
No.JACXFAU-101-74
Performing Organization Nam* and Address
Jack Faucett Associates
5454 Wisconsin Avenue
Chevy Chase, Maryland 20015
10. Proiect/Tcsk/Vork Unit No.
PE THAOQ^ PI AQT._rn
11. Contract/Grant No.
68-01 1850
2. Sponsor ing Organization Name and Address
Environmental Protection Agency
Implementation Research Division
Washington, D.C. 20460
13. Type of Report 8t Period
Coveted
Final Report
14.
5. Supplementary Notes
traces Quantitative estimates of the internal cost savings to be de-
rived from changes in the pricing of electric power are devised and eva-
luated. The econometric literature on electricity demand is surveyed,
and elasticity values are selected which are parameters for the overall
benefit measures. A method for using reported utility data to estimate
the cost of delivered power--at the system peak and off the system, and
for each customer class--is devised. Data on five electric utilities is
used to make estimates of the potential benefits from improvements in the
pricing of electric power, for each customer class in each system. The
estimated potential benefits are sufficiently large to merit load curve
studies by block f,or residential customers. Such studies are necessary
preliminaries to a definitive assessment of the proposals for so called
inversion.
17. Key Voids and Document Analysis. 17*. Descriptor*
Electric Power
Rate Structure
Environmental Benefits
Load Curves
Peak-Load Pricing
ITb, Identifiers/Open-Eaded Terms
Ue. COSATI Field/Group
21. Mo. of Pagea
187
18. Availability. Statement
^..Security Class (This
Report)
H. Security Class li'Sis
Page
22. Price
FORM NTIS-39 (REV. 8-721
USCOM4-DC 40US>I»71
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