SV/P3YO
Electric Power Pricing Policy
Worild Bank Staff Working Paper No. 340
July 1979
Prepared by; Mohan Munasinghe
Energy, Water and Telecommrunications Department
Central Projects Staff
Copyright © 1979
The World Bank
1818 H Street, N.W.
Washington, D.C. 20433, U.S.A.
The views and interpretations in this document are those of the authors
and should not be attributed to the World Bank, to its affiliated
organizations, or to any individual acting in their behalf.



The -diews and interpretations in this document are those of the author
and shiould not be attributed to the World Bank, to its affiliated orga-
nizations or to any individual acting in their behalf.
WORLD BANK
Staff Working Paper No. 340
July 1979
ELECTRIC POWER PRICING POLICY*
This paper presents a framework for electric power pricing which
is especially appropriate to the developing countries. It contains a review
of the basic theory of marginal cost pricing applicable to the power sector,
and a summary of the current state-of-the-art. The adaptation of the theory
for practical application in relation to the objectives of power pricing
policy in the LDC context, results in a two stage procedure for tariff
setting. First, a set of prices based on the strict long-run marginal costs
(LFMC) of supply which meet the economic efficiency criterion are computed.
Second, the strict LRMC is adjusted to arrive at an appropriate realistic
tariff structure which satisfies various constraints. Explicit models are
presented which permit modifications to be made to the strict LRMC on the
basis of: (a) economic-second best considerations (especially with regard
to the pricing of substitute fuels), and (b) social considerations relating
to subsidized prices for poor consumers. The tailoring of tariff policy to
meet sector financial needs and other requirements such as simplicity of
metering and billing are also discussed.
Prepared by: Mohan Munasinghe
Energy, Water and Telecommunications Department
Central Projects Staff
Copyright Q1979
The World Bank
1818 H Street, N.W.
Washington, D.C.
* Paper presented at the LDC Energy Management Training Seminar, State
University of New York-Brookhaven National Laboratory, Stony Brook,
New York, November 1978. The author is grateful to Denis Anderson
and Fred McCoy for valuable comments on an earlier draft of this paper.



TABLE OF CONTENTS
Page No.
A.   INTRODUCTION AND OVERVIEW ..... . .............................         1
A.1 Requirements of a Power Tariff..    2
A.2  Long Run Marginal Cost (LRMC) Based Tariffs ............           3
A.3  Practical Tariff Setting ..............................            5
A.4  Summary ...i........... .                                          7
B.   ECONOMICS OF MARGINAL COST PRICING  ........................            9
B.1  Basic Marginal Cost Theory               ........ .               10
B.2  Capital Indivisibilities and Peak Load Pricing .13
B.3  Extensions of Simple Models               .......                 15
B.4    Shadow   Pricing   . ...... . ............ . ...... . .......   18
C.   CALCULATING STRICT LRMC ................... o .........                25
C.1  Cost Categories and Rating Periods    ..26
C.2  Marginal Capacity Costs .. ....  ..... o. ...         .27
C.3  Marginal Energy Costs      .. . ..       ... ... . ..    32
C.4  Consumer Costs .3................ ...                             33
D.   ADJUSTED LRMC TARIFF STRUCTURE  ........34
D.1 Second Best Considerations                    ..35
D.2 Subsidized or Lifeline Rates    .               .37
D.3  Financial Viability                  ............ o....... * ....................    39
D .4 Other Considerations                      .       .40
D.5  Metering and Billing                         .o ...... ......     41
Appendix 1.  ALLOCATION OF CAPACITY AND ENERGY COSTS
AMONG PEAK AND OFF-PEAK USERS
Appendix 2.  MODEL FOR OPTIMAL ELECTRICITY PRICING IN A
DISTORTED ECONOMY
Ref erences



ELECTRIC POWER PRICING
by
MOHAN MUNASINGHE
Section A
Introduction and Overview 1/
Modern societies have become increasingly dependent on various
types of energy sources, among which electric power has occupied a dominant
position. Traditionally, electric power pricing policy in most countries
has been determined mainly on the basis of financial or accounting criteria,
e.g.,, raising sufficient sales revenues to meet operating expenses and debt
service requirements while providing a reasonable contribution towards the
capital required for future power system expansion.
However, in recent times several new factors have arisen, including
the rapid growth of demand, the increase in fuel oil prices and prices of
fossil fuel and nuclear plant, the dwindling availability of cheaply exploit-
able hydro-electric resources, and the expansion of power systems into areas
of loDwer consumer density at relatively high unit costs. These developments
have led to increasing emphasis being laid on the use of economic principles
in order to produce and consume electric power efficiently, while conserving
scarce resources, especially in the developing country context. In partic-
ular, a great deal of attention has been paid to the use of marginal cost
pricing policies in the electric power sector.
1/   This section summarizes basic pricing policy principles developed in
the EWT Department over the last 6 years, through a program of applied
research work and country case studies.



The objectives of power tariff policy in the national context, and
a pricing framework based on long run marginal costs (LRMC) which meets these
requirements, are summarized in this section. In Section B, the economic
principles underlying the LRMC approach are described, and in Section C, a
framework for calculating strict LRMC is presented. Finally, the process of
adjusting LRMC to devise a practical tariff structure which meets other
national constraints is discussed in Section D, followed by several technical
appendices.
A.1 Requirements of a Power Tariff
The modern approach to power pricing recognizes the existence of
several objectives or criteria, not all of which are mutually consistent.
First, national economic resources must be allocated efficiently, not only
among different sectors of the economy, but within the electric power sector
itself. This implies that cost-reflecting prices must be used to indicate
to the electricity consumers the true econLomic costs of supplying their
specific needs, so that supply and demand can be matched efficiently.
Second, certain principles relating to fairness and equity must
be satisfied, including: (a) the fair allocation of costs among consumers
according to the burdens they impose on the system; (b) the ensuring of a
reasonable degree of price stability and avoiding large fluctuations in price
from year to year; and (c) the provision of a minimum level of service to
persons who may not be able to afford the full cost.
Third, the power prices should raise sufficient revenues to meet
the financial requirements of the sector, as described earlier.  Fourth, the
power tariff structure must be simple enough to facilitate the metering and



- 3 -
billing of customers. Fifth and finally, other economic and political
requirements must also be considered, e.g., subsidized electricity supply to
certain sectors to enhance growth, or to certain geographic areas for pur-
poses of regional development.
Since the above criteria are often in conflict with one another, it
is necessary to accept certain trade-offs between them.  The LRMC approach to
price setting described below has both the analytical rigor and inherent
flexibility to provide a tariff structure which is responsive to these basic
objectives.
A.2 Long Run Marginal Costs (LRMC) Based Tariffs
A tariff based on LRMC is consistent with the first objective, i.e.,
the efficient allocation of resources. The traditional accounting approach is
concerned with the recovery of sunk costs, whereas in the LRMC calculation it
is the amount of future resources used or saved by consumer decisions which is
important. Since prices are the amounts paid for increments of consumption,
in general they should reflect the incremental cost thereby incurred. Supply
costs increase if existing consumers increase their demand or if new consumers
are connected to the system. Therefore, prices which act as a signal to
consumers should be related to the economic value of resources to be used in
the future, to meet such consumption changes. The accounting approach which
uses historical assets and embedded costs implies that future economic re-
sources will be as cheap or as expensive as in the past. This could lead to
over-investment and waste, or under-investment and the additional costs of
unnecessary scarcity.



-4-
In order to promote better utilization of capacity, and to avoid
unnecessary investments to meet peak demands (which tend to grow very
rapidly), the LRMC approach permits the structuring of prices so that they
vary according to the marginal costs of serving demands:
-    by different consumer categories;
-    in different seasons;
-    at different hours of the day;
-    by different voltage levels;
-    in different geographical areas; and so on.
In particular, with an appropriate choice of the peak period, struc-
turing the LRMC based tariffs by time-of-day generally leads to the conclusion
that peak consumers should pay both capacity and energy costs, whereas off-
peak consumers need to pay only the energy costs. Similarly, analysis of LRMC
by voltage level usually indicates that the lower the service voltage, the
greater the costs imposed on the system by consumers.
The structuring of LRMC based tariffs also meets sub-categories (a)
and (b) of the second (or fairness) objective. The economic resource costs
of future consumption are allocated as far as possible among the customers
according to the incremental costs they impose on the power system. In the
traditional approach, fairness was often defined rather narrowly and led to
the allocation of (arbitrary) accounting costs to various consumers. Because
the LRMC method deals with future costs over a long period, e.g., about 10
years, the resulting prices (in constant terms) tend to be quite stable over
time. This smoothing out of costs over a long period is especially important
because of capital indivisibilities or lumpiness of power system investments.



-5-
The use of economic opportunity costs (or shadow prices, especially
for capital, labor, and fuel) instead of purely financial costs, and the
consideration of externalities whenever possible, also underline the links
between the LRMC method and efficient resource allocation.
The development of LRMC based tariff structures which also meet the
other objectives of pricing policy mentioned earlier, are discussed below.
A.3 Practical Tariff Setting
The first stage of the LRMC approach is the calculation of pure or
strict LRMC which reflect the economic efficiency criterion. If price was
set strictly equal to LRMC, consmers could indicate their willingness-to-pay
for more consumption, thus signalling the justification of further investment
to expand capacity.
In the second stage of tariff setting, ways are sought in which the
strict LRMC may be adjusted to meet the other objectives, among which the
most important one is the financial requirement. If prices were set equal
to strict LRMC, it is likely that there will be a financi4l surplus. This
is because marginal costs tend to be higher than average costs, during a
period when the unit costs of supply are increasing.  In principle, financial
surpluses of the utility may be taxed away by the state, but in practice the
use of power pricing as a tool for raising central government revenues is
usually politically unpopular and rarely applied. However, such surplus
revenues can also be disposed of in a manner which is consistent with the
other objectives. For example, the connection charges can be subsidized
without violating the LRMC price, or low income consumers could be provided
with a subsidized block of electricity to meet their basic requirement, thus
satisfying socio-political objectives. Conversely, if as in some cases,



- 6 -
marginal costs are below average costs (e.g., due to economies of scale),
then pricing at the strict LRMC will lead to a financial deficit, which will
have to be made up,for example, by higher lump sum connection charges, flat
rate charges, or even government subsidies.
Another reason for deviating from the strict LRMC arises because
of second-best considerations. When prices elsewhere in the economy do not
reflect marginal costs, especially in the case of substitutes and complements
for electric power, then departures from the strict marginal cost pricing
rule for electricity services would be justified. For example, in rural
areas alternative energy may be available cheaply in the form of subsidized
kerosene and/or firewood. In this case, pricing electricity below the LRMC
may be justified, to prevent excessive use of the alternative forms of energy.
Similarly, if incentives are provided for the importation of private gener-
ators, while their fuel is also subsidized, then charging the full marginal
cost to industrial consumers may encourage them to purchase captive power
plant, which is economically less efficient from the national viewpoint.
Since the computation of strict LRMC is based on the power utilities' least
cost expansion program, LRMC may also need to be modified by short term con-
siderations if previously unforeseen events render the long run system plan
sub-optimal in the short run. Typical examples include a sudden reduction
in demand growth and a large excess of installed capacity which may justify
somewhat reduced capacity charges, or a rapid increase in fuel prices, which
could warrant a short term fuel surcharge.
As discussed earlier, the LRMC approach permits a high degree of
tariff structuring. However, data constraints and the objective of simpli-
fying metering and billing procedure usually requires that there should be



a practical limit to differentiation of tariffs by: (a) major customer cate-
gories (e.g., residential, industrial, commercial, special, rural etc.);
(b) voltage levels (e.g., high, medium and low); (c) time-of-day (e.g., peak,
off.-take); (d) geographic region, etc. Finally, various other constraints
also may be incorporated into the LRMC based tariff, such as the political
requirement of having a uniform national tariff, subsidizing rural electrifi-
cation, and so on. However, in each case, such deviations from LRMC will
impose an efficiency cost on the economy.
A.4 Summary
To summarize, in the first stage of calculating LRMC, the economic
(first best) efficiency objectives of tariff setting are satisfied, because
the method of calculation is based on future economic resource costs (rather
than sunk costs), and also incorporates economic considerations such as shadow
prices and externalities. The structuring of marginal costs permits an effi-
cient and fair allocation of the tariff burden on consumers. In the second
stage of developing a LRMC based tariff, deviations from strict LRMC are
considered, to meet important financial and other social, economic (second-
best) and political criteria. This second step of adjusting strict LRMC is
generally as important as the first stage calculation, especially in the
developing country context.
The LRMC approach provides an explicit framework for analyzing
system costs and setting tariffs. If departures from the strict LRMC are
required for non-economic reasons, then the economic efficiency cost of these
deviations may be estimated even on a rough basis, by comparing the impact
of the modified tariff relative to (benchmark) strict LRMC. Furthermore



-8-
since the cost structure may be studied in consideral e detail during the
LRMC calculations, this analysis helps to pinpoint w aknesses and ineffi-
ciencies in the various parts of the power system, e.g., overinvestment,
unbalanced investment, or excessive losses, at the generation, transmission
and distribution levels, in different geographic areas, and so on. This
aspect is particularly useful in improving system expansion planning.
Finally, any LRMC based tariff is a compromise between many dif-
ferent objectives. Therefore, there is no "ideal" tariff. By using the LRMC
approach, it is possible to revise and improve the tariff on a consistent and
ongoing basis, and thereby approach the optimum price over a period of several
years, without subjecting long-standing consumers to "unfair" shocks, in the
form of large abrupt price changes.



- 9 -
Section B
Economics of Marginal Cost Pricing
The origins of m,rginal cost pricing theory date back as far as the
path,breakiag efforts of Dupuit and subsequently Hotelling; Ruggles provides
a comprehensive review of work in this area up to the 1940's. 1/ The devel-
opment of the theory, especially for application in the electric power sector,
received a strong impetus from the work of Boiteux, Steiner, and others, from
the 1950's onwards. 2/ Recernt work has led to more sophisticated investment
models which permit determination of marginal costs, developments in peak load
pricing, consideration of the effects of uncertainty and the costs of power
shortages, and so on. 3/
1/  P. Dupuit, "De l'Utilite et de sa Mesure," La Reforma Soziale, Turin,
(1932); H. Hotelling, "The General Welfare in Relation to Problems of
Railway and Utility Rates," Econometrica, vol. 6 (July 1938), pp. 242-
269; and N. Ruggles, "The Welfare Basis of the Marginal Cost Pricing
Principle," Review of Economic Studies, vol. 17 (1949-50), pp. 29-46,
and "Recent Developments [n the Theory of Marginal Cost Pricing," ibid.,
pp. 107-126.
2/   See for example:  M. Boiteux, "La Tarification des Demandes en Pointe,"
Revue Generale de l'E'aectricite, vol. 58, (1949), P. Steiner, "Peak Loads
and Efficient Pricing," Quarterly Journal of Economics (November 1957);
M. Boiteux and P. Stasi, "The Determination of Costs of Expansion of an
Incerconnected Systeai of Production and Distribution of Electricity," in
James Nelson, Ed., tlarginal Cost Pricing in Practice, Prentice-Hall,
Englewood Cliffs, N.J. (1964); O.E. Williamson, "Peak Load Pricing and
Optimal Capacity under Indivisibility Constraints," The American Economic
Review, vol. 56, No. 4 (September 1966), pp. 810-827; and R. Turvey,
Optimal Pricing and Investment in Electricity Supply, Cambridge M.I.T.
Press (1968).
3/   See for example:  Symposium on Peak Load Pricing, in The Bell Journal of
Economics, vol. 7 (Spring 1976), pp. 197-250; R. Turvey and D. Anderson,
Electricity Economnics, Johns Hopkins (1977), M.A. Crew and P.R. Kleindorfer,
"Reliability and Public Utility Pricing," American Economic Review,
vol. 68 (March 1978); R. Sherman and M. Visscher, "Second Best Pricing
with Stochastic Demand," ibid.; Marginal Costing and Pricing of Electrical
Energy, Proceedings of the State of the Art Conference, Canadian Elec-
trical Association, Montreal (May 1978); and M. Munasinghe, Economics of
Power Syste' Reliability and Planning, Johns Hopkins Press, Baltimore
(1979).



- 10 -
This section consists of a review of the basic economic principles
of marginal cost pricing and a summary of the current state-of-the-art.
Further details of the theory may be found in the references given earlier.
B.1 Basic Marginal Cost Theory
The rationale for setting price equal to marginal cost may be
clarified with the simple supply-demand diagram shown in Figure B.1. Let
EFGD0 be the demand curve (which determines the kWh of electricity demanded
per year, at any given average price level), while AGS is the supply curve
(represented by the marginal cost MC of supplying additional units of output).
At the price p, and demand Q, the total benefit of consumption is
represented by the consumers willingness-to-pay, i.e., the area under the
demand curve OEFJ. The cost of supplying the output is the area under supply
curve OAHJ. Therefore, the net benefit,,or total benefit minus supply cost, is
given by the area AEFH. Clearly, the maximum net benefit AEG is achieved when
price is set equal to marginal cost at the optimum market clearing point G,
i.e., (Po,Q0).
In mathematical terms, the net benefit is given by:
NV 13  fpJ     jNI MC(d.
0 
Where p(Q) and MC(Q) are the equations of the demand and supply curves respec-
tively maximizing NB yields:   i (NM) /d Q  :b (Q) - M  C (4)   0
which is the point of intersection of the demand and marginal cost curves
(Po9Q0).
The analysis so far has been static, and therefore we now consider
the dynamic effect of growth of demand from year 0 to year 1, which leads to
an outward shift in the demand curve from D  to D .  Assuming that the correct
o     1



- 11 -
market clearing price p  was prevailing in year 0, excess demand equal to GK
wil:L occur in year 1.  Ideally, the supply should be increased to Q1 and the
new optimum market clearing price established at p1.  However, the available
information concerning the demand curve D may be incomplete, making it diffi-
1
cull: to locate the point L.
Fortunately, the technical relationships underlying the production
function usually permit the marginal cost curve to be determined more accu-
rately. Therefore, as a first step, the supply may be increased to an inter-
mediate level Q', at the price p'. Observation of the excess demand MN indi-
cates that both the supply and the marginal cost price should be further
increased. Conversely, if we overshoot L and end up in a situation of excess
supply, then it may be necessary to wait until the growth of demand catches
up with the over-capacity. In this iterative manner, it is possible to move
along the marginal cost curve towards the optimum market clearing point. It
should be noted that, as we approach it, the optimum is also shifting with
demand growth, and therefore we may never hit this moving target. However,
the basic rule of setting price equal to the marginal cost and expanding
supply until the market clears, is still valid. 1/
1/   This simple rule has to be modified when there are constraints in the
economy; in particular, the consequences of shadow pricing of inputs,
second best considerations, and subsidized social prices for poor
consumers, are clarified in Appendix 2.



uvt~~~~~~~~~t             I
Untt
Price
N~~~~~~~~~~~N
I             I   :.t\                D
o                       QO  QQ                              kWh
Figure B.1. Supply and Demand Diagram for Electricity Consumption
Prit
3
Po ___D 
Figure B.2. The Effect of Capital Indivisibilities on Price



- 13 -
B.2 Capital Indivisibilities and Peak Load Pricing
Next, the effect of capital indivisibilities or lumpiness of invest-
ments, is examined with the help of Figure B.2. This analysis recognizes the
fact that,owing to economies of scale, capacity additions to power systems
(especially generation) tend to be large and long-lived. Suppose that in
year 0, the maximum supply capacity is Q, while the optimum price and output
combination (p , Q ) prevails, corresponding to the demand curve D  and the
short run marginal cost curve SRMC (e.g., fuel, operating and maintenance
costs). Now if capacity is to be increased from Q to Q, there will be a sharp
spike in the marginal cost curve.
As demand grows from D  to D1 over time, the price must be increased
to p1  to clear the market.  When the demand curve has shifted to D2 and the
price is p2, plant is added on to increase the capacity to Q.  However, as
soon as the capacity increment is completed and becomes a sunk cost, SRMC
falls to its old trend line.  Therefore, p3 is the optimum price corresponding
to demand D3.  Generally, the large price fluctuations during this process
will be unacceptable to consumers. This practical problem may be avoided by
adopting a long run marginal cost (LRMC) approach, and recognizing the need
for peak load pricing, as described below.
The basic peak load pricing model shown in Figure B.3 has two demand
curves; for example,D k could represent the peak demand during the x daylight
and evening hours of the day when electric loads are large, while D   would
op
irLdicate the off-peak demand during the remaining (24-x) hours when loads are
light. The marginal cost curve is simplified assuming a single type of plant
with the fuel, operating and maintenance costs given by the constant a, and



-14-
LU;t
PoIQt  <   <D           p~~~Dk
o                                              k Wih
Figure B.3. P



- 15 -
the LRMC of adding to capacity (e.g., investment costs suitably annuitized
and distributed over the lifetime output of the plant) given by the constant
b. The static diagram has been drawn to indicate that the pressure on
capacity arises due to peak demand D k' while the off-peak demand D   does
not infringe on the capacity Q. The optimum pricing rule now has two parts
corresponding to two distinct rating periods (i.e., differentiated by the
time of day);
peak period price        ppk = a + b
off-peak period price:  p   5 a
The logic of this simple result is that peak period users, who are the cause
of capacity additions, should bear full responsibility for the capacity costs
as well as fuel, operating and maintenance costs, while off-peak consumers
only pay the latter costs (see also Appendix 1).
B.3 Extensions of Simple Models
The models presented so far have been deliberately idealized and
simplified to clarify the basic principles involved. Extensions of these
models which incorporate and analyze the economics of real-world power systems
more realistically are reviewed below.
First, the usual procedure adopted in marginal cost pricing studies
may require some iteration. Typically, a long-range demand forecast is made
assuming some given future evolution of prices, a least cost system expansion
plan is determined to meet this demand, and LRMC is computed on the basis of
latter. However, if the estimated LRMC which is to be imposed on consumers is
significantly different from the original assumption regarding the evolution
of prices, then the first round LRMC estimates must be fed back into the
model to revise the demand forecast and repeat the LRMC calculation.



- 16 -
In theory, this iterative procedure could be repeated until future
demand, prices, and LRKC estimates become mutually self-consistent. In
practice, uncertainties in price elasticities of demand and other data may
dictate a more pragmatic approach in which the LRMC results would be used
to devise power tariffs after only one iteration. The behavior of demand is
then observed over some time period and the LRMC re-estimated and tariffs
revised to move closer to the optimum, which may itself have shifted meanwhile,
as described in subsection B.1. The price feedback effects are most important
in the so-called shifting peak case, when peak load pricing may shift the
demand peak from one rating period to another. In general, problems arising
from changes in the level of demand at any given time of day due to differen-
tial pricing during other rating periods have been recognized, and are being
investigated.
Second, the interrelated issues of supply and demand uncertainty,
reserve margins, and costs of shortages raise certain problems. The least
cost system expansion plan to meet the demand forecast is generally deter-
mined assuming some (arbitrary) target level of system reliability (e.g.,
loss-of-load-probability or LOLP, reserve margin, etc.)   Therefore, marginal
costs depend on the target reliability level, when in fact economic theory
suggests that reliability should also be treated as a variable to be optimized,
and both price and capacity (or equivalently, reliability) levels should be
optimized simultaneously. The optimum price is the marginal cost price as
described earlier, while the optimum reliability level is achieved when the
marginal cost of capacity additions (to improve the reserve margin) are equal
to the expected value of economic cost savings to consumers due to electricity



- 17 -
supply shortages averted by those capacity increments. These considerations
lead to a more generalized approach to system expansion planning as shown
below. 1/
Consider a simple expression for the net benefits (NB) of elec-
tric:ity consumption, which is to be maximized:
NB(D,R) = TB(D) - SC(D,R) - OC(D,R)
where TB = total benefits of consumption if there were no outages; SC = supply
costs (i.e., system costs); OC = outage costs (i.e., costs to consumers of
suplply shortages); D = demand; and R = reliability.
In the traditional approach to system planning both D and R are
exogenously fixed, and therefore NB is maximized, when SC is minimized, i.e.,
least cost system expansion planning. However, if R is treated as a variable:
d(Na) W -a  (S Ct + o                   (ra--)s+-oc). !b  = o
is the necessary first order maximization condition.
Assuming    a,               elds :       sC)  5 _ -CR
Therefore, as described earlier, reliability should be increased by
adding to capacity until the above condition is satisfied. An alternative
way of expressing this result is that since TB is independent of R, NB is
maximized when total costs: TC = (SC + OC) are minimized. The above
criterion is one which effectively subsumes the traditional system planning
rule of minimizing only the system costs. 2/
1/   For details see M. Munasinghe, "A New Approach to System Planning,"
- =IEEE Transactions on Power Apparatus and Systems, vol. PAS-78, (July-
.August 1979).
2/   The emphasis on outage costs requires greater effort to measure these
costs; see M. Munasinghe and M. Gellerson, Economic Criteria for
Optimnizing Power System Reliability Levels," The Bell Journal of Eco-
nomics, vol. 10 (Spring 1979); and M. Munasinghe, "The Costs of Elec-
tric Power Shortages to Residential Consumers," Journal of Consumer
Economics (forthcoming).



- 18 -
Third, some problems are raised by the dichotomy of having to choose
between short and long run marginal costs, i.e., SRMC versus LRMC. The short-
run (SRMC) may be defined as the cost of meeting additional electricity con-
sumption, with capacity fixed, while the long run marginal cost (LRMC) is the
cost of providing an increase in consumption (sustained indefinitely into the
future) in a situation where optimal capacity adjustments are possible. When
the system is optimally planned and operated (i.e., capacity and reliability
are optimal), SRMC and LRMC coincide. However, if the system plan is sub-
optimal, significant deviations between SRMC and LRMC will have to be resolved
within the pricing policy framework. Finally, if there are substantial out-
age costs outside the peak period, then the optimal marginal capacity costs
may be allocated among the different rating periods in proportion to the
corresponding marginal costs. 1/
B.4 Shadow Pricing
In the idealized world of perfect competition the interaction of
atomistic profit maximizing procedures and atomistic utility maximizing con-
sumers gives rise to a situation that is called pareto-optimal. In this
state, prices reflect the true marginal social costs, scarce resources are
efficiently allocated, and for a given income distribution, no one person
can be made better off without making someone else worse off. 2/
1/   It has been suggested that capacity costs should be allocated to dif-
ferent rating periods in inverse proportion to LOLP, but this would be
unsatisfactory because aggregate reliability indices such as LOLP are
poor proxies for pro-rating outage costs.
2/   See for example:  E. J. Mishan, Cost Benefit Analysis, Praeger, New York
(1976) part vii.



- 19 -
However, conditions are likely to be far from ideal in the real
world. Distortions due to monopoly practices, external economies and dis-
economies (which are not internalized in the private market), interventions
in the market process through taxes, import duties and subsidies, etc., all
result in market (or financial) prices for goods and services, which may
divrerge substantially from their shadow prices or true economic values. More-
over, if there are large income disparities, the passive acceptance of the
existing skewed income distribution, which is implied by the reliance on
strict efficiency criteria for determining economic welfare, may be socially
and politically unacceptable. Such considerations necessitate the use of
appropriate shadow prices (instead of marklet prices) of inputs to the elec-
trLcity sector, to determine the optimal investment program as well as LRMC,
eslpecially in the developing countries where market distortions are more
prevalent.
The basic concepts of shadow pricing are summarized below, with
special reference to so called efficiency (shadow) prices which emphasize effi-
cient resource allocation and neglect income distributional considerations. 1/
In order to derive a consistent set of shadow prices for goods and
services it is necessary to adopt a common yardstick or numeraire to measure
economic value. For example, a rupee's (or dollar's) worth of a certain good
purchased in a duty free shop is likely to be more than the physical quantity
1/   For details including a discussion of social shadow prices which incorpo-
rate income distributional effects, see: M. Munasinghe and J. J. Warford,
"Shadow Pricing and Power Tariff Policy," in Marginal Costing and Pricing
of Electrical Energy, op. cit., pp. 159-180. A more general reference is:
L. Squire and H. van der Tak, Economic Analysis of Projects, Johns
Hopkins Press, Baltimore (1975).



- 20 -
of the same good obtained for one rupee (or one dollar) in a retail store,
after import duties and taxes have been levied. Therefore, it is possible to
intuitively distinguish between a border priced rupee, which is used in inter-
national markets free of import tariffs, and a domestic priced rupee, which
is used in the domestic market subject to various distortions. A more sophis-
ticated example of the value differences of a currency unit in various uses
arises in countries where the aggregate investment for future economic growth
is considered inadequate. In such a case, a rupee of savings (which could be
invested to increase the level of future consumption) may be considered more
valuable in the national context than a rupee devoted to current consumption.
One numeraire that has proved to be most appropriate in many in-
stances is a unit of uncommitted public income at border prices, which is
essentially the same as freely disposable foreign exchange available to the
government, but expressed in terms of units of local currency converted at the
official exchange rate. 1/ Therefore, the discussion in the next section is
developed in terms of this particular yardstick of value. The border priced
numeraire is particularly relevant for the foreign-exchange scarce developing
countries, and represents the set of opportunities available to a country to
purchase goods and services on the international market. The numeraire and
shadow prices are in real terms, i.e., net of inflation.
The estimation and use of shadow prices is facilitated by dividing
economic resources into tradable and non-tradable items. The values of
1/   See I.M.D. Little and J. A. Mirrless, Project Appraisal and Planning for
Developing Countries, Basic Books, New York (1974), Chap. 9, and L. Squire
and H. van der Tak, op. cit., chap. 3. A numeraire based on private con-
sumption is advocated in: P. Dasgupta, A. Sen and S. Marglin, Guidelines
for Project Evaluation (UNIDO), United Nations, New York (1972).



- 21 -
directly imported or exported goods and services are already known in terms
of their border prices, i.e., their foreign exchange costs, converted at the
official exchange rate. However, locally purchased items whose values are
known only in terms of domestic market prices, need to be converted to border
shadow prices by multiplying the former prices by appropriate conversion
factors (CF). 1/ The free trade assumption is not required to justify the
use of border prices since domestic price distortions are, in effect, adjusted
by netting out all taxes, duties and subsidies.
The most important tradable inputs used in the electric power sector
are capital goods and petroleum-based fuels; in each case world market or
border prices (c.i.f. for imports and f.o.b. for exports) may be used as
shadow prices where appropriate. In some countries other fuels, such as coal
deposits, are available, for which there may be no clear-cut alternative (ex-
port) market. In these cases, the marginal social cost (MSC) of production
e.g., resource cost of extracting the coal, may be used. The most important
non-tradable primary factor inputs are labor and land, which are discussed
later. The shadow prices of other non-tradable goods and services from many
sectors can be determined in terms of their MSC through appropriate decompo-
sition. For example, suppose one rupee's worth (in domestic market prices)
of the output of the domestic construction sector may be broken down succes-
sLvely into n components (such as capital, labor, materials, etc.), which
are themselves valued at rupees a1, a2, ..., a  (in terms of border prices).
1t   In the subsequent discussion the pair of terms:  border and shadow
prices, will be used synonymously, as well as the pair: domestic and
market prices.



- 22 -
Since the conversion factor of any good is defined as the ratio of the border
price to domestic price, the construction conversion factor equals:
In the case of non-tradables which are not important enough to
merit individual attention, or lack sufficient data, the standard conversion
factor (SCF) may be used. The SCF is equal to the official exchange rate
(OER) divided by the more familiar shadow exchange rate (SER), appropriately
defined. Conversion of domestic priced values into border price equivalents
by application of the SCF to the former, is conceptually the inverse of the
traditional practice of multiplying foreign currency costs by the SER (instead
of the OER), to convert to the domestic price equivalent. A convenient
approximation to the standard conversion factor is the ratio of the official
exchange rate to the free trade exchange rate (FTER), when the country is
moving toward a freer trade regime. This estimate of the SCF therefore
reflects the average level of import duties and exports subsidies, and is
usually less than unity.
Consider a typical case of unskilled labor in a labor surplus
country, e.g., rural workers employed for dam construction. The foregone
output of workers used in the electric power sector is the dominant component
of the shadow wage rate (SWR). Complications arise because the original rural
income earned may not reflect the marginal product of agricultural labor, and
furthermore, for every new job created, more than one rural worker may give up
his former employment. Allowance must also be made for seasonality of activi-
ties such as harvesting. In theory, if the laborer has to work harder in a
new job than before, then the disutility of foregone leisure should be included
in the SWR, but in practice this component is ignored. Overhead costs incurred,



- 23 -
such as transportation expenses, should also be considered. The foregoing
may be summarized by the following basic equation for the efficiency shadow
wage rate:
ESWR - a.m + c.u
where m and u are the foregone marginal output and overhead costs of labor
in domestic prices, and a and c are corresponding conversion factors to
convert these values into border prices.
In the case of land inputs, the appropriate shadow value placed on
this primary factor depends on its location. In most cases, it is assumed
that the market price of urban land is a good indicator of its economic
value in domestic prices, and the application of an appropriate conversion
factor, e.g., the SCF, to this domestic price will yield the border price
cost of urban land inputs. Rural land which has an alternative use in agri-
culture may be valued at its opportunity cost, i.e., the net benefit of fore-
gone agricultural output. The marginal social cost of other rural land is
usually assumed to be negligible, unless there is a specific reason to the
contrary, e.g., the flooding of virgin jungle because of a hydroelectric
dam may involve the loss of valuable timber or spoilage of a recreational
area which has commercial potential
The shadow price of capital is usually reflected in the discount
rate or accounting rate of interest (ARI), which is defined as the rate of
decline in the value of the numeraire over time. In practice the opportunity
cost of capital (OCC) may be used as a proxy for the ARI, in the pure effi-
ciency price regime. The OCC is defined as the expected value of the annual
stream of consumption (in border prices), net of replacement, which is yielded
by the investment of one unit of public income, at the margin.



- 24 -
If the LRMC is calculated by shadow pricing the inputs using
border prices, it is necessary to make a further adjustment to convert this
shadow priced LRMC into an equivalent optimal electricity price which will
be perceived and interpreted by consumers like any other domestic market
price. Thus, if only economic efficiency considerations are considered, a
typical expression for the optimal market price based on LRMC would be:
Pe*  =  (MCBe/b)
As explained in Appendix 2, the value of b for a given consumer
group depends on the expenditure pattern of these electricity users, and
therefore  it is possible to have different prices p * for various categories
of electricity consumers, e.g., residential, industrial, etc., based on the
same value of MCB . However, it may sometimes be simpler to use an economy
wide average value of b, such as the SCF, for all electricity consumers, espe-
cially when detailed information on different consumer categories is unavail-
able. In such a case, since SCF < 1 usually, the optimal market price is
greater than the border priced LRMC, i.e., p e* > MCB . 1/
1/   A simple numerical example will illustrate this point.  Suppose that
based on the world import price for high speed diesel fuel and the
running costs of peaking gas turbines, the border priced LRMC of peak
period energy is MCB = Pesos 1.6 per kWh, i.e., USJ8 per kWh times the
official exchange rate (OER) of Pesos 20 per US$. Let the appropriate
shadow exchange rate (SER) which reflects the average level of import
duties and export subsidies (e.g., FTER) be Pesos 25 per US$. There-
fore SCF = OER/SER = 0.8 and the optimal market price for peak period
energy: pe* = 1.6/0.8 = Pesos 2 per kWh.



- 25 -
Section C
Calculating Strict LRMC
Strict LRMC may be defined broadly as the incremental cost of
cptimum adjustments in the system expansion plan and system operations
attributable to an incremental demand increase which is sustained into the
future. 1/  However, LRMC must be evaluated within a disaggregated frame-
work. This structuring of LRMC is based chiefly on technical grounds and
may include: differentiation of marginal costs by time of day, voltage level,
geographic area, season of the year, and so on. The degree of structuring
ancl sophis-ication of the LRMC calculation depends on data constraints and
the useftul.ess of the results, given the practical problems of computing and
applying a complex tariff; e.g., in theory, the LRMC of each individual
cornsumer at each moment of time, may be estimated.
The calculation of strict LRMC is discussed below, 4,tih the struc-
turing framework limited to one which is of operational val,e I4 a typical
developing country.  Points at which the computation may be pMrsued at a more
sophisticated level are indicated in the text. The methoaciogy u. computing
1/   The word increment is used to convey the concept of a small but dis-rete
lump of costs or demand, since the term marginal is often itlterpreted in
the strictly mathematical sense, with reference to ,n iMfinitesimal change.
In the present context, both words may be used interchangeably, tq d-enote
a discrete change.



- 26 -
LRMC is summarized but no attempt has been made to present a complete case
study, because of space limitations. 1/
C.1 Cost Categories and Rating Periods
Three broad categories of marginal costs may be identified for
purposes of the LRMC calculations: capacity costs, energy costs and con-
sumer costs. Marginal capacity costs are basically the investment costs of
generation, transmission and distribution facilities associated with supplying
additional kW. Marginal energy costs are the fuel and operating costs of
providing additional kWh. Marginal customer costs are the incremental costs
directly attributable to consumers including costs of hook-up, metering and
billing. Wherever appropriate, these elements of LRMC must be structured by
time of day, voltage level and so on, as mentioned earlier.
The first step in structuring is the selection of appropriate rating
periods. By examining the system load duration curves, it is possible to
determine periods during which demand presses on capacity, e.g., at a partic-
ular time of day, or in a given season of the year. To clarify the following
presentation, we make the simplifying assumptions that the system under study
does not exhibit marked seasonability of demand (or supply, where hydro gen-
eration is involved), and that these are only two rating periods by time-of-
1/   Several recent case studies are available, involving LRMC calculations in
a variety of situations including: R. Turvey and D. Anderson, Electricity
Economics, op.cit.; C. J. Cicchetti, W. J. Gillen and P. Smolensky, The
Marginal Cost and Pricing of Electricity, Ballinger Publishing Co.,
Cambridge, Mass. (1977), and M. Munasinghe, "Marginal Cost Based Tariff
Calculations in Developing Countries," EWT Dept. Report, World Bank,
Washington, D.C. (1979).



- 27 -
day, i.e., peak and off-peak. 1/ Other aspects of structuring will be intro-
duced later during the analysis.
C.2 Marginal Capacity Costs
Consider Figure C.1 which shows the typical annual load duration
curve (LDC) for the system ABEF in the starting year 0, as well as the two
rating periods: peak and off-peak. As demand grows over time, the LDC
increases in magnitude, and the resultant forecast of peak demand is given
by the curve D in Figure C.2, starting from the initial value MW . The LRMC
of capacity may be determined by asking the following question: what is the
change in system capacity costs AC associated with a sustained increment AD
in the long run peak demand (as shown by the shaded area of Figure C.1 and
the broken line D + AD in Figure C.2). Consequently, the LRMC of generation
would be ( ' C), where the increment of demand AD is marginal both in time,
and in terms of MW. 2/
1/   If the duration of the peak period is defined too narrowly, peak-load
pricing is more likely to cause a shift in the peak to the off-peak
period (see also sub-section B.3). For a review of the application and
results of peak load pricing policies in European countries, see:
B. M. Mitchell, W. G. Manning, Jr., and J. P. Acton, Peak Load Pricing,
Balliner Publ. Co., Cambridge, Mass. (1978). Some very recent results
of time-of-day pricing studies in the U.S. are given in: A. K. Miedama,
S. B. White, C. A. Clayton and D. P. Lifson, "Analysis of Experimental
Time of Use Electricity Prices," Tenth Annual Conference on Current
Issues in Public Utility Regulation, Williamsburg, Va. (December 1978),
Research Triangle Institute, North Carolina.
2/   In theory, AD can be either positive or negative, and generally the
ratio ( AC/ AD) will vary with the sign as well as the magnitude of AD.
If many such values of ( AC/ AD) are computed, it is possible to average
them to obtain LRMC.  However, the easiest procedure would be to consider
only a single representative positive increment of demand.



- 28 -
In an optimally planned system, the change in the expansion program
to meet the new incremental load wouJ.d normally consist of advancing the
commissioning date of future plant or inserting new units such as gas turbines
or peaking hydro plant (see Figure C.2). If system planning is carried out
using a computerized model, it is relatively easy to determine the change in
capacity costs AC by simulating the expansion path and system operation, with
and without the demand increment AD. 1/ Even if such a computer model is
unavailable, it is usually possible to use simple considerations to derive
marginal capacity costs. For example, suppose gas turbines are used for
peaking; then the required LRMC of generating capacity (LRMC   n  C   ) is the
cost of advancing 1 kW of gas turbines, which may be estimated in terms of
the cost per kW installed, annuitized over the expected lifetime. This figure
must be adjusted for the reserve margin (RM%) and losses due to station use
(L  %). Thus, a typical expression would be:
LRMC4ve  C&~. = { A05tP         A} . (I + RM/IIo)|(I  -  L/O/ioO)
In our simple model, all capacity costs are to be charged.to peak
period consumers. 2/  Therefore, if the capacity costs of base load generating
units are to be included in the calculations,it is very important to net out
potential fuel savings due to displacement of less efficient plant by these
1/   If a more sophisticated tariff structure having more rating periods is
used, then the LRMC in any rating period may be estimated by simulating
the computerized system expansion model with a sustained load increment
added to the LDC during that period, i.e., just as in the case of the
peak period analysis.
2/   As discussed in Section B.3, if expected outage costs are significant
in a rating period outside the peak period, then it is possible to
allocate marginal capacity costs over several rating periods.



A                -2-
I /
plours   AtZ~~~~~~~~(wrs
^  : -                2~~Of- Pea
Figurf! C.I1. Typical Annual Load l)uration Curve (LDC)
,3-mk   i               I       anned    I
Fu                                                      I
/~~/
li!I.I
Figure 0 .1. Typicalt Annueal Loadr DuratindCre C
=~    . .-



- 30 -
new base load units. 1/ The rationale underlying this conclusion is clarified
in Appendix 1, using a simplified system model.
Next, the LRMC of transmission and distribution (T&D) are calcu-
lated. Generally, all T&D investment costs are allocated to incremental
capacity, because the designs of these facilities are determined principally
by the peak kW that they carry rather than the kWh. 2/ The concept of struc-
turing by voltage level may be introduced at this stage. Consider three supply
voltage categories: high, medium and low (HV, MV, LV). Consumers at each
voltage level are charged only upstream costs. Therefore, capacity costs at
each supply voltage must be identified.
For example, assume that data is available on the investment costs
associated with extra high voltage (EHV) and the HV transmission facilities.
Next, the average incremental costs 3/ (AIC) of EHV and HV transmission could
1/   From a practical point of view, it is clear that if peak consumers are
incorrectly charged the high capacity costs of expensive base load units
(e.g., nuclear), then it may encourage them to install their own captive
gas turbine plant. Even intuitively, such a pricing policy would not
appear to be very sensible.
2/   Particularly at the distribution level, the size of a given feeder may
depend on local peak demand which may not occur within the system peak
period. This complicates the problem of allocating distribution capacity
costs among the various rating periods (see for example, M. Boiteux and
P. Stasi, op. cit.)
3/   Suppose that in year i, AMWi and I  are the increase in demand served
(relative to the previous year), anA the investment cost respectively.
Then, the AIC of capacity is given by:
AIC  -L'Z le/(t-r)'          'AN/ci :  o   ee/ r)LI
where r is the discount rate (e.g, the opportunity cost of capital) and
T is the planning horizon (e.g., > 10 years). We note that in the AIC
method the actual additional increments of demand are considered as they
occur, rather than the hypothetical fixed demand increment AD used (more
rigorously) in calculating generation LRMC. However, because there is no
problem of plant mix with T&D investments, AIC andthe hypothetical incre-
ment method will yield similar results, while AIC is usually much easier
to calculate using rapidly available planning data. For a more detailed
description of AIC, see: R.J. Saunders, J.J. Warford and P.C. Mann,
"Alternative Concepts of Marginal Cost Pricing for Public Utility Pricing:
Problems and Applications in the Water Supply Sector", Staff Working
Paper No, 259, World Bank, Washington D. C. (May 1977).



- 31 -
be computed, and annuitized (using the discount rate) over the lifetime of
the plant (e.g., 30 years) to provide an estimate of this element of marginal
costs ( &LRMC HV). Then, the total LRMC of capacity during the peak period,
at the HV level would be:
LRMC        = LRMC          /(1-L  /100) + IALRMC
HV Cap.       Gen. Cap.      HV               HV
where LHV % is the percentage of incoming peak power that is lost in EHV and
and HV network.
This procedure may be repeated at the MV and LV levels. Thus the
LRMC of capacity to medium voltage consumers is given by:
LRMV Cap.   LRMCHV Cap /(1-L mv/100) + ALRMCMV
where ALRMCmv is the element of incremental MV capacity costs (e.g., AIC of
distribution substations and primary feeders), L mv% is the percentage of in-
coming peak power that is lost at the MV level.
The LRMC of T&D calculated in this way is based on actual growth of
future demand, and averaged over many consumers. However, some exceptions
should be noted. First certain transmission li es may be specifically asso-
ciated with particular generating sites (e.g., remote hydro), and therefore
could be considered a generation cost rather than a transmission cost.
Second, some transmission may be associated with specific loads, and there-
fore the costs of such facilities should be allocated accordingly. For
example, suppose that a particular system has two geographically distinct
load areas: a central area consisting of a group of cities, and a remote
area which is predominantly rural. Then the concept of a generation power
pool can be used to calculate a common generating cost for serving both areas,
but different transmission costs may be determined for each area by allocating



- 32 -
the costs of transmission links appropriately. Third, it may be possible
to identify facilities which are specific to certain consumers, and these
could be allocated to consumer costs; e.g., a special sub-transmission link
and substation for a large industry. This last point is also important in
dividing the distribution costs between LV and consumer costs; e.g., a given
customer may have a very long service drop line which should be specifically
allocated to this user, rather than being included in the LV AIC calculation.
C.3 Marginal Energy Costs
With reference to Figure C.1, it may be deduced that LRMC qf energy
during the peak period will be the running costs of the machines to be used
last in the merit order, to meet the incremental peak kWh represented by   D.
In our simple model, this would be the fuel and operating costs of gas tur-
bines. These costs have to be adjusted by the appropriate peak loss factors
at each voltage level, as in the case of marginal capacity costs.
Similarly, the LRMC of off-peak energy corresponding to a load
increment during the off-peak period would usually be the running costs of the
least efficient base load or cycling plant used during this period. 1/ We
note that the loss factors for adjusting off-peak costs will be smaller than
the peak period loss factors; resistive losses are a function of the square of
the current, and current flows are greatest during the peak period. 2/
1/   Exceptions to this generalization would occur when the marginal plant
used during a rating period was not necessarily the least efficient
machine that could have been used. For example, less efficient plants
which have long start-up times and are required in the next rating
period, may be operated ealier in the loading order than more efficient
plant. This would correspond to minimization of operating costs over
several rating periods rather than on an hourly basis.
2/   See for example:  C. J. Cicchetti, W. J. Gillen and P. Smolensky,
op. cit.



- 33 -
Some complications arise particularly in the case of all-hydro and
mixed hydro-thermal systems. First, a predominantly hydro system may be
energy constrained, i.e., it may be short of reservoir storage rather than
generating capacity. Thus all incremental capacity is needed primarily to
generate more energy because the energy shortage precedes the capacity con-
straint. In this case, the distinction between peak and off-peak costs,
and between capacity and energy costs, tends to blur. Because hydro energy
consumed during any period (except when spilling) usually leads to an equi-
valent drawdown of the reservoirs, it may be sufficient only to levy a simple
kWh chage at all times, e.g., by applying the AIC method of total incremental
system costs.
Second, where hydro is involved, marginal energy costs have to be
determined carefully. These costs would be close to zero, at times when water
is being spilled or mandatorily run-off for other purposes (e.g., irrigation).
HDwever, in a mixed hydro-thermal system, if the hydro is used to displace
more expensive thermal plant, then the running cost of the latter is the
relevant marginal energy costs.
Third, if the pattern of operation is likely to change rapidly in
the future (e.g., shift from gas turbines to peaking hydro as the marginal
peaking plant, or vice versa), then the value of the LRMC of energy would have
to be calculated as a weighted average, with the weights depending on the
share of future generation by the different types of plant used.
C.4 Consumer Costs
These costs are those which can be readily allocated to customers.
Fixed customer costs consist of non-recurrent expenses attributable to items



-34 -
such as service drop lines, meters and labor for installation. These costs
may be charged to the customer as a lump sum or distributed payments over
several years.
Recurrent customer costs occur due to meter reading, billing,
administrative and other expenses. These could be imposed as a flat charge,
on a repeated basis, in addition to the usual kW and kWh charges. In general,
the allocation of incremental (non-fuel) operation, maintenance and adminis-
trative costs among the three basic categories of costs: capacity, energy and
customer, varies from system to system and requires specific analysis. How-
ever, these costs are usually small and will not greatly affect the results.
Section D
Adjusted LRMC Tariff Structure
Once strict LRMC has been calculated, the first stage of tariff
setting is complete. In the second stage, the actual tariff structure which
meets economic second best, social, financial, political and other constraints
must be derived by modifying strict LRMC, and this topic is dealt with below.
This process of adjusting LRMC will, in general, result in deviations in both
the magnitude and structure of strict LRMC. Changes in tariff structure at
this stage will be based mainly on socio-political factors, e.g., differen-
tiation by type of consumer (residential, commercial, industrial and so on),
or by income level (poor, middle and high income residential). Practical con-
siderations such as the difficulties of metering and billing will also affect
the final tariff structure.



- 35 -
The constraints which necessitate deviations in the final tariffs
relative to strict LRMC fall into two categories. 1/ The first group consists
of distortions which may be analyzed basically within an economic framework,
i.e., second best considerations and subsidized (or lifeline) tariffs for low
:ncome consumers. In these cases, it is possible to quantify the extent of
the deviation from strict LRMC by using an appropriate pricing model and
explicit system of shadow prices. The second group includes all other con-
siderations such as financial viability, socio-political constraints and
problems of metering and billing where strict economic analysis is difficult
to apply. These two groups of constraints may be interrelated, e.g., sub-
sidized tariffs can simultaneously have economic welfare, financial and
socio-political implications.
D.1 Second Best Considerations
Where prices elsewhere in the economy, especially in the case of
substitutes and complements for electric power, 2/ do not reflect marginal
costs, a "second best" departure from a strict marginal cost pricing policy
fcor electricity services may be required. For example, the subsidies
for imported generators and/or diesel fuel,which exist in many developing
1J   We note that strict (shadow priced) LRMC also deviates from the LRMC
calculated on the basis of financial costs, because shadow prices are
used instead of the market prices of electricity sector inputs. This
is done to correct the distortions in the economy. Therefore, thie
constraints which force further departures fron strict LRMC (in the
second stage of the tariff setting procedure) may also be considered
consequently as distortions which impose their own shadow values on the
calculation. See M. Munasinghe and J. J. Warford, op.cit., for details.
2!   More generally, price distortions affecting inputs into the production
of electric power and outputs of other sectors which are electricity
intensive (e.g., aluminium) should also be considered. The former
category may be dealt with by direct shadow pricing of inputs, while
the latter requires more detailed analysis (although such cases are rare).



- 36 -
countries, may make it advantageous for users to set up their own captive
plant, even though to the economy as a whole this is not the least cost way
of meeting the demand. The appropriate solution in this case might be for
the government to revoke such subsidies or restrict imports of private
generating plant. However, if transportation policy dictates the need to
maintain subsidies for diesel fuel, or if strong pressure groups make such
changes politically unfeasible, the low cost of (subsidized) private genera-
tion may require the setting of an optimal grid supplies electricity price,
which is below strict LRMC. The extent of the deviation from strict LRMC is
determined by the magnitude of the subsidy and degree of substitutability of
the alternative energy source (see Appendix 2 for details).
A related question concerns the availability of subsidized kerosene
which in many developing countries is aimed mainly at providing basic energy
requirements for low income consumers at prices they can afford. 1/ In part,
the subsidy may also prevent low income households especially in rural area
from shifting to use of non-commercial fuels, e.g., wood, the over-use of
which leads to deforestation and associated environmental consequences, or
animal dung, which has a high opportunity cost as a fertilizer. If we assume
the kerosene subsidy as given, then once again the price of electricity must
be reduced proportionately.
1/   However, a number of unfortunate side effects may follow, including the
practice of mixing kerosene with gasoline, which is typically sold at a
higher price per gallon. The income distributi6n effects of such a
policy may also be perverse. For example, in some countries the rela-
tively wealthy have benefitted from the subsidy by converting prime
movers which use other fuels, such as motor car engines, to kerosene use.



- 37 -
D.2 Subsidized or Lifeline Rates
In addition to the second best economic arguments (e.g., associated
with subsidized kerosene), socio-political or equity arguments are often
advanced in favor of "lifeline" rates for electric power, especially where
the costs of electricity consumption are high in comparison to the relevant
income levels. While the ability of electric power utilities to act as dis-
criminating monopolists gives them an advantage in addressing these issues,
it is clear that the appropriateness of the "lifeline" rate policy and the
size of the rate blocks requires detailed analysis. Such an analysis would
involve the study of a whole chain of interrelated energy and other effects,
which are generally of a higher order of complexity in developing countries
thasn in the developed-country context.
Domestic
Price
G
12 > Il
P                                        \       H
e   _ _ _ _.i\
A
F          B
5 ~ ~   '                      ' I-- 
Ql   <mn.                          Q2       Quantity
Figure D.1: ECONOMIC BASIS FOR THE SOCIAL OR LIFELINE RATE



38 -
The concept of a subsidized "social" block, or "lifeline" rate,
for low income consumers has another important economic rationale, based on
the income redistribution argument. We clarify this point with the aid of
Figure D.1 which shows the respective demand curves AB and GH of low (11) and
and average (I 2) income domestic users, the social tariff P  over the minimum
consumption block 0 to Q min  and the marginal cost based price level P . All
tariff levels are in domestic market prices.  If the actual tariff P - P e
then the average household will be consuming at the "optimal" level Q29 but
the poor household will not be able to afford the service.
If increased benefits accruing to the poor have a high social value,
then, although in nominal domestic prices the point A lies below P  , the con-
sumer surplus portion ABF multiplied by the appropriate social weight w could
be greater than the shadow price of supply. The adoption of the increasing
block tariff shown in Figure D.1, consisting of the lifeline rate P , followed
by the full tariff P  , helps to capture the consumer surplus of the poor user,
but does not affect the optimum consumption pattern of the average consumer. 1/
In practice, the magnitude Q i  has to be carefully determined, to avoid sub-
siding relatively well-off consumers; it should be based on acceptable cri-
teria for identifying "low income" groups, and reasonable estimates of their
minimum consumption levels (e.g., sufficient to supply basic requirements for
lighting and minor appliances). 2/  The level of P  relative to strict LRMC
1/   Ignoring the income effect due to reduced expenditure of the average
consumer for the first block of consumption, i.e., up to Q mi.
2/   In most developing countries Q i would be less than 100 kWh per month.



- 39 -
may be determined on the basis of the poor consumer's income level relative
to some critical consumption level, as shown in Appendix 2.  The utility's
revenue constraints would also be considered in determining P  and Q in.
This approach may be reinforced by an appropriate connections policy (e.g.,
subsidized house connections, etc.).
D.3       Financial Viability
The financial constraints most often encountered relate to the
revenue requirements of the sector, and are often embodied in criteria
such as some target financial rate of return on assets, or an acceptable
rate of contribution towards the future investment program. In principle, for
state-owned power utilities, the most efficient solution would be to set
price equal to marginal cost and rely on government subsidies (or taxes) to
meet the utilities financial needs. In practice, some measure of financial
autonomy and self-sufficiency is an important goal for the sector. Because of
the premium that is placed on public funds, a marginal cost pricing policy
which results in failure to achieve minimum financial targets for continued
operation of the power sector, would rarely be acceptable. The converse and
more typical case, where marginal cost pricing would result in financial
surpluses well in excess of traditional revenue targets, most often leads to a
situation which is politically embarrassing. Therefore in either case,
changes in revenues have to be achieved by adjusting the strict marginal cost
tariffs.
It is intuitively clear that discriminating between the various con-
sumer categories so that the greatest divergence from the marginal cost price
occurs for the consumer group with the lowest price elasticity of demand, and



- 40 -
vice versa, will result in the smallest deviations from the "optimal" levels
of consumption consistent with the strict marginal cost pricing rule. 1/
Generally, in developing countries the necessary data for the analysis of
demand by consumer categories is rarely available, so rule-of-thumb methods
of determining the appropriate tariff structure have to be adopted. However,
the fiscal implications of an increasing cost industry (i.e., marginal costs
greater than average costs) should be exploited to the full. Thus electric
power tariffs (especially in a developing country) constitute an excellent
means of raising public revenues in a manner which is generally consistent
with the economic efficiency objective, at least for the bulk of the consumers
who are not subsidized, while at the same time helping to supply basic energy
needs to low income groups.
D.4 Other Considerations
There are several additional economic, political and social con-
siderations that may be adequate justification for departing from a strictly
marginal cost-based tariff policy. The decision to electrify a remote rural
area, which may also entail subsidized tariffs because the beneficiaries are
not able to pay the full price based on high unit costs, could be made on
completely non-economic grounds, e.g, for general socio-political reasons such
as maintaining a viable regional industrial or aricultural base, stemming
rural to urban migration, or alleviating local political discontent. How-
ever, the full economic benefits of such a course of action may be much
1/   See W. J. Baumol and D. F. Bradford, "Optimal Departures from Marginal
Cost Pricing," Am. Econ. Rev., June 1970, pp. 265-283; and M. S. Feldstein,
"Distributional Equity and the Optimal Structure of Public Prices,"
Am. Econ. Rev., 1973, pp. 32-36.



- 41 -
greater than the apparent efficiency costs which arise from any divergence
between actual price and marginal cost. Again, this possibility is likely
to be much more significant in a developing country than in a developed one,
not only because of the high cost of power relative to incomes in the former,
but also because the available administrative or fiscal machinery to redis-
tribute incomes or achieve regional or industrial development objectives by
other means is frequently ineffective.
For the same reason, it is particularly difficult to reform pricing
policy where low incomes and a tradition of subsidized power combine to create
extreme difficulties in raising prices to anywhere near marginal costs. In
practice, price changes have to be gradual, in view of the costs which may be
imposed on those who have already incurred expenditures on electrical equipment
and made other decisions, while expecting little or no changes in traditional
power pricing policies. The efficiency costs of "gradualism" can be seen as
an implicit shadow value placed upon the social benefits that result from this
policy.
D.5 Metering and Billing
Owing to the practical difficulties of metering and billing, the
tariff structure may have to be simplified. For example,the number of
customer categories, rating periods, consumption blocks, voltage levels, and
so on, will have to be limited.
The degree of sophistication of metering (e.g., by time of day)
depends on the net benefit of metering, problems of installation and mainte-
nance, and so on. Thus, for very poor consumers receiving a subsidized rate,
a simple current limiting device may suffice, because the cost of even simple
kWh metering may exceed the net benefit equal to the lower supply cost of



- 42 -
reduced consumption, less the decrease in consumption benefits. In general,
various forms of peak load pricing (i.e., maximum demand or time-of-day
metering) would be more applicable to large MV and HV industrial and commnr-
cial consumers. 1/
Most LV consumption, especially for households, is metered only on
a kWh basis, with the price per kWh based on a combined energy and "rolled in"
capacity charge (e.g., using appropriate coincidence and load factors). More
sophisticated meters, such as time-of-day meters which incorporate synchro-
nous clocks, may be affected by power outages. At the other end of the scale,
current limiting devices are easier to tamper with. Some developing countries
may lack technically skilled labor for installation and maintenance of sophis-
ticated meters, or even reliable meter readers. Therefore, choice of appro-
priate metering is usually very country specific, and is likely to involve
many practical considerations.
1/ For details of metering, see: Electric Utility Rate Design Study, Rate
Design and Load Control, NARUC study, Palo Alto, California (November
1977), pp. 67-77.



- 43 -
Appendix 1
Allocation of Capacity and Energy Costs Among Peak and Off-Peak Users
The simplified model of a typical electric power generation system
is used below to show from a conceptual viewpoint, how a long run marginal
cost (LRMC) analysis based on the optimal system expansion plan yields the
following idealized conclusions. 1/
1.   Peak users should pay off-peak LRMC of capacity as well
as energy costs.
2.   Off-peak users should pay only off-peak LRMC of energy.
3.   LRMC of peak capacity   LRMC of base load capacity
net fuel savings due to this base
load plant.
1/   A more realistic system model would have to consider a number of
complicating factors such as a larger number of rating periods and
plant types, non-coincidence of the rating periods with the economic
crossover points between different plant types, economies of scale
and variable heat rates for a given plant type, hydroelectric plant
including pumped storage, reserve margins and stochasticity of supply
and demand, and so on. The most important difference with respect to
the general case is that some capacity costs would have to be borne by
consumers outside the peak period. However, the bulk of the capacity
costs would still be allocated to peak period users. A simplified
exposition of this result is provided in: J. T. Wenders, "Peak Load
Pricing in the Electric Utility Industry," The Bell Journal of Economics,
Vol. 7, (Spring 1976), pp. 232-41.



-44-
Tot4
Cos ki                         f       /T             ta
b 
9                                                  HTurs of loperationt
bW        ~~IN
°   H                         @~~~~~~9760    Houvrs tezrg",r
Piture 1.1. Plant Costs and-Annual Loadi Duration Curve (LDC)



- 45 -
Consider an all thermal generation system having the annual load
duration curve (LDC) shown in Figure 1.1. There are only two types of plant
whose linearized cost characteristics are given in the table below, and also
in the figure. We ignore for the moment, all losses, reserve margin, etc.
Capacity cost per
kW installed             Operating Costs
Plant Type             (annuitized)                 per hour
1. Peaking (e.g. Gas
Turbines:  GT)           a                           e
2. Base Load
(e.g. steam)             b                           f
Total cost of 1 kW which is used h hours per year:
GT : a + e.h
Base:  b + f.h
Let H be the hours of operation which corresponds to the crossover
point for which GT and Base Load plant total costs are equal.
Therefore, a + e.H - b + f.H
b-a
H =(e-f ) .......................................
The most economic use of plant can be determined by examining the
LDC, OABCEF:
(1) For planned base load operation (i.e. more than H hours per
year), use base load plant; X kW
(2)  For planned peak operation (i.e. less than H hours per year),
use GT; (Y-X) kW
Total annual costs of meeting the demand depicted by the LDC is:-
C  = X (b+f.T) + (Y-X)    (a+e.H)
0



- 46 -
Case 1:   Only peak period demand increases by 1 kW (as shown by shaded
area AGNB in Figure 1.1):
The optimal system planning response is to increase GT by 1 kW.
Total annual cost is C1 - X (b+f.T) + (Y+1-X) (a+e.H)
Therefore, increase in cost:  C 1-C  = a + e.H
This is the increase in system costs incurred because of the
1 kW increase in marginal (or incremental) demand during the
peak period, and thus the peak period user must pay this cost.
The peak costs consist of:
(1) Capacity charge - a per kW per year
(2) Energy charge - e per kWh.
It may be seen that peak users payment - a+e.H - increase in
system costs.
Case 2:   Only off-peak period demand increases by 1 kW (as shown by shaded
area CIJE in Figure 1.1).
The optimal system planning response is to add 1 kW more of base
load plant. But now there is 1 kW less of GT required than before.
Total annual cost: C2 - (X+1).(b4f.T) + [Y-(X+1)] (a+e.H)
Therefore, increase in cost:  C   -c  (b4f.T) - (a+e.H)
2o0
- (b-a) + (f-e).H + f (T-H).
Sustituting for H from equation on (1.1)
C2-Co   (b-a) + (f-e).(b-a)/(e-f) + f.(T-H)
C2-C * f(T-H)



- 47 -
Therefore, the increase in system cost incurred due to the 1 kW
increase in marginal off-peak demand is equal to the energy cost of operating
the base load plant during this period, and thus off-peak users must pay only
this energy charge f per kWh. There are no capacity costs incurred by off
pealk users, since off peak users payment - f(T-H) - increase in system cost.
In particular, we note that the base load capacity cost (b) is
exactly offset by the total cost saving due to GT which is not required any
more (i.e., capacity cost 'a' plus net fuel cost saving (e-f).H inside the
shakded area LKIC). In other words: Peak capacity cost - Base load capacity
costs - net fuel savings: a - b - (e-f).H
Case 3:   Both peak and off-peak demand increases by 1 kW.  This case is
a linear combination of Cases 1 and 2, and therefore consumer
charges are:
(1)  Peak capacity charge:    a per kW per year;
(2)  Peak energy charge:       e per kWh;
(3)  Off-peak energy charge:  f per kWh.
Clearly, total peak and off-peak users payment - b+f.T - increase in system
cost. These results may be generalized to include more types of generating
units, and rating time periods; e.g., n plant types and n rating periods,
where these rating periods are chosen to coincide with the economic crossover
poLnts between competing types of plant.



- 48 -
In this case LRMC prices would be:
O to H    =  peak period   :   capacity charge a1 per kW per year, and
1~~~~~~~~~~~~~~~~~~
energy charge e1 per kWh
H  to H   '  2   period    :   only energy charge e2 per kWh
1     2                                              2
H    to T    nt  period    : only energy charge e~ per kWh
n-In



- 49 -
Appendix 2
Model for Optimal Electricity Pricing in a Distorted Economy
In this appendix, a general expression for the socially optimal
electricity price is developed based on the border prices, to compensate for
distortions in the economy. From the general equation, results for optimal
electricity pricing are derived, for cases which reflect:
(a) a perfectly competitive economy (classified results);
(b) economic second best considerations; and
(c) subsidized social prices or lifeline rates for poor
consumers.
NlaYrket
-hr ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~-
Figure 2.1 SUPPLY AND DEMAND FOR A GOOD



- 50 -
The supply and demand for electricity is shown in Figure 2.1, where
S is the supply curve represented by the marginal cost of supply (evaluated
at domestic market prices of inputs), and D is the corresponding demand curve
for a specific consumer. Starting with the initial combination of price and
consumption (p, Q), consider the impact of a small price reduction ( dp),
and the resultant increase in demand ( dQ), on the net social benefits of
electricity consumption.
Before evaluating the net social benefit of this price change, let
us define several parameters. First, suppose we calculate the marginal cost
of electricity supply MC without shadow pricing the inputs, i.e., in market
prices.  Then a  is defned as the electricity conversion factor (ECF) which
transforms the (market priced) marginal cost of electricity supply MC into the
corresponding real economic resource cost, i.e., when all the inputs to the
electricity sector are correctly shadow priced, the (border priced) marginal
supply cost is MCB  = (a .MC).  Second, we assign a specific social weight W
to each marginal unit of consumption (valued in market prices) of a given
individual i in the economy, e.g., if this electricity user is poor, the
corresponding social weight may be much larger than for a rich customer, to
reflect society's emphasis on the increased consumption of low income groups.
Third, if the given individual's consumption of goods and services other than
electricity (valued in market prices), increases by one unit, then the border
priced marginal social cost of economic resources used (or the shadow cost to
the economy) is b-



- 51 -
As a result of the price reduction, the consumer is using dQ units
more of electricity, which has a market value of (p. dQ) (i.e., area IFGH). 1/
However, the consumer's income has increased by the amount PQ - (P- P)
(Q + dQ), and assuming none of it is saved, this individual's consumption of
other goods and services will increase by the amount (Q. dp-p. dQ), also
valued in market prices (i.e., area BEFG minus area IFGH). Therefore, the
consumer's total consumption, i.e., electricity plus other goods, will in-
crease by the net amount (Q. dp) in market prices. This is the traditional
increase in consumer surplus benefits. The shadow value of this increased
consumption is W  . (Q. dp) where W   is the social weight appropriate to this
consumer's income/consumption level.
Next consider the resource costs of these changes in consumption.
The shadow cost of increasing electricity supply is (a .PMC. dQ), (i.e., a
times area IJKH), and the resources used up to provide the other additional
goods consumed b .(Q. dp - p. dQ), where a  is the conversion factor for
electricity production, and b  is the conversion factor for other goods con-
sumed by this consumer. Finally, the income change of the electricity pro-
ducer must also be considered, but this effect may be ignored if we assume
quite plausibly that the producer is the government.
The total increase in net social benefits due to the electricity
price decrease is given by:
NB = W (p. dQ) - ap.(MC. dQ) + (W c- bc).(Q. dp - p.dQ)
11   The little triangle LFG may be neglected throughout this analysis because
its area is ( dp. dQ)/2, where both  dp and  dQ are small increments.



- 52 -
Therefore:
( dNB/ dp) = Q [(W  - b ) + n.b ] - n.a. .(MC/p)
where n = (p. dQIQ. dp) is the elasticity of demand (magnitude).
The necessary first order condition for maximizing net social benefits, in
the limit, is d(NB)/dp-O. This yields the optimal price level:
p* = a . MC/[b c+ (W c   bc)/n]      (2.1)
This expression may be reduced to a more familiar form, by making
some simplifying assumptions.
Case 1:   Perfectly competitive economy where market prices and shadow prices
are the same, and income transfer effects are ignored, i.e., no
social weighting.
Therefore, a  - W  = b  = 1, and equation (2.1) reduces to:
p * = MC                  (2.2)
c
This is the classical result (discussed in subsection B.1), where net social
benefits are maximized when price is set equal to marginal cost at the market
clearing point (p ,QC ) in Figure 2.1.
Case 2:  Income transfer effects ignored, because the marginal social benefit
of consumption is equal to the marginal social cost to the economy
of providing thip consumption.
Therefore, W = b , and equation (2.1) becomes:
c    c
Pe* = (ap.MC) / bc = MCBe/b          (2.3)
This is the optimal marginal cost based electricity price, when efficiency
(shadow) prices are used which emphasize the efficient allocation of resources
and neglect income distributional considerations.
As mentioned earlier, the marginal social cost of electricity
supply (MCBe) may be evaluated in a straightforward manner by applying the



- 53 -
appropriate shadow prices to the least cost mix of technically determined
inputs used in producing electricity.  However, the conversion factor b-
depends crucially on the type of consumer involved.
For residential electricity consumers, b  represents the consump-
tLon conversion factor (CCF), which reflects the resource cost or shadow
value of one (market priced) unit of the household's marginal consumption
basket.  If the CCF<1, then p *>(MCB ).
Another interesting case illustrates the application of equation
(2.3) to correct for economic second-best consideration arising from energy
substitution possibilities. As an extreme case, suppose all expenditures
diverted from grid supplied electricity will be used to purchase alternative
energy which is subsidized by the government (e.g., kerosene for lighting,
or diesel for autogeneration).  In this case, b  is the ratio of the border
priced marginal cost of alternative energy to its market price; and may be
written:
MICB
b   =     ae
ae
Thus from equation (2.3): 1/
Pe*   MCB e. (P  /MCB  )             (2.4)
e    e   ~ae    ae
1/   The logic of this expression may be clarified by considering the case
when the actual p >p *. Then the shadow cost of one unit of expenditure
on electricity iSeMCg /Pe, while if this sum was used to purchase alter-
native energy the shadow cost would be MCB  /p  .  Since p >p *, MCB /p >
MCB  /p  , and the country is better off i       remor  electricity ts used
insead of the alternative energy.  Therefore,  e should be reduced to
pe*.  Similar reasoning can be used to show that if p <p *, then p  should
be increased to the value Pe*                            e  e          e



- 54 -
Since the alternative energy is priced below its border marginal cost, i.e.,
b > 1, then p e* < MCB also. Therefore, the subsidization of substitute
energy prices will result in an optimal electricity price which is below its
shadow supply cost.
If it is not possible to determine the consumption patterns of
specific consumer groups, then b  could be defined very broadly as the average
conversion factor for all electricity users, e.g., the SCF, as discussed in
subsection B.4.
Case 3:   General
Equation (2.1) is the optimal electricity price when social (shadow) prices
are used, which incorporate income distributional concerns.
Consider the case of a group of very poor consumers for whom we may
assume:  W  >> b (n-1).  Therefore, equation (2.1) may be written:
P * m n.MCB /W
An even greater simplification is possible if it is assumed that n = 1; thus
P * = MCB /W
'8 e c
For illustration, suppose that the income/consumption level of these poor
consumers (c) is 1/3 the critical income/consumption level (c) which is like
a poverty line. Then a simple expression for the social weight is:
W  c 3
c   c
Therefore p5* = MCB /3, which is the "lifeline" rate or subsidized tariff
approprt  t e
appropriate to this group of low income consumers.



- 55 -
REFERENCES
1. W. J. Baumol and D. F. Bradford, "Optimal Departures from Marginal Cost
Pricing" American Economic Review, June 1979, pp. 265-283.
2. M. Boiteux, "La Tarification des Demandes en Pointe," Revue Generale de
l'Electricite, vol. 58 (1949).
3. M. Boiteux and P. Stasi, "The Determination of Costs of Expansion of an
Interconnected System of Production and Distribution of Electricity," in
James Nelson, ed., Marginal Cost Pricing in Practice, Englewood Cliffs,
N.J., Prentice-Hall (1964).
4. C. J. Cicchetti, W. J. Gillen and P. Smolensky, The Marginal Cost and
Pricing of Electricity, Ballinger Publishing Co., Cambridge, Mass (1977).
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7.  P. Dupuit, "De l'Utilite' et de sa Mesure," La Reforma Soziale, Turin,
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8. Electric Utility Rate Design Study, Rate Design and Load Control, NARUC
Study, Palo Alto, California (November 1977), pp. 67-77.
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Public Prices," American Economic Review, 1973, pp. 32-36.
10. H. Hotelling, "The General Welfare in Relation to Problems of Taxation
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11. 1. M. D. Little and J. A. Mirrless, Project Appraisal and Planning for
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State of the Art Conference, Canadian Electrical Association, Montreal
(1978).
13. A. K. Miedama, S. B. White, C. A. Clayton and D. P. Lifson, "Analysis
of Experimental Time-of-Use Electricity Prices," Tenth Annual Conference
on Current Issues in Public Utility Regulation, Williamsburg, Va.
(Dec. 1978), Research Triangle Institute, North Carolina.
14. E. J. Mishan, Cost Benefit Analysis, Praeger, New York (1976), part vii.
15.  B. M. Mitchell, W. G. Manning, Jr., and J. P. Acton, Peak Load Pricing,
Ballinger Publishing Co., Cambridge, Mass. (1978).



- 56 -
16. M. Munasinghe, "A New Approach to System Planning," IEEE Transactions on
Power Apparatus and Systems, vol. PAS-78 (July-August, 1979).
17. M. Munasinghe, Economics of Power System Reliability and Planning, Johns
Hopkins Press, Baltimore (1979).
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Countries," EWT Dept. Report, World Bank, Washington, D.C. (1979).
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Consumers," Journal of Consumer Economics (forthcoming).
20.  M. Munasinghe and M. Gellerson, "Economic Criteria for Optimizing Power
System Reliability Levels," The Bell Journal of Economics, vol. 10
(Spring 1979), pp. 353-365.
21.  M. Munasinghe and J. J. Warford, "Shadow Pricing and Power Tariff
Policy," in Marginal Costing and Pricing of Electrical Energy, op. cit.,
pp. 159-180.
22. N. Ruggles, "The Welfare Basis of the Marginal Cost Pricing Principle,"
Review of Economic Studies, Vol. 17 (1949-59), pp. 29-46.
23. N. Ruggles, "Recent Developments in the Theory of Marginal Cost Pricing,"
ibid., pp. 107-126.
24. R.J. Saunders, J.J. Warford and P.C. Mann, "Alternative Concepts of
Marginal Cost Pricing for Public Utility Pricing: Problems of Applica-
tion in the Water Supply Sector", Staff Working Paper No. 259, World
Bank, Washington D. C. (May 1977).
25.  R. Sherman and M. Visscher, "Second Best Pricing with Stochastic Demand,"
American Economic Review, vol. 68 (March 1978), pp. 42-53.
26. P. Steiner, "Peak Loads and Efficient Pricing," Quarterly Journal of
Economics (November 1957).
27.  R. Turvey, Optimal Pricing and Invetment in Electricity Supply,
M.I.T. Press, Cambridge, Mass. (1968).
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Baltimore (1977).
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The Bell Journal of Economics, vol. 7 (Spring 1976), pp. 232-241.
30. 0. E. Williamson, "Peak Load Pricing and Optimal Capacity under
Indivisibility Constraints," The American Economic Review, vol. 56,
No. 4 (Sept. 1966), pp. 810-827.



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337     The Population of Thailand:  Its Growth        S. Cochrane
and Welfare
338     Capital Market Imperfections and               V.V. Bhatt,
Economic Development                           A.R. Roe
339     Behaviour of Foodgrain Production              J. Sarma
and Consumption in India, 1960-77              S. Roy