20120614Exergy, Simplot, Clearwater to Idaho Power 7-10.pdf

Peter J. Richardson ISB # 3195
Gregory Adams ISB # 7454 *
RICHARDSON & O'LEARY PLLC 2012
515N.27thStreet
Boise, Idaho 83702
Telephone: [phone]
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gregrichardsonandoleary.com
peter(richardsonandoleary.com
Attorneys for Clearwater Paper Corporation, J. R. Simplot Company
and Exergy Development Group, LLC
BEFORE THE IDAHO PUBLIC UTILITIES COMMISSION
IN THE MATTER OF THE ) CASE NO. GNR-E-11-03
COMMISSION'S REVIEW OF PURPA QF )
CONTRACT PROVISIONS INCLUDING ) CLEARWATER PAPER
THE SURROGATE AVOIDED ) CORPORATION, J. R. SIMPLOT
RESOURCE (SAR) AND INTEGRATED ) CORPORATION AND EXERGY
RESOURCE PLANNING (IRP) ) DEVELOPMENT GROUP OF IDAHO,
METHODOLOGIES FOR CALCULATING ) LLC's ANSWER TO IDAHO POWER
PUBLISHED AVOIDED COST RATES COMPANY'S SECOND
PRODUCTION REQUEST
COMES NOW, Clearwater Paper Corporation ("Clearwater") the J. R. Simplot
Company ("Simplot") and Exergy Development Group of Idaho, LLC ("Exergy") in response to
the Second Production Request of the Idaho Power Company ("Idaho Power") to Clearwater and
provides the following answers:
1- CLEARWATER ET AL RESPONSE TO IDAHO POWER'S SECOND PRODUCTION REQUEST
REQUEST FOR PRODUCTION NO. 7:
In Dr. Reading's Direct Testimony, pages 10 through 12, Dr. Reading makes several
references to and citations from the "Grey Books" which were published prior to the passage of
the Public Utility Regulatory Policies Act of 1978. Please provide a copy of these "Grey
Books."
RESPONSE TO REQUEST FOR PRODUCTION NO. 7:
See attached.
2- CLEARWATER ET AL RESPONSE TO IDAHO POWER'S SECOND PRODUCTION REQUEST
REQUEST FOR PRODUCTION NO. 8:
In Dr. Reading's Direct Testimony, page 10, lines 10-12, Dr. Reading states, "These
'Grey' books provided much of the theoretical background that was used in establishing avoided
cost rates by regulatory commissions." Please provide all documentation supporting that claim,
and a list of all the commissions which relied upon the "Grey Books" in establishing avoided
cost rates.
RESPONSE TO REQUEST PRODUCTION NO. 8:
Dr. Reading does not have a list of Commissions that used the "Grey Books", but is
aware the North Carolina Commission used them. The copies provided in response to Request
for Production No. 7 are copies obtained from the North Carolina Staff. In a recent case in North
Carolina, Progress Energy referred to a "Grey Book" as one source used in determining PURPA
rates. Dr. Reading was a member of the Idaho Commission Staff in the 1980s and participated in
numerous meetings and interactions with PUC Staff members from other states' commissions
that were familiar with NERA's publications. Some Commissions invited NERA Staff to testify
or consult when determining PURPA rates.
3- CLEARWATER ET AL RESPONSE TO IDAHO POWER'S SECOND PRODUCTION REQUEST
REQUEST FOR PRODUCTION NO. 9:
In Dr. Reading's Direct Testimony, page 10, line 12, Dr. Reading states, "As explained
by NERA in one of the "Grey Books' . . ." Please provide a definitive reference to which of the
"Grey Books" Dr. Reading is referring and a citation to the page and paragraph.
RESPONSE TO REQUEST FOR PRODUCTION NO. 9:
How to Quant[y Marginal Cost: Topic 4, Page 3.
4- CLEARWATER ET AL RESPONSE TO IDAHO POWER'S SECOND PRODUCTION REQUEST
REQUEST FOR PRODUCTION NO. 10:
If not already provided in response to Idaho Power's Request for Production No. 1,
please provide a copy of the Topic 4 "Grey Book," cited in Dr. Reading's Direct Testimony,
pages 11 through 12.
RESPONSE TO REQUEST FOR PRODUCTION NO. 10:
See Response to Request for Production No. 7.
DATED this 14th day of June, 2012.
RICHARDSON & O'LEARY PLLC
By: ;;E)
'aiISB#' Peter J. Rich
RICHARDSON & O'LEARY, PLLC
5- CLEARWATER ET AL RESPONSE TO IDAHO POWER'S SECOND PRODUCTION REQUEST
CERTIFICATE OF SERVICE
I HEREBY CERTIFY that on the 14th day of June, 2012, a true and correct copy of the
within and foregoing CLEARWATER PAPER CORPORATION'S RESPONSE TO THE
SECOND PRODUCTION REQUEST OF IDAHO POWER COMPANY was served as shown
to
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Williams Bradbury, PC
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Robert A. Paul
Grand View Solar II
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James Carkulis
Exergy Development Group of Idaho, LLC
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Blue Ribbon Energy, LLC
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#15 NERA 1.3
A FRAMEWORK FOR MARGINAL COST-BASED
TIME-DIFFERENTIATED PRICING
IN THE UNITED STATES:
TOPIC 1.3
Prepared by
National Economic Research Associates, Inc.
Prepared for
ELECTRIC UTILITY RATE DESIGN STUDY:
A nationwide effort by the Electric Power Research
Institute, the Edison Electric Institute, the American
Public Power Association, and the National Rural
Electric Cooperative Association for the
National Association of Regulatory Utility Commissioners
February 21, 1977
FMWy c
H trcic,- RATE DESIGN STUDY
A nationwide effort by
the Electric Power Research Institute.
the Edison Electric Institute,
the American Public Power
Association, and the National
Rural Electric Cooperative
Association for the National
Association of Regulatory Utility
Commissioners.
Post Office Box 10412
Palo Alto, California 94303
[phone]
A FRAMEWORK FOR MARGINAL COST-BASED
TIME-DIFFERENTIATED PRICING
IN THE UNITED STATES:
TOPIC 1.3
Prepared by
National Economic Research Associates, Inc.
80 Broad Street
New York City, New York 10004
'I
February 21, 1977
NOTE TO READERS
This report was prepared by National Economic Research
Associates, Inc. It contains information that will be
considered by the Project Committee along with other reports,
data and information prepared by several other consultants,
the various task forces and other participants in the rate
design study. This document is not a report of the Project
Committee and its publication is for the general information
of the industry. The Project Committee will report its
findings to the National Association of Regulatory Utility
Commissioners in a comprehensive report that will be published
in the spring of 1977.
The report of National Economic Research Associates contains
the findings and reflects the views of the consultant. The
distribution of the document by the rate design study does
not imply an endorsement by the Project Committee or the
organizations, utilities or commissions, participating in
the rate design study.
National Economic Research Associates (NERA) was retained to
examine portions of the Plan of Study (e.g., "The Analysis of
Various Pricing Approaches," If5pic l. A task force was organized
to provide additional information. NERA reports its findings here
on Topic 1.3, A Framework for Marginal Cost-Based Time-Differentiated
Pricing in the United States. The findings of the task force appear
in a companion document entitled The Analysis of Various Pricing
Approaches that will be released simultaneously with the NERA report.
Further, work by a second consultant on this topic, Ebasco Services,
Inc., will be reported separately.
Topic 1 is described in the Plan of Study as:
Topic 1 The Analysis of Various Pricing Approaches
The first topic (1.1) would be a "state-of-
the-art" review as to the purpose of rates and possible
uses of price as policy instruments, particularly with
respect to various aspects of peak-load pricing. The
development of the roles of fully allocated historic
cost pricing and long-run incremental cost pricing would
be examined and the rationales supporting them appraised.
The starting point would be the premise that
rates must be just and reasonable and that they must
effect an overall balance between the interest of the
owners of the enterprise--the stockholders--and the
ratepayers. Thus, absent some fairly radical statutory
development, there must be an overall revenue constraint in raternaking. Second, there is the general precept that
rates must not be unduly preferential or unduly discrim-
inatory. This introduces a principle of equity. The
:1.
general constraint here is that differentials
between classes of service and rates within classes
must be based on some notion of cost of service.
Whether this is the more traditional, fully allocated
historic cost of service or "fully allocated" marginal
cost of service is a matter to be considered later.
Third, there is the historic concept of continuity
in ratemaking under which customers are said to have
a right to be protected against unnecessarily abrupt
changes in the structure of rates.. The justification
for this assertion arises from the capital-intensive
nature of electric utilization, where customers have
to make substantial investments which are theoretically
based, in part at least on their price expectations.
To this might be added an extension of the concept of
equity; somehow it does not seem to some "fair" to
disturb unduly customers' expectations.
Finally, simplicity and clarity are considered
to be an essential of proper ratemaking, not only from
the standpoint of the customers' ability to understand
rates, but also from the standpoint of rate adminis-
tration by the commission and the companies.
Often these various precepts are in conflict
with each other and the regulator must choose which
precept he considers the most binding. Here there is
little statutory guidance, but rather the regulator's
judgment is brought into play.
Into this set of somewhat conflicting signals
has been injected the economic role Of price, more
particularly in the last five years. A version of
marginal cost, based on long-run incremental cost (LRIC),
has been introduced into various rate proceedings in
guiding certain of the utility companies as to the
directions in which rates should move. Moreover, even
before this, utility companies were moving in the
direction of peak responsibility pricing, with demand
charge ratchets, off-peak rates, summer-winter differ-
entials, etc.
Most recently, capital shortages, increasing
costs of fuel and equipment, and declining load factors
have led to more frequent and more insistent asking of
the question as to whether pricing as generally practiced.
has contributed to an uneconomic growth of the peak, and
whether basic changes in the price structure might help
to curb this tendency.
A reasoned debate is taking place in academic
and trade journals as to the purposes and effects of
rates based on these different principles. An overview
of the theoretical basis of the different positions,
and a comparison of the ratemaking philosophies would
be a useful first step to clarifying the problem.
The second topic (1.2) would be to review the
theoretical and/or applied work done in the United States
Prance, England, Germany, Sweden and other countries in
connection with peak-load pricing. This review would
then examine experience with peak-load pricing where it
has been applied. Particular emphasis would be directed
toward an examination of these tariffs in terms of the
peak-limiting and capital-saving results and their
possible applicability to conditions in the United States.
In addition, some United States utilities have
introduced interruptible rates, summer-winter differ-
entials and/or ratcheted demand metering. The basis
for these and their effectiveness will be examined and
their relationship to traditional ratamaking and peak-
lOad pricing will be reviewed.
Assuming that these two investigations show a
promising basis for pursuing time-related rates further,
the third topic (1.3) would be to develop a methodological
framework to be employed in developing time-related rates
in the United States electric industry. This would be in
the form of a preliminary working paper, with the emphasis
not on "should" this course be followed, but rather
"how" to proceed.
Without prejudging the contents of this paper,
the sequence of the likely, necessary steps is outlined
here, since it is important to the understanding of what
follows. The first step would require a determination
of the periods to be used in a peak-load pricing rate
schedule and, therefore, for which Costs are to be
determined. Typically, this would involve several
seasons during the year and several times of day. Only
if the rate schedules are reasonably simple can they
be effective. Step 2 would involve the determination
of appropriate running costs (fuel and other variable
costs) for each of the pricing periods selected in
Step 1. Step 3 would involve the determination of the
various categories of appropriate capacjy costs
(generation, transmission and distribution). In. Step 4,
the allocation of these costs (some of which are joint)
would be made to the various rating periods on the basis
of appropriate criteria. Step 5 would involve putting
these various costs together, for each rating period,
to devise a cost-based rate for each period; and finally,
these preliminary rates would be adjusted into a practical
set of proposals which blend these rates with other
111
pertinent regulatory standards, in the light of
practical metering capabilities (the subject of
Topic 7). It is not the intention of the fore-
going description to foreclose consideration of
alternative pricing methods. There should be an
explicit consideration, for example, at least in
principle, of the possibility of basing rates on
short-run incremental costs.
The National Economic Research Associates report is responsive
to the requirements of Topic 1. Their findings, as reflected
in their report, will be weighed by the Project Committee in
reaching its conclusions. Many of the issues in the rate de-
sign study are controversial, in some cases data are lacking
and in certain instances value judgments are necessary. Thus,
readers are cautioned to make their own careful assessment of
NERA's work and to consider other sources of information as well.
Readers are reminded that some of the materials contained in this
report will be an advocate's point of view.
iv
NOTICE
This report was prepared by National Economic Research
Associates, Inc. as an account of work sponsored by the
Electric Power Research Institute, Inc. (EPRI). Neither
EPRI, members of EPRI, National Economic Research
Associates, Inc. nor any person acting on behalf of either:
(a) makes any warranty or representation, expressed or
implied, with respect to the accuracy, completeness, or
usefulness of the information contained in this report,
or that the use of any information, apparatus, method, or
process disclosed in this report may not infringe pri-
vately owned rights; or (b) assumes any liabilities
with respect to the use of, or for damages resulting from
the use of, any information, apparatus, method, or process
disclosed in this report.
ABSTRACT
The report "A Framework for Marginal Cost-Based
Time-Differentiated Pricing in the United States" discusses
the theory of marginal cost pricing and its relation to the
problems utility commissions face in setting just and rea-
sonable rates for electricity. It applies basic concepts
of microeconomics to the problems of estimating marginal
costs in that industry showing how this results in time-
differentiated costs. It discusses theoretical problems
associated with costing, including capacity responsibility,
charges for long-lived assets and distribution costs. Fi-
nally, it discusses the theoretical considerations involved
in deriving rates from costs including problems of second
best and the revenue constraint.
Vi
TABLE OF CONTENTS
Page
I. SUMMARY 1
II. THE RATIONALE FOR MARGINAL COST PRICING 13
III. FURTHER DEVELOPMENT OF THE MARGINAL COST THEORY 30
A.Joint and Common Costs 30
B.External Costs 39
C.Shortage Costs 41
D.The Role of Demand Elasticity 42
IV. METHODOLOGICAL ASPECTS OF MEASURING MARGINAL
COSTS FOR AN ELECTRIC UTILITY 49
A. Marginal Costs of a Generating System 51
1. Marginal Costs and Total Costs 58
2. Marginal Costs and Cost Allocation 59
3. Short-Run Changes and Long-Run Changes 61
B. Marginal Capacity Costs 63
C. Treatment of Taxes 71
D. Reserve Margins, Maintenance and Related
Issues, and Their Impact on Responsibility
for Marginal Capacity Costs 73
1.General Overview 73
2.Use of LOL? 77
E. Distribution and Transmission 82
1. Customer Costs--Covering the Territory 82
2. Customer Costs--Metering, Billing and
Hook-Up 86
3. Demand Costs in Distribution 87
4. Coincidence and Diversity 88
F. Annual Charges 90
G. Treatment of Hydro 94
Vii
Page
V.THE DEVELOPMENT OF THE METHODOLOGY--LRIC TO
TIME-DIFFERENTIATE) MARGINAL COSTS 100
VI.RATEMAKING ASPECTS OF MARGINAL COST PRICING 106
A. Introduction 106
B. Coincidence and Diversity 108
C. Special Problems 112
1.Needle Peaking and Temperature 112 2.Rates for Small Consumers 114 3.Fuel Adjustment Clauses 116
D. The Second-Best Issue in Ratemakirtg 117
E. The Revenue Gap and the Least Distortion Rule 124
ATTACHMENT A: A SIMPLIFIED MODEL OF TIME-OF-DAY/SEASONAL
PRICING
ATTACHMENT B: THE "TURVEY CALCULATION"
ATTACHMENT C: AN ECONOMIC CONCEPT OF ANNUAL COSTS OF LONG-
LIVED ASSETS
viii
L
A FRAMEWORK FOR MARGINAL COST-BASED
TIME-DIFFERENTIATED PRICING IN THE UNITED STATES
I. SUMMARY
It has been suggested that the real argument in the
"Great Rate Debate" lies not in disagreement with economic
theory, but realistically in problems of application.' This
summary of our report presents the basic concepts of economic
theory as they apply in theory and practice to electric rate-
making.
Utility rates can be viewed from two broad perspec-
tives: equity or efficiency. After the total amount of the
utility's revenue requirements is determined, rates must be
determined for each group of customers so that the revenue
requirement is achieved. In order to establish these rates,
one must have some objective in mind, and however stated,
that objective is either some conception of what is fair, or
a more efficient allocation of resources, or some combination
of those two.
We shall not dwell here on the meaning of the words
"equity" or "fair." We shall turn, instead, to an examination
of rate structures on the assumption that we seek an efficient
allocation of resources--and then return to the question of
whether such an objective cannot be accommodated to a rea-
sonable conception of equity.
' Frank S. Walters, "The Great Rate Debate," Public Utilities
Fortnightly, December 16, 1976.
-2-
It is the economist's contention that some prices
allocate better than others; specifically, that marginal cost
pricing produces an efficient allocation of resources. Regu-
lators of an industry which uses 16 percent of the nation's
annual capital investment and 27 percent of its raw energy
sources might do worse than have econoriic efficiency in mind
in seeking rates which will most enhance the public interest.
We submit that economic efficiency is a reasonable basis for
ratemaking which, in the public interest cannot be ignored,
and argue that it also leads to prices which satisfy equity
criteria that are often considered important by regulators.
First, however, we explain why marginal cost pricing is thought
to be economically efficient.
Marginal cost pricing is a central concept in eco-
nomic theory. The theory states that if the price of every
commodity is set equal to its marginal cost, society's scarce
resources are allocated so as to maximize the satisfaction of
consumers. Under such an allocation, no consumer can be made
better off without making some other consumer worse off. It
is a very well-established theory--even those economists who
object to its application in particular circumstances would
not dispute its theoretical validity. In common sense terms,
the rule can be thought of as asserting that the price should
signal the cost to society of producing one unit more of a
good, or what society will save by producing one unit less.
For if the price is higher than the resource cost, some people
will not consume something for which they would have been
-3-
willing to pay the resource cost; while if the price is too
low, some consumers will consume commodities which cost so-
ciety more than they are worth to the consumers and too many
scarce resources will be devoted to producing that item.
In electric production, the product is demanded in
a cyclical fashion and is to a large extent unstorable, so
that although the same machines may be used to produce elec-
tricity in the day and at night, daytime and nighttime elec-
tricity are best thought of as separate products with joint or
common costs. When two products with different costs of pro-
duction are priced at the same level, there is a tendency for
too little to be consumed of the overpriced product while too
much is consumed of the underpriced product. In the case of
electricity, the costs of expanding the system to meet peak
demands have been far greater than the price charged. Con-
sumers have been receiving the wrong signal. They make deci-
sions based on a price of peak electricity which is too low,
causing them to increase their consumption beyond the point
where the costs of resources and the value of output of addi-
tional consumption are in balance. At the same time, night-
time electricity is relatively inexpensive to provide, but by
signaling that it is more expensive, the price discourages
people from using it.
That is the coupon sense to the economist's theo-
retical notion of marginal cost pricing, but there are certain
assumptions underlying the theory, and certain conditions
-4-
which should be reviewed before applying marginal cost prices
in any particular case.
First, the economist's rule of marginal cost pricing
is a rule for economic efficiency, and economic efficiency
may in some cases be rejected in favor of other goals. How-
ever, if economic efficiency is a goal, the conditions under
which marginal cost pricing will produce an efficient alloca-
tion of resources are:
- That the income distribution is acceptable, or
that it can be changed without departing from the rule that
price equals marginal cost;
- That consumers and producers act rationally,
consumers acting to maximize their satisfactions and producers
to minimize their costs; and
- That all other relevant goods and services in the
economy are priced at marginal cost.
The first two propositions are fairly easily dealt
with. Strictly speaking, the efficient allocation of resources
we speak of is a "local maximum," given the income distribu-
tion. A different income distribution would give a different
mix of goods and services and marginal cost pricing would then
lead to an efficient allocation of resources given that income
distribution. The economist cannot say which is the best in-
come distribution, nor does he assert that the present distri-
bution is good or bad. It must be admitted that the economist's
belief in the basic reasonableness of allocating by price is
-5-
II
dependent on the assumption that the income distribution is
also reasonable. To the extent that the income distribution
is perceived to be unjust, allocations based on price will be
perceived to be unjust. However, social justice is mainly the
province of legislatures: public utility commissions generally
are not required or expected to use electricity rates to im-
prove the income distribution.
The second assumption, of consumer and producer
rationality, has sometimes been contested on empirical
grounds, particularly the assumption that producers act to
minimize their costs. In the case of electric utilities, we
can only assume that even if the utility management does not
aim to minimize costs, the commission will try to enforce
that objective.
The theory also assumes that other goods and serv-
ices in the economy are priced at marginal cost. This is the
"problem of the second best" and is primarily relevant in the
case where close substitutes are priced above or below their 1f%
marginal cost; however, complementary goods--inputs to the
production pkocess and markets for goods which use electric-
ity as an input--should also be reviewed. As a result, in
certain cases, departures from the rule price equals marginal
cost may be called for. Since goods and services in a compe-
titive economy will tend to be priced at marginal cost, it is
mainly cases of monopoly or regulation which would be relevant
to decisions to deviate from marginal cost. These should be
made in the context of the specific circumstance appropriate
-6-
to any ratemaking application. The decision to deviate from
marginal cost is, however, still based on marginal cost con-
siderations.
Our proposal for rate structure reform in the elec-
tric utility industry does not generally involve pricing at
marginal cost. Revenue constraints based on historic costs
will, except by chance, dictate rates based on marginal cost
principles rather than rates precisely equal to marginal cost.
In our report we claim only that even when second-best con-
siderations have been taken into account, prices guided by
marginal costs offer the best method of improving resource
allocation and of signaling consumers what their electricity
consumption is costing society, while prices based on other
considerations have no general beneficial allocative signifi-
cance at all.
The marginal cost methodology we propose is based
throughout on the planning and operation of a utility system
and the cost of decisions taken at the margin. Each system
is different, but the same economic principles apply to each
analysis. These principles and their application have been
carefully enunciated and refined in numerous rate cases and
generic hearings on rate structure, and have been used as a
basis for rate decisions by several commissions.
It is the application of marginal cost principles
to electricity production which leads to proposals for time-
of-day rates and in some cases to seasonal variations.
Additional consumption during some periods may require both
-7-
additional capacity and fuel, while at other times addi-
tional consumption may only require more fuel utilization.
In reality, there is a graduated peak responsibility which
depends on the load and the equipment configuration. For
utilities whose load is very flat, marginal costs may not
vary very much over the cycle, and time-of-use prices would
not be indicated for such companies; however, for most com-
panies there is substantial variation in marginal cost by
time of use.
Since the total revenues allowed by the regulatory
commission will be independent of the rate structure method-
ology chosen, the "average" consumer will generally pay the
same total dollar amount under time-of-use pricing as under
average cost pricing. Those who consume relatively more at
peak will pay more, and those whose consumption is mainly off
peak will pay less. However, consumers will be free to alter
their patterns of demand to save themselves money at the same
time as they save the system money.
-1
One of the basic differences between historic V
practices and what we are currently proposing is that as
economists we believe that prices do more than simply allo-
cate costs to those who "caused" them. While it is true that
historic methods based on peak responsibility did allocate
costs to peak users by charging higher average prices to those
whose class characteristics were more on peak, those prices
did not provide a signal to consumers that power costs more
at the peak, because the price was the same at all times.
-8-
Nor did the prices provide an incentive to get off the peak
because the consumer could not save money by doing so. The
economist insists that price has an economic function: it
provides signals and incentives to which buyers do in fact
respond, and since they do respond, it is better .to send them
signals which will tell them something useful about the con-
sequences of their actions.
The consumer then may welcome time-of-use pricing
because it offers a lower price for off-peak electricity as
a way out of ever-increasing electric bills, while utility
management sees it as a way to reduce the uneconomic growth
of the peak. Marginal cost pricing is not simply a theoreti-
cal, some would say theological, construct: both consumers
and producers can benefit, and that is precisely what econo-
mists mean by a "net gain in welfare." It would, of course,
be possible to differentiate prices by time of use based on
some other concept than marginal cost, but there is no other
system that we are aware of that offers a consistent and ra-
tional basis for deciding the appropriate price differentials.
We should caution, however, that the purpose of
marginal cost pricing is not to level the load, but to char ge
L the right price. If the price reflects the cost then the
"right" load curve reflects what the customers want and are
willing to pay for. If people do not want to eat at 3: 00.
a.m., we do not propose jiggling the rates until they do.
If they will pay what it costs to cook at 6:00 p.m., then
-9-
the resulting demand pattern is economically efficient. Of
course, we do expect that, since demand is responsive to
price, there would be some response to time-of-use prices,
but it is by no means the aim to shift the load, least of all
to level the load. Conversely, in a utility where the load
is level or nearly so, there might be little time-of-use cost
differentiation and hence there would be little or no purpose
in differentiating prices by time of use.
There may still be those who feel that while mar-
ginal cost pricing can be shown to be efficient and perhaps
even reasonable as a basis for rate structure reform, given
the central role electricity plays in the economic system,
it is somehow unfair in a more metaphysical sense. At this
point then it may be helpful to consider the ways in which
marginal cost pricing satisfies criteria which many regula-
tors, consumers and producers feel must be taken into account
for rates to be just and reasonable.
First, it is the very same principle under which
the total revenue balance between stockholder and customer
is thought to be fair: the return is just large enough to
attract an adequate supply of capital to meet demand; the regu-
latory process simulates a competitive market in adjudicating
the rival claims. Where a competitive market flourishes, the
question of fair prices is not often raised, save in times of
extraordinary crisis such as famines and wars, or for special
types of services such as medical care. Prices in competitive
-10-
markets are generally thought to be equal to the marginal
cost of production and paralleling this, the economist's pro-
posal is that marginal cost pricing, or the simulation of a
competitive market, be used to adjudicate rival claims on
electric power between different customers, between use at
different times of day and seasons of the year, and be-
tween different uses. Regulated prices which are based on
the simulation of a competitive market are therefore neither
more nor less equitable than prices which are determined in
competitive markets.
Second, the use of marginal cost pricing principles
might be considered fair in a more specific sense in electric-
ity production. All consumers use electricity from the same
generating plant. For years people have pondered how to di-
vide up the cost of the plant fairly. Many books and trea-
tises have been written and at least 29 alternative methods
have been proposed. Marginal cost analysis offers a solution
to this problem using economic principles, which certainly
seems on its face to be eminently fair, since it involves
each consumer paying the extra costs of putting him on the
system, while all consumers jointly pay all the costs.
A third aspect of the fairness of marginal cost
prices is more widely argued. The principles of peak respon-
sibility for assigning plant costs to customers is asserted
by many to give unfair "free rides" to off-peak customers.
Sometimes the principle of peak responsibility has been
-11-
essentially misunderstood: there is not one moment of time
at which responsibility for the plant is established, but
rather a graduated responsibility which measures how likely
it is that an increase in demand at any time will cause more
capacity to be added. It is only at those times when there
is no probability (in practical terms) that there will be
any necessity for new capacity to be added in the long run,
in response to an increase in demand that no capacity charges
should be made. In addition, since rates reflect the marginal
rather than the average energy costs in each period, the
energy" charges themselves generally make a contribution to
the capital costs since marginal energy costs are higher than
average energy costs in each period.
The fourth and perhaps most genuinely troublesome
equity problem is the question of the revenue gap. That is
'Co say, revenues derived from rates set at marginal costs
will almost certainly not equal the revenues allowed by a
regulatory authority. Since commissions neither wish to
grant windfall profits to the companies they regulate, nor
to bankrupt them, this gap must be eliminated. The economist
suggests that it is appropriate to eliminate the gap by
setting rates furthest from marginal costs in such a way that
consumption is affected the least, i.e., to create the least
distortion in the allocation of resources.
It appears to be the fear of some large commercial
and industrial users that, when eliminating the gap, regulatory
-12-
bodies will be subject to political pressures in adjusting
the prices away from marginal costs so as to adversely affect
them. Specifically, where the gap is an excess, they are
afraid that their rates will be held at marginal costs while
residential rates are reduced.
There is, depending on the size of the revenue gap,
a genuine area of judgment remaining here for commissions,
but it would be naive to suppose that it is any different in
genesis or extent than the area of judgment used by the allo-
cator in more traditional costing methods. The economist has
a general rule that the adjustment should be made so as to
distort the demand least--where demands are highly responsive
to price, the price should be closest to marginal cost. This
does not, however, lead to a single solution, but to a general
approach.
Our case for marginal cost pricing is based on its
effects on the allocation of society's scarce resources, in
particular that marginal cost pricing will lead to an effi-
cient allocation of resources. We believe that efficiency
is certainly one important consideration that regulators must
take into account in setting prices that are "in the public
interest." We also recognize that regulators, consumers
and electricity producers may have other criteria which also
may properly be given consideration. But by beginning with
economically appropriate rates they can then focus on the
economic cost of pursuing these other objectives.
II. THE RATIONALE FOR MARGINAL COST PRICING
Industries which are subject to regulation are often
characterized by heavy overhead costs and economies of scale
which tend to lead to monopoly. Moreover, such industries are
usually characterized as being "vested with public interest."
The electric industry fits this description well. The basic
importance of electric energy to the community has never been
more keenly appreciated, and the special characteristics of
electric distribution which lead to its being granted statutory
monopoly status are clear and seldom contested. Regulators are
empowered to set prices which will prevent monopoly profits ac-
cruing to the statutory monopoly while at the same time ensuring
that the company is sufficiently profitable to continue to at-
tract capital and provide service. The mandate set down by
statute for regulators in most jurisdictions is to promulgate
just and reasonable prices for the services that are "in the
public interest."
How can regulators ensure that rates are reasonable
and just, and in the public interest? It would probably be
fruitless to try to gain agreement on a definition of fair,
reasonable and just. Philosophers have debated the issue for
centuries. They have argued many arguments and failed to
come to an agreement. Some think with Plato that equity
means "let each man receive what he deserves and let the
better rule the worse," whereas others after Marx would agree
-14-
that it means "from each according to his abilities, to each
according to his needs." Aristotle thought that equity was
the natural law which permitted exceptions to be made, whereas
Hobbes felt that it was the law forbidding exceptions. The
only agreement we will get about equity is that there is no
agreement. We may agree with John Selden who put it succinctly
in 1689:
Equity is a roguish thing. For Law we
have a measure, know what to trust to;
Equity is according to the conscience of
him that is Chancellor, and as that is
larger or narrower, so is Equity.
Our only hope is to offer proposals and explicate the features
which seem to make proposals reasonable, then allow commis-
sions in their judicial role to determine whether the propos-
als are in fact fair, just and reasonable.
When we try to examine what might be behind the
notion that regulators should try to set a fair price, we
have to recognize that it is in part the existence of the monop-
oly itself which leads to fears that the price could be set
"unfairly." In a competitive market, prices are restrained
by the forces of competition. If a producer can make a very
high return, above what is required to keep him in business
or above what his money could earn elsewhere, then other
producers also will be attracted to the market and will beat
down the price to just the level where the price equals the
cost of the last unit produced plus a return on the capital
invested. But a monopoly, if unrestrained, can earn excessive
-
-15-
or monopoly profits by raising the price or restricting the
supply. In our competitive economy, monopoly power is there-
fore controlled by antitrust laws or by regulation, because
monopoly profits are thought to be exploitative of the con-
sumer, or unfair. On the other side of the coin, prices
which are determined in a free market generally are thought
to be neither "fair' nor "unfair"--they essentially are
neutral, and except in special cases, we do not consider it
necessary to regulate the price of even essential commodities
(although we may regulate the quality) if the prices are
market determined. One criterion for a "fair " price under
regulation might therefore be that it be the price that a
competitive market would produce, with no monopoly profits
permitted. This does not, of course, mean no return on
capital; it simply means no excessive return over what is
required to attract new capital.
If monopoly profits are what make prices "unfair,"
we can see that equity between stockholders and customers is
the first consideration in a just and reasonable rate. This
means that a monopoly must be restrained to earn only enough
to attract further capital from investors. In those indus-
tries where competition is infeasible, the regulatory process
seeks to impose fair rates by keeping the total revenues in-
cluding return on capital to the level which will just cover
costs and attract capital as a competitive market would. In
-16-
this way an equitable balance between stockholders and con-
sumers is commonly thought to be served.
The total revenue decision, then, affects equity
between customer and stockholder; the rate structure question
on the other hand affects equity among various consumers. A
typical large electric utility has perhaps a million consumers,
ranging from very large industrial concerns to very small
households. How can fairness be served best? The customers
as a whole must pay the stockholders as a whole the full cost
of service. But which customer should pay how much? When
equipment lasts many years and serves many customers, how can
the costs best be allocated to different customers and dif-
ferent years? A large system offers economies of scale and
benefits of diversity--who should get these benefits? Should
everyone be treated the same? What would it mean to treat a
large industry "the same as" a small household?
These and other questions lead to the generally
acceptable answer that prices should be based on cost. It
would be possible, of course, to base prices on income, or
not to charge at all, but no one is seriously suggesting in
the United States, for example, that customers should pay an
income-related electric tax and use all the electricity they
want. In other words, most people agree that it is reasonable
to charge customers by reference to the amount of electricity
they use and the costs of producing that electricity--you get
what you pay for.
J
-17-
But ratemaking does not simply have the static
purpose of allocating out fair shares of total revenues;
there is further logic to basing prices on costs. Not only
do prices raise money to pay for the total system, but price
also affects the demand for the product. The price is the
basis on which the consumer decides how to allocate income to
the purchase of goods and services. The higher the price of
a good, the less will be purchased: this is the principle
of demand elasticity. Because there is demand elasticity,
the price of the product determines how much will be bought,
and price helps to determine the allocation of society's
scarce resources among the countless competing uses for them.
The price is a signal: the price serves an a].locative pur-
pose.
It is the economist's contention that some prices
allocate better than others; specifically, that marginal cost
pricing produces an efficient allocation of resources. When
prices are set equal to marginal cost, given the prevailing
distribution of income, society's scarce resources are allo-
cated so as to maximize the satisfaction of consumers. Regu-
lators of an industry which uses 16 percent of the nation's
annual capital investment and 27 percent of its raw energy
sources might do worse than have economic efficiency in mind
in seeking rates which will most enhance the public interest.
We submit that economic efficiency is a reasonable basis for
ratemaking, and we will argue below that it also leads to
-18-
prices which satisfy eq1iity criteria that are often considered
important by regulators. First, however, we must explain why
marginal cost pricing is thought to be economically efficient.
Marginal cost pricing is a central concept in eco-
nomic theory. The theory states that if the price of every
commodity is set equal to its marginal cost, society's scarce
resources are allocated so as to maximize the satisfaction of
consumers. Under such an allocation, no consumer can be made
better off without making some other consumer worse off. It
is a very well established theory--even those economists who
object to its application in particular circumstances would
not dispute its theoretical validity. In common sense terms,
the rule can be thought of as asserting that the price should
signal the cost to society of producing one unit more of a
good, or what society will save by producing one unit less.
For if the price is higher than the resource cost, some people
will not consume something for which they would have been will-
ing to pay the resource cost, while if the price is too low,
some consumers will consume commodities which cost society
more than they are worth to the consumers; too many scarce
resources will be devoted to producing that item.
In electricity production, the product is demanded
in a cyclical fashion and is to a large extent unstorable, so
that although the same machines may be used to produce elec-
tricity in the day and at night, daytime and nighttime elec-
tricity are best thought of as separate products with joint
or common costs. When two products with different costs of,
production are priced at the same price, there is a tendency
for too little to be consumed of the overpriced product while
too much is consumed of the underpriced product. In the case
of electricity, the costs of expanding the system to meet
peak demands have been far greater than the price charged.
Consumers have been receiving the wrong signal. They make
decisions based on a price of peak electricity which is too
low, causing them to increase their consumption beyond the
point where the costs of resources and the value of output
of additional consumption are in balance. At the same time,
nighttime electricity is relatively inexpensive to provide,
but by signaling that it is more expensive, the price dis-
courages people from using it.
That is the common sense to the economist's theore-
tical notion of marginal cost pricing, but there are certain
assumptions underlying the theory, and certain conditions
which should be reviewed before applying marginal cost prices
in any particular case.
First, the economist's rule of marginal cost pricing
is a rule for economic efficiency, and economic efficiency may
in some cases be rejected in favor of other goals. However,
if economic efficiency is a goal, the conditions under which
marginal cost pricing will produce an efficient allocation of
resources are:
-20-
- That the income distribution is acceptable, or
that it can be changed without departing from the rule that
price equals marginal cost.
- That consumers and producers act rationally,
consumers acting to maximize their satisfactions and producers
to minimize their costs; and
- That all other relevant goods and services in the
economy are priced at marginal cost.
The first two propositions are fairly easily dealt
with. Strictly speaking, the efficient allocation of resources
we speak of is a "local maximum," given the income distribution.
A different income distribution would give a different mix of
goods and services and marginal cost pricing would then maxi-
mize efficiency given that income distribution. The econo-
mist cannot say which is the best income distribution, nor
does he assert that the present distribution is good or bad.
It must be admitted that the economist's belief in the basic
reasonableness of allocating by price is dependent on the
assumption that the income distribution is also reasonable.
To the extent that the income distribution is perceived to be
unjust, allocations based on price will be perceived to be
unjust. However, social justice is mainly the province of
legislatures: public utility commissions generally are not
required or expected to use electricity rates to improve the
income distribution. Nor do electricity rate structures appear
-21-
to be a particularly effective instrument for persuing income
redistribution goals.2
The second assumption, of consumer and producer
rationality, has sometimes been contested on empirical
grounds, particularly the assumption that producers act to
minimize their costs. In the case of electric utilities, we
can only assume that even if the utility management does not
aim to minimize costs, the commission will try to enforce
that objective.
The theory also assumes that other goods and
services in the economy are priced at marginal cost. This
is the "problem of the second best" and is primarily relevant
in the case where close substitutes are priced above or below
their marginal cost; however, complementary goods--inputs to
the production process and markets for goods which use elec-
tricity as an input--should also be reviewed. Since goods
and services in a competitive economy will tend to be priced
at marginal cost, it is mainly cases of monopoly or regula-
tion which would be relevant to decisions to deviate from
marginal cost. The decision to deviate from marginal cost is,
however, still based on marginal cost considerations.3
This is discussed in more detail in Section VI-C'.
See, for example, Joe D. Pace, Lifeline Rates or Energy Stamps,
presented at NERA Conference on Peak-Load Pricing and Lifeline
Rates, New York, New York, June 17, 1975; or Joe D. Pace, Testi-
mony before the Public Service Commission of New York, Case No.
26806, February 1976.
-22-
Economists' proposals for rate Structure reform in
electricity do not generally involve pricing at marginal cost.
Revenue constraints based on historic costs will, except by
chance, dictate rates based on marginal cost principles rather
than rates precisely equal to marginal cost. The economist's
claim is only that even when second-best considerations have
been taken into account, prices based on marginal costs offer
the best method of improving resource allocation and of signal-
ing consumers what their consumption is costing society, while
prices based on other considerations have no general beneficial
allocative significance at all
It is the application of marginal cost principles to
electricity production which leads to proposals for time-of-day
rates and in some cases to seasonal variations. Additional
consumption during some periods may require both additional
capacity and fuel, while at other times additional consumption
may only require more fuel utilization. In reality, there is
a graduated peak responsibility which depends on the load and
the equipment configuration. For utilities whose load is very
flat, marginal costs may not vary very much over the cycle,
and time-of-use prices would not be indicated for such com-
panies; however, for most companies there is substantial
variation in marginal cost by time of use.
Since the total revenues allowed by the regulatory
commission will be independent of the rate structure method-
ology chosen, the "average" consumer will generally pay the
-23-
same total bill. Those who consume relatively more at peak
will pay more, and those whose consumption is mainly off peak
will pay less. However, consumers will be free to alter their
patterns of demand to save themselves money at the same time
as they save the system money.
The consumer then may welcome time-of-day pricing
because it offers a lower price for off-peak electricity as a
way out of ever-increasing electric bills, while utility
management sees it as a way to reduce the uneconomic growth
of the peak. Marginal cost pricing is not simply a theoreti-
cal, some would say theological, construct: both consumers
and producers can benefit, and that is precisely what econo-
mists mean by a "net gain in welfare."
In recent months, many proponents of other methods
of cost analysis have suggested that it is possible to dif-
ferentiate the costs of serving at different times based on
traditional fully , distributed cost measures. It is, of course,
always possible to come up with an arithmetic division of his-
toric costs which "seem fair," perhaps because it has some
magic number property such as 1/3, 1/3, 1/3. But such systems
are only arbitrary allocation schemes which do not take into
account the efficiency implications of prices. They will have
no necessary relationship to the marginal costs which will
give consumers economically sound signals on which to base
their decisions.
-24-
We should caution, however, that the purpose of
marginal cost pricing is not to level the load, but to charge
the right price. If the price reflects the cost then the
"right" load curve reflects what the customers want and are
willing to pay for. If people do not want to eat at 3:00 a.m.,
we do not propose jiggling the rates until they do. If they
will pay what it costs to cook at 6:00 p.m., then the resulting
demand pattern is economically efficient. In short, there is
no "ideal" load curve that can be derived by looking only at
the costs of production. Of course, we do expect that, since
demand is responsive to price, there would be some response to
time-of-use prices, but it is by no means the aim to shift the
load, least of all to level the load. Conversely, in a utility
where the load is level or nearly so, there might be little
time-of-use cost differentiation and hence there would be little
or no purpose in differentiating prices by time of use.
There may still be those who feel that while mar-
ginal cost pricing can be shown to be efficient and perhaps
even reasonable as a basis for rate structure reform, given
the central role electricity plays in the economic system, it
is somehow unfair in a more metaphysical sense. At this point
then it may be helpful to consider the ways in which marginal
cost pricing satisfies criteria which many regulators, con-
sumers and producers feel must be taken into account for
rates to be just and reasonable.
-25-
First, it is the very same principle under which
the total revenue balance between stockholder and customer
is thought to be fair: the return is just large enough to
attract the last unit of capital; the regulatory process
simulates a competitive market in adjudicating the rival
claims. Where a competitive market flourishes, the question
of fair prices is not often raised, save in times of extra-
ordinary crisis such as famines and wars, or for special types
of services such as medical care. Prices in competitive mar-
kets are generally thought to be equal to the marginal cost
of production and paralleling this, the economist's proposal
is that marginal cost pricing, or the simulation of a competi-
tive market, be used to adjudicate rival claims on electric
power between different customers, between use at different
times of day and seasons of the year, and between different
usec. It may be argued that regulated prices which are based
on the simulation of a competitive market are neither more
nor less equitable than prices which are determined in competi-
tive markets.
Second, the use of marginal cost pricing principles
might be considered fair in a more specific sense in electric-
ity production. All consumers use electricity from the same
generating plant. For years people have pondered how to divide
up the cost of the plant fairly. Many books and treatises
have been written and at least 29 alternative methods have
-26-
been proposed." Marginal 'cost analysis solves the problem
using economic principles in a way that we will examine be-
low, but which certainly seems on its face to be eminently
fair, since it involves each consumer paying the extra costs
of putting him on the system, while all consumers jointly pay
all the costs.
A third aspect of the fairness of marginal cost
prices is more widely argued. The principles of peak respon-
sibility for assigning plant costs to customers is asserted
by many to give unfair "free rides" to off-peak customers.
Sometimes the principle of peak responsibility has been essen-
tially misunderstood: there is not one moment of time at
which responsibility for the plant is established, but rather
a graduated responsibility which measures how likely it is
that an increase in demand at any time will cause more capacity
to be added. It is only at those times when there is no proba-
bility (in practical terms) that there will be any necessity
for new capacity to be added in response to an increase in
demand, that no capacity charges should be levied.5
" See Attachment A to NERA's report on Topic 1. 1, "An Overview
of Regulated Ratemaking in the United States," February 2, 1977.
There is another aspect to the off-peak capacity charge:
a utility whose revenue requirement is based on historic
patterns can increase its earnings by increasing its load
factor if capacity costs are included in off-peak charges. (This is, of course, because marginal revenues exceed mar-ginal costs in those cases.) However, this is a double-
edged sword: if load factor should decline, earnings ero- sion will inevitably set in.
-27-
In some utilities, a relatively high load factor
and the need for maintenance will lead to a situation where
loss-of-load probabilities are measurable in the off-peak
period. In that case, there is no free ride: since the off-
peak consumer by increasing his use may in fact cause capacity
to be added in the long run he is responsible for a portion
(albeit a smaller portion than the peak user) of capacity costs.
In addition, some estimate of off-peak elasticity must be made,
for a low price based on current costs could attract new loads
and result in higher costs. Initially at least some caution
must be exercised in reducing the off-peak rate to reflect
only marginal running costs in the off-peak period.
The fourth and perhaps most genuinely troublesome
equity problem is the question of the revenue gap. That is
to say revenues derived from rates set at marginal costs will
almost certainly not equal the revenues allowed by a regula-
tory authority. Since commissions neither wish to grant wind-
fall profits to the companies they regulate, nor to bankrupt
them, this gap must be eliminated. The economist suggests
that it is appropriate to eliminate the gap by setting rates
further from marginal costs where consumption is affected
the least, i.e., to create the least distortion in the alloca-
tion of resources.
It appears to be the fear of some large commercial
and industrial users that when eliminating the gap, regulatory
-28-
bodies will be subject to political pressures in adjusting
the prices away from marginal, cost so as to adversely affect
them. Specifically, where the gap is an excess, they are
afraid that their rates will be held at marginal costs while
residential rates are reduced.
There is, depending on the size of the revenue gap,
a genuine area of judgment remaining here for commissions,
but it would be naive to suppose that it is any different in
genesis or extent from the area of judgment used by the allo-
cator with the green eyeshade in more traditional costing
methods. The economist has a general rule that the adjust-
ment should be made so as to distort the demand least--where
demands are highly responsive to price, the price should be
closest to marginal cost. This does not, however, lead to a
single solution, but to a general approach. Possible solu-
tions to this problem are examined in Section VI-E.
The economist's case for marginal cost pricing is
based on its effects on the allocation of society's scarce
resources, in particular that marginal cost pricing will lead
to an efficient allocation of resources. We believe that
efficiency is certainly one important consideration that
regulators must take into account in setting prices that are
"in the public interest." We also recognize that regulators,
consumers and electricity producers may have other criteria
which also may properly be given consideration. We have
examined several that are often raised and indicated the
implications of marginal cost pricing for them. In the
following section, we review some of the theoretical con-
siderations more closely before turning to the methodological
aspects in Section IV.
-30-
III. FURTHER DEVELOPMENT OF THE MARGINAL COST THEORY
A. Joint and Common Costs
We have examined the reasons marginal cost should be
the basis for price; we now turn to a further elaboration of
the four aspects of the theory of marginal cost pricing--the
treatment of joint costs, the treatment of externalities, the
concept of shortage costs and the use of demand elasticity--
before considering the more concrete aspects of measuring mar-
ginal cost in the electric industry. In order to keep the
thread of the discussion, we will, however, banish some of the
proofs or discussions of finer points to the attachments to this
topic, not because they are unimportant, but because to some
readers the statement of the results will be convincing enough
to accept, while those readers who require more detail can stop
and work through the subsidiary exposition in the attachments.
It is first necessary to dwell a little on the de-
tails of the theoretical treatment of marginal costs, and partic-
ularly the economic approach to joint costs and common costs.
Treatment of joint costs is a major source of the pricing
arguments in the electric industry since so much of the plant
and equipment serves more than one consumer and more than one
class of customers.
This is a fairly typical situation in many types of
production. Sheep produce both wool and mutton. Should the
wool user or the mutton user pay the cost of raising the
sheep? The production of cotton can yield both cotton and
-31-
cottonseed oil. Who should pay the costs of raising the har-
vest? Is it simply guesswork or "feel" which determines the
economic price, or does "equity" demand a 50/50 split?
Agreement on satisfactory methods of resolving this
problem has been elusive. In a rate case in 1953, when
Commonwealth Edison was challenged by the City of Chicago to
present exhibits showing separately "Cost of providing elec-
tric energy for each class of customer in the City of Chicago"
and also showing separately "Cost of providing electric energy
for each class of customer in the territory outside the City
of Chicago," the company responded with an affidavit by James
C. Bonbright, who asserted:
This analysis would be .a truly formidable
undertaking probably involving months of
time and giving rise to problems of cost
allocation that are simply insoluble by
any technique of cost accounting that has
won general acceptance among experts.6
However, as part of the same brief, Commonwealth included an
analysis, authorship unattributed, which listed 29 methods of
applying capacity costs to classes of customers. That analysis
flas been appended as Attachment A to NERA'S Topic 1.1 report.
Although Bonbright was pessimistic about the "arbi-
trary nature of any apportionment of joint costs," he asserted that,
"[a] more promising alternative is that of a 'differential
James C. Bonbright, Affidavit for the Illinois Commerce
Commission, on behalf of the City of Chicago (requested
by the Commonwealth Edison Company), Case 41130,
October 1, 1953.
I
-32-
cost' analysis, under which estimates are made of incremental
or marginal costs with no attempt to make the sum of the costs
imputed to the various classes of service equate with aggre-
gate costs."
Bonbright's 1961 book expanded briefly on this
theme; he was still exasperated by the property of differen-
tial or marginal costs not meeting revenue requirements.
The usual assumption is that, if the in-
cremental costs of all services, separately
measured, were added together, they would
fall materially short of covering total
costs--an assumption based on the belief
that most public utility enterprises
operate under conditions of decreasing
costs with increasing output. When this
assumption is valid, it implies that a
public utility company cannot cover its
total revenue requirements without charging
more than incremental costs for at least
some of its services.'
He remained, however, disdainful of the alternative:
The nonadditive character of the costs
specifically allocable, on a cost-
responsibility basis, to the different
classes and amounts of public utility
services has often been disguised by
the acceptance of elaborate full-cost
apportionments which begin with total
costs and apportion these costs among
the various classes of service as one
might divide a pie among the members
of a dinner party, leaving no residue
for the kitchen. These "fully-
distributed-cost" apportionments are
especially familiar in the railroad
field, where they have been made under
James C. Bonbright, Principles of Public Utility Rates,
(New York: Columbia University Press, 1961), p. 299.
I
-33-
formulas developed by experts in -the
Interstate Commerce Commission. One
such apportionment seems to indicate
that the railroads of the United States,
taken altogether, have been suffering
annual losses of many millions of
dollars per year on their passenger
business. The usefulness of these
apportionments is a debatable subject
But, in any case, their merits
must rest on a claim that they repre-
sent, not a finding of the costs defi-
nitely occasioned by this class of
service rather than that, but rather
a fair or equitable division of total
costs. Even the cost analysts who make
these full-cost apportionments recog-
nize this fact implicitly when they
concede, as they usually do, that a
company may find it profitable to sell
some classes of service at less than
their imputed costs.e
Bonbright seems finally to conclude that apportionment of
joint costs is a branch of ethics, and offers his familiar
eight criteria for judging the appropriateness of a rate
structure.9
a Ibid.
These criteria, stated on page 291 of Bonbright's above-
cited book, are:
1.The related, "practical" attributes of
simplicity, understandability, public
acceptability, and feasibility of appli-
cation.
2.Freedom from controversies as to proper
interpretation.
3.Effectiveness in yielding total revenue
requirements under the fair-return standard.
4.Revenue stability from year to year.
5.Stability of the rates themselves, with a
minimum of unexpected changes seriously
adverse to existing customers.
- continued -
-34-
While Bonbright and some subsequent economists"
have nodded in the direction of marginal cost analysis for
use in utility pricing, but concluded that it was impractical,
Boiteux and others in Turvey in Britain 12 and Kahn
in the United States'3 have developed the essential tools for
the analysis of marginal costs of electricity.
When various products are produced from the same
machine or process, the joint costs have to be recouped in
' -continued-
6.Fairness of the specific rates in the
apportionment of total costs of service
among the different consumers.
7.Avoidance of "undue discrimination" in
rate relationships.
S. Efficiency of the rate classes and rate
blocks in discouraging wasteful use of
service while promoting all justified
types and amounts of use.
10 E.g., Charles F. Phillips, Jr., The Economics of Regulation
(Homewood, Illinois: Richard D. Irwin, Inc., 1969) .
11 Marcel Boiteux and Paul Stasi, "The Determination of Costs
of Expansion of an Interconnected System of Production and
Distribution of Electricity," Marginal Cost Pricing in
Practice, J. Nelson, ed. (Englewood Cliffs, New Jersey:
Prentice-Hall, Inc., 1964). Also Y. Balasko, "On Designing
Public Utility Tariffs with Applications to Electricity,"
manuscript (EDF), 1974; and P. Caillé, "Marginal Cost
Pricing in a Random Future as Applied to the Tariff for
Electrical Energy by Electricité de France," Presexitad
before the French-American Energy System Planning and
Pricing Conference, Madison, Wisconsin, September 23 to
October 4, 1974.
12 Ralph Turvey, Optimal Pricing and Investment in Electricity
Supply (London: George Allen and Unwin, Ltd., 1968).
13 Alfred B. Kahn, The Economics of Regulation, Volume 1 (New
York: John Wiley & Sons, Inc., 1970)..
-35-
some proportion by the prices of the products. In a competi-
tive market there is no real question of allocating the common
or joint costs to the products. So long as the joint products
cover their joint marginal costs when offered for sale in the
market, then it does not much matter to the producer whether
one product carries all the overhead while the other is essen-
tially a by-product, offered for sale at little more than the
cost of transporting it to market. The prices are set by the
market for each separate product. What actually happens is
that the relative demands for the separate products determine
the relative prices--steak is more expensive than shin because
more people want it.
It is this same effect of relative demands which
over a longer period induces changes in the technology.
Whereas in a short time frame it may be technically impossi-
ble to prpduce one product without producing another, over a
longer period someone devises a way to produce relatively
more of the product in heavy demand while not producing
the same amount more of the other. Again, in a competitive
market, this is a response to the relative prices--it is
worth producing more of the product in heavy demand if the
price will cover the costs of extra production.
In regulated industries the problem is reversed:
given that there is no marketplace dictating the price, the
problem is to determine the appropriate allocation of costs
to the joint products. In the limiting case, where proportions
-36-
of products produced are economically invariant, ony the
relative demands for each product would be relevant to
determining the conditional marginal costs and the associated
prices of each product. There is no clearly separable re-
sponsibility for the joint costs if one looks at the produc-
tion process alone." The solution is then to set the rela-
tive prices to clear the market as far as possible. The
case which would be relevant in electricity production would
be the case where production were entirely limited to one
production technique; for example, baseload plants. In this
case, the correct solution would be to apportion capacity
costs so as to level the load and leave no capacity "lying
idle. "Is
However, in response to differences in demand for
peak and off-peak electricity, the technology has in fact
developed Which allows the relative demands to be accommodated
by economically variable technology. it is possible to in-
crease peak output using technology which would not be appro-
priate for longer use. Where the technology is variable, the
relative demands affect the costs through the technical
" For the solution of this limiting case, which Kahn refers
to as "joint costs" as distinguished from "common costs"
where proportions are variable, see the discussion in The Economics of Regulation, pages 77-83.
15 There is one qualification: demand for off-peak consump-
tion might be so small that no price equal to or greater
than marginal energy costs will level the load. In this
case, the appropriate off-peak price is the marginal energy
cost and the appropriate peak price is the marginal energy
cost plus the full marginal capacity cost.
-37-
adaptation of the system, and the prices in each period should
reflect the associated technological and cost tradeoffs.16
Many firms in the electric industry and elsewhere
now try to optimize their production systems through linear
progr amming using programming techniques. Baumol has pointed
out in his discussion of linear programming that the marginal
cost is automatically derived in the process of determining
the minimum cost system. He describes how programming, which
is simply a mathematical technique, may be used to help busi-
nesses with the problem of solving problems such as transpor-
tation routing or blending gasoline or plant location deci-
sions, by finding the least cost or maximum profit solution
when numerous variables and bottlenecks have to be considered,
and shows how, when the best solution has been achieved, the
cost imputed to each output is, in effect, what has to be
given up to achieve a little more bf that output, or what we
have called the marginal cost.
16 For a general development of peak-load pricing with a
variable proportions production technology, see John C.
Panzar, "A Neoclassical Approach to Peak Load Pricing,"
The Bell Journal of Economics and Management Science,
Fall 1976.
-38-
It is noteworthy, then, how these time-honored
concepts of economic theory, the marginal product
and the opportunity cost, have sneaked back into
the analysis. No one has put them into the
analysis of the primal production problem which
proceeds largely in terms of the relevant physi-
cal and technological considerations. This
indicates, in fact, that no matter how techno-
cratic the bias of the planner and how abhorrent
to him are the unplanned workings of the free
market, every optimal planning decision which
he makes must have implicit in it the rationale
of the pricing mechanism and the allocation of
resources produced by the profit system. 17
This result is not confined to capitalist economies
which place perhaps excessive faith in a market system. While
we have argued that marginal costs are reasonable because they
emulate the workings of a free market, Bauznol points out that
even in planned economies it has been hard to escape the logic
of marginal costs.
It is noteworthy that these results have led
to the open and well-publicized reintroduction
of marginal analysis into Soviet economics by
Russian mathematicians working on the applica-
tion of linear programming to economic planning.
This analysis for electricity generation is de-
scribed in detail in Section IV-A, where a simplified model
of time-of-day/seasonal pricing is presented. The model is
in fact a very simple linear programming model, by which, in
17 William Baumol, Economic Theory and Operations Analysis,
2nd ed. (New Jersey: Prentice-Hall, Inc., 1965), p. 114.
Ibid.
-39.-
the process of developing ,a minimum cost system to meet the
demand, the extra cost of increasing demand at any hour can
be found. This marginal cost is then the appropriate price
for each of the "products" or hours.
B. External Costs
The marginal cost includes "all sacrifices, present
or future, and external as well as internal to the company,
for which production is at the margin causally responsible."9
The effects of externalities are properly a part of the mar-
gina]. costs. If production of electricity causes pollution,
then in economic terms there is a cost of production which
is not internal to the company, and the consumers of elec-
tricity should pay this cost. However, for reasons we Set
out below, we believe that in computing marginal costs at
the present time and under present environmental regulations,
it is not necessary to calculate a factor to represent en-
vironmental externalities which would then be added to the
computed marginal cost of production to represent the full
marginal cost to society.
If pollution abatement were done in a perfectly
economic fashion, all consumers of every commodity would be
required to pay a charge based on the costs of pollution
associated with that commodity. One way of doing this would
19 Alfred E. Kahn, P. 75.
I ..-.- --.-..------
-40-
be through a taxation program. Taxes could be levied accord-
ing to the marginal damage of pollution discharges. Faced
with effluent charges private decisionmakers would then take
the costs of pollution into account when making decisions on
how to produce output. The prices charged in a competitive
market would be composed of at least two and generally three
components: the "ordinary" marginal costs of production, the
marginal charges levied on effluents, and the costs of abate-
ment efforts. Abatement efforts would occur up to the point
that the marginal cost of abatement and the marginal cost of
effluents are equal to one another. If the effluent charges
had been set properly, marginal private costs and marginal
social costs would be equal. If abatement costs were very
high relative to effluent charges firms might not respond
with abatement efforts, finding it more profitable to produce
as before, but pay the marginal damage charges. If cleanup
costs were very low relative to effluent charges, extensive
abatement would take place to avoid as much of the effluent
charges as would be economic. In such a world where the
costs of pollution had been properly "internalized" we could
estimate marginal social costs simply by estimating marginal
private costs (including effluent charges). To say otherwise
is merely to say that the government agency responsible for
pollution control has not done its job properly.
While the effluent charge approach to dealing with
the pollution problem has a certain conceptual attraction,
-41-
there are a number o.f important practical problems associated
With it. We are not recommending such a strategy, but it
serves to illustrate the point that the economically optimal
level of pollution control may well be below the level which
would be obtained if a strategy of near-zero emissions by
regulatory fiat were adopted, as it has been in recent years
in the United States. In the current circumstances, the in-
ternal costs of the utilities may well represent an overpayment
for externalities. Furthermore, when pollution control stra-
tegies are nationally applied in such a way that virtually no
other industry is forced to include uninternalized externali-
ties in prices, there are good reasons on second-best grounds
for not including them in electric prices either. These are
not overwhelming theoretical reasons for ignoring uninternal-
ized externalities, but for a public utility commission to
try to second guess pollution control authorities would be an
exercise in futility anyway, and given the practical realities
we suggest computing only marginal private costs.
C. Shortage Costs
Shortage costs or curtailment costs are the burden
imposed on society when electric supply is inadequate to meet
the demand. Industries are forced to shut down; inconvenience
and discomfort are caused to individuals. Explicitly or im-
plicitly, those who decide on levels of reserve margin for
electric systems have tolerable levels of discomfort or pro-
duction loss in mind. They may not systematically measure
-42-
shortage costs in determining reserve margin, but the calcula-
tion is implicit: in order to avoid excessive costs of out-
ages, the company installs extra capacity. When the extra
cost of increased reliability is equal to the probable cost
of the inconveniei ace caused by shortages, the reserve margin
is adequate.
Unless plans have been poorly laid, marginal short-
age costs will equal the cost of the last unit of capacity
added to avert a shortage. It is not generally the purpose
of ratemaking deliberations to determine whether there is an
excess or deficit of capacity, although if one of the condi-
tions clearly exists, rates may be adjusted to try to utilize
the excess or ration the deficit. If there is excess capacity,
the per-kilowatt rates may be lowered; if there is too little
capacity, the per-kilowatt rates should be raised. This is
the same thing as saying "bring price into line with marginal
shortage costs" (what the last consumer will pay rather than
go short).
D. The Role of Demand Elasticity
The basic factual assumption which underlies the
theory that marginal cost pricing will produce an optimum
allocation of resources is the assumption that the price of
a commodity has an effect on the amount which is purchased
(the demand for that commodity). This sensitivity to price,
which is sometimes nontechnically called "price resistance,"
is referred to by economists as "price elasticity of demand,"
-43-
and demands which exhibit great sensitivity to price are
called "elastic" while commodities whose demand exhibits no
sensitivity at all to price are called "totally inelastic."
Elasticity is measured as a ratio of percentage change in
quantity to percentage change in price: this ratio will almost
invariably be negative (when price goes up, quantity goes down).
Although it seems intuitive and also by observation
that some elasticity exists for virtually all commodities, it
is sometimes hard to measure the extent of price elasticity,
especially since observed data which relate quantity demanded
to price are affected also by income levels, recessions, the
price of other goods and changes in taste. Therefore, methods
of analysis which hold constant other factors must be used to
isolate the effect of price alone and this in turn requires
large amounts of data.
It so happens that the nature of electricity produc-
tion, the wide variation of price across the United States and
the uniform reporting requirements of the FPC have yielded more
data on the price/quantity relationship of electricity demand
than exists for virtually any other commodity, and studies in
recent years have amply confirmed the existence and extent of
price elasticity for electricity. These studies are discussed
in some detail under Topic 2 of this study. They uniformly
demonstrate that demand is affected by price, and hence that
the underlying assumption of the economist that price does
affect the allocation of resources is confirmed. These
-44-
elasticity studies, however, have further usefulness in their
application to planning and pricing policies of the industry.
The general relevance of price elasticity in economic
policy affecting the electric utility industry may be consid-
ered to have two dimensions, one having to do with the level
of activity of the industry (total kilowatt-hour sales) and
the other having to do with the structure of the industry at
different times of the day or different seasons, and as
between different types of customers (the shape of the load
curve). Under the first category, we include the general
question of long-range planning for the firm. This involves
how the sales and peak-load requirements of the firm change,
given expected changes in electricity prices, and what impli-
cations this growth has for appropriate system planning.
Conversely, the second general area relates to the subject
of appropriate economic design of rate structures. Virtually
all of the work which has been done on price elasticity relates
to the first area, and even then only to growth in kilowatt-
hour sales and not kilowatt peak demand,20 at least in the
sense of any direct projections.
20 Note that in the economist's term, demand measures the
units of consumption of a good or service a consumer
desires within a given time period, as for example, in
kilowatt-hours. In the utility industry, however, the
term "demand" is generally defined as "the rate at which
electric energy is delivered on a system" and is expressed
in kilowatts. Our discussion will always be in terms of
kilowatt-hours rather than kilowatts except when the con-
text makes it clear that kilowatt demand is referred to.
-45--
Price elasticity studies which relate to the
question "toward what level of sales and kilowatt demand
are we headed?" may be termed "average" elasticity studies.
The end results of these studies almost always provide indica-
tions of how various customers adjust their average consump-
tion, given average changes in some measure of electricity
price. These adjustments may also be aggregated into a
forecast of average growth of kilowatt-hour sales of the
utility to all of its customers.
The role of price elasticity considerations in
rate structure policy arises in a formal way in connection
with the development of marginal cost and time-of-use pricing.
Price elasticity considerations have some degree of relevance
in both the determination of costs and the setting of rates
based on those costs.
In estimating appropriate marginal costs, both
demand and supply elasticity have to be taken into account
to some extent, because the correct level of marginal costs
on which to base prices is that level where demand and supply
are approximately in equilibrium. For example, if current
price at the time of system peak is below currently esti-
mated marginal cost, and if there is any elasticity of demand,
then setting the price at marginal cost will cause demand to
drop. In some cases, this would then indicate a lower supply
price for the lower level of demand and an equilibrium point
must be estimated using such knowledge as is available of
-46-
system cost characteristics and demand elasticity. This
should not present a serious problem even with the limited
amount of information on time-of-day price elasticities
available. Since short-run price elasticities are small
relative to long-run price elasticities, changes in consump-
tion patterns should be gradual and allow us to make adjust-
ments in rates over time as we learn more about consumer
responses. The limited knowledge about time-of-day price
elasticities does call for prudence in setting initial rates
and also requires that extensive load research efforts be
instituted along with the implementation of time-of-day
rates.
In these cases it is helpful to think of what is
actually happening. If we assume that there is an underlying
demand and supply relation (the conditional marginal cost
function) for peak electricity, shown by the DD and SS curves
in the figure below, the current price p 1 is below the equi-
librium price at which demand and supply would be equated.
However, because the quantity q 1 is demanded at price p 1 ,
when we measure the current cost of supplying qt' we find
that it is p 2 . If we were then to raise the price from p 1
to p 21 the quantity demanded would decline to q 2 , and at that
level of demand, the supply price P3 would be lower than p.,
(but higher than pi).
-47-
Price
P2
P3
P I
q2 q, Quantity
There is thus an iterative process, in which using
such knowledge as is available about demand elasticity and
supply prices, an estimate must be made of the equilibrium
level at which supply and demand are equal.
Once costs are determined, however, price elas-
ticity may play a role in the design of rates based upon
those costs. This is, of course, a reference to the so-called
"inverse elasticity rule." The relevance of this rule stems
from the fact that we are dealing with an electric utility
with a fixed revenue requirement which must be satisfied and
may be illustrated as follows. Consider the circumstance
where setting all rates at respective marginal cost would
-48-
produce total revenues in excess of the approved level of
revenues for the electric utility. The regulated utility
should then set each of its rates below marginal cost. Where
the demand is relatively elastic, the rates should not be a
great deal less than marginal cost, where demand is relatively
inelastic, the rates should be lower relative to marginal costs.
In other words, where the demand is mostly elastic the price
should come closest to marginal cost so as to minimize the
encouragement of growth in demand at rates which do not cover
the value of the resources consumed in meeting it. In markets
where the demand is less elastic, the rates should correspond-
ingly be that much lower than marginal costs, because in
these markets lower rates will least encourage uneconomic
consumption. This is an entirely general and theoretical
result, and the problems of its application are considered
further in Section VI-E.
-49-
IV. METHODOLOGICAL ASPECTS OF MEASURING MARGINAL COSTS FOR AN ELECTRIC UTILITY
We have examined the theoretical basis for marginal
cost pricing, and considered some of the theoretical problems
with an eye to their application in the electric utility in-
dustry. We now proceed to a discussion of the methodology of
how one can develop costs, bridging the gap between the pure
theory and the real-world problems that face us in the costing
process of an actual company. These problems will be dealt
with more fully under Topic 4, but the broad outlines and the
reasoning behind the methodology will be discussed in the sec-
tions below.
Before proceeding with the discussion of the marginal
costing methodology that we propose to apply, we must not for -
get that the purpose of the costing exercise is to set prices
that can actually be implemented. We should keep in the back
of our minds a number of important considerations regarding
the kinds of prices we will be setting which in part determine
the nature of the costing exercise.
First and foremost, we are assuming that by and
large we will be establishing rate schedules before the fact.
That is, rates must be established before consumption actually
takes place and will not vary instantaneously as the relation-
ship between supply and demand varies over time. In addition,
for administrative reasons we will be restricted to a fairly
small number of rating periods. Although we can, after the
fact, identify a particular hour of the year in which the
-50-
peak demand actually occurred, it is generally unknown exactly
when it will occur or exactly how high it will be before the
fact. We do have some expectations concerning the height of
the peak, what the variance of demand is, as well as a good
idea of what the potential peak hours will be. These are
the same kinds of expectations that must be used by system
planners in designing the system and providing for reserve
capacity and maintenance scheduling. Since in most cases we
are forced to establish a set of rating periods and associated
prices before the fact, the identification of homogeneous
groups of potential peak hours and the associated expected
marginal costs are crucial for establishing rating periods
and estimating marginal cost-based prices.
In the discussion below, we attempt to build up pur
costing methodology by abstracting first from the full com-
plexity of the planning and costing process. For example,
although uncertainty about demand, forced outages, maintenance
and reserve requirements are important aspects of both the
planning process and our costing process, the early discussion
in this section abstracts from these considerations of uncer-
tainty and deals primarily with a deterministic system to
allow us to concentrate on the economics of the generating,
transmission and distribution technology itself. Important
considerations regarding uncertainty, load diversity, reserve
margins, etc., are treated in more detail afterward. In the
earlier sections that follow, we also speak rather loosely
-51-
about "peak" and "off-peak" periods, while in reality we will
be developing a pricing model in which rates during virtually
all periods make some contribution to total system capacity
costs through a combination of both marginal energy charges
(greater than average energy costs) and shortage costs.
A. Marginal Costs of a Generating System
The problem bf apportioning joint or common costs
of a generating system has exhausted many theoretical and
practical ratemakers. How can we ensure that electric users
as a whole pay for all electric costs, and at the same time
make an appropriate apportionment of those costs between
consumers. Many alternatives have been suggested, most
of which recognize to some extent that use at the time of
system peak causes the system to be expanded. On the other
hand, it is clear that the system is not constructed to serve
only the peak; not only does the system also serve other hours,
but crucially, a system constructed to serve only the peak
would be quite different from a system constructed to serve
both peak and off-peak.
What we have is in fact a system producing joint
or common products (peak and off-peak electricity), and since
the system can be designed to accommodate differing proportions
of peak and oaf-peak demand, the economist would analyze the
problem as a common cost problem (rather than a joint cost
problem)2 L and would look for the marginal cost of increasing
21 See Section 111-A above.
-52-
consumption of each product separately, while holding the
others constant. To see what this would mean for an electric
generating system, we have to follow through the planning
Process and see what marginal cost pricing would entail in
an optimally planned or minimum cost system. In the planning
process, marginal costs are important because they determine
how much will be built and at what cost: consequently, when
we conceptually reproduce the planning process, we are able
to identify and measure marginal costs for pricing purposes.
When we have simulated the planning process, we will
have a conceptual model of a generating system, and we will he
able to test such questions as:
- Under marginal cost pricing, how can revenues
cover total costs?
- Shouldn't the 100-percent-load-factor customer
receive a price break (i.e., not pay full peak
rates) because of his full and constant use of
facilities?
- How should you spread the cost of covering the
risk of outage, and what is the appropriate
capital cost to be spread?
- Since plant expansion, even to meet peak growth,
has traditionally been in the form of base plant,
what is the appropriate capacity charge to be
levied, and when (i.e., during what time periods)
should it be levied?
- Should a consumer who uses only off-peak power
be charged any capacity costs?
- What is the appropriate cost to charge consumers
who take all their power only at peak times?
-53-
- Is there a way to determine the cost causation
by customer class so we can set rates that will
closely match total costs with allowed revenue?
Let us assume that the generation planner's only aim
is to minimize the total costs of the system, and that they
have before them an array of possible plants which can be
purchased. The plants vary in the initial cost, expected
useful life and running costs per kilowatt-hour. We can
assume away economies of scale of plants, although we admit
that they probably exist, by assuming that a planner can
arrange to rent or share in a plant of the most economic
size, if that size would be too big for the given system,
at a proportional annual cost per kilowatt.
The problem is then to minimize system costs for
a given load curve. For each possible plant there is a
series of total costs per kilowatt which rises according to
the number of hours a plant is used, and cuts the y-axis at
the level of the annual charge (Figure 1).
For the case (Figure 3) in which there are three
possible types of plant, the comparison of the three cases
gives the optimal running hours for each type. Plant P
(peaking plant) will not be economical for more than h 1
hours. Plant I (intermediate plant) will be cheaper for up
to 1i 2 hours, Plant B (baseload plant) should be run for the
whole year.
-.54-.
In principle we could specify an infinite number of
possible plants, some perhaps too expensive to be considered
at all. Thus, a plant with the characteristic shown by dotted
line (E) (Figure 2) is in fact too expensive to be chosen for
any number of hours in the system.22
Figure 2.
TC/ICW
h
TC = C + rh
Where: TC = Total Cost
C = Annual Capital Cost
h = Number of Hours Run
r = Running Costs
22 Or, it may be an older plant economically ready for retirement.
ri Sure 3
rs
-.55-
/ Figure 2
(E /
?C/ICW •bh
:ies
h
Peaking
Plant
Intermedi-
ate Plant
flaseload
Plant
Tc/KW
hl ha h
-56-
When the optimal number of running hours for a
given type of plant is known, inspection of the load curve
will show the system planner how much capacity of each type
will be needed. This then determines the lowest cost system
for the company.
Now of course, the real-world planners have to
deal with more problems than this. The running costs may be
expected to change more for one type of fuel than another
over the life of the plant, and hence a system which is
minimum cost today may be nonoptimal tomorrow. Changes
which are known, and expected or even simply guessed at,
may be taken into account by discounting future cost (both
capital and operating) streams under alternative choices of
equipment and comparing the discounted total costs of given
systems to find the minimum cost solution. Again, since
capacity has to be added in discrete increments, the system
at any given point in time may have more or less of a parti-
cular type of capacity than an optimal system would indicate.
This is, of course, because there are economies of scale for
individual plants added at the margin--it would never make
sense to add just one kilowatt. When we assume away economies
of scale we assume that excess capacity can be rented or sold
in the short term, so that the net system, including purchases
and subtracting sales, may be reasonably close to optimal.
We will call a system planned according to this simpli-
fied model an "optimal system." It represents the lowest cost
-57-
system available to meet a given load pattern. We now have
to consider how the system is run, and what constitutes a
marginal cost in this context.
Our pricing rule is to price at marginal cost--the
cost of producing a little more or the savings from producing
a little less. This cost will be different from hour to hour,
according to which machine is last on the line. At night, the
marginal cost will be the fuel and variable running cost of
a baseload machine. During the day, the marginal cost will
generally be the running cost of an intermediate machine,
and at peak it will be the running cost of a peaking machine.
This is the familiar dispatch cost which is routinely calcu-
lated for interutility sales. At peak, however, we also
encounter the need to expand capacity, and each hour at peak
should also be charged the cost of expanding capacity. The
appropriate cost is, however, the marginal cost of capacity,
the machine that will meet loads of shortest duration in the
least cost way. It will generally be a peaking plant. Extra
demand at the peak alone does not require a new nuclear plant:
the marginal cost of peak demand is the cost of meeting an
increase only at the peak.23 '2 '
23 A more detailed exposition is given in Section IV-B below.
24 Note, however, that the price during the "intermediate"
period makes a contribution to total capacity costs since
the marginal running cost during this period is greater
than the average running cost.
I
-58-
When we examine the way most systems are planned,
it is evident that it is not only the one peak hour which is
responsible for capacity additions but the whole configuration
of demand reflecting uncertainty in demand and equipment out-
ages. In some companies, this is reflected in the calculation
of a loss-of-load probability, or something similar, which is
built up by summing the outage probability in each hour. We
therefore consider peak responsibility to be a graduated respon-
sibility, and assign the marginal cost of capacity to each hour
in proportion to its loss-of-load probability (LOLP).25 Since
LOLP tends to vary with load (it is highest when the load is
highest) but declines much more sharply than load, it leads
to an apportionment of capacity costs mainly in the peak and
"shoulder" or near peak periods. The capacity Costs may be
charged as kilowatt charges or rolled in to the kilowatt-hour
charges.
Using this pricing scheme (with the marginal capac-
ity cost spread over the peak hours only, for simplicity),
we can investigate the questions posed above for our simulated
system.
1. Marginal Costs and Total Costs
If the output of an optimal system is priced accord-
ing to the marginal cost rule, revenues will exactly equal
system cost (properly defined). Proof of this is given in
25 Discussion of loss-of-load probability is reserved for
Section IV-D below.
L
-59-
Attachment A. What this, means in practice is that all hours
in which the peaking plant is the marginal machine are charged
at the marginal cost, even though some of the kilowatt-hours
sold at this time are generated by plants with a lower running
cost. In this way, the higher capital costs of the baseload
machines are partly recovered in the peak-hour price. Another
way of looking at it is that expensive machines are put on to
save energy costs. Similarly, in the shoulder period, the
running cost of the marginal (intermediate load range) machine
(plus, perhaps, some part of the capital cost of the peaker,
depending on the allocation of capital costs) will exceed the
average running cost of generating at that hour, and thereby
contribute to the capital cost. For the baseload period, the
running cost of the last machine on the line (with a small
adjustment for curtailment cost, if this is appropriate) is
the appropriate price. For a system which is fully adjusted
to demand, this will produce revenues which equal total costs.
2. Marginal Costs and Cost Allocation
It is a generally accepted principle of ratemaking
that there should be no unreasonable price discrimination and
it is accepted that differences in price which follow differ-
ences in cost are reasonable. Let us then see how costs fall
in the pricing system we propose and whether costs warrant it.
The customer who has a very high load factor is
traditionally assumed to impose lower unit costs on the sys-
tem than the customer with a lower load factor. If we add a
-60-
customer with a 100-percent-load factor to our optimal sys-
tem, we clearly add a baseload unit. This unit has a
capital cost and a running cost for 8,160 hours. we show
in Corollary A of Attachment A that this total cost exactly
equals the sum of the revenues from marginal cost pricing
when the consumer pays the peak price for the peak hours, the
shoulder price for the shoulder hours and the off-peak price
for the off-peak hours. So the 100-percent-load-factor cus-
tomer pays his fair share.
What of the consumer who uses electricity only on
peak? It is more straightforward to see that the price he is
charged is equal to the capital and running cost of the peak-
ing machine, which is the cheapest way to meet his limited
demand.
The customer who consumes only off-peak electricity
is charged only the running costs (unless some curtailment
cost is appropriate). This is the case that somehow strikes
rate people as inappropriate. We show in Corollary E of
Attachment A that without the off-peak consumer, the optimal
system would not include the baseload plant which serves him.
The additional cost of the baseload plant is exactly offset
by the fuel savings in the rest of the system, and therefore
the additional cost to the system of the off-peak consumer is
represented by the running costs alone.
26 Ignoring maintenance costs, as throughout the analysis in
this section.
-61-
Rate people frequently feel apprehensive about the
low charges indicated for off-peak rates. This is partly a
disdain for "free rides," a concern we have addressed earlier.
Here we have shown that the off-peak customer pays just what
it costs to adjust the system to serve him, which seems to be
fair. We are, however, aware of continuing discomfort on this
point, and are generally convinced that the apprehension ex-
presses an intuitive estimate of high off-peak elasticity. The
prices for off-peak power should reflect the equilibrium cost
after adjustment, and if elasticity of off-peak use is high,
the prices indicated by the current marginal cost may be too
Low. Reducing prices to current marginal cost might induce
consumption leading to reoptimjzatjon of the system and higher
costs in the present off-peak time, and some room should be
left in the off-peak rates for such a process.
3. Short-Run Changes and Long-Run Changes
So far, we have only discussed costs of use of a
given system. Evidently as a system grows, it is important
that prices represent also the cost of adding capital equip-
ment to meet increased demand. We can demonstrate, using the
simplified model, that if a system is optimal and growth in
demand is accurately forecast, then short-run marginal cost
equals long-run marginal cost. This is true for even growth,
uneven growth and no growth.
The short-run marginal cost is defined as the
change in costs corresponding to a small change in demand
-62-
without capital adjustment; if there is capacity available,
the short-run cost is the running cost of the last unit on
line. If demand presses against capacity, the cost is the
shortage cost (which normally equals the capital cost of
the last machine on line).27
The long-run marginal cost is measured after changes
in capital equipment have been made to adjust to increased
demand in the long run, and takes into account the capital
costs of increased production.
If planning has been properly done, the long-run
marginal costs will equal the short-run marginal costs. This
may seem odd, but on reflection it is really not odd at all:
if the cheapest way of meeting increased demand is to run
existing machines, then they will be run to the point at
which the extra cost of running them plus possible shortage
costs are equal to the cost of meeting the extra load by
changing the capacity. If the extra running costs plus
shortage costs rise above the point at which it is worth sub-
stituting capacity for running costs, then if the planner has
anticipated this, his goal of minimum cost will be met by
putting in the extra capital capacity.
Using the simple model, we can see how this is true
in the electric industry. If growth has the same,load duration
curve as the current system, then the capital equipment needed
27 This concept is developed further in Section IV-B below.
-63-
for the optimal system discussed above is reproduced in minia-
ture for the increment. The sum of the short-run marginal
costs equals the sum of the marginal costs when the system has
been fully adjusted. It also holds for each set of hours.
Suppose growth occurs only at the peak. Then only
peaking plants will be added, and the price of running cost
and capital cost of a peaker at the peak will exactly recover
the total costs of adding and running the peaking plant.
If the growth is expected to occur in the off-peak
hours, the system plan has to be reoptimized. The new opti-
mal plan will include more baseload and less intermediate
capacity. Providing this has been accurately forecast, the
extra capital cost of the baseload plant will be exactly offset
by the reduced running costs in the intermediate period. This
is shown in Corollary B of Attachment A.
We have shown how marginal cost pricing of the
generating system leads to rather straightforward and logical
results. It is not a mysterious concept, but simply the appli-
cation of competitive business practices to an efficiently
planned system.
B. Marginal Capacity Costs
In the previous discussion of the marginal costs
of generation, it was asserted that the marginal running costs
for each hour plus the capital cost of a peaking plant gener-
ally represented the marginal costs of generation. A full
explanation of the marginal capacity costs was not, however,
-64-
given. In this section, we try to explain the basic concepts
which have been used by various analysts, particularly Boiteux
and Turvey, and their followers.
The French analysts began with an electric system
which was not growing very fast, and Boiteux 28 first proposed
that the marginal cost of capacity should be considered equal
to the manning and maintenance costs of the oldest unit re-
tained on the line to meet the peak, which would otherwise
be retired. However, as the system grew the analysis shifted
to the "long-term cost of development." Since the analysts
were interested in the appropriate annual charge for a ma-
chine, they performed a conceptual experiment of considering
what the extra cost would be of having a single kilowatt one
year early, and moving up the entire stream of costs. This is
the basis for the more abstract annual charge analysis de-
scribed in Section IV-P of this report, which was originally
proposed by Boiteux. Of course, the fixed charges on the type
of baseload plant the French were adding to their system would
be partly offset by fuel savings on older, less efficient
plants which would produce one kilowatt-hour less each hour,
and thus a net annual cost of capacity would be calculated.
In an optimally planned system which had retirable capacity,
2B Marcel Boiteux and Paul Stasi, "The Determination of Costs
of Expansion of an Interconnected System of Production and
Distribution of Electricity," Marginal Cost Pricing in
Practice, J. Nelson, ed. (Englewood Cliffs, New Jersey:
Prentice-Hall, Inc., 1964).
-65-
the original Boiteux formulation of the manning and the main-
tenance cost would be equivalent to the later formulation--the
net long-term development cost.
With the development of ever more flexible capacity
and the rapid growth of systems, the cheapest way of adding
capacity to meet the peak became the gas turbine machine. It
was not necessary to push up an old plant and calculate fuel
savings. Turvey 29 in Britain developed a more realistic analy-
sis using peaking machines. The comparison the planner makes
is between purchasing baseload plant, intermediate plant and
peaking plant. The baseload or intermediate plant offers fuel
savings (as compared with the peaking plant) as a way of meet-
ing peak demand, whereas the peaking plant offers no fuel say-
ings. It can be shown that when capacity is at minimum cost,
the annual cost of one kilowatt of any new capacity net of
fuel savings is equal to the cost of a peaking plant. (See
Attachment B for a further discussion on the Turvey methodology.)
At this point a further theoretical refinement, the
shortage cost, entered the French analysis • 30 Economists have
often made a distinction between long-run and short-run costs
29 Ralph Turvey, Optimal Pricing and Investment in Electricity
Supply (London: George Allen and Unwin, Ltd., 1968).
See Y. Balasko, "On Designing Public Utility Tariffs with
Applications toElectricity," manuscript (ED?), 1974; and
P. Caillé, "Marginal Cost Pricing in a Random Future as
Applied to the Tariff for Electrical Energy by ElectriCite
de France," Presented before the French-American Energy
System Planning and Pricing Conference, Madison, Wisconsin,
September 23 to October 4, 1974.
-66-
of consumption. We have alluded to this on page 61 above.
The long run is a capital adjustment concept, whereas the
short run is the period in which capital stock adjustment is
not possible. For a system which has been well planned, if
the world has turned out to be as it was expected to be, the
short-run marginal cost should be equal to the long-run
marginal cost.
Thus we have the theorem that short-run marginal
cost equals the long-run marginal cost at those
outputs where the actual amount of the fixed
factor coincides with the optimal amount. If
we call the fixed factor "capacity" this theorem
can be restated by saying that marginal short-
and long-run costs coincide when capacity is
optimal. This is an important theorem because
it shows that the argument about whether public
enterprises should set prices equal to long-run
or short-run marginal costs is only meaningful
when capacity is not optimal.31
In the short run in an electric system, there is
either a cost to the utility of producing power, or, if there
is insufficient capacity, there is a cost to the consumer of
there not being enough. In the long run, when equipment can
be adjusted, the per-kilowatt cost of extra demand at peak
times will be the cost of adding capacity.
In a well-planned system, the long-run cost of
adjusting capacity to produce an extra kilowatt of output
should be just equal to the short-run cost incurred by those
who would have to do without in the event of there not being
3 1 Ralph Turvey, "Marginal Cost," The Economic Journal,
Vol. 79, No. 314, June 1969, p. 283.
-67-
enough. This latter concept is what we have referred to as the
"shortage cost." It could in principle be measured directly,
and the French attempt to do so; a utility could look at its
plan for load shedding and calculate the loss in value added
for industries which it would shed in a situation of potential
power failure; it might then plan to add capacity to the point
at which the cost of the last unit of capacity added equals
the probable cost of a failure. In the United States, the
reserve margin for generation and transmission is decided by
reference to a set of reliability criteria. These criteria
may be only implicitly related to the cost of curtailment, but
they do represent someone's judgment on how much people are
prepared to pay to prevent brownouts, which is another way of
saying the same thing.
So in the short run, before capacity can be adjusted,
the marginal cost is the cost of energy for the hours served
plus the premium which must be charged to constrain demand to
available capacity. This premium generally reflects the mar-
ginal shortage cost. In the long run, after capacity can be
adjusted, the marginal cost is the cost of energy plus the
cost of capacity at peak. In an optimal systn, the long-run
costs equal the short-run costs; in fact, the following are
all equal on an annual basis:
- The cost of a peaker.
- The net cost of an intermediate load plant
(capital less fuel savings).
- The net cost of a baseload plant
(capital less fuel savings).
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- The rental cost of any unit of capacity
(peaking, base or intermediate load plant), in "the market," with fuel savings taken
into account.
- The long-run marginal cost of system
peak demand.
- The short-run marginal cost of system
peak demand (curtailment cost).
any real system, there are likely to be temporary
mismatches, if only because of the discontinuous nature of
plant adjustment. After the addition of a new baseload plant,
the short-run costs will probably be lower than the long-run
costs: the running costs will be lower because of the new
efficient capacity, and the probability of outage (and hence
probable shortage costs) will be low. As the demand grows, the
costs approach and exceed their long-run level, triggering more
capacity additions. Rather than follow the short-run costs in
their oscillations around an equilibrium level, for tariff-
making purposes we can imagine a plant continuously adapted to
demand in which the long-run marginal cost of capacity is also
the appropriate short-run cost of curtailment.
In general, the marginal cost of capacity will be
the cost of a peaking plant. Exceptions will occur in cases
where the load characteristics are such that peaking plant.
would never be used to meet the peak, even in long-run
equilibrium, as for example in a company with a high annual
load factor. In this case, the plant with the next lowest
capital cost should be used as the marginal cost of capacity.
-69-
Running costs at the peak will be commensurately lower. Also,
the cost will be charged over a larger number of hours since
the high load factor will cause many more hours to have a
significant LOLP. A utility with a very high load factor may
therefore show little variation in hourly costs.
Problems arise with this approach only if there is
a chronic imbalance in the system. In cases of permanent
over-capacity, the correct approach is to adopt the short-
run costs of providing service, in order to make the best
possible use of existing capacity without burdening current
users with capital costs of equipment they neither want nor
need. This would be an important consideration in railroad
pricing, for instance. However, in some electric companies,
we are looking not at oscillations around equilibrium nor at
chronic imbalances, but temporary traumatic imbalances induced
mainly by the oil price rise which may, however, take several
years to correct. In the meantime, the short-run marginal fuel
costs are above their equilibrium level, while the excess of
capacity which develops as companies seek to install baseload
alternatives to oil causes the short-run curtailment cost to
fall below the long-run capacity cost.
In this situation, the correct solution may be to
peg kilowatt-hour prices to the short run to reflect the fact
that oil is currently being used to meet additional demand,
while pegging kilowatt prices to the long-run equilibrium
level. The short-run cost of a kilowatt is, however, well
-70-
below the long-run cost because of the excess capacity (outage
probabilities are very low or zero). The system could accom-
modate increases in demand at peak times without jeopardizing
reliability for some time, and even when capacity is added,
it will at least initially offer such substantial fuel savings
that the net cost of capacity will be below the cost of a
peaker. Hence if the problem were simply the static problem
of economizing existing capacity as well as possible, the
capacity charge could be relatively low since there is no
need to ration capacity in the short run. However, since
customers will make long-run decisions based on the price
signal, it is important not to leave them with the impression
that extra kilowatts are always going to be as inexpensive as
they are currently. The offer of five-year contracts at a
lower per-kilowatt price may also be considered as a method
of reflecting the excess capacity in a temporary way. Again,
in cases where the revenue constraint is such that excess
revenues would result from sales at marginal cost, and it is
necessary to adjust energy charges or capacity charges in
order to meet the constraint, it is the capacity charges which
should be reduced, while the energy charges continue to re-
flect high current costs.32
32 See Section VI-E below.
-71-
C. Taxes
Is a tax a marginal cost or is it not? If we reduce
the question for simplicity to two types of taxes, property
taxes and income taxes, we can see the principles more clearly.
The local property tax is generally thought of as a tax which
covers the cost of local services. Police protection, sani-
tation services, fire protection needs, educational needs for
the offspring of workers, are increased by the existence of a
plant, and to that extent may be thought of as a marginal cost.
The plant imposes costs on society which are to some extent
recouped by the property tax, although the match of costs with
taxes will be far from perfect. However, where local taxes
on utilities are particularly heavy in comparison with other
Jurisdictions, perhaps because the local government has con-
cluded that utilities are locationally relatively inelastic
with respect to taxes, it may be necessary to make some judg-
ment about how much of the local taxes can reasonably be
assumed to be related to the cost of services provided to the
utility before computing the marginal cost. The excess will
of course still be part of the revenue requirement.
With income taxes an argument is sometimes made
that the income tax is a tax on surplus and not a cost of
doing business, and therefore should not be computed as part
of the marginal cost. Further, it is sometimes argued, if
federal taxes are, from a national perspective, a cost partly
similar to property taxes on a local level, they are a cost
-72-
not of capacity alone but of the whole system, and should not
be computed in the capacity charge only, but instead should
be ignored in computing capacity costs and included only in
the revenue requirement.
However, this would ignore the complexity of the
federal tax system and of the regulatory system. For most
firms in the economy, the opportunity cost of capital in-
cludes federal income taxes which are computed before divi-
dends are declared. At the margin a firm must include the
taxes in its computation of the rates of return it will re-
quire to make an investment profitable. It would, therefore,
introduce distortions into the system to suggest that the
marginal cost of capital to regulated utilities should not
include federal taxes, when they are included in the prices of
other goods and services. This is perhaps more of a second-
best argument than a costing argument, but on these grounds
we believe taxes should be included in the computation of
marginal capacity costs.
-73-
D. Reserve Margins, Maintenance and Related Iss
and Their Impact on Responsibility for Marai.
1. General Overview
When an electric utility makes plans to construct
plant, it aims to build sufficient margin to allow for contin-
gencies. These contingencies include the need for maintenance,
the possibility of forced outage on machines, and the likeli-
hood that demand may be somewhat higher than predicted because
of random factors such as a particularly hot summer or severe
winter. There is a variety of methods or rules of thumb used
to determine the appropriate reserve margin. However, there
are two observations about the results which seem to be
generally true.
First, the (correct) reserve margin should not be
thought of as excess capacity. It is there to be used. The
higher the reserve margin, the greater the reliability with
which a given kilowatt-hour is provided; the decision about
the correct reserve margin is really a decision about how
much reliability is economically desirable; since more reli-
ability generally costs more, some estimate has to be made of
when to stop. The criterion, which again is often only impli-
cit, is that capacity should be expanded up to the point that
the marginal cost of capacity and the expected marginal cost
of shortage are equal. Depending on the characteristics of
the system, this rule gives us an implicit reserve margin.
It may be the case that different consumers would be willing
-74-
to tolerate different levels of reliability. Some industries
would be prepared to take an interruptible service if the
price were lower, while others will go so far as to build
their own backup generators to further reduce the already
small probability of a power failure. It would be possible
to provide tariffs which distinguished kilowatts by their
reliability, and indeed, some interruptible rates of this
sort are already offered. In any case, the cost of an appro-
priately determined reserve margin is properly part of the
marginal capacity cost of the utility.
Second, the marginal cost of capacity and reserve
cannot be attributed solely to the one hour of peak demand.
Planning criteria based on reliability take into account the
need for adequate capacity at all hours, and while the hour
of peak demand is generally the hour of greatest exposure
(although not invariably), other hours bear a risk which is
mainly, although not exclusively, related to the level of
demand. We, therefore, think of the responsiblity for capac-
ity as being a graduated peak responsibility rather than one
singularly attributable to a single hour, and use the relative
value of logs-of-load probability in each hour to estimate the
graduated responsibility for capacity costs.
This is again something of a surrogate. Loss-of-energy
probability might be a more satisfactory measure of the
probable shortage costs at different periods, since the
marginal costs of outages may well be positively related
- continued -
-75-
In some cases, however, planning criteria are a
mixture of physical and legal requirements, as for example
when membership of a pool requires a company to maintain only
a certain specific reserve level above its own maximum. The
pool requirements may be based on a more comprehensive analy -
sis, but each individual company has only the one dimensional
rule of thumb to follow, and will add capacity based only on
its own peak. From the point of view of the individual com-
pany, however, the relevant probability for capacity respon-
o sibility purposes becomes the probability that any individual
hour will in fact be the peak hour, which is not the same as
the loss-of-load probability for each hour. In these circum-
stances, individual appraisals of the company's relation to
the pool have to be made and flexibility of the rules allowed
for. In a well-functioning pool, dispatch cost and loss-of-
load probability will be the same throughout the pool except
for transmission costs, but systems in transition must be
considered case by case.
The LOLP is derived 14 by comparing the available
capacity with the demands on that capacity, including the
33 -continued-
to their size. However, few utilities in our experience
calculate such data, and consultation with system planners
has convinced us that LOLP is a reasonable substitute if
LOLP is computed to include all relevant probabilistic
elements in supply and demand.
Attachment A to NERA's report on Topic 4, "How to Quantify
Marginal Costs," March10, 1977.
-76-
demands which are probabilistic rather than determinate.
Starting with the load duration curve, which gives a most proba-
ble level of demand for energy at each hour, the planner adds
demand for planned maintenance; this gives a determinate total
demand level. (Plants out of service for maintenance can,
of course, be subtracted from capacity rather than added to
demand: it nets out to the same thing.) The probabilistic
elements of supply and demand must then be figured in also.
On the supply side, each machine has a history of forced out-
age from which the probability of its being out for unplanned
reasons can be estimated. Looking at the system as a whole,
a probability distribution can be arrived at which shows the
(probable) amounts of forced outage on the system at any
given level of demand. The level of demand itself may also
be variable, particularly perhaps with respect to weather, and
the probability distribution of demand may also be estimated.
While all companies aim to have more capacity than the deter-
minate peak demand projection, they have to estimate how many
times they will have a conjunction of these probabilistic
events: how often, for instance, will three plants be sub-
ject to random outage in the peak period? Or, how often will
freak weather be likely to make the temperature soar just
when the largest machine is out for planned maintenance in
weather which would normally be balmy? Probabilistic methods
can enable these questions to be answered and enable the
planner to calculate the loss-of-load probability at each
hour for various possible levels of reserve.
-77-
It follows from this that the loss-of--load probabil-
ity is likely to be highest when the load is highest, although
this is not invariable. Hydro-based companies may find their
peak exposure at times when the water level is low, so that
increases in demand at those times would require new capacity,
since even though demands at other times may be higher, they
can more easily be met. Also, companies with relatively high
load factors may find that when planned maintenance is consid-
ered, the loss-of-load probability is relatively even all year
round, at least in the daytime hours, so that an increase in
demand at any time would require capacity additions.
2. Use of LOL?
Depending on the particular system under study, we
can get various amounts of information about the probability
that the load at any particular time will exceed the level of
available capacity. These estimates reflect information on
the probability distribution of demands over the year, mainte-
nance schedules and forced outage rates. In making use of
these probability estimates, we recognize the general principle
that the price at any period of time should reflect the ex-
pected marginal cost of energy plus the expected marginal
shortage cost.35 Following the approach used by the French 36
See M. A. Crew and P. R. Kleindorfer, "Peak Load Pricing
With A Diverse Technology" and P. L. Joskow, "Contributions
to the Theory of Marginal Cost Pricing," The Bell Journal
of Economics and Management Science, Spring 1976.
36 See Y. Sa].asko, "On Designing Public Utility Tariffs with
Applications to Electricity," manuscript (EDF), 1974; and
- Continued -
-78-
we also recognize that under a number of simplifying assump-
tions, the expected marginal shortage cost can be expressed
in terms of the marginal cost of capacity, in effect allocat-
ing the marginal .cost of capacity to all periods which have a
significant shortage probability in accordance with the relative
probabilities in the different rating periods.
Briefly the argument goes as follows: assume that
we can summarize the uncertainty in demand, forced outages,
and maintenance requirements associated with each hour (i) of
the year by a probability distribution which for any level of
capacity gives us a probability Pi that demand will exceed
available capacity in each hour. Other things being equal,
the larger the amount of capacity we build, the lower will be
the shortage probabilities. Let us assume that the marginal
cost of not being able to supply a kilowatt of demand because
of capacity constraints is given by d dollars in each period
(allowing the d's to vary across periods does not change the
nature of the results) and the marginal capacity cost is given
by C dollars per kilowatt. Efficiency requires us to expand
capacity. up to the point at which the marginal cost of capacity
is equal to the marginal benefit of adding that capacity, which
continued
P. Caillé, "Marginal Cost Pricing in a Random Future as
Applied to the Tariff for Electrical Energy by Electricité
de France," Presented before the French-American Energy
System Planning and Pricing Conference, Madison, Wisconsin,
September 23 to October 4, 1974.
-79-
in turn is given by the expected marginal shortage cost summed
over all hours of the year. This condition is given by (1)
below:
(1)EPjd = C.
Now consider the decision to consume an extra
kilowatt-hour during any hour. With probability P, there
will not be enough capacity to provide the service so that
there are expected shortage costs associated with this deci-
sion of:
(2)Pjd,
but (1) tells us that if the system has been expanded effi-
ciently, then:
(3)C
and (2) can be rewritten as:
Pi
(4)Pd EP C
which gives the expected shortage cost associated with the
decision to consume one more or one less kilowatt-hour during
each hour. Our initial reaction, therefore, is to set the
rate (Ri) during each period such that it is equal to the
expected marginal energy cost (aj) plus the expected marginal
shortage cost given by (4):
Pi + (5)Rj = a1
and
(6)ER1Ea+C
-80-
which is equivalent to the result for the sum of the prices
for the simple deterministic model discussed in the previous
sections.
However, we are not quite finished. Referring back
to the optimal expansion relationship (1), we realize that
associated with this condition is some level of reserve margin
r measured by the difference between peak capacity and expected
(mean) demand. The larger the variance of the probability
distribution, other things being equal, the larger will be the
reserve margin. The cost of this reserve margin as yet does
not appear anywhere in the rates. This is because the question
that we asked is what is the cost of consuming one more or one
less kilowatt-hour in each period with certainty or alterna-
tively without any variance component. If we had asked instead
what is the cost of adding a one-kilowatt reproduction of the
existing demand configuration with identical stochastic charac-
teristics so as to maintain the same level of system risk, we
would have to include a reserve margin and the marginal cost
would be (l+r)C dollars.
We have accounted for the variance in load and the
associated reserve margin by including the reserve margin in
the marginal cost of capacity so that our rates now become:
4
(7)Ri = a 21- A(l+r)C Ep i
and
(8)ERi = Ea + (l+r)C
-81-
Note at this point that rates during all periods make
some contribution to the total capacity costs of the system
through a combination of the marginal energy costs ai generally
being higher than the average energy costs during any hour and
the allocation of the marginal costs of capacity using the
loss-of-load probabilities. These relationships may also give
us a basis to charge differential rates to customers who do
not want to pay for the level of reliability that the system
has been designed for--perhaps by opting for interruptible
rates--although we have not as yet explored this possibility
in any detail.
One final simplification must be mentioned in con-
clusion. We are not proposing to set different rates for
every hour of the year. In addition, the probability distri-
bution of load losses is similar for a small number of groups
of hours. We have, therefore, chosen to isolate three or four
homogeneous groups of hours, each containing hi hours which
have the same loss-of-load probabilities for any level of
system capacity. Therefore, for computation purposes,
Pjhj (l+r)C, is the share of marginal capacity costs charge-
able to the hours h, where hi is the number of hours in each
rating period and P 1 is the associated loss-of-load probability.
An example of how computations are done using this
procedure is given in NERA's report on Topic 4.
-82-
E. Distribution and Transmission
In distribution, unlike generation, the marginal cost
of one kilowatt to each consumer is different, depending on loca-
tion, terrain, distance from a pole, building characteristics,
etc. Since in costing we abstract from many of these differences,
the methodology will depend largely on the distinctions the dis-
tribution planner feels appropriate to make. In any case, we
are looking for the current annual cost of serving a customer
and the current cost of one kilowatt of demand at peak.
In the analysis of distribution costs, we again look
at the planning of the system. The system has to cover the ter-
ritory, irrespective of how much load is carried, and it also
has to carry the load.
1. Customer Costs--Covering the Territory
There are two elements to customer costs: the cost of
metering and billing, and the cost of covering the territory.
We take the latter first.
There is a certain level of investment requi.red to
,carry even the most minimal level of service to customers which
is not required where there are no customers. Ttçost of poles,
clearances and undergrounding, where required, is rightly charged
to the customers served, since if they were not there the expendi-
tures would not be required. This is most obvious in the case
of a new subdivision, where an investment has to be made to ex-
tend service to the subdivision, and it is clearly a marginal
-83-
cost of serving the new. consumers. Generally, this cost will
not be charged as a onetime lump sum charge for service, but
will be spread Over the life of the equipment with adjustments
made for repairs and replacements. The minimum system part of
the customer cost is then the appropriately annualized cost of
providing and maintaining the investment in minimum service.
With respect to the new subdivision we can raise sev-
eral questions relating to cost responsibility. First, there
is the problem of joint or common costs. If there are twelve
homes in the subdivision, how should they divide the joint cost
of the minimum system within the subdivision. The elements
which vary with number of kilowatts should be separated as
kilowatt costs, and the hook-up from Street to house, which
would not exist without the customer, should be conceptually
segregated, leaving the shared facilities' costs. The rule
is then to charge costs which do not vary with the number of
customers 17 with reference to intensity of demand of different
customers. We generally make the assumption that all cus-
tomers have equal intensities of demand, and therefore would
divide the customer charges equally between all twelve homes
in the subdivision.
It would be rare in the United States to find a case
where the 'taking of electric service itself were sensitive to
See Section Ill-A above.
-84-
the customer charge, but it is conceivable that a case might
exist or arise where a group of customers could only be induced
to take service at a price lower than that dictated by equal
shares of the customer charge. As an example, suppose eleven
of the twelve wanted electric service and the twelfth for some
reason did not particularly care. If the total cost were, say,
$60.00 the equal charge would be $5.00 per customer, whereas
with only eleven the charge would be $5.45 per customer. Since
the addition of the twelfth MjiX cost nothing (in terms of the
minimum system), any contribution to overhead by the twelfth
would reduce the charges to the others. This is the classic
joint cost problem. Everyone could be made better off if the
reluctant twelfth would participate even at a lower price.
However, as we have stated, in normal circumstances, we simply
assume that everyone wants service at an equal share of the
cost, and that no one whose addition to the system would cost
nothing is thereby excluded.
We can see that if the subdivision held only six
houses, or alternatively held twenty-four, that the $60.00
cost would result in charges of $10.00 or $2.50 respectively.
The density of development affects the appropriate level of
customer charge, and some utilities may choose to make such
distinctions, costing separately for less densely populated
areas of the territory. However, the economies of increasing
density may run out. In cities undergrounding may be more eco-
nomical because of density of load than overhead distribution,
-85-
or may be required by law irrespective of load densities, in
which case the per-customer cost may rise again. Utilities
may, after a brief review, decide that costs do not vary
sufficiently across the territory to warrant separate cost-
ing; in any case, some commissions prohibit charges which
vary from area to area.
It is also possible that the land-use characteris-
tics of the various classes of customers affect the extent of
the minimum system; this may be taken into account by a study
of system characteristics, and a weighting system established
to divide the customer costs. For example, the typical com-
mercial establishment may use only half a pole, each residence
one pole and each industrial facility two poles. This would
offer a basis for weighting customer costs other than simply
counting each customer as one. This sort of study is not,
however, frequently done.
What of the consumers who are already on the system?
If any individual customer chose to discontinue service, the
cost saving would be minimal and hence, it may be argued that
the minimum system cost is not a marginal cost. However, this
apparent anomaly comes about because of the long-lived nature
of the investment and because of the jointness of the costs.
The system serving a group of customers was installed to last
a long time, and their payment for it in monthly installments
is in the nature of a contract--they might instead have been
-86-
asked to pay their share of joint marginal costs at the time
of installation in a lump sum, which they might have financed
together with their mortgages, paying the bank in monthly in-
stallments- Instead, the utility financed it, and the monthly
charge represents the "mortgage payment." Furthermore, it is,
as we have seen, a characteristic of joint costs that the loss
of one consumer does not reduce the total costs: this does
not mean that there are no marginal costs, it simply means
that the marginal costs are joint between consumers, and the
- .-.-.. ----.-
cost of the individual consumer is conditional on the demand
of the others. Furthermore, the system is constantly being
repaired and replaced; and while the utility has an obligation
to provide service, customers are liable for the cost of pro-
viding the service. So we cannot argue that existing customers
impose no marginal costs: they too must pay for the resources
used to serve them.
2. Customer Costs--Metering, Billing and Hook-Up
The annual costs of the meter and the line from the
street to the house together with the costs of billing which are
undeniably specific to an individual should, in principle, be
charged to that individual, although in practice individual
assessments may only be charged in atypical cases. Other meter-
ing and billing costs are joint between many consumers: the
meter reader covers dozens of customers on a route; if one
ceased to take service the saving would be minimal, but if they
all ceased to exist, the meter reader would not be needed. The
-87-
joint marginal metering and billing costs are then treated in
the same way as the joint costs of the minimum system. If size
differences impose different costs, differentiation may be made:
otherwise all customers are assessed equally.
3. Demand Costs in Distribution
When the territory has been covered, the cost of carry-
ing kilowatts depends on the cost of copper or aluminum wire and
the cost of transformers, etc. There are many intertwined
elements of scale economies, joint costs, diversity and dis-
continuity in the analysis of distribution costs, but although
we should try to understand the various complications, we can
reduce the actual computations to fairly simple proportions.
In planning for a distribution system, it makes eco-
nomic sense to plan we].]. ahead. The labor involved in replacing
wires as demand grows is too expensive to warrant sizing wires
to current demand: a tradeoff is made between the extra cost
of installing more wire capacity than is needed this year and
the cost of continually replacing it. Also, while a wire which
is sized exactly to maximum demand will carry the load, the
losses are reduced if the wire is sized larger, and a similar
tradeoff can be made on the optimum size of wire to carry a given
expected load at minimum cost of wire and losses. These two
tradeoffs lead to most distribution systems being sized some-
what larger than the maximum current load, not simply to provide
a reserve margin but because of the economics of the distribution
system itself.
-88-
Transformers are used on the distribution and trans-
mission" systems to lower the voltage level, and the costs of
transformation are properly assigned to those who use the lower
voltage levels: a primary/secondary distribution distinction
can be made with the costs of secondary composed of the cost
of primary plus transformation to secondary. The losses in-
volved in transformation also raise the costs per kilowatt as
voltage level decreases. On the other hand, there are modest
economies of scale in transformer sizes, so that at each volt-
age level the fixed charge per kilowatt attributed to distribu-
tion may be charged as a declining block rate or accorded a
quantity discount. This is the only example in our general
scheme of analysis where economies of scale enter the costing
process directly.
4. Coincidence and Diversity
The same wires carry the current to many different
customers. Systems do not, however, have to be sized to carry
the sum of consumers' maximum demands because of system diver-
sity. The distribution engineer, for instance, will estimate
that if service is required for a new subdivision of thirty homes,
each sized at 12 kilowatts, then each house will obviously require
a 12-kilowatt line, and should be charged the full per-kilowatt
cost at that level. But the subdivision itself will be able to
$8 There is no hard and fast distinction between distribution
and transmission. The FPC insists on reporting cutoff at
69 kilovolts, but lower or higher voltages may be the func-
tional cutoff level in some companies.
I
-89-
be served by a line much smaller than 360 (30x12) kilowatts:
because there is a very tiny likelihood of all thirty homes ever
needing 12 kilowatts at the same time, the feeder system can be
sized at, say, 216 kilowatts with virtually no risk of serious
overloading. This then allows us to say that the coincidence
factor of the individual with the group is 216/360 or 0.60.
The maximum demand of 216 kilowatts on the feeder to
our hypothetical subdivision will be the demand at the time of
the subdivision's peak, and the cost attributable to each consumer
will be the expected value of the consumer's demand at the time
of this group's peak, or 0.6 x 12 = 7.2 kilowatts. Even if the
subdivision peaks at a different time from the rest of the sys-
tem which serves it, the cost of the distribution line to the
subdivision still depends on the expected demand at group peak.
The members of the subdivision may be assumed to be
more similar to each other than they are to the rest of the sys-
tem (this is an assumption which can be empirically tested, but
it seems well established). We, therefore, assume that the
best estimate of a consumer's demand at system peak, as far as
local distribution costs go, is the consumer's own maximum times
the coincidence factor of the group.39 It is preferable to
charge for local distribution costs by measuring the con-
sumer's own maximum demand, reduced by the coincidence factor,
Coincidence - Slndjvjdual maxima
factor - Group peak
-90-
because that is more likely to be related to demand at local
group peak which is the cost-incurring factor.
Marginal transmission costs per kilowatt can be
estimated fairly simply from the relation of additional
transmission investment to additional load. Since this is
also data which would be used in planning, an analysis of
past trends and expected future costs can be used to estimate
the cost per additional kilowatt of load. This cost is prop-
erly related to the system peak load, and may be spread using
loss-of-load probability in the same way as the marginal cost
of generating capacity.
F. Annual Charges
Machines for producing electricity and equipment for
transmission and distribution are bought to last 30 years or
so. Generations of customers use the same machine. In this
section, we investigate the appropriate annual charge rate to
be used for estimated marginal cost in a world with inflation
and technological change.
The series of charges on a long-lived asset are
composed of return on capital (interest and dividends), de-
preciation of the machine, and taxes. The pattern of these
charges is generally such that cash flows required to finance
a plant are greater in the first year than in later years.
This is because straightline depreciation usually used
for ratemaking purposes will reduce the plant book value
from year to year and hence the basis on which the return
is earned declines.
L
-91-
In computing annual costs, however, it has been
customary to take the present worth of this prospective
stream of payments and compute the constant annual charge
which would have the same present worth. This works well
in times of no inflation or technical progress, but the
presence of either of these factors renders the leveling
procedure a poor approximation of the marginal economic
cost of using the machine for a year.
When a choice is made to purchase a new machine, we
can think of it as the choice between purchasing it this year
or next year. If the machine is installed this year, a stream
of charges is incurred with replacement 30 years from now, 60
years from now, and so on. If it is installed next year, a
stream of charges begins next year with replacement 31 years
from now, 61 years from now, and so on. The difference in
cost between those two options is the marginal cost of the
machine for the year. This has been variously called the
"fair rental cost" or the "amortization "
It turns out that the difference between a stream
of costs starting today and one starting next year is equal
to the familiar mortgage formula" ensuring equal annual
payments over the life of the equipment, which shows how
f' (1+r)' •I 40 A = Kr!
L (l+r) -1 J
where A = amortization
K = price of plant
r = interest rate
n = expected life of plant.
-92-
reasonable the engineers annualization practice has been.
However, there are limits to the applicability of the simple
formula. It only gives the marginal cost if the purchase
price in this year is equal to the purchase price of the same
machine installed next year. This is true if there is no in-
flation or technical progress. But if there is a price change
expected between this year and next year, the marginal cost of
a new machine will not be adequately estimated using this
procedure.
If technical progress is expected the rental cost
for this year is raised.41 It is raised because by buying
this year rather than next, a certain price reduction is for-
gone. The forgone price reduction is part of this year's
cost. By parallel reasoning, if inflation is expected, the
rental cost of thi4 year is reduced. Buying the machine this
year rather than next has at least saved the higher price
which will be demanded next year.
n The formula is:
I (l+r)
At = K0 (r-i+p) (l+i_p )t L l+ )fl - (1j_p)flJ
where i = inflation rate
p = rate of technical progress
t = age of plant.
-93-
This is not as paradoxical as it seems. If the
inflation which affects the plant whose marginal cost we are
calculating also affects the rest of the economy, then the
interest rate which we would normally use to calculate the
levelized annual charge will normally have risen to include
an inflation premium. Computing annual charges with the in-
flation premium in the interest rate actually overstates the
first year cost of owning the machine, and our improved meth-
odology for computing annual charges will simply extract that
inflation premium.
The net result is that instead of equal annual charges
whose present worth is equal to the present worth of the cash
flows, we derive a series of charges rising at the rate of
inflation (but still with the same present worth). It there-
fore starts out below the levelized stream at the beginning of
the life and rises at i percent each year if inflation is ±
percent. The indicated annual charge for each year would in
fact be equal to the first year's charge on a new machine in
that year. By the time the machine is replaced at a much
higher cost, the annual charges on the new machine continue
in unbroken series, rising at the inflation rate. To think of
it another way, each generation of consumers should pay the
same in real dollars for the use of the machine.
This method of computing the marginal cost for one
year of long-lived equipment gives a lower current annual
charge than the generally used "levelized" computation. The
I i
-94-
adjustment is approximately equivalent to reducing the interest
rate by the inflation rate.
A further explanation of the derivation of the for-
mula is given in the paper "An Economic Concept of Annual Costs
of Long-Lived Assets," included as Attachment C to this report.
G. Treatment of Hydro
In principle, hydro power may be one of three types:
run of the river plants, which take as much water as is avail-
able strictly as it comes; pondage plants, which store water
for maximum value use; and pumped storage plants which create
a pond to be let out at peak times.
As with all other marginal cost analyses, we look
first at the planning process. When the plant is planned, it
is assumed that the initial construction costs and the running
costs of the plant will be largely offset by the value of
the more expensive fuel which can be displaced by the water
when it is run through the turbines.
This is most evident in the case of pumped storage.
For each day of the year, an operating decision is made on
how much water to pump, if any. The decision rests on two
parameters: the cost of (nighttime) pumping and the value
of the displaced peaking fuel. If the marginal plant at
night without pumping is, say, a coal plant, the marginal
cost of pumping fuel is the coal cost times the efficiency
factor (about 1.3 or 1.4). As more plants are brought on to
pump, the marginal cost of pumping rises (or it may rise
simply because other demands have caused more plants to be
-95-
brought on as the dawn approaches). We, therefore, have a
daily supply curve of pumped energy.
At the same time, a demand curve is being generated.
The first kilowatt-hour of pumped energy has a high value,
since it can displace the highest cost generators on line
during the day, but as more and more kilowatt-hours are
stored, the marginal value of each declines. Since it takes
1.3 kilowatt-hours of pumping energy to produce one kilowatt-
hour of released energy, pumping will continue until the
marginal fuel for pumping costs 1/1.3 times the marginal fuel
displaced.
DISPATCHING PUMPED STORAGE
(TYPICAL UTILITY)
Price
energy
/
(Efficiency
had factor /
Demand
(Value of energy
displaced)
Quantity
I I
-96-
From these supply and demand schedules (which are
routinely generated by a typical utility for dispatching
pumped storage), it can be seen that a "transaction surplus"
is generated (shaded area). All the kilowatt-hours below g
are worth (displace) more than they cost. It is this trans-
action surplus which was estimated when the plant was planned;
if the planning was properly done, the capital cost of the
plant was equal to the discounted sum of the daily transaction
surpluses over the life of the plant.
By calculating the value of the fuel displaced,
rather than simply the value of the pumping fuel, we obtain
a budgetary equilibrium from a planning point of view. The
last unit of fuel displaced will equal the last unit of fuel
pumped (times the efficiency factor), but the higher value
units, by being valued at the displacement cost, will thereby
cover the capital costs of the plant.
In this way, by inspecting the placement of SnX
hydro power in the merit order of plant dispatch, we can
impute a value to the hydro power. The reasoning is easy to
see in the case of pumped storage. For pondage and run of the
river, the same imputed value computation applies; the reason-
ing rests on the planning logic. If a planner were trying to
estimate whether to build a pondage dam, the demand curve or
displacement curve might look the same as the one set out
above. The fuel "supply curve" would, however, be very close
to zero, since no pumping is involved.
-97-
Why then not continue building pondage hydro forever until the
displaced energy was worth zero? Simply because natural re-
sources become ever more expensive as they are used up, and
the total lifetime transaction surplus cannot meet the initial
cost of the plant. Such pondage as is available is used to meet
the highest possible demand in the merit order, displacing fuel
costs as high as possible, and thus covering its capital costs
through the transaction surplus. This logic enables us to im-
pute a "shadow cost."
To make the imputation, we simply review how the
planner has dispatched the available hydro and compare that
with the familiar current tradeoff between capital and fuel
faced by the planner.
Total Cc
per K
I
P
termediata
Mt
- - Hours
-98-
We then impute the shadow cost of hydro power on
the basis of the running costs of the generators that would
have been used if no hydra power had been available. The
average shadow value of the hydro power is a weighted average
of the fuel costs of the plants above and below it in the
merit order, the weights being the shares of power generation
that would have been provided by those plants. An example of
the calculation is given in NERA's report on Topic 4.
Run-of-the-river hydro by its nature cannot be used
to displace a maximum of high priced fuel. It runs continu-
ously, depending on the water availability, and displaces both
cheap and expensive fuel. eseldom need to impute a shadow
cost to it since it is seldom" dispatched at the margin.
This analysis of hydro power serves well in mixed
systems where hydro potential has long been exhausted and the
existing hydro power is sandwiched in the dispatch between
fossil units. It also may impute a market value to hydro in
cases where a utility can choose to sell, to its less fortunate
neighbors who are dependent on fossil power. However, for
the sake of completeness, we should review the implications
of the theory in the case where an isolated system can still
build hydro for its own use.
The marginal energy cost of hydro, viewed from the
planning stage, is the cost of expanding the .basin and any
associated facilities to produce additional energy. It is a
joint cost among all units of energy produced over the life
-99-
of the hydro plant. A per-unit energy charge is a fair ap-
proximation, but it should rise over the years to reflect
replacement costs, when these are rising. The capacity, or
the rate of flow of energy, can be altered by adding water
wheels, within limits, during the life of the project. (The
per-kilowatt cost of a water wheel is close to the cost of a
kilowatt of peaking capacity.)
Pricing a hydro-based system is further complicated
bthe variable nature of the water supply. The maximum sup-
ply period on an annual basis may not coincide with maximum
demand, and it may be desirable to build a storage basin.
However, in years of abundant water flows, some water may be
spilled during the peak water supply period. Conversely, in
a low water year, supplemental sources may have to be employed.
If rates are to be fixed ex ante over the hydro cycle, costs
then have to be estimated on a probabilistic basis. Alterna-
tively, it would be possible to reflect marginal costs more
accurately by developing rate schedules related to low, high
and average water years: this would be equivalent to extend-
ing the time-differentiated concept beyond the one-year period
usually considered appropriate, and revenue cycles would have
to be adjusted accordingly. Whether it would be desirable to
structure rates in this way would depend upon the costs of
administration.
-100-
V. THE DEVELOPMENT OF THE METHODOLOGY--LRIC TO TIME-
DIFFERENTIATED MARGINAL COSTS
We have discussed why it is important in designing
electric rates for a given utility to use its long-run mar-
ginal cost of supplying electricity as a cost standard, and
we have presented a methodology for calculating marginal costs.
A word is in order as to how this methodology has evolved over
the past eight years or so. This will enable the reader to
distinguish between this methodology and earlier descriptions
of the computation of marginal costs.
In the late 1960s with technological progress
still reducing generating costs, with economies of scale
still indisputably present, and with inflation at a very low
rate, average costs of electricity were considerably higher
than marginal costs. This was particularly true with re-
spect to off-peak usage. There was, therefore, clear
justification for pricing such usage at less than average
costs; but commissions were reluctant to approve such rates
lest they be exposed to the charge of fostering discrimina-
tory practices. It was to allay this concern that certain
utility companies sought to present the economic cost justi-
fication for these load-factor improving rates, relying on the
very same costing theory we advance here, i.e., that marginal
cost is the proper method to test the rates' proprety.42
42 Some early NERA testimony using marginal costs were:
I. N. Stelzer, Prepared Testimony before the New York
- continued -
-101-
It was in these early proceedings that the first versions of
long-run incremental costs, soon dubbed LRIC, were introduced.
This was defined as:
All costs associated with the addition of a
given quantum of service.... The concept
refers to the long run; any costs which may
be added as a result of adding or expanding
a service, including those costs which will
not immediately be incurred, are included in
the total incremental cost of a service offer-
ing. In other words, these (total incremental]
costs are long run in the sense that they in-
clude the addition to total costs when the
company has fully adjusted its operations and
facilities to the most efficient means of
meeting the increased total demand.3
At that time electric sales were growing rapidly
and the prime consideration was the cost of taking on new
load. Costs were computed in the form of annual kilowatt
charges for meeting the new demand at the time of the system
peak, the compatible energy costs, and the related customer
costs. No attempt was made to allocate these annual costs
between the different periods of the year, though rudimentary
support for summer/winter differentials was developed.
42 -continued-
Public Service Commission, Case No. 24726, 1968;
C. H. Frazier, Testimony before the Pennsylvania Utility
Commission, Docket RID 16, September 1972; and
C. H. Frazier, Testimony before the Pennsylvania Utility
Commission, C. 18859, September 1970.
' I. M. Stelzer, J. Joskow, "Utility Ratemaking in the
Competitive Era," delivered at a seminar on Some Economic
Aspects of Public Utility Regulation, sponsored by New
York Telephone Company, Cornell University, September 8,
1966, p. 3.
-102-
This methodology developed from rate case to rate
case as computational improvements suggested themselves. For
instance, it was recognized that nuclear plants with their
much higher first costs were being introduced to affect energy
cost savings as well as to meet new load requirements, and
allowances were made for this effect. Refinements were intro-
duced as to the methodology for separating distribution costs
which vary with demand from those costs which were strictly
related to customer coverage. Developments such as these cul-
minated in the cost presentation in 1973 before the Wisconsin
Public Service Commission in the Madison Gas and Electric rate
case (Docket 2-U-7423). This presentation was the final pre-
sentation in the LRIC costing saga.
That particular period of late 1973/early 1974
marked a turning point in the energy world, with the combina-
tion of a three- to four-fold increase in energy costs and
1974's very severe inflation causing capacity (and energy)
costs to surge to new heights. The need for rate relief be-
came urgent; but customer resistance concomitantly reached a
new high. Environmental groups reacted to the circumstances
and were actively interested in the ratemaking process. "Time-
of-day," "peak-load" pricing was prescribed as the solution,
purportedly to moderate the increased need for generating capac-
ity and to curb the alleged wasteful use of electricity.
To respond to this challenge, many utility companies
engaged in the study of the proper costing techniques needed
rl-
-103-
to support time-of-usage pricing. It is as a result of this
area of study that the methodology here proposed was evolved.
It has been offered in a number of jurisdictions, in the
years 1975-1976, as the appropriate standard for marginal cost
ratemaking. The treatment of annual charges recommended in
Section IV-F of this report has been generally discussed but
not formally presented in previous testimony; it is the treat-
ment that will be used by NERA in Topic 4 work.
In terms of overall annual costs, the two methods
(LRIC and time-differentiated marginal costs) produced gener-
ally the same results, but the individual cost components do
vary. Thus, the advanced methodology more systematically
applies a part of the capacity cost to the load being served
outside of the normal peak months, though this was always
recognized as necessary to some degree. Also, a more sys-
tematic method was developed for including in the energy cost
element the recognition that a substantial part of the capital
cost is incurred for the purpose of saving energy cost and not
merely to meet peak loads. The general effect of these changes
has been (paradoxically) to place a somewhat lower emphasis on
the demand (capacity) cost element, and on the costs at the
particular time of the system peak, correspondingly somewhat
greater emphasis on the energy cost element, and on service
during the off-peak months. A comparison of the methodologies
is summarized in the following table:
-104-
A QUICK GUIDE TO LRIC AND TIME-DIFFERENTIATED
MARGINAL COSTING
Time-Differentiated
Costing LRIC Marginal Costs
Capital cost of Mean expected plant Least capital intensive
generation cost per Kw over plant used on system,
planning horizon, usually a peaker.
Current dollars.'' Current dollars,
Annualization Levelized at cur- Annual charge reduced
(Carrying rent rates of by (approximately)
charges) interest, including rate of inflation,
taxes. includes taxes.
Fuel costs Average fuel cost. Marginal fuel cost
Current prices. (always > average).
Current prices.
Distribution and Mean per-Kw cost of recently installed
transmission capacity.
Customer costs (Judgmental) Minimal system.
Capacity respon- Some measure of Loss-of-load proba-
sibility peak. bility.
These costing methods have been evolving for some
eight years now. It is not claimed that the final improve-
ments have been made, for hopefully this very study will
contribute to that progress. We are satisfied, however, that
the methodology described above is soundly conceived, well
tested under real-world conditions, and now an appropriate
one to assign the marginal costs of providing service to the
different seasons of the year and times of day.
As the LRIC methodology progressed, capital credits to
reflect fuel savings were introduced.
rI-
-105-
In analyzing the costs of particular companies,
data availability may dictate some variations in estimating
procedures. Such variations are discussed in more detail in
NERA!S report under Topic 4 where the results of cost studies
for four companies with different characteristics are presented.
-106-
VI. RATEMAKING ASPECTS OF MARGINAL COST PRICING
A. Introduction
Once marginal costs have been determined, we
face the problem of suitably reflecting them in rate struc-
tures. This problem is particularly pressing for large con-
sumers who would clearly be the first candidates for con-
version to time-of-day rates, since development of metering
may itself hinge on rate design discussions. (See Topic 5
for a more detailed discussion of this subject.)
In making rates, it will of course be important to
recognize constraints such as the overall revenue target, con-
tinuity, simplicity and so on, but it will in most cases be
best to work from the costs to a set of unconstrained or
"ideal" rates which as faithfully as possible reflects the
marginal cost structure of the utility. These "rates " could
be simply $X per kilowatt, $Y per kilowatt-hour, $Z per cus-
tomer, derived directly from the marginal costing process.
(The per-kilowatt-hour and the per-kilowatt costs would nor-
mally be differentiated by time of use.) By consideration of
the demand pattern of the utility we can then estimate the
total revenues which would be derived if the marginal cost or
"ideal" rates were charged as the price. These "total mar-
ginal cost revenues" can also be derived for each class of
customer using load research data.
Development of a preliminary rate format depends
on two sets of data: marginal cost data and load research
-107-
data. The cost data will show how cost varies in several
dimensions; the load research data will show in what respects
customers' demands are sufficiently similar to warrant averaging
their expected costs in the tariff, and in what respects they
are so diverse as to warrant variations in the tariff.
Some of these decisions will already have been
made in the costing process. For example, virtually every
consumer will incur distribution costs different from
every other consumer. Differences of terrain, density, loca-
tion, and even of building materials will affect the actual
cost of distribution for each consumer; but an early decision
is made to ignore these differences, or to acknowledge two
or three major differences in the costing process and hence
in the rates. Thus, some companies retain urban/rural dis-
tinctions, while others charge the customer the cost of
connection at greater than 100 feet from a pole. In many
cases, commissions have decreed the allowable distinctions
as a matter of policy, while in other cases, the decision
can be made by taking a rough cut at the marginal costs to
determine whether significant differences of cost exist.
Similarly, the marginal cost can be projected
for each hour of the next several years, but early in the
costing' process a decision is made to group similar hours
into periods, so that by the time the question of making
(unconstrained) rates arises, some of the averaging has
already been done. It must be stressed that the need to
-108-
average arises from the desire for simplicity of tariffs,
and because there is a cost to developing, measuring and
communicating more complex price signals. In general, the
larger the customer, the more it will be worth the trouble
for both the consumer and the utility to make finer cost
distinctions; the smaller the consumer, the less justified
are complex tariffs and metering. However, this also depends
on the extent to which load research shows that customers are
relatively similar, since both equity and efficiency require
that customers with very different cost characteristics
should not pay the same rates even if they are small.
In the following sections we discuss coincidence
and diversity and their implications for ratemaking, the
treatment of second best, revenue constraint adjustments and
other additional problems such as the needle peak and setting
rates for small customers.
B. Coincidence and Diversity
The sum of all consumers' maximum demands on a
system can only equal or exceed the system's maximum demand;
this is true of any system, not simply electric systems,
and is due to the fact that there is diversity between demands.
On an electric system, the estimation of diversity and
coincidence of demands play a considerable role in sizing
the system.
-109-
We discussed earlier the impact of diversity on
sizing the distribution system, and concluded that the
closer to the consumer, the more likely it is that his own
maximum demand would be responsible for the sizing and hence
the cost of the system serving him, but as the distance from
the consumer increases, the cost depends on the diversity of
the group and on the consumer's expected demand at the time
of group peak. It would be possible to measure this di-
rectly, but in general, load research leads us to simplifj'
by asserting that the individual's own maximum demand times
the group's average coincidence factor is a fair approxima-
tion of the cost incurrence for local distribution close to
the consumer.
As we move further away from the consumer, the
"group" whose peak determines the system size becomes larger,
the similarity of customer and group becomes smaller and the
coincidence of the customer with the group peak declines. In
fact, as the "group" becomes larger and larger and becomes
the "system," the customer's expected demand at system peak
may not be systematically related to the consumer's own maxi-
mum. Neither, at this distance, does the consumer's own
maximum have a particular significance. Certain random
factors in a consumer's demand will be offset by random factors
in other consumers' demands, and measuring the consumer's own
maximum in order to determine the consumer's contribution to
system peak can actually introduce inefficiencies such as those(
-110-
we encounter from time to time: cost-sensitive managers spend
many thousands of dollars to prevent temporary demand increases
which can raise the consumer's maximum demand reading. This
may make sense to the managers who reduce their bill, but it
makes no sense to the utility: by just the amount that the
customer's load factor is apparently improved, system diversity
is thereby decreased. .A.sigralthat individual maximum demand
is important, henin fact it has very little signifcanceat
gyAtemlevel, induces economic inefficiency.
Neither is the ex post integrated demand, at what
is later determined to be the system peak, the proper factor
to measure when considering the customer's contribution to
the system capacity requirements. It may appear that with
tape measurements it should be possible simply to determine
in arrears the moment of system peak, and to charge for kilo-
watts demanded at that moment. But although this is probably
better than the individual's maximum as a guide to system
cost responsibility, it does not deal with the problem that
at the moment of system peak, any individual may be consuming
a typical amount, an unusually large amount, or nothing at
all. And none of these possibilities would make any dif-
ference at all to his reponsibility for system peak, since
the system is sized to meet his expected demand, not his
randomly measured actual demand at a particular moment.
The expected demand on the system is best given by
the mean demand over several peak hours, or even the entire
n
-111-
peak period. If the entire peak period is used, the generation 1
and transmission cost per kilowatt is then the sum of the kilo-
watts demanded at each hour in the peak period times the cost
per kilowatt, divided by the number of hours in the period,
which is exactly equivalent to dividing the kilowatt charges
into each kilowatt-hour of the peak period, or "rolling in"
the kilowatt charge for the central system into the kilowatt-
hour charge.
This latter approach has been used by the French
in making their industrial tariff. The charges in the French
tariff consist of a fixed annual charge per maximum kilowatt,
which corresponds to the "semi-individualized" system, or
the part of the system nearest the consumer, for which the
consumer's own maximum demand is responsible, and a charge per
kilowatt-hour which represents the rolled-in charge for the
"collective" system, or the part of the system furthest from
the consumer, where his diversity with others renders his own
maximum irrelevant. The French have also tried to relate
diversity to the load factor (a concept which has been examined
in the United States at various times), and offer rates which
in effect vary the rate with the load factor as a proxy for
diversity. The rates and the theory behind them are examined
more fully in Attachment F to NERA'S report on Topic 5,
"Ratemaking," March 11, 1 97 7 .
While we believe the French approach has consider -
able merit, the alternative, which we have called the x-hour
integrated demand rate, may perhaps have more appeal in the
-112-
United States where demand charges are in current use. The
proposal is essentially to extend the period of integration
from its current 15 minutes to 1 hour to a 4, 5, 6, 7 or 8
hour period during the peak hours, in order to more accurately
measure the expected cost during the system peak period. The
reasoning for this is explained more fully in Attachment B
to NERA's report on Topic 5.
C. Special Problems
1. Needle Peaking and Temperature
A needle peak is one or a series of short periods,
totalling, say, 40 hours, in which demand is considerably
above a plateau of high demand. There is a fear in the utili-
ties that this may become a pervasive pattern if higher per-
kilowatt-hour rates are offered in the summer. We now believe
that the needle-peaking potential is not nearly so pervasive
as is sometimes implied, and as we had previously feared.
From our studies of the load characteristics of many util-
ities, we observe that the long flat summer peak seems to be
much more typical.
However, for those companies where needle peaking
potential might exist, we must understand the genesis of the
problem: the peak peak period is a period of above-average
costs, but it cannot be pinpointed in advance since it is
more related to weather than to a particular time of day;
hence, the obvious solution is that the peak period be delin-
eated not by time of day but by temperature. The principle
-113-
is correct, but the availability of metering is problematic.
In the absence of suitable metering, we are forced to average
costs over the entire peak period and thereby create a
miniature peak-load pricing problem--the peak peak will be
underpriced, the near peak overpriced, and we may therefore
confidently expect too much demand at the peak peak and too
little at the near peak. Not only this, but some observers
suspect that peak peak elasticity is lower than the near
peak so that the change that can be expected would be a
greater reduction in the near peak than in the peak peak.
This means that revenues are lost, but capacity is not "saved."
Energy savings would exactly match revenue losses in the energy
component of the charge for peak hours, but capacity cannot be
adjusted in the short term. In terms of revenues, the company
has to guess the elasticity in order to make up its revenues.
Or, to put it another way, the equilibrium cost per kilowatt
in the peak period after the rate change may be higher than the
measured cost at present.
In principle, the answex to these two problems
(absent temperature-sensitive rates) is relatively straight-
forward: since we are trying to price at the equilibrium
level anyway, costs should be adjusted using our best esti-
mate of elasticity.
The practical question arises because of the new
concentration of revenues in the peak period under peak-load
pricing. This is the reason for implementing change slowly,
by steps. steps. It makes sense, for example, to institute a mini-
mum bill to aid revenue stability during the adjustment; go
only two-thirds of the way to marginal costs as a first step;
if there is a revenue excess, back off first in the peak
period to allow the rate to be adjusted and monitored over
several years.
2. Rates for Small Consumers
Small consumers, like large consumers, may have
costs differentiated by time of day and season, but it will
not always be wise to introduce metering to enable these
differences to be fully reflected in rates. It is relatively
simple to offer seasonal differentials at this level, but time-
of-day differentials may not be appropriate while metering
costs are high. There are several possible approaches to this
problem.
First, a rate may be "synthesized," which simply
averages time-differentiated costs for the typical consumer,
weighting by the typical consumer's peak and off-peak con-
sumption. The option of a time-of-day meter may be offered
in addition for those who believe they can benefit from it and
are willing to pay or at least share in the additional meter-
ing cost. In order to give the utility some idea of how many
consumers would want to install meters, it may be wise to use
load research data as follows.
For each consumer, estimate the total bill under
full time-of-day metering and under the synthesized rate. By
I1
-115-
subtracting the two, we can observe that some will gain and
some will lose by metering as opposed to the synthesized rate.
Plotting a frequency curve of gains and losses, we will find
a curve which will be more or less a bell-shaped curve around
a mean of zero:
Number
of
Customers
Monthly Gain or Loss to Consumer from TOD Metering
The "gainers" from time-of-day metering will be those whose
consumption is more off peak than the mean, while the "losers"
will be those whose consumption is concentrated in the peak
hours. If we then superimpose the monthly cost of metering on
either side of the mean, we will discover the number of cus-
tomers who would stand to gain more than the metering cost by
paying for a meter (shaded area). These customers can prob-
ably be shown, from the load research data, to be customers
-116-
with particular characteristics of size or appliances, and
the utility's offering of an optional meter may include a
description of the type of customer who would normally benefit
from optional metering.
On the other side of the curve, there may be a
group of customers, who can also be identified as a type or
class, who are actually costing the utility more than it
would cost to put in metering which would track their costs
more closely.
Of course, it is also possible that the load re-
search data would show that the ratio of peak/off-peak use
varies so little between small consumers, that the whole fre-
quency distribution of gains and losses falls within the
cost of the meter, and that the meter can be justified only
by the shifts in consumption it may induce.
3. Fuel Adjustment Clauses
Since in computing marginal costs the fuel cost of
the marginal machine is an important element, it is clear that
if costs of different types of fuel change in different pro-
portions, the marginal cost of different hours will change
nonproportionally. In principle, it would be possible to
design a fuel adjustment clause which took this into account
and maintained the price equal to marginal cost. However,
we advise against doing this in practice for two reasons:
first, if rate cases continue to come close together, the dis-
tortions caused by average adjustment clauses in conjunction
-117-
with a marginal cost-based rate will be relatively minor.
Second, a revenue excess or deficiency problem would have to
be worked through at every adjustment, creating an adminis-
trative monster. For instance, if oil is marginal for 1,000
hours, but represents only 5 percent of total fuel, a 20 per -
cent increase in the price of oil alone would raise the mar-
ginal energy cost of the 1,000 hours by 20 percent, and total
revenues attributable to energy charges by perhaps 3 percent.
At the same time, total fuel costs have increased only 1 per-
cent. This sort of adjustment should be made from time to
time, particularly if energy price increases get very high,
but need not be attempted monthly.
D. The Second-Best Issue in Ratemaking
The second-best issue can be briefly summarized as
follows. Economic theory suggests that when price equals
marginal cost in -all markets, an optimum (efficient) alloca-
tion of resources will result for the economy as a whole.
It was once thought that if one could not have the best allo-
cation of resources, with all prices equal to marginal cost,
then Setting as many prices as possible close to marginal cost
might be a way of getting a second-best allocation. But
it was then shown by Lipsey and Lancaster 45 that this was
"
5 R. G. Lipsey and K. Lancaster, "The General Theory of
Second Best," Review of Economic Studies, Vol. 24, No. 1,
1956, pp. .11-32.
-118-
not necessarily a second best. That is, by setting price
equal to marginal cost in a particular industry, one might
actually be moving away from what was best and making the
situation worse.
While Lipsey and Lancaster's formulation of this
truth is highly mathematical, some real-world examples from
a different industry can readily be imagined to demonstrate
their point: suppose we were asked to formulate an optimal
pricing scheme for the New York City subway system, and
suppose that the (internal) marginal costs of the subway
system could easily be calculated. We would be foolish to
claim that changing to a system of marginal cost pricing
would increase the general level of well-being in New York
City, let alone optimize it, unless we had first reviewed
the rest of the transportation system. If we proposed, for
example, to raise the peak-load price while the roads and
bridges offer free access to cars, we would expect to see
underutilized subways and traffic jams on the roads. Simi-
larly, bus fares, parking fees (and fines), and other related
services must be examined. If parking space on the streets is
priced well below what it costs in terms of congestion, air
pollution, accident hazards, etc., then it makes no sense to
try to "optimize" by pricing subways at a price which simply
tends to increase parking. This is the common sense of the
second-best problem.
.
-119-
Fortunately, the problem of second best is not so
paralyzing a difficulty as it may at first appear; one should
not draw the conclusion from the theory of second best that
no policy based on that economic principle can be developed.
The implication of the theory of second best is that one must
consider the implication of any policy on both the particular
market in question as well as other markets in which demand
is affected by the price in the first market. Special consid-
eration must be given to those markets in which prices are
known to deviate from marginal cost.
First, not all other products are relevant to the
price of electricity. If yoyos are not sold at marginal cost,
it has no bearing on electric prices. Only goods which are
substitutes for electricity (such as oil and natural gas), in-
puts to the electric production process (such as coal and
uranium), complements to electric use (such as electric appli-
ances) and products which use electricity in their manufac-
ture (such as aluminum) need to be considered. Since compe-
titive markets can be assumed to bring price to marginal
cost, we need mainly to consider the effect of markets in
which regulation or monopoly are significant elements.
In the case of natural gas as a substitute for
electricity, we may believe, for instance, that the natural
gas price is held below marginal cost. Pricing electricity
at its marginal cost could conceivably push people into de-
manding gas at prices which do not reflect what the additional
-120-
gas costs society, which would not be economically efficient
for the whole society. In that case, the best solution from
an economic point of view would be to price gas also at its
marginal cost: if this is impossible, the second-best solu-
tion is to price electricity below its marginal cost for uses
where it competes with gas.
A further second-best consideration is the pricing
policies of neighboring jurisdictions. This is perhaps the
most important practical problem in the application of marginal
cost pricing to electric rates. Studies by Guth" have shown
that the price elasticity of demand for electricity for indus-
trial uses is relatively low (in the range of -0.2 to -0.5),
once one has removed locational effects. But since locational
elasticities may be quite high (in the neighborhood of -1.0),
the application of marginal cost pricing to industrial rates
may require us to take into account the policies of other
jurisdictions, since, otherwise, industries may be induced to
relocate. If marginal costs are lower in other areas and if
the prices elsewhere reflect marginal cost, then relocation
may be economically beneficial to the society as a whole.
But if other jurisdictions are pricing below marginal cost,
this may be something which should be considered in setting
Louis A. Guth, "Price Elasticity of Demand for Electricity,"
Testimony before the Public Service Commission of New York,
Case No. 26806, June 30, 1975.
-121-
prices in one jurisdiction. " It is ultimately the reason
that the federal government may mandate marginal cost pricing.
The correct policy to pursue in making the second-
best adjustment is to set the price of electricity equal to
marginal cost as a starting point and to apply "corrections"
to these prices in response to those departures from marginal
cost elsewhere which are known to have significant effects on
the demand and cost structure of electricity and are not them-
selves the object of government policies to reduce other non-
optimai.ities in the economy.
The following relatively simple formula may be
used to try to evaluate whether or not a particular price
change will lead to an improvement in resource allocation: 48
47 Some would argue that if another jurisdiction seeks to
subsidize some industries by pricing below marginal cost,
there is no obvious reason why the jurisdiction in ques-
tion should follow suit. It depends on whether the bene-
fits of retaining the industires in the jurisdiction are
worth the distortionary costs of the subsidy.
48 See Ralph Turvey, "Price Changes and Improved Resource
Allocation," The Economic Journal, Vol. 84, No. 336,
December 1974 and generally Arnold Harberger, "Three
Basic Postulates for Applied Welfare Economics," Journal
of Economic Literature, Vol. IX, No. 3, September 1971.
-122-
e pe
Net Benefit (Qe - QC) _°_i! I - MC + iz (Qi t) (P. - MC. )
1 0 2 e I 0 1. 1.
Where: Q = the quantity of electricity consumed at
the old price (P).
= the quantity of electricity consumed at
the new price (?)•
Qi = the quantity of some other commodity whose
0 cons\imption depends on the price of elec-
tricity, at the initial price of electricity.
= the quantity of this other commodity at
the new price of electricity.
Pi = the prevailing price of the other commodity
1 .
MC. = the marginal cost of the other commodity i.
The first term in the expression above represents
a measure of the change in economic efficiency in the elec-
tricity market itself. The second term provides a "second-
best" correction by summing the second-best effects over all
commodities, i, whose demand is affected by the price of elec-
tricity.
For example, if all other commodities are priced
at marginal cost, the second term disappears. If the
original price were less than marginal cost and were changed
to a price equal to marginal cost, the value of the first
expression would be positive (a negative times a negative).
If, on the other hand, there were some market, i, where
price was less than marginal cost and which was a substitute
for electricity, the effect of increasing the price of
-123-
electricity would be to increase consumption of that commodity.
The second term would now be negative and the sign of the
entire net benefit equation ambiguous. It would be necessary
to have more detailed information on the relative sizes of
the price responses in the electricity market and its comple-
ment market and the size of the deviations of price from
marginal cost to come to a definitive conclusion. Other
situations involving complements or prices greater than
marginal cost can be analyzed in the same way.
Primary practical concern about second-best prices
has revolved around the relationship of oil and natural gas
prices to their marginal costs. With empirical information
about the price responsiveness of oil and natural gas con-
sumption to electricity prices and the relationship of price
to marginal cost, the net benefit equation could be used to
indicate whether or not a particular movement increased
economic efficiency and also to search for an electricity
price that maximized the net benefit equation.
In conclusion, second-best considerations may corn-
plicate pricing policy, but they do not make rational pricing
policy impossible. By using the net benefit relationship
above, it should be possible to get a fairly good feeling
for whether a price change will make things better or worse
and also help us to zero in on an optimal second-best price
for electricity that accounts for distortions elsewhere.
-124-
E. The Revenue Gap. and the Least Distortion Rule
The critical problem in the acceptability of mar-
ginal cost pricing has been the treatment of the revenue
requirement/cost gap. In most cases, revenue requirements
will fall short of or exceed the revenue generated if all
prices are set at their appropriate marginal costs, and
adjustments will have to be made. It may be helpful first
to review the genesis of the gap and the size of the adjust-
ment, before discussing how to treat it.
In the economic literature, which deals mainly
with marginal costs in relation to the scale of production,
great attention is paid to the effects of economies of scale.
In an industry which exhibits economies of scale (or what is
the same thing, decreasing costs), the marginal cost of each
successive unit will be below the average cost per unit for
the system as a whole. This leads to pricing questions
centered around the idea "if price is best set at marginal
cost, who will pay the overhead?" This question led, in the
1930s, to a revival of interest in marginal cost pricing
theory when Hotelling"9 suggested, with reference to tolls
on New York city bridges, that price should indeed be set at
marginal cost (which he assumed to be zero or, anyway, very
Harold Hotelling, "The General Welfare in Relation to
Problems of Taxation and of Railway and Utility Rates,"
Econometrica, 1938, pp. 242-268.
-125-
low). His answer to "who should pay the overhead" was that
taxes should be raised to pay it.
This solution aroused copious discussion, but was
not generally accepted as feasible: some utilities, however,
proposed that where economies of scale and technical progress
were reducing marginal costs, it would be feasible and econom-
ically efficient to offer service at marginal cost for those
customers with very elastic use; in electricity, this was
especially relevant for uses which were in direct competition
with other fuels. It was essentially the policy which had
been followed when the electric industry was vying for indus-
trial consumers whose alternative was self-generation.
(Although some "promotional rates" probably were set below
marginal cost, most utility managements realized that they
could not long survive with a growing load which did not
cover its marginal costs.) Electric heat rates based on
(lower than average) marginal cost were supported, because
electric heat was assumed to be elastic compared with basic
lighting use.
However, it is not clear that, had marginal costs
been systematically calculated during the period when average
costs (in the economists' sense) were declining, revenues de-
rived from marginal cost rates would have resulted in a rev-
enue deficit despite the contrary assumption by academics.
This is because the revenue requirements as calculated by
commissions have no logical or theoretical relationship to
-126-
the economists' definition of an average cost. The revenue
requirement is based on the history of the company and on ac-
counting practices which have no necessary relation to the
principles of economics. The average cost concept as used by
the economist is essentially the answer to the question:
"How would average costs vary with scale if electric utility
systems were constructed de novo today?" It is therefore im-
possible to make a general theoretical statement about the
relation of historic-cost-based revenue requirements and mar-
ginal costs.
However, in empirical work done in recent years,
there appears to be a strong though not universal tendency
for revenues which would be derived from marginal cost rates
to exceed the revenue requirement. The old (academic) prob-
lem of what to do with the overhead has reversed itself into
the practical problem of what to do with the excess.
This tendency seems to be derived from three major
sources. First, although the electric utility industry is
undoubtedly characterized by economies of scale, recent econ-
ometric studies indicate that most large firms have achieved
the scale level at which there are few further scale economies
to be made. Second, the effect of environmental controls has
been to increase the costs of new plant. Third, the effect
of price increases in capital, labor and materials for new
plants has been to raise marginal costs faster than the his-
toric cost rate base.
-127-
Let us consider the effects of inflation in greater
detail. The effect of inflation is clearly to raise the money
cost of plants from year to year: this would not in itself
mean that marginal costs would exceed revenue requirements,
except for the fact that depreciation policies have been
fundamentally erroneous from an economic point of view.
Depreciation in an economic sense should be the
contribution made by the users in a given year for the use
of a machine in that year, and should therefore reflect the
change in value of the asset over the year. When technology
is moving fast and new improvements reduce the cost of re-
placements, the value of the asset will decline fast. If,
conversely, prices of new equipment are rising, then economic
depreciation may in fact be negative: the economic value of
a machine may actually rise in a particular year. If the
economic value were correctly stated on the books, the gross
return on the net book value plus the variable cost of operat-
ing the old plant would produce a cost of service exactly
equal to that of a new plant. This would then eliminate most
of the revenue gap.
In periods when inflation is pushing the reproduc-
tion costs beyond the historic cost, and when old plant is
nonetheless depreciated on the books by straightline methods,
marginal costs are likely to exceed revenue requirements
based on original cost. The revenue requirements are based
not only on current expenditures for fuel, labor, etc., but
-128-
also on those depreciation schedules which overestimate the
loss in value early in the life of the plant. The resulting
valuation of the rate base on which return is earned is a
hodgepodge of variously depreciated properties bearing no
relation to current value. It should surprise no one that
revenue requirements will almost never equal marginal costs,
and will generally be below them 5° in periods of inflation.
The reverse is true in periods of technical progress.
Inflation also has one further effect. The bonds
which were sold at 3 percent when there was no inflation
are now holding down revenue requirements, because interest
rates have since risen to include an inflation premium.
Marginal debt prices are above average historic debt prices.
The same is not true of equity capital since the regulatory
process permits the return on old equity to equal the rate of
return on new equity. These then are the sources of the gap.
What is the best way to meet it?
The rule for economic efficiency is that marginal
prices be set at marginal cost. If there is a revenue
constraint, the general rule is that price adjustments must
be made so as to distort demand patterns the least. If a
particular quantity (q c ) of a commodity would be purchased
° Because of the very high revenue requirement in the early
years of plant service, a small company adding a large
plant, particularly a nuclear plant, may find its marginal
cost below its revenue requirement.
-129-
at the marginal cost price, then the second-best solution
is as follows:
The rate should be set so that the con-
sumption taken under the new rate (the
second best rate) for each category of
service is a uniform fraction of the
amount of consumption (q] that would
have been taken in each category had
the marginal cost based rates been set.
The rule is credited to Frank Ramsey in
Economic Journal of 1927. Notice that the general rule
looks at quantity departures from the optimal rather than
directly at price departures.
It is evident that the degree to which the quantity
consumed will deviate from the first-best solution (qu) for
any given deviation of price from marginal cost, is dependent
on the degree of responsiveness of the demand in question to
the price of the commodity. It is the "degree of responsive-
ness" which economists call "elasticity." Demands which
respond most readily to price are termed "elastic," while
demands which remain roughly constant in quantity irrespec-
tive of price are termed "inelastic with respect to price."
If a demand is totally inelastic, then the quantity consumed
is independent of the price.
Baumol and Bradford, in a later article, showed
that if cross-elasticities of demand between products were
zero, then the rule (a special case of the Ramsey rule) be-
came the "inverse elasticity rule" of setting prices in dif-
ferent markets so that their departure from marginal cost was
-130-
inversely proportional to elasticity of demand in those mar-
kets.5
Returning first to the basic Ramsey rule, there is
a first-best way which is theoretically appropriate for meeting
the revenue constraint. If the excess can be redistributed
in a way which has no effect upon consumption (eccept indi-
rectly through income effects but not substitution effects),
the first-best condition is met. There is, in fact, a the-
oretical way to do this by means of what are called "lump sum
payments" or payments which are totally independent of the
electric price.
Forgetting the political or practical constraints,
first-best solutions from an economic efficiency point of view
might 'include (in no particular order): energy stamps for the
poor, customer dividends independent of consumption levels,
construction funds for the utility, contribution to local govern-
ment or a lottery. An interesting alternative was recently pro-
posed whereby large customers are rebated based on their con-
sumption of three years previously. This avoids the "inequity"
of the "dividend" option above, where the 250 kilowatt-hour cus-
tomer gets the same rebate as the 250,000 kilowatt-hour consumer
--some size factor is introduced but with sufficient uncertainty
to remove it somewhat as a factor influencing current consumption.
W. .1. Baumol and D. F. Bradford, "Optimal Departures from
Marginal Cost Pricing," The American Economic Review,
Vol. LX, No. 3, June 1970.
-131-
Very few conunissiorts would feel free to fully adopt
these prescriptions without legislation, although some commis-
sions are working under legislation which mandates or permits
"lifeline rates," or construction work in progress (CWIP) in
the rate base, either of which has, at least to some extent,
the same effect.
Recognizing that the first-best solution (first-best,
that is, from an economic point of view) is probably impracti-
cal, at least, at the present time, we have to examine how ad-
justments can be made in the rates to follow as closely as
possible the prescription that q mc be maintained. In the case
of an excess, some rates have to be reduced below marginal cost.
The governing principles are examined in this section: the
practical applications are found in NERA's report on Topic S.
In order to meet the goal of minimum deviation from
we return to the optimal departure from marginal cost rules
of Ramsey and Baumol and Bradford. We find that we should reduce
the price of all demands, but more for those with the least
price elasticity (including all "cross-price" effects), and less
for those with the greatest price elasticity. "Price closest to
marginal cost for the most elastic demands," is the shorthand
form of the rule.
The rule as it stands is very general. Should we look
for a class of customers whose demand is inelastic with respect
to price, or should we look for a type of use which is inelastic
with respect to price, or are we talking about an element of the
bill?
-132-
We remind ourselves that all three have been used
in the history of ratemaking when the question was who should
pay the overhead. The industrial class was considered elastic
because of the potential for self-generation; the electric
heat class was considered elastic because of competition from
other fuels. These two classes were at certain times afforded
the (low) marginal cost precisely because the quantity sold
was assumed to be very sensitive to the price. Conversely,
the early blocks of the rate were considered to represent the
inelastic load, and the higher early block charges represent 1;
an effort to recoup the overhead from the least elastic de-
mands. This is consistent with our general rule that adjust-
ments be made so as to affect the amount (qm) the least, and
it has been good business practice for many years in competi-
tive business, where it is known as "charging what the traffic
will bear."
When the question is not who will pay the overhead,
but who will benefit from the excess, the general rule remains
the same; adjust so that the quantity demanded remains as
'close as possible to
Suppose we investigate the elasticity of classes of
customer. There are several pitfalls here. Are we interested
in the elasticity of consumption after the decision to take
service has been made, or before? Is the locational decision
of industry a relevant part of the elasticity? When
-133-
investigators measure the price elasticity of electric demand,
they find the following as general orders of magnitude:
Residential -0.5
Commercial -0.5
Industrial -0.5
Industrial, with
locational effect -1.0
The locational effect is the tendency of industries with high
electric use to congregate in an area of low electric prices.
This effect tends to mask the response to smaller price dif-
ferentials once the location decision is made, and, therefOre,
corrections are made to isolate the effects of price changes
on industry already located.
The locational effect suggests that industry is quite
sensitive to the total bill, although, having located, the
effect of the price on total amount consumed may be about the
same for industrial consumers as for other users. Which is
the correct elasticity to use in applying the inverse elas-
ticity rule in one jurisdiction? The answer is not clear.
The same type of problem arises in looking at the
elasticity of various types of use. On a priori grounds, we
may suppose that when other fuels can substitute for
electricity in a particular use (principally heating and
water heating), elasticity of demand for electricity will be
greater than when there are no close substitutes, as in
lighting use, for instance. But this again is a total
bill elasticity. Once the decision is made to use electric
-134-
heat it is not clear that the quantity used is more or less
responsive to marginal price than is lighting use.
Thus, the application of the inverse elasticity
rule to classes of customer or even types of use may become
quite problematical.52 This is true conceptually as we have
shown. It is also true empirically, since the measurements
of elasticity still carry a fair margin of error and a class
of customers will be comprised of consumers with many differ-
ent characteristics.
The alternative is then to look at the elements of
the bill and use the basic concept of a lump sum payment as
discussed above, but one which is applied in the rate rather
than one which does not reduce rates at all. Let us be clear
what "the lump sum payment solution" is, when the lump sum is
attached to the price, rather than, say, distributed as a lot-
tery. If the cost structure is $X per kilowatt, $Y per kilowatt-
hour, and $Z per customer, the rate structure then appears as
follows (in very barebones form):
$X per kilowatt
$Y per kilowatt-hour
$Z per customer
Less $L per customer,
Subject to no bill being less than zero.
There is a further, slightly more obscure reason for the
conceptual problem. Strictly speaking, in order to cal-
culate departures from the first-best q, we need cross-
elasticities of demand also. Baumol and Bradford assume
them to be zero, but particularly when peak-load pricing
is introduced, this assumption will not be valid.
-135-
What are the advantages to this approach? The main
advantage is that it retains the marginal price at marginal
cost. The extra unit of consumption will always be priced at
what it costs the utility to provide it, with the economic
efficiency advantages we described earlier. The economic
effect of the rebate of $L per customer is the same as if
we had increased the customer's income; the effect will pre-
sumably be spread through consumption of many goods and ser-
vices, and will therefore have less tendency to raise q mc
than if the excess revenue $L were used to reduce the $X per
kilowatt or $Y per kilowatt-hour. In other words, we assume
that consumption is less elastic with respect to a lump sum
refund.
It can be seen that there would be several possible
ways to affect this rebate in the rate structure. If $L (the
rebate) were less than $Z (the customer charge), then the
customer charge could simply be rebated. If, however, $L were
greater than $Z, it would be necessary to reduce the price of
the early blocks of kilowatts or kilowatt-hours below the mar-
ginal cost. This would look like an "inverted rate."
In some utilities, it will be the case that if the
customer charge component of the rate were rebated, then the
revenue gap would be almost entirely eliminated and this is
a solution which has been recommended by some experts. It has
the effect of treating the basic distribution system as a public
-1.36-
utility, similar to the highway network, financed by general
taxation.
There may, however, be problems of equity in this
approach. The "customer costs" are an equal division among
all consumers who use the distribution system of the joint
marginal costs of distributing a minimum amount of electric-
ity. If only customers who use the distribution system are
"forgiven" part of the distribution system costs, while all
customers are charged marginal costs for kilowatts and
kilowatt-hours, the revenue responsibility balance as between
consumers is affected. All rates are raised to marginal cost,
while only those customers using the distribution system are
rebated the system excess revenues.
It must be stressed that this is not an economic
efficiency problem, except in a broad sense. The alternative
is, of course, to allow the rebate $L to apply to all consumers,
whether or not there is a lump sum element ($Z per consumer)
in the usual rate form for that class of customer. If there
is no customer charge in the rate, the early blocks may be
reduced.
If all consumers were fairly similar in size, the
flat rate rebate, by treating everyone equally, would provide
a reasonably equitable solution. We have, however, the fur-
ther problem that consumers differ vastly in size, and while
a $10 rebate might represent more than 50 percent of a resi-
dential bill, it would be no more than a drop in the ocean on
-137-
an industrial bill. Therefore, the suggestion may be made
again, on equitable rather than economic grounds, that all
classes of customers participate in the revenue excess in pro-
portion to their total bills, and that rates be constructed
to reflect a rough proportionality. A full proportionality
is self-defeating. A 10-percent rebate on the bill, for
instance, simply reduces the marginal price 10 percent, but
relating rebates to wide-size brackets reduces the "inequity"
of lump sum payments.
In the final analysis, there is no single answer to
the question of who should get the "economic rent" which accrues
from unanticipated inflation and changing environmental regula-
tions. The question of how to dispose of it is, of course,
of great importance, particularly to the people who stand as
potential recipients of that rent. among those, we might name
the stockholders of the company, the bondholders of the company,
the management of the company, the industrial consumers, the
commercial consumers, the residential consumers, the government,
etc. As the economic rent becomes larger, the significance of
who gets the rent becomes more and more important.
Under marginal cost pricing, the rent is explicit and
the means of dividing up the rent is a matter for discussion
and decision by the commission using certain well defined eco-
nomic concepts for guidance. If an alternative method is used
which automatically conforms the proposed rates to a revenue
requirement, that rent is there, nevertheless, and that rent
-138-
has been divided up between the consumers by some method which
is not explicit.
ATTACHMENT A
Attachment A
A simplified model
Of
timemofmday/seasonal pricing
The theory of marginal cost pricing posits that the
price charged for electricity at any time should equal the
cost of providing a small amount more, or the savings from
providing a small amount less. Since in a complex system
with a cyclical demand there are different costs at different
times, we have to find a way to estimate the different costs.
Fortunately. the engineers got there before the economists
and produced a variable technology adapted to the variable
demand. The technology permits different equipment to serve
demands of different durations, and by simulating the
planning process by which equipment is chosen, it is
possible to derive the conditions for a minimum cost system.
If the marginal cost principle of pricing is then applied to
this simplified system. we can lest various hypotheses about
the relation of revenues to costs under marginal Cost pricing
we can examine the fairness of charges to consumers with
different load patterns we can show how different load
patterns vary in cost and how growth affects cost.
The following theorem and corollaries snow in a very
Simplified and schematic way how a kilow3tt•hour pricing
scheme based on marginal Costs for each hour of the
year wtU:
1.Cover total costs. in fact, exactly equate revenues
with COStS.
2.Be equitable to particular types of consumers.
Tne proposed pricing rule is that the price to be
criargoa for ea:n ictowalt producec ti a given hour Ct the
year ShOuld te the hourly running cost of the last machine
on line at tnat point, plus an amount equal to the annual
cost of one kilowatt of peaking capactty. charged tor the
peak hour only ITO be a little more realistic, since trie exact
hour of me peai is unkno.vn. the annual capital cost of the
next ki'owa:t is spread over all trio hours wrien the peak is
equally ltkt', to occur.)
The theorem is proven for a Schematically simple but
represer.tat;e system con:a?nIng three plants. This system is
assumed to have ceert designed to minimize me cost Of
meeting an a ;anousty CetermneC load curve. This
assumption is important since it gives trio conditions unce:
whict. the pr.c:rig rule produces revenues which exactly
cover trie cap.:a and running costs of tne system All the
proofs in th.s paper refer to this opt-mat system.
We are entirely aware that the real world has systems
which are tesa fl-an optimal. and that thiS simplified model
can only be of limited app!:Cation Nor will marginal costs
eiactly equate with total coStS when technocat progress,
inftaf:ori and other factors are introduced. Nonetheless, it has
proved heptuf in analyzing nonoptimality also, and is
presented as a conceptual 1301
THEOREM
Rule
In an opt.mally planned system prices should be set
equal to me marginal cunning cost at any given hOur plus
the capital cost of meeting I extra Kw of peak demand
cha'ged at the peak hoUr only.
Result
The revenues, so obtained will exactly equal the annual
capital Costs plus the annual running costs 01 the system.
Proof
Let tt-.e to'towing symbols be used in a syStem with
3 plaiut types available
Annual Hours/
Capital Running Year
Cost Costs Running Kw
$/Kw $;Kwh Time Capacity
Peaking
Plant X x a A
Cycling
Ptant V y a+b B
8a.etoad
Plant 2 z a'b+c C
Total running time lii a b • c - 8.750 hOurs
Totalcapaoty K-A+8C
II X. Y. Z. x. y. z are g;ven. t can be shc'.vn that in an
optimally p!anrutd system. tria prices 0010w eal g,,-.e the
required revenues.
Peak hours: a hours at (x ,. X 'a) S t(wh
Middle hours: flOurS at v S' i(wh
Low hOurs: c hours at z S '<wfl
This is true whatever me vatuOs of A 5 and C.
1 Cond't;o".S for an otmzi system

Total costs X+xh I ICy: of
capacity
y L

2 I

a a
a h. b hi
Use peaking plants when
X+xh<Y+yh
Since X. Y. X. y are known
I)
Then A is determined by the load curve and the value of a
Similarly, use Cycling plants when
Y+yfl<Z4'zh
2)
Y+yh
Z4' zh
c Hours
-3-
Then B is determined by the 10CC curve and Inc value of (3b)
2. it plant has been optimized, and price has been set
according to rules set Out above, revenues will equal total
annual capital + running costs
Revenues
Period
in WliCh
Marginal Plant
Machine is: in Use Output Price Revenues
PeaKngunil A..B-C
Cycling Unit B • C (B • CV Y (B + C)by a
Basaioad Unit C Cc Z Cez
!Rivenues
Costs
Annual Hours Running Total
Capital in Kwh Cost Running
Costs Cost $ Use Generated per Kwh Cost
Pe3'ng
pla-t AX a As x Aax
Cycling
plant BY a+b B(a - b) y $(a4b)y
Baselcad
oiani CZ 3-0C C(a+o.c) z C(a-D'C)Z
. Cao'tal . Running
E tevenues - E Running i. r Capital
iA.C.Cijii..Xa).(9.C)D,.CU. aa.ela.si ,Ca ,o.ca.Al.DY.CZ
6*.c.8.Ca4-Ct. e .CZ.8,.c4i.CU 3)
In 1) above
then X - Y-a(x-y) . . .4)
In 211 above ' a + b
then Z(a4by2)+V ..,5)
Substituting from 4) and 5) into 3)
a.cnv.aft.11.Ie. .c•co• fiv.CV.Ct.i.i,IIy.fl. ø.v.cu.Co.
Rearranging and cancelling common terms
BY + CY + Bay + Cay Coy .-IBY 's. CV + Cay + Cby + Bay
QED
Relative costs determine optimal running hur$ and Price
Total costs I Kw of capacity
S
{Yf _________
vr:
a III C Hours
Load cusve and hours of use determine quantities
of equipment and revenue
Kw( x (x+ ) $ per !(wh
Ak0 per Kv1h
B 0
erKv,h
i ia a
a b C flours
Note:
I. The result is independent of the fn3gnatuoe of A. B wtc
C and Of Mott total. The Kw capacity of each type of
machine depends only on tne load cuive.
2. The optimal hours 01 running oacn class of mjchuu.
depend only Only on inc retalive costs
3. The assignment Of capital costs to me bouts when Inc
peaking machine is used. and equally Over thoSe hours.
is arbitrary.
The cute more rigorously defined is mat each kilowatt
hour should be charged (the probability at failure) x (the
cost of the next Kw to meet the failure)
This may -mean sprcadng the caoitaf cost of inc
Kw over more hours of the year. or ieiver However, if
peaking cnarges covet too few nOws a new peak may
POP up.
Corollary .A
•A user who has a flat load curve and used M Kwh hour
continuously throughout inc year will- be paying exactly
his lair share.
For if his demand flaø been met by add;tion of a
basaload plant with M Kw capacity
Fair Share Cost - MZ - M(a - o - cz
Actual Cna';es. M(a(x'+ X a I by - cz)
This is lair if
MZ-i Mat Mat-' Mcz .- Max • Mby - MCZ - MX .6)
In
fn.2) above!-- a. b
Adding 1)'-.2'Z-X u.:ax-r.by-az-bz .7)
Substituting in 6) from 7)
MZ Mat 'Mz.+ MCZ - Max - MDy• MCZ • M(2-ax-by at • bZ)
Cancelling common terms
MZ-+ Mat..' Mbz-i. Mcz- MZ + Mat Mbz Mcz OED
h
Hours
Corollary 8
U two firms differ only ;n their load curve cbatacteristcs
with the difference Only in the bottom of me load curse. it
can be shown that the same pricin; rule yields each firm
sufficient to cover its COStS.
Kw It use
B'
C
Cs
S has mote baseload need than S and consecuenI,
installs C Kw of baseload and S Kw 0' :n:erme'ate Want
where $ instals C° and 8' respectively
The difference in capital and runring costs between
the systems wilt equal the difference in revenue unaer the
pricing system.
For the shaded reclangle
Costs S-S' difference in capital costs difference in
running costs
(C-C')Z + (8-87 (C-'C')z(a 'e b + C)
+ ($-B')y(a 4 b)
Si
Revenues S-S' - (C-C')cz
Since C-C' - -(8-81
and Z-V - (y-zXa + b) from I)
In 8) Costs S-S (C-C')Z-Y + at + bz + cz-ay-by)
- (C-C1(a + bxy-z) - at + Ba + C2-ay-byj
(C-C')cz
Revenues S-S' OED
Corollary C
The fuel savings from the baseload and cycling plant
Quiet part of the capital cost at the piant so that te net
cost per Kw is equal to the cost of the peaking plant.
In other words
Go
Hours
Kw
Hours
-5-
Capital cost of peaking plant
- Capital cost of Cycling plant less tuel savings from
running the cycler rather than the peaker.
- Capital cost of basetoad plant less fuel savings from
running baseload rather than the cycler and the peaker.
Proof
In
X - Y-&(X-y) CEO
In 2)E - a+b
Adding 1)4.2)
X - Z-a(x-z)-b(y-z) OEO
Corollary D
As a system grows, if its configuration is optimal at
the becjnnrig and end of the growth. the revenues from the
growth w;tl equal the COSt of the growth. This is true for
oven or uneven growth.
1) or even growth of G Kw in each period
These are equal if
G(Z+(a+b+cIz)-G(az+by.cz+X) .9)
from 7) Z-X - by-aE-Dz + ax
Substituting in 9) G(Z + (a + b + c]z) - G(Z + ax bZ CE)
2) For uneven growth of C. G. 0 at peak. intermeaiite
period and oll.peak
Kw 11m a in sog
LI
System before growth System alter growth
Peaking plant A Kw A Kw
Cycling plant S Kw S Kw
hlaseload plant C Kw C+G Kw
Cost of growth ' G(Z + (a + b + cjz)
loimnues from growth G(a(x 4 by + CZ)
System before growl System after grown
Peaking A A... G -G
Cycling S S+G-G
Baseioad C
Total Kw A+8'-C A-B+C-G
Cost of net growth in peaking caacty (0 -CXX - ax]
Cost of net growth in cycling ceacrty - (C -G )(V - a -
Cost of net growth in basetoad caac:iy C 112 (a b + cz,
Revenues from net growth -C3a(x -) - G.by -G cz
Costs equal revenues if
(G-G.)(X + ax) + (G -G.XV (a + bjy) + G(Z + a + b cJa)
G.a(x .1. ) + Gøy + G.cz
G.(X+ ax) .s.G.(Y •p(a... b)y-X-ax] G(Z .a b .c)i-Y-(a' b)yI
- G.a(x +) + G.by + G.cz
Since Y-X - 3(x-y)
Z-Y - (y-z)( t b)
G.(X + ax) + Gby + Gicz - Ga(x +) + G.by + Gcz OED
This means that the cost of growth in each period and in
bral are equui to me running costs in each hour plus thO
COSt of the peaking plant.
-6-
Corollary B
A consumer who uses only off-peak power should not
be charged any capital Costs, only the running cost.
Corollary F
But what if the consumer requires all his oo.er at
the peak? Then charging him the Capital costs cove's tne
incremental Cost to thO system.
Kw
Kw
lithe off-peak consumer did not exist then tne system
configuration wou'd be different The net total cost to the
system of the changed conhgura:ion is equal to the running
cost in the oflpeak hours. or Ccz.
Proof
lithe consumer had not existed. system would have
been
A Kw Peaking
(B C) Kw cycling
0 basetoad
Cost without him - AX (B i' C)Y + Aax + (8 + CXa + b)y
It the consumer now exists. and the system as teoptimszed
Cost with him .AX+BY4 CZ4Aax'a-B(as b)y#C(a+b+c)E
Difference In costs with him and without him
-CZ-CYr(a+bi c)z-C(a+b)y
CZ-CY + C(aZ 4 bz 4' cz-ay-by)
- CZ-CY-C((a + bXy-z) c:)
- C(Z-Y-Z .1' Y) + Ccz
- Ccz
This is what we ask him to pay.
System w.moui l"im -B- C
$ystsu wdfl awn - • B • C
System costs minoui him -9Y.CZ-Ba-a,y-Ca.o-:::
System costs ,am him ' AX -BY - CZ • AA* - -027 - -: •
Oittetencc m sjsiem costs - AX • - Aaii .X.a
This is What we ask h:m to pay.
ILLUSTRATION
ILLUSTRATIVE EXAMPLE TO DEMONSTRATE
THAT BY CHARGING THE CAPITAL COST OF
PEAKING CAPACITY DURING PEAK HOURS. THE
RUNNING COST OF PEAKING CAPACITY DURING
PEAK HOURS AND THE RUNNING COST OF THE
MARGINAL MACHINE AT OTHER TIMES, THE
TOTAL COSTS OF AN OPTIMIZED SYSTEM WILL
BE RECOVERED.
ASSUME:
I) A System whose load duration profile permits
each type of production plant to operate the
optimum number of hours (The optimum number
of running hours (Or any plant is that number of'
running hews beyond which some other type of
plant would operate at 0 tosser total cost)
ma
2)The lotiowing symbols are used
Peak. Base.
ing Inlet. load
Capital $ Kw P I S
Annual cnacge °.i AC. AC AC.
Running COStS $ Kwh p i b
Hours of running time h. h; hi
System cofl'iguraison (1(w) K K K,
3)In thuS eampie me f011OWi.1g values. approximating
those of an actual utility, are taken
Peak- Base-
ing That load
140 300 500
209b 15% 1546
.03 .015 .004
.2 .3 .5
A. COMPUTATION OF OPTIMUM RUNNING HOURS:
1)PEAKING CAPACITY
SP(AC.) + Sp(h ) - Sl(AC) Si(h).
S;ve for to -
Sp(h.)-S.(h) - SI(AC )-SP(AC.,)
h' j-SP(AC.
Sp-Si
Substitute te assumed costs
Pr S300( 15)-$140(.20)
-

$.03-5.0*5
11 33 nrs. $015 .015
2)INTERMEDIATE CAPACITY
SI(AC) Ss(h) S3(AC-) + Sb(1)
Solve br h -
SICIr. )-Sb(h ) - S8(AC.)-Sl(AC)
Pr - Si-Sb
Substitute the assumed costs-
Pr S500( ! 5)-329(..i $01 5-5.004
h. •S75445f :01* -2727 Pus.
3)BASELOAO CAPACITY
Baseloud cunning tiour - 0.760 hrs.
B.REVENUES ARE RECOVERED
With prices set equal to cunning costs 01 the margri.
machine 13C. 1.5c. 0 44 per Kwh] in eac'i period. )iuS a
capital component equal to the cost or 1 Kw of peaking
capacity, the total costs are recovered,
COMPUTE TOTAL ANNUAL COST
1Kw
I33}(S.o3;(.2)ss2.4o
o.exw
P17
NTEAMISDlATEE30.I5)c.3)4.272?IS.0lS)c.3)sH 77 0.5Kw OMA
IASELQAO=SSOO(, ISK.5) .87S0(S.004)(3)555.02
11331irs. 2727hr$.
TOTAl. ANNUAl.. COST=s12,40+s25.77,s$s.02593. Ii
COMPUTE TOTAL ANNUAL REVENUES:
1Kw
o.sr.w
WI
LSKw .
(I700-2727flL004)(.5)=S 12.07
is w 11331i*S. 272 7hrs. bi
TOTAL ANNUAL REVENUESS61.99+$19.1 3+S$2.07St3.19
C.A 100-PERCENT LOAD FACTOR CUSTOMER IS
FAIRLY CHARGED
Using the values in the fllus:raIicn. we show we CC
percent load factor customer pays rus lair share uncar
marginal ccst pricing.
If the 100 percent toad factor consumer were ao
the system would need to add a baseload unit at a cc.ci o
$500 (,1S)+8.760(004)- $110 per year
Under marginal cost pricing ho would pay:
$28 (spread over the peaking hours)
+ $0.03 x I • 133 (peak running time)
+ $0.015 x (2.727-1.133) (intermediate running timeS
+ SO.004 x (8.760-2.727) (off-peak cunning time)
-$t tO per year
This can be shown to be Jtuo for all opl.rnnl syskut
Capital S Kw
Annual Charge %
Running costs S. Kwh
System configuration
(I Kw System)
-8-
$0.03
I Kw
S

S0.015
to F a
1,133 2,727 8,760
Hours
D. THE OFF-PEAK CONSUMER PAYS ONLY THE
RUNNING COSTS
It the off-peak consmoc did not exist. ne system
would have mere intarmeia:e ceoactty an tess oasooa0
capacity The off-peak coner causes a re;Acement of
intermediate capacity wh basetoad c.ac:;y whth has a
higher capital cost and a lower operating cost. ThiS is the
only difference to System COStS
1 Kw
Hours
Taking costs for ShaUnd area only
Total cost of plant optimized with off-peak consumer
-5500(15)+8.760(.004) .sito
Total cost of plant Optimized with3ul off-peak consumer
- S300(. 15)+ 2.721(015). S85.9
Dillerence - $24.1
Olt.pcak Ct3IJiS ploposc!d for oll.peat. consumer
- $004 x 6.033
$24.1
ATTACHMENT B
Attachment B
THE "TURVEY CALCULATION"
The "Turvey calculation," or the "moving forward/
moving backward calculation," has crept into marginal cost
folklore because Dr. Ralph Turvey of England, formerly
economist to the Electricity Council, performed such a cal-
culation to determine the marginal cost of capacity at a
seminar held at Wisconsin Power and Light in 1975. It appears
to have been adopted by Charles Cicchetti of the Wisconsin
Energy Office, and also was adopted at one point as an alter-
native formulation by NERA,2 with the caveat that it should
only be used for an optimal system. NERA has since had
second thoughts about using the computation at all.
The "Turvey calculation" is never carefully speci-
fied in any of Turvey's published work. F.urthermore, Turvey
himself disavowed the calculation as "his method" in cross-
examination in New York. 3 This paper is an attempt to trace
through Turvey's thoughts on measuring long-run marginal cost
to see where his "moving forward/moving backward calculation"
We have benefitted greatly from Dr. Turvey's published work
and numerous discussions with him over the past few years.
The discussion that follows deals with a relatively minor
point that has caused a great deal of confusion, but should
not be taken as a general criticism of the important contri-
butions made in this area by Dr. Turvey.
Leo T. Mahoney, "Cost Analysis for Use in Peak-Load Pricing,"
Testimony before the New York Public Service Commission,
Case No. 26806, August 1975.
See the cross-examination of Ralph Turvey before the New
York Public Service Commission, Case Nos. 26806 and 26887,
Tr. J-694 to J-696.
-2-
comes from. Turvey's ideas are developed in two publications:
first, in his book Optimal Pricing and Investment in Electric-
ity Supply' and, second, in his June 1969 The Economic Journal s
article.
The simplest and most straightforward definition
of long-run marginal cost is given by Turvey on page 44 of
his book:
Long run marginal cost, in present worth terms,
is simply the present worth of all system costs
as they will be with the increment in load which
is to be costed, less what they would be without
that increment.
A somewhat different but related definition of
marginal cost appears on page 289 of The Economic Journal
article:
That is to say, marginal cost for any year
is the excess of (a) the present worth in
that year of system costs with a unit perma-
nent output increment starting then, over (b)
the present worth in that year of system costs
with the unit permanent output increment post-
poned to the following year.
The two definitions are essentially the same as
long as there is no secular cost-saving technical change.
The second definition is applicable if there is such techni-
cal change because it recognizes that marginal cost will
change over time--specifically that it will decline.
' Ralph Turvey, o ptimal Pricing and Investment in Electricity
Supply (London: George Allen and Unwin, Ltd., 1968).
Ralph Turvey, "Marginal Cost," The Economic Journal,
Volume 79, No. 314 (June 1969), pp. 282-299.
Recognition of of the basic correctness of this approach leads
to the Turvey/Boiteux treatment of annual charges outlined
earlier in this report. (See Section IV-B.)
Operationally, the two rules provide a straight-
forward procedure to follow for estimating marginal cost.
You look at your system expansion plan given your current
expectations and then replan the system given a load incre-
ment. In the first definition the load increment is thought
of as an exogenous but permanent increment in system load.
In the second definition you could think of the load either
in this way or as advancing the demand profile for the system
one year and replanning accordingly. You then compare the
present worth of system costs with and without the load incre-
ment. This gives a measure of total marginal costs, not just
the marginal cost of capacity.
It should be noted at this point that the actual
"Turvey calculation" employed in practice satisfies neither
of these definitions. It seems to be based primarily on the
second definition of marginal cost and the associated develop-
ment in The Economic Journal article. The calculation done
by Turvey in Wisconsin for a Wisconsin Power and Light seminar,
and also espoused by Cicchetti, is to move forward the supply
side of the expansion plan, but not the demand side of the
expansion plan. The expansion plan is moved up one year and
the difference between the present discounted value of future
costs under the prevailing plan and the plan moved up one
-4-
year is calculated given the prevailing demand forecast.
The proponents would argue that this then gives us a
measure of the (annual) marginal cost of capacity for the
system. The logic here appears to be that by not also ad-
vancing the load one year you can net Out the marginal
energy costs and have only the marginal capacity costs re-
maining. This is not, however, demonstrated anywhere in
Turvey's writings.
The Economic Journal article is often cited as the
source of this "Turvey calculation." While most of the arti-
cle really seeks to develop the second definition of marginal
cost, the so-called calculation itself may have arisen as a
by-product of the exercise performed on pages 292-295 of the
article. Although on the surface this appears to be a proof
of some sort, it really is not. The discussion there recog-
nizes that we will be indifferent between replacing an old
machine with one year of life left, this year rather than
next year, if the running costs of the old machine for the
year are exactly equal to the total costs (properly discounted)
of adding and operating the machine now rather than next year.
It is simply asserted then that the total cost of adding and
operating the machine now rather than next year is the mar-
ginal cost of an additional unit of output this year. All
that has really been done here is to put his definition of
marginal cost (second definition) into symbols.
-5-
It may be instructive to compare the explanation by
a French writer, Caill&, which clearly envisages a thought ex-
periment involving one kilowatt added to an optimal system.
The requirement that production facilities be
in line with the consumption forecast then leads
to the following property: advancing the intro-
duction from July 1, 1976, to July 1, 1975, of
an increase in capacity of one kilowatt, by the
type of facility then being used to augment
generating capacity, produces a balance in the
budget. On the other hand, the advancement is
associated with a fixed cost which includes
financial charges, depreciation for the first
year of existence, and fixed operating costs.
In addition, fuel costs must be taken into
account for use of an up-to-date kilowatt of
capacity. The counterpart of this extra kilo-
watt of capacity is a saving, during each hour
it is drawn on, as determined by the load diaqram,
of the marginal cost of fuel in an operating
situation, and of the curtailment cost in the
alternative case.' [Emphasis added.]
The "Turvey calculation" moves a whole plant up one year, not
one kilowatt, and takes no account of changes in curtailment
cost.
While it offers the attraction of using "real
world" numbers, the "Purvey calculation" is not a method
of calculating long-run marginal costs. First, while
it appears to be forward-looking, it is not independent
of history. Except for a system that is completely opti-
mal, the figure one arrives at depends on the history of
the system. We know from simple economic theory that the
6 P. Caillé, "Marginal Cost Pricing in a Random Future as
Applied to the Tariff for Electrical Energy by Electric-4té
de France," Presented before the French American Energy
System Planning and Pricing Conference, Madison, Wisconsin,
September 22 to October 24, 1974, p. 110.
-6-
price in any market in long-run equilibrium is determined by
the costs of firms entering the industry using the best prac-
tice (least cost) technology. Competitive market prices will
be determined by the costs of new entrants in equilibrium.
The relevant marginal cost for determining efficient market
prices in economic theory is completely forward-looking and
independent of history. We will not get an appropriate mea-
sure of long-run marginal, cost by looking at the total costs
of existing firms unless input prices and technology have re-
mained constant. Second, the marginal cost is the cost of
one extra kilowatt, not a whole extra plant. When a whole
plant is moved out of its planned timing without a concurrent
change in expected demand, the resulting "system" is not the
minimum cost system. Costs must be higher than those in the
plan--that is why the plant was not planned for a year earlier
in the first place.
A further and perhaps the major problem with the
"Turvey calculation" is that it is not an equilibrium cost.
If a system is out of equilibrium, as when it has excessive
amounts of oil plants, the net Cost of a unit of capacity
(annual capital cost less fuel savings) may be negative.
Plant should of course be added when fuel savings exceed the
total, cost of the new plant. As old plant is replaced, fuel
savings opportunities diminish, and finally the net cost
reaches zero. At this point, plant should be added to reduce
the shortage cost induced by growth. In any event, as plant
J
-7-
is added, the net cost per kilowatt will rise until the system
equilibrium is reached. At this point, the net cost will be
at the long-run marginal cost. This rising net cost of ca-
pacity does not represent a long-run marginal cost, but is
cost incurred along an adjustment path to equilibrium. Turvey
and Cicchetti both recognize that this is a problem, but thus
far have offered no consistent approach to its solution.
ATTACHMENT C
Attachment C
AN ECONOMIC CONCEPT OF ANNUAL COSTS
OF LONG-LIVED ASSETS
Electric plant is constructed for many years' service.
In pricing, we need to determine an appropriate annual charge
consistent with the marginal cost calculation. This problem
is known in the economic literature as the "fair rental" prob-
lem, also sometimes referred to as the problem of determining
"amortization." We use "fair rental," "amortization" and
"annual charge" interchangeably.
Boiteux deals with amortization in his 1957 paper
which appeared in English in International Economic Papers
in 19601; Turvey enlarged on the paper in an article in The
Economic Journal, 19692; Littlechild offered a general
mathematical solution in The Economic Journal in l970;
and Baumol, writing in the Bell Journal in Autumn 1970 asserted
that Littlechild had "effectively given order to the entire
discussion." The literature is, however, pretty much limited
to these few pieces.
Maurice Boiteux, "The Role of Amortization in Investment
Programming," International Economic Papers, 1960, pp. 147-162.
2 Ralph Turvey, "Marginal Cost," The Economic Journal, Volume
79, No. 314 (June 1969), pp. 282-299.
S. C. Littlechild, "Marginal Cost Pricing with Joint Costs,"
The Economic Journal, Volume 80, No. 318 (June 1970), pp.
323-335.
" William Baumol, "Optimal Depreciation Policy: Pricing the
Products of Durable Assets," The Bell Journal of Economics
and Management Science, Volume 1 (Autumn 1970), pp. 638-656.
-2-
Can we derive any guidance from this literature
in coming to a suggestion for an annual charge which is com-
patible with our marginal cost computation? The following
analysis is derived from the articles cited above, but takes
inflation specifically into account and offers some calculated
examples, and some further corollaries.
The clue is to look at the problem as one of assign-
ing joint costs between joint products--in this case the
joint products are production in different years; the joint
cost is the cost of the machine which is available for one
year because it is available for other years.
The general solution to the "joint cost problem"5
is in terms of relative intensities of demand; Littlechild
uses this to solve the amortization problem in the general
case by use of linear programming, deriving a solution similar
to peak-load pricing, in which assignment of costs follows
the level of demand:
,.. J4..
The amount set aside for amortization I
varies from period to period, depending S on demand, and may even be zero in some j I'
periods. With varying demand one should
not try to recoup a constant proportion I . of capacity costs each year. Rather, 4.:
price should be set to fully utilize " ....
capacity (subject to price not being below . .. 6.1
marginal production cost) and capacity .I...., '. cost should be chosen so that, over the ,. a'-"
life of the asset capacity costs are just recouped.6
See for example the discussion in A. E. Kahn, The Economics
of Regulation, Volume 1 (New York: John Wiley & Sons, Inc.,
1970), P. 79.
6 Littlechild, p. 330.
-3-
This, of course, is not out of line with any of
our assertions, but since electric capacity is not generally
planned to be other than "fully utilized" (the "correct"
reserve margin should not be thought of as excess capacity),
it is hard to envisage planning for other than a regular
pattern of use from year to year.
The more interesting concept is in the special
case where demand for the capital good is assumed to be
constant (in real terms) from year to year. Examination of
the implications for this case may enable us to see what the
Boiteux-Turvey-Littlechild-Baumol analysis implies for annual
charges and depreciation policy.
General Scheme of Analysis and Conclusion
This paper derives a formula for an annual charge
which represents the full cost of buying a machine this year
rather than next year, taking account of the stream of re-
placements.
The amortization or annual charge thus computed has
the following properties:
1.It is a constant annual charge in the simple
case of no inflation, no technical progress.
2.It rises annually at the inflation rate if
there is inflation, or at the rate of inflation less tech-
nical progress if both are present.
3.The amortization appropriate to an old plant
-j
in any year equals the first year carrying charge on a new
'I
-
plant in that year. 1 'ri
-4-
This last property is the most felicitous of all, for it
allows us to impute annual charges to old machines--they
will be equal to the annual charge on a "similar" new
machine. A "similar" machine provides the "same " product.
We may think of it as a machine with the same running cost
per kilowatt-hour.
This then leads us back to the simplified model
of time-of-day/seasonal pricing. The optimization pro-
cedure was based on the cost of new plants, and some of the
criticism has been based on ignoring the existence of old
plants. But if the appropriate annual charge is in fact
the same for an old machine as a new machine, given running
costs, then the "problem" of optimizing with old machines
disappears.
The following pages lay out the logic of the cal-
culation; details are given in the Appendix in this Attachment.
Amortization--NO Technical Progress, No Inflation
We assume first:
(1)a plant which lasts a given number of years
then falls apart
(2)no inflation or technical progress affects
the cost of replacements
(3)no effects of maintenance costs, increasing
with age, on the replacment decision
(4)no excess capacity--the machine is used as
planned
-5-
(5) the only. factor determining the value of used
equipment is the approach of its demise. (This
assumption would not be valid in the case of
used cars, for example, when clearly taste and
fashion have an important influence on the
value of older cars. But for most types of
equipment the psychological value of a "new"
as opposed to a "used" machine can probably
be ignored.)
What is the full cost, or rental value, of owning
a piece of equipment for a year? It is the initial cost,
plus the discounted stream of replacement costs of buying
the plant this year rather than next year.
If K 0 is the initial cost in year zero, and r is
the rate of interest:
Cost if purchased now:
=K 0 + K 0 + K 0
(1+r)5 (1+r)1 °
Cost if purchased next year:
= J + K0 + K 0 +....
(l+r) (l+r)6 (1+r)
This year's cost is the difference between these two streams
discounted to the beginning of this year. This is the rental
or amortization cost. Let At be the amortization for year t,
discounted to the beginning of year 0.
-6-
By subtraction (shown in the Appendix), we have:
A D = K r r (1+r)
A1 K _r (1+r)5 1 thus,
(l+r)2.(l+r)5 - i i
At =K r r (l+r)r
(l+r)t+l(l+r)fl - I
At in this case was defined as the present worth of
the amortization for each year. If we sum the present worth
of the amortization for each year we have:
=
In other words, amortization computed under this
formula would fulfill the general condition that the present
worth of the expected returns should equal the original in-
vestment.
While the discounted amortization, At, for each
year is declining by r percent, the absolute value of the
amortization is constant. Let us call this
A = A (j+r) A (l+r) = A 1+r)3 ....= = C 1 2 3 1 2 3
Row does its constant value compare with the tradi-
tional method of calculating an annuity on a value of K. at
r percent for n years? Annuity value, end-of-year payment
is given as:
Kr
I -
(l+r)
-7-
which, rearranged, is equal to (1+r)A 0 . This difference is
due to A. having been computed for the beginning of the year,
whereas the annuity formula is an end-of-year formula. We
will be careful to distinguish in the future.
This result is interesting, because the annualized
cost of the plant is generally computed from a nonconstant
stream of costs; the annuity value is considered an approxima-
tion, whereas, as we have seen, it is the true value in the
simple case.
No Technical Progress, With Inflation
Now we have to ask, what happens in inflationary
circumstances? The cost of replacement in current dollars
is rising. Assuming inflation is anticipated to be i over
the life of the machine, replacement costs will be
for a machine with an n-year life. Using the same reasoning
as in the simple case, we derive the fair rental cost for
the first year.
Let the value of a one-year-old plant be K 1 . Then
the cost of new plant this year plus replacements:
K0 + K0(1+j) + Ko(l+i) +
(1+r)' (1+r )2n
A new plant next year will entail a stream of costs:
(1+1) 2n+1 K 0 (].+i) + K 0 i1+r n+l• + 0 (1 +)2fl+l
The appropriate rental cost or amortization for the year
would be the cost of having the plant rather than not having
-8-
the plant for that year, or the difference in these two
streams. Since the calculations are now becoming lengthy,
we will send them all to the Appendix and simply state the
comparable results.
No Inflation
Constant amortization.
At At_i
Discounted sum of annual amor-
tization payments = original
cost (condition for investment
to be worth making in year 0).
After replacement, amortiza-
tion payments continue to be
equal to payments before
replacement.
The amortization on an old
plant in any year equals the
first-year carrying charge on
a new plant in that year.
Inflation at i%
Amortization increases annu-
ally at i%.
At = Xt_1(l+i)
Discounted sum of annual amor-
tization payments = original
cost (condition for investment
to be worth making in year 0).
After replacement, amortiza-
tion payments continue unbroken
at i% higher than the previous
year.
The amortization on an old
plant in any year equals the
first-year carrying charge on
a new plant in that year.
This last property is important. Correctly valued
capital stock, whatever its original cost, will have equal
rental charges for all machines of the same type whatever their
vintage. This makes intuitive sense, also. If two machines
can do the same job and produce the same output, the rental
charge should not depend on the age of the machine.
Figure 1 shows a comparison of the first-year costs
under inflation with those which would be computed if interest
rates, but not inflation, were taken into account. What this
Shows is that the amortization payment in the first year
should be lower if future inflation is taken into account.
IF
-9-
This discrepancy becgmes greater for longer lives and higher
interest rates.
Technical Progress
The treatment of technical progress is the reverse
of the treatment of inflation. Technical progress is defined
as a real reduction in the price of the same capital good over
time, resulting in a reduced replacement cost. In this case
the annual amortization, or rental cost, is increased in the
first year, and declines annually. The common sense expres-
sion of this is given in a case we have often discussed--if
two-dial meters which have a physical life of 20 years will
be overtaken within five years by a technology which will ef -
fectively offer the equivalent of the two-dial option at a
very low or even zero cost (because the new technology can
also do other things), then the present generation of meters
must be fully depreciated (reduced to zero value) in five
years. The general expression for amortization, if technical
progress is reducing costs by p percent annually is:
I-
At =K 0 (r+p)(l_p)t I_(l+r)

(l+r)t+l [(l+r)' - (l_p)J
With both inflation and technical progress we have:
At = K(r_i+p)(l+i_p)t[ (1+r)

(l+r)t (l+r)fl - (l+i_p)1J
-10-
The effect of these results is as follows: in a
time of inflation, the appropriate price for use of an asset
will start lower than the cash flow or the levelized cost and
will rise from year to year. The early users will pay the same
in real dollars as the later users.. This is consistent with our
general approach of considering what a competitive market would
do: a businessman who estimates that the market price of his
output will rise at the rate of inflation will take that into
account in deciding the economic feasibility of purchasing an
asset below cash flow requirements, and may price accordingly
for several years.
One qualification must, however, be made. We have
assumed that the machine is like a one-hoes shay which produces
at a constant rate and simply dies at the end of its life. In
fact, machines do lose efficiency, both by being more suscepti-
ble to breakdown and repair, and also by being relegated to
lighter duty as technical progress increases the efficiency of
newer plants. (We should not, however, overemphasize these
effects, for the one-hoss-shay model is actually fairly appro-
priate to electric capacity.) The effect of taking physical
depreciation into account is to raise the constant dollar price
in the early years as compared with the later years, or miti-
gate somewhat the reduction in marginal cost from the constant
annuity value which results from taking inflation into account.
The two diagrams which follow show the effect of our
revised annual charge formula on the stream of annual charges.
-11-
In Figure 1, we show a 3.0-year asset at eight percent: the
cash flow per $100 declines from $11 to $3 in a straight
line. The equivalent levelized value (the stream with the
same present worth) is at $9. The stream of charges, in-
cluding inflation at five percent, rises from $5 at the
beginning of the life to $22 at the end.
To see how much the effect of inflation depends on
the life of the plant and the actual level of inflation,
Figure 2 plots out the ratio of first-year charge to equiva-
lent leve].ized charge as a function of the life of the plant
and the rates of interest and inflation. It can be seen that
the effect is greatest for long-lived assets and high rates
of inflation and interest.
FIGURE 1
0
x
FIGURE 1
ANNUAL COST OF 30-YEAR PLANT
UNDER VARYING DEPRECIATION
SCHEDULES
--
NMI
• ____ EWA
ME
• __ __ min
IN
E!J iimi .11 I -
ME
ME EE== OEM -
FIGURE 2
FIGURE 2
1.0
0.9
0.8
0.7
0.6
A0
A0 0.5
0.4
0.3
0.2
0.1
FIRST YEAR'S AMORTIZATION ON PL1
H - WITH INFLATION AS A RATIO
TO_WITHOUT_INFLATION
______• ::•: !.. _________
Including inflation always reduces the first-
year charges. The proportion by which they
are reduced is very small for plants with
longer lives. As interest rates and infla-
tion rates rise, the discrepancy gets larger.
First-year amortization on a 30-year plant
at rlO%, 17% would be one half of the
T: charge if inflation were not considered.
.ffTTI.-i t I I I I I L- •t: IIi I F I I_.
NT- -
r= 4%, i=l%
r= 5%, i=2%
r 6%, i=3%
r= 7%, i=4%
r= 8%, i=5%
r= 9%, i6%
r 10%, i 7%
r 11%, i 8%
r 12%, i 9%
5 15 30 50 100
EXPECTED LIFE OF PLANT (YEARS)
a'
CONTENTS OF APPENDIX
Page
Notation 3.
Sums of Series Employed in Proofs 2
Summary of Proofs 3
Proofs 4
-1-
NOTATION
A = Annual discounted charge for use of plant
rental cost = amortization
where A0 = annual cost for year 0 discounted to
beginning of year 0
A t = annual cost for year 1 discounted to
beginning of year 0
= annual cost for year t discounted to
beginning of year 0
= Annual, undiscounted cost of plant
D = Depreciation
where D0 = depreciation in the first year of life
D 1 = depreciation in the second year of life
= depreciation in the t+i year of life
I = Interest on the beginning-of-year remaining
value of plant
K = Price of plant
where K0 = price of new plant
1(1 = price of one-year-old plant
Kt = price of t-year-old plant
RV = Remaining value of plant
= rate of inflation
r4 = expected life of plant
r = interest rate
t = age of plant
= calculated with inflation (applies to A, D, I,
K and RV)
superscript = years of inflation (applies to A t D, I, K and RV)
-2-
SUMS OF SERIES EMPLOYED IN PROOFS
Where a = (1+r); b
E a
kQ ank a-1
2
k=1 a" a'-1
3.: bkn_ a
k=o
b 4.
* k=1 a-b
t=r-1
5.Z at = 1-an
1-a
t=zi- 1
6.1 at =
t=1. 1-a
7.1
t+1=1 at+i an
t=n-1bt r 2. 1 afl-b"
j. t= a-' La -bJ an
16m
-3-
SUMMARY OF PROOFS
I. WITHOUT INFLATION
1.Derivation of At
A 0 = Kr T(1+r}5
l+r t(1+r) 5 -iJ
(14-r) 2 (.'.L+ r) 5 1j
At = 0 r (1+r)'
(1+r)t+1L(I~r)fl _1j
2.Sum of Discounted Annual Costs Over Equipment's Life = K0
3.Annual Undiscounted Cost in Each Year is Equal
4.Annuity Formula = Undiscounted Annual Value
Kr
=At(l+r)
1
II. WITH INFLATION
S. Derivation of A
A0 = K0 (r-i) I (1+r)5
(l+r)
At = K0 (r-i) (1+i)t - I (l+r)
(1+r) t+l Ll+r- (l+i) n
• 6. Sum of Discounted Values of A"*t = K0
7. Annual Undiscounted Cost Rises Each Year by (l+i)
B. Annuity Formula Does Not Equal Undiscounted Annual Value
-4—
PROOFS
I. WITHOUT INFLATION
1. Derivation of A t
Cost of putting in the plant at beginning of year 0
=K0 +_K0 +3
+

(1 4r) (1+0 14
Cost of putting in the plant at beginni'.g of year 1

X0 + K3 + K0 +...
(let) 2
Difference in cost discou,tec to beginning of year 0. for year 0
A0 = K0 - K 0 + K - -
1+r (1+r)5 (l+r)
A0=K0 1 1- 11+0r __. - .
L (1+r)l 1+r)'
A0 =E0 r !i+ i. + 1

i ( (1+r) (1+r)1°
AOKA r 1

- k=o l+r (l+rj Tk
r I(l+r) Sim*L

1r(1+r) 51J kO ank a-)
Similarly, cost of putting in plant at beginning of year 2
=XO + K0 + :<,,

(1+Z)2 (i+r)' (1+r)'2
Difference in cost discounted to begnnin of year 0, for year i
= K0 - K0 + K0 - K0 r (1': (1+:) (1+r)'
A Ko r
(1+:) 2 L1+t -x
Sithilarly for each year 0, 1, 2, 3, 4.

Generally At K0r 1+t)
(1+r) tl (i+r)
-5-
2. The Sum of the DISCOUNTED Annual Costs Over Egupment*S Life,
Equals the Purchase Price
A0 + A l + A 2 + A s + A =

(r + r + - r + r + r

[,(l+r)
(1+r 5_].J Li~r (1+r) (1+r) (l+r) (1+r)'!
K0
1(1+r)
(1.)t+1fl r
'-iJt+i=i (1+r)t+l
= K 0 S I1 - 1
_I since
[
(I+.r)
u+r 5-1_,L (1+r) Si t+l=l 41 t
= K 0 (1+r) $ 1+r) -1
L1+r 1 -1J (l+r)'
3.The Annual Undiscounted Cost in Each Year is Eq ual
A0 = A 1 (l+r) = A(1+r)2 = A 3 (1+r)3 = A(1+r)' by inspection
4. e Annual Undi3counted Cost Equals the
K for Five Years at r Percent
Annuity value = fC 3 r
end ofyear

A= K 0 r
(1+r)
A = K0r (l+r)
-. = (1+r)A0 (1+r) -1
tv Val
-6-
II. WITH INFLATION
5. Derivation of A
Cost of equipment in year 0:
= Kg + Kg (l+j)5 + xg (]+j)t0
(10 5 (l+r)'
Cost of equipment in year 1, discounted to beginning of year 0:
Kg (l+i) + Kg(l+i)' +

- (1+r) (l+r) 6 (l+r) '
Difference in costs
- (1+i) + (].+j)5 - (j+j)6
1.. (l +r) -Fl +r) s (1+r) J
= K_R1~r>_1+t414jtC1+r-.1.j' 1

+. I

(l~r)[ (1.+r)1
= Kg(r-i) ri + (14.i)5+1
_•1
(].+r) L (i+r)5 -'
Kg (r-i) z (l+i) sk
- (l+r) k=o-
=

KOO
F,+
1+r)
(j.+r) ) 5-(l+i) 6J
Cost of equipment in year 2, discounted to beginning of year 0:
+

(j.+r) (l+r)
Second year annual cost, discounted to beginning of year 0
K3 (L+i)2 + (L+i)' - (l+i)'

Lu+r (1+0 2 (l+r) (1+r)7 J
K(r-i)(l+i) rt+ (].+i)5 -

(1+r)2 L (1+r)5 J
Xg(r-i) (l+i) Z (l+i)

(1+r)2 k=O(1)sk
K(r-i)(l+i) r (1+r)3
-

(1+r)2 L1+r-u+iJ --
since ko
In general £ = K(V_i)(l+i)t r_(l+r) rl
(l+r) t+l L14r - (l+i) flJ
-7-
6. The Sum of the Discounted Annual Costs =
t=n-i
(l+r)r (i ..j)t
(1+r)-(j+j)fl 0 (1+r) t +1
Ii 1
L1+ij+J L (].+r)

tria-)
I t
7.The Undiscounted Value of the Annual Payment
At = K8(r-i) (1j)t [

lr)
(i+i}
The undiscounted annual value is not constant; it rises
by (14.i) each year.
8.Annuity Formula Does Not Equal Undiscounted Annual Value
K = Kg(r-i) (.+i;t
i ti 1- (l+r)' L