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Document Numbe(

ELASTICITY OF DEMAND: TOPIC 2

Prepared by Task Force No. 2

Prepared for ELECTRIC UTILITY RATE D~SIGN STUDY~

A nationwide effort by the Electric Power Research Institute, the Edison Electric Institute, 'the American

Public Power A3sociation, and the National Rural Electric Cooperative Association for the

National Association of Regulatory Utility Commissioners

January 31, 1977

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ELASTICITY OF DEMAND: TOPIC 2

Prepared by Task Force No. 2

Ernest G. Ellingson, Task Force Chairman

January 31, 1977

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ELECTRIC· UTILITY RATE DESiGN STUDY . A nationwide effort by tr ·.'Electric Power Research Institute, th~ ~dison Electric Institute, the kmerican 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 (415) 493-4800

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NOTE TO READERS

This report was prepared by Task Force 2. It contains infor­mation that will be considered by the P1:oject Committee along with other reports, data and information prepared by other task forces, several consultants, 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 Task Force 2 contains the findings and reflects the views of that group. The distribution of the document by the rate design study does not im~ly an endorsement by the Project Committee or the organizai:ions, utilities or commissions, participating in the rate design study.

Task Force 2 was formed to examine a portion of the Plan of Study (i.e., "Elasticity of Demand," Topic 2). Two consultants--National Economic Research Associates and .John W .. Wilson and Associates-­were engaged to Provide additional information on "Elasticity of Demand" (i.e., Topic 2). The findings of these consultants appear in companion documents.

Topic 2 is described in the Plan of Study as:

Topic 2 Considerations of Demand Elasticity for Electricity

It is, of course, impossible to measure the effects o£ a proposal that has not been implemented, yet, proponents of time-based rates have asserted that they will have bene­ficial effects while opponents assert either that the effects would be negligi!1le compared with the cost of implementation or that negative benefits vlould ensue ..

The assertion that something wuuld happen in re­sponse i:o time-based rates, wehther the something were good or bad, is an assertion that there is a price elasticity of demand.. The assertion that nothing would happen is a denial that, for electricity prices, elasticity is significantly greater than zero.

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Demand elasticity plays a significant. role in as­sessing the potential shift of customer usage from one time period to another due to price differentials, in determining the revenue effect and the changing costs from such usage shifting, and possibly in the adjustment of rates derived frqm incremental cost pricing to the level acceptable u.-qder the overall revenue requirement constraint of regulation.

Topic 2.1 would be the preparation of a comprehen­sive statement of the several roles of the price elasticity of the demand £or electricity in peak-load pricing, iriclud;ng time-of-day pricing and possibly pr:tcing based on marginal or incremental costs.

Topic 2.2 would then be to marshal the available evidence on the price elasticity of electricity to determ~ne whethar it has been shown to have a value significantly greater than zero, for each of the various classes of cus­tc?~rs, large and small. The several studies which have estimated electric demand elasticities in the United States would be examined and evaluated. There have been a dozen or so such studies of varying quality, which mostly, how­everp consider the effect of price on total kilowatt-hour consumption. It is not contemplated that new research will be undertaken for this topic. Rather, the results of exist­ing studies will-be reviewed, particularly to make an eval­uation of the maximum effec·t that changes in price would have on demand at the peak.

A second phase of this study, and the moJ:~e impor~ tant one, would be to examina more directly the evidence on the elasticity of peak demand. It is this area which is important in evaluating che effectiveness (or lack of it) of peak-load pricing. Lit.tle has been published on this aspect, but experience over the last several years may have yielded data which can provide useful results~

There are two possible sources of data that might yield reasonable inferences concerning differences between elasticities at the peak and the average elasticities. First, especially since October 1973, a large number of utilities have maintained comparative records of both peak (kilowatt) and energy (kilowatt-hour) for both aci:ual and projected send-out.. These data will need to be analyzed in the lig-ht of the increasing sensitivity of usage to weather conditions and of differential price changes during this period, as companies turned more and more to summer-winter rates. An attempt \vill be made to test the generally advanced thesis that "conservation'~ and/or price elasticity had a more marked effect on kilowatt-hour usage than 011 peak demand.

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In s.1ort, the task will be to analyze these data to see whether useful conclusions can safely be drawn. This study wil ... examine the data in the light of three main concerns exprt..ssed by proponents and opponents of peak-load pricing:

a. Can shifts in demand limit long-term capital needs of utilities?

b. If the shifts in demand occur before capital programs can ~e adjusted, will there be serious revenue erosion in tr..e short term?

c. Is time-of-day pricing likely to accentuate a "needle peak 11 and therefore cause revenue erosion with no long-term capital conservation benefits? If so, are there alternative devices such as a fuller use of interruptible rates to avoid this result?

An additional topic (2.3) in the elasticity area (to be sequentially phased in at a later point) arises from the probability that the existing data and the analysis to be conducted will provide insufficient measurement of peak elasticity. Whether or not a program of field experiments should be undertaken to provide further data and information is a matter for additional consideration, perhaps either in conjunction with topic 3 or on the part of individual systems or regulatory agencies. In any event, it seems clear tha·t with or without su~h additional experiments there will need to be developed a statistical monitoring system to collect data relevant to the measurement of peak elasticity. These data might come from such a planned program of experiments or from experiments undertaken by individual utilities or from other experiments sJon to be conducted, such as those under the sponsorship of the Federal Energy Administration. This would also include monitoring the effects of rate changes where they are introduced without experiments.

The Task Force 2 report is responsive to the requirements of Topic 2. Their findings, as reflected in their report, will be WE'!.Lg-hed by the Project Committee in reaching its conclusions. Many of the issues in the rate design 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 Task Force 2's work and to consider other sources of information as well

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TABLE OF CONTENTS

Page

I. Introduction. • . . . . . 1

The Concept of Elasticity of Demand . . . . . . . 2

Cross Elasticity of Demand. . .. . . . . 5

Income Elasticity • • • • e • • • • . . .,; ~ 7

Marginal Price. 8 . . . . . . . . . . . . . .

Estimating the Demand Curve . . . . . . . . . . . Structural Form and Specification cf the Model. 11

Results of Existin0 Studies • • • 12

II. The Relationship Between Elasticity of Demand and Pricing Policies. • . . • • • • • • ••• 13

Limitations on the Use of Elasticity •• . . . . . . . 13

The Inverse Elasticity Rule • . . . . . . . . 15

III. Conclusion. 17 . . . . . . • • 4 .. . . .

IV. Some Recent Developments •. . . . . . 18

Appendix. A Surrunary of Some of the s·tudies . . . . . . 20

Bibliography .. 27 . . . . . .. • fll 0 • •

Task Force 2 Members. 29 . . . . . . . . . . . . . . .

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I. INTRODUCTION

The objectives of this report are to discuss the couc~pt of price

elasticity and to summarize tbe results of some empirical studies of the

relations.hip between the demand for eler:tricity and the price of electrl.-

city.

The increased interest in energy research by economists has caused a

large number of studies directed towards tJ-..e demand and supply of energy in

different markets. One area that has received considerable attention is

the demand for electricity (both Kwh and Kw). The construction of meaning-

ful models of electricity demand is extremely important for long-run strategic

pJanning by electric utilities. The existing models generally attempt to

mes,sure the degree of responsiveness of K'tvh consumption to changes in the

price of electricity. This information is useful for measuring the effect

of :rate changes on total revenue generated from Kwh sales. ~1ost of the

models include the prices of substitute fuels as variables to explain varia-

tions in Kwh consumption. The ~:· stimat::;:-4 coefficients of these variables

can be used to assess the likely impact of changes in the price of a competing

fuel, e .. g .. , natural gas. The models also include other economic variables

as precii.ctor-t of Kwh cor_.~umption. These other variables 'tvould include

disposable incpme, industrial production~ gross national product, etc. The

estimated effects of these variables can be used to forecast the consequences

., of changes in these variables.

Anticipated electricity demand ( Kw) is the primary factor deterr1ining

future capital expenditur-es ln the electric utility industry. Properly

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sp!;!cified models of electricity demand can yield information about necessary

future expenditures for plant and equipment. Furthermore, price elasticitp

of demand can provide a guid.e for adjusting electricity prices away from

long-run incr.emental cost when the revenue generated 'by prices equal to

long-run .incremental cost exceeds or is smaller than the revenue requirement&

The Concept of Elasticity of Demand

Elasticity of demand is a measure of the effect a change in the relative

price of a commodity has on the demand for that COIIlillodity. The price elasti-

city of demand for electricity is the ratio o~ ~he percentage change in the

quantity of electricity demanded caused by a one percent change in the rela-

tive price of electricity, assuming all other things that could affect the

demand for electricity are held constant. The term relative price of

electricity means the price of electricity relative to the price of all other r

goods. If the no~inal price of electricity rose by 10% and all other prices

rose by 20%, a fall in the relative price of electricity has occurred. Thus

in any study of electricity demand~ real prices of electricity must be _used,

i.e. prices weighted by an appropriate pric..: index.

It follows from the "law of demand" that the quantity demanded of a

coP.Jmodi ty will increas_e (decrease) when the price of a CO!ITIUwdity falls

(rises) ,everything else remaining constant. For this reason, the elasticity-

o.f demand will always be negative. If the price rises, the price change is

positive and the change ir1 quantity demanded is negative. For convenience

elasticity is disct.tssed in absolut'e terms, i.e. ignoring the algebr.iic

sign. Ho~ve.ver, Table 1 has values for elasticity of demand that are

acco:n!_)anied by a negative sign.

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A demand curve can have an infinite variety o.f shapes. However, the

"law of demand" dictates that all must be dowmvard sloping_. Figures 1 and 2

are examples of two demand curves.

Figure 1 Price

Quantity Demanded

Figure 2

Price

A'

Quantity Demanded

Figure 1 describes a linear relationship between ~rice and quantity, i.e.,

if price declines· by one 11nit; quantity demanded iJ:!.creasE;s by a constant

number of units. Figure 2 describes a demand curve that is curvilinear~

i.e., if price declines by one unit; quantity demanded increases by varying

aJ;nounts depending on the level of price.

For convenience the following discussion will make use of linear demand

curves (Figure 1), but the reader should not interpret this to mean that most

demand curves take this form.

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Economists usually describe demand for a commodity as being inelastic,

elaStic, or unitary elastic. The demand fer a commodity is described as

inelastic when elas·ticity of demand is less than one, elastic when elasticity

is greatQr than one, and unitary elastic when elasticity is equal to one.

The change in revenue resulting from a price change is directly affected by

elasticity of demand. For example, ir dewand is elastic (iGe. greater

than 1) a 10% price increase will cause quantity demanded to fall by more

than 10%.., thus total revenues v.rill fall.. Obviously, a price increase "tvould

cause revenues to rise (remain consta~t) if demand were inelastic (unitary

elastic).

Figure 3 can be used to discuss the: concept of price: elasticity 0f

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$10

$7

$4

Fio-u rr.: ~ 0 ···~

l I

5 12 19 Quantity Demanded

If price decreases from $10 to $~ quantity demanded increases from 5 units

to 12 units; Tpe percentage change in price is -30% ( l~

change in quantity is 140%. Thus elasticity of demand is

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140 ~30 = 4. 66 ..

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If price declines from $7 to. ·$4; _quant:ty demanded incr~ases from 12 units to

19 units, (the linear relationship implies that quantity demanded .increases

by 7 whenever price decrease.s by $3), the elasticity of demand is calculated

in the same manner as above:

7 .12

49 36

1 • .36

Notice that even though the slope of the demand curve is constant, the elasti-.

city of demand varies along the demand curvee thus, a linear relationship

betv7een price and quantity implies variable elasticity of demand. A constant

elasticity of demand implies variable slope, i.e., a curvilinear demand curve.

Cross Elasticity of Demand

Cross elasticity of demand i-5 defined as the ratio of the percentagE7

change in quantity demanded· of one commodity to a one percent change in price

of some other related commodity. The demand for electricity is affected by

the price of competing fuels and the price of appliances that use either

electricity or other fuels. Thus, a 10% change in the price of natural gas

would affect the quantity demanded of electricity. It is reasonable to

believe, because of a priori knowledge, that an increase in the price of

natural gas would cause the demand for electricity to increase. The cross

elasticity of demand would be positive, i.e. both the numerator and denominator

of the ratio are positive. When the cross elasticity of demand between two

commodities is positive,the goods are described as gross substitutes. When

it is negative,the goods are described as gross complements. The price of

appliartc~s, both those that use electricity and those that use alternative

fuels, would affect the demand for elec~ricity. Therefore an empirical

estimation of the elasticity of demand c~n be judged to some extent by the

presence or absence of relevant variables •

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Cross elasticity of demand can be illustrated by using Figure 4. The

previous illustrations have assumed that all other variables that: could

affect demand are being held constant. In.order to investigate c~oss

elasticity of demand, this assumption must be relaxed. Figure 4 describes

the effect of an increase in the price of natural gas on the demand f~r

electricity ..

Price of I Electricity

5¢

Figure 4

500 (Kwh) 700 (Kwh) Electricity Demanded

Demand curve (A) in Figure 4 assumes the price of natural gas is $1 .. 00

per mcf. Demand curve '(B) is drawn assuming the price of natural gas is $2.00

per me£.

A 100% increase in the price of natural gas is assumed to cause a 40%

increase in the quantity demanded of electricity~ The cross elasticity of

40 dP.mand is ( --

100 = .4).

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Income Elasticitx

Income elasticity measures the relationship between changes in income and

~he demand for a good. The ii1fluence of income on the demand for electricity

is described in Figur~ 5. Figure 5 is dratm assu.rning an increase in income

will cause the quantity of electricity demanded to inc~ease.

Figure 5

Price

5¢.

SOOKwh lOOOKwh Electricity Demanded

Demand curve A is dratvn assuming income of $1,000/month. L.emand curve

B is drawn assuming income is $1,500/month. Electricity demanded increases

from 500 Kwh to 1,000 Kwh. A measure of inco~e elasticity can be calculated

analogously to price elasticity. The percentage change in income is 50%.

The percentage change in Kwh is 100%. Income elasticity is calculated to be

100 ( 50= 2.0).

· The discussion up to this point has. implicitly described the response

of consumar demand as instantc~1eoun with a change in the prices of electricity

or so:n2 related co'lllnodity. Although ther~ -.;·7ill be so:na imu.?.dia te response,

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one would expect the response to be larger the longer the time period a price

change is in effect. If a consumer has already invested in a stoC'k of appli­

ances, an increase in the price of electricity may cause him to use the

appliance less. When the appliance wears out he may stop using it altogether.

Furthermore, an increase in the real price of ~lectricity may cause con­

su-:ners to employ appliances that use electricity more efficiently. There­

fore elasticity of demand has a time dimension as well. Economists describe

elasticity as short-run elasticity and long-run elasticity.

Marginal Price

The nprice'' most relevant for the measurement. of elasticity is the marginal

price. Marginal price can be defined as the pay-ment required to obtain one

additi~nal unit of a commodity. Economic models of consumer behavior dictate

that the equilibrium quantity demanded of a co:runodity depends on the price of

the marginal unit. Of course, other prices of the co~odity influence the

consumption choice but the influence i:3 contained in an "income" effect.

For example, a grocery store may have oranges for sale. It may offer one

orange for 15 cents, 2 oranges for 25 cents. The price of an orange is not

12.5 cents if one buys two oranges. The price of an additional orange once

one orange is to be purchased iR 10 cents. The consumer reaches equilibrium

when the value (to the consumer) of an additional orange is equal to the price

of an additional orange. If the value of au additional orange was greater

than the pr~ce of the dranga, the consumer would obviously im?rove his lo~

by 'buying it. If the additional value ~vas less, the consumer ~v~uld obviously not

purchase it.

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Electr:Lcity has been priced in a similar manner, i.e. declining block

rates. The first X Kwh's are higher priced than additional Kwh's. If one

is to estimate "price" elasticity of demand the correct variable to use is

marginal price. However, marginal price depends on the block in which .

consumption is occurring and differs £rom customer to customer. Furthermore,

the equilibrium level of consumption is determined not only by marginal

price but by all other prices in the schedule.. An e.stimate of elasticity

should be a measure ·Of response to a change in the margin.9.l price, all other

things remaining the. same. However, a change of prices in blocks other than

the marginal block may also affect consumption. Thus, it may be desirable

to have average price as a variable as well as marginal price. But,it is

clear that marginal price should be used in any estimate of price e~asticity

of demand.

Estimating the Demand Curve

Unfortunately the empirical world does not allmv us to see the entire

demand nor does it allow us to measure all ·the variables that have an effect

on electricity demand. In fact the empirical world only allows us to see

points in space. Figure 6 is a plot of prices and quantity demanded.

Price

Figure 6

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Quantity Demanded

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One could estimate a line that passed through those points and call the line

a demand curve. Such a curve.would be similar to the one in Figure 7.

Price

Figure 7

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Quantity Demanded

However, Figure 7 may not be an accurate portrayal of the demand curve because

variables other than price may have changed alsoo The reader should recall

the "everything else remaining constantn assumption.

Income may have been changing, the prices of other goods may have been

changing, or some other variable such as family characteristi.cs may have

changed. Figure 8 could be the 11 real 11 demand curve. Notice that the response

to price changes is smaller (the lines are steeper) and that the demand curve

position is not constant. (The demand curve has shifted due to the influence

of variables other than price.) Figure 8

Price

A

Quanti~y Demanded -10-

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The reader will notice in the short summaries of existing studies that

various forms of the demand for electricity have been estimated. One wight

be tempted t .J conclude tha-t economists may not even agree on the 11law of

de)Iland." Most economists can agree bn direction of phenomena but not on

the form of the phenomena. Economics predicts: economists make_predictions.

Economic theory does not dictate a specific fo~ of the demand function,

although it does provide information about the direction of change. For

example, economic theory tells us that the quantity demanded of a co!:nmodity

will increase if the price of the co~odity falls, all other things remaining

the same. It does not provide information on the size of the quantity change

resulting from a given price change, or whether the relationship will be

linear or curvilinear. Thus, econometricians must assume a form of the

demand function, or by trial and error, select a form that provides a good

fit to the data.

St~~ctural Form and Speci~ication of the Model

Some models that have been estimated have equations of a structural form

that provide direct estimates of the elasticity of demand while others have

developed variable elasticity estimates, i.e. elasticity varies with price

or quantity.

A double logarithmic form provid~s a direct estimate of elasticity in

that elasticity is assumed to be invariant with respect to price. This form

assumes that the logarithm of quantity demanded depends, inter alia, on the

logarithm of price. T!:le estimate of the parameter attached to price is the

estimate of price elasticity.

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A linear relationship can also be assumed~ This form ass~mes that the

quantity changes resulting from a unit price change is constant. This implies

that elasticity varies with price. At low prices (large quantities) a unit

change in price would be a larger percentage change than at higher prices

(lower quantities). The percentage change in quantity induced by the price

change would be smaller at large quantities (low prices) than at smallF.:r

quantities (higher prices). Thus elasticity of demand decreases as price

(quantity) falls (increases). Of course, other forms are possible, each

having different implications regarding elasticity of demand.

Close attention should be paid to the specification of the form of the

relationship in reviewing any elasticity of demand study. Some speci:=i.cations

may be faulty even though the fit to the data is good because estimates of

parameters violate a priori knowledge. For example, a negative estimate of

income elasticity of electricity demand could occur using a particular for.n .

0'!le might become suspic.ious of the form if he believed that, all other things

remaining the same, electricity consumption increases with increased income.

Results of Existing Studies

Table 1 contains a list of the results of a number of electrici;;.y demand

studies. Both long-run and short-run elasticities have been estimated by some

of the studies. Table 1 also contains a list of variables (other tha·"' price)

used in each of the studies as well as a column describing the type of data

used in each study.

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TYPE OF DEMAND

Residential llouthakkcr Fisher ti Knysen Houthokker & Taylor Wilson

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~1ount 1 Chapman 6 Tyrrell Anderson Lymnn

llouthukker, Verleger, Sheehan llalvorscn Grt ffin Tyrrt!ll G Chern Nelson Berman G Graubnnd l~oods

FEA (15)

~ Commerc1 al PJ ~olii~Chnpmnn & Tyrrell

Lyman Halvorsen Griffin T}•rrcll tl Chern 1\'cwds Ff:A

Industrial ~her f, Kaysen

Baxter 4 Rics ·Anderson

Mount, Chapman & Tyrrell Lyman llnlvorscn Griffin Tyrrell f, Chern Woods Fl:A

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RDC~jmw 2/S/76

Nn -Not estimated NA -Not uvnilublo A -Average price ~ -Marginal price

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tr l>

TARt,!! 1 Summary of f:lcctri~;cc Elasticity Tables

PRICE ELASTICITY Short-Hun

-lt. 89 -0.15 -0.13 NE

-0.14 Nl!

-0.90 NE -0.06 NJ: NE 0 NE

NE

(-0.90)

-0.17 (2.10)

NE -!!.04 NE NE NE

NE NE NE

-0.22

NE -0.04 NU -0.3 NE

(-1.40)

Long-Run

NE 0 -1.89 -2.00

-1.20 -1.12

~1.02

-1 •. 33 -0.52 -0.99 -1.6 -l.O -1.5

-0.77

-1.36

-0.944 -0.51 -1.23 -1.0 -0.87

-1.25 -1.50 -1. 94

-1.82

-2.37 -IJ.51 -1.28 -0.7 -0.33

TYPE OF PRICE ANALYZED

~~ A A A

A A A

~I A ~~ A A A A

A

A A A ~t A A

A A A

A A A ~I

A A A

OTII!:R I~!POI!TANT VARIABLES IN STiJOY

l!ouschold income, G!is price, Appliance Income, Gas price, Stock of appliances Personal consumption per capita Gas price, Family income, Degree days, Number of

rooms per hou:;c Populntion, Income, Ga~ price, Temperature Gns, oil lind coni prices, income, Avernge family

sIt<!, Tt'mpct•a t 11 rc Gas price, Price index, Income, Temperature Person1l consumption per capita Nft.. NA Income, Population, Gas price Gus price, tncomc Income, Appliances, Gus price, Temperature In~·ouu.l, Appt iaacc saturation, Oil and gas price,

Prh·c index Gas price, Oil price, Income, Population

Population. Income, Gas price, Temperature Gus price, Price index, Income, Temperature NA NA Income, Population, Oil·and coal price, Gas price Cotnmcrdal emplnymcnt, Gus price Gas price, Oil price, Income, Population

Cupi t:ll, Lal.ior inputs Coal price, Coke rrice, Oil price, Manufacturing

wage rotc · Population, Income, Gas price, Temperature Gns price, Price index, income, Temperature NA . NA £1:1s price, Jntlustdal output Industrial output, Coal, oil and gas price Gus price, Residential oil price, Coal price,

Economic vnriahlcs

TYPE OF DATA

City States Aggregate u.s. S~ISA

States States

Utility Service Territory States .. NA NA States Cities Customer County

Census Region

States Utility Servicr Territory NA NA States County Census Re-gion

States Dy Industry (SIC) States

States Utility Service Territory NA NA States SIC, County Census Regions

SMSA "" Standard Metropolitan Statistical Area

SIC - Standard Industrial Classification

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The results on Table 1 indicate that:

1. The price elasticity of demand_ for elec.tricity, for

all I:! lasses of consume.rs, is .much larger in the long-

run. than in the short-run.

2. The average long-run elasticity for all consumer classes

appears to be greater than one, based on the average of

the t·esul ts of the studies.· The average long-run elasti-

city for .each class is about -1.3.

3. While not indicated in the summary table, many studies

indicate the existence of long-run cross-elasticities with

respect to other fuels, in the +0.1 to +0.3 range.

4. In spite of the existence of the:.:2 estimated elasticity

values, it should be clearly pointed out that their use

for a particular utility could grosply misrepresent

actual values. Elasticities are highly dependent on

socio-economic and industry mix characteristics. Thus,

while· these results are good references, indivi1.:ual

utilities should investigate their mm customers' response

to price changes.

II. THE RELATIONSHIP BETWEEN ELASTICITY OF DEMAND AND PRICING POLICIES

Limitations on the Use of ElasticitX,

The demand studies that currently exist use annual Kwh consumption

as the dependent variable. The 11 law of ~t:lmand", hm·rever, applies to

a single commodity. If Kwh's at different times of the day and year are

,, -13-

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perceived by custo;:ners to be different conunodities, aggregation of Kwh

purchases over these time periods does not permit one to claim he has estimated I

a demand function--except under a special circumstance. If the marginal I prices of the goods change in the same proportions then the goods can be I

aggregated. A shift in the rate design (slimmer-winter differentials) during

the period studied would violate a necessary condition for aggregation.

Furthermore, even if the rat~ design hasn't changed it is obvious that the

elasticity estimate would not apply if a rate design change is being con-

templated. L changt. in th~· summer-winter mix cannot be forecast given an

elasticity coefficient that has been estimated assuming proportionate price

changes. In fact, a proportionate price change will not allow a determination

of the changes in the time pattern of consumption.

The elasticity estimates that have been developed may be us~ful in

forecasting revenues provided_winter-su~~er differentials are not large, or

if the changes in vlinter-s:.Ja.:uner rates are in the same proport;i.on*

The demand models that ~·xist do not giv-~ complete information for

plann5.ng plant additions. Plant mix is determined by the shape of the load

curve, inter alia, not the area underneath the load curve (annual Kwh's).

Two different load curves can have the same total Kwh's but imply different

optimal generating mixes. An estimated demand model of annual Kwh sales

cannot be used to forecast the need for specific types of plants, e.g ..

nuclear, coal, and gas turbines, unless so::ne assumptions are made concerning

the shape of the load curve. Hotvever, the shape of the load curve is deter-

mined to some extent by the price of electricity and the prices of competing

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fuels. (A demand model that would be useful for planning would specify

consumption by time of day and/or season as the correct dependent variable.)

Furthermore, the models that exist have not been derived from behavioral models

that recognize time of consumption as a determinant of deroaDd. All of the

models assume implicitly that a Kwh cons~med at any time is perceived by the

consumer as equivalent to a Kwh consumed at any other time. Although the

assumption is powerful in the sense of simplifying the model, it appears the

assumption mitigates some of the usefulness of the model for planning purposes.

This assumption introduces some confusion if marpinal cost pricing is used and

the estimated demand elasticities are nc;r-d. to adjust prices to reflect the

revenue requirement set by the regulatory commission, i.e. the inverse elasticity

r.1le.

The Inverse Elasticity Rule

The inverse elasticity rule is a debatable method for actjusting prices

to obtain quasi-optimal allocation of resources. An excellent criticism of

the rule can be found in testimony by Alan Chalfantl before the New Ycrk

Public Service Commission. Hmvever, even if one accepts the rule as being

a legitimate way of altering prices, one must be cautious about the elasti-

citie·s used in the adjustment process. The inverse elasticity rule (ignoring

cross elasticity effects) can be stated as: Quasi-optimal output can be

obtained by adjusting the price of goods i-versely proportionate to their

elasticities of demand. If t;;.;ro goods are produced but cannot be sold at

---~------------------

1 . Alan Chalfant, Testimony Before the New York Public Service Commission,

Case No. 26806.

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the!r_.marginal cost (selling them r.~ that price would violate a revenue

constraint). then prices must deviate from marginal cose. The p:r..fce of the

commodity with t9e more elastic demand would have a smalle~percentage

deviation from marginal cost than would the price of the good with the less

elastic demand.

It is important to realize that electricity production has different

marginal costs at different times of the day and year. Furthermore, it may be

reasonable to assume that electricity consumed at on~ point in time is per-

ceived by consumers (residential, commercial, or industrial) as a different

c~Jl'P'.0dity t:han electricity consumed at some other point in time. Thus,

"the inverse elasticity rule as developed by Baumel and Bradford2 is one that

applies to different times of the day and year. The existing elasticity

estimates are not different by tl.in~ of day or time of year. Th~s_2 they are

relatively useless for applying the inverse elasticity ruleo

An application of the inverse elasticity rule to customer classes call.

appear to be a correct application. For example, if the industrial class

demand was more ine1a~tic than the residential class demanci, then the

indu$trial price wculd deviate more from margiwal cost than the residential

price. However, marginal cost is different from time period to time period

for the utility system_and~ ignoring transmission losses, identical for differ-

ent classes ·in any_ time ;::>eriod. Since the inverse elasticity rule is based on

deviations from marginal cost 1 it seems obvious that one needs time differ-

ent:iated elasticiti.es before he could recoiJ1.mend correct deviations from

marginal cost.

2william J. B~llmol and David J. Bradford, "Optimal Departures from Marginal Cost Pricing.:t n The American Economic ~eview, LX (June, 1970) >

pp. 265-283.

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-·-"·"""'-----"'""*,..•--=--..--·--.. ..... ,.r ... .,t_. • .,..;.,.,.., .• _,.t *"'"*"""''"""~""~~ ....... ~ ... ...,_."""""',._...,..,._,'$,.~-··-·"""-'*. ""'"""'"''"" ...... ...,.,..,. • .;.u,,,.."=· ""'""'-' .• ..._ ... ~··v...,,...,._ .... .,...,......,..., . ...,. ... .,. • .,;,·----·-~~ ..... -·IIOi;d'"'""'· ""*' ..;.· ii.k•· , ...... ,_,..;'ase:M.i··...,rtf~'-~;;.\;.O.:.:·,'.:.,;;·"··..;.ed;,;..;.· '*..;.~-.· ... : J.,..,..,.i,,..,.,..r.ioi••(•·tariio·htl'lii·~G.!lf!P-Plliil't!L~-

Of course, the usefulne'ss ·of any model .for pre-dicting consumer response

to a price change depends on th~ price structure used.in selling the coTil!!l.odity.

If time of day tariffs are imposed, the elasticity estimates that exist will

be useless for estimating the response to the new tariffs. It is unlikely

that time of day tariffs would have declining blocks. Furthermore, inter-

temporal cross elasticities probably exist but cannot b~ measured under

existing rate structures.

It would appear that some information about custo:ner respo!1se to time

of day tariffs would be necessary before such tariffs were put into place

on a large scale. Thus, so:ne experiments should be structured to obtain useful

information about customer re~ponse to different ra!=e levels as well as different

rate structures. For example, if the time of day rate structure includes a·

demand charge during the times when a peak is likely to occur, the consumption

pattern as well as total K~vh are likely to be different than they 'tvould be

if a sim?le time differentiated Kwh charge is used ..

III. CONCLUSION

The Task Force believes that the existing elasticity studi~s shed little

light on response of customers to changes in rate structures that reflect

different costs by time of day. Furthermore, the deficiency of the existing

studies prevents application of the inverse elasticity rule. The existing

·estimates can be used to a limited e~tent to forecast revenues. Hm·1ever,

revenue forecasting 't·Pttld depend on rate structures maintaining a similar

relationshipo It appears that more accurate revenue forecasting can be dona

with a model estimated for a specif-!.c utility rather than one estimated over

a national or regional cross section.

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IV. SOME RECENT DEVELOPMENTS

NERA' s final report on Topic 2 included an analysis of VEPCO' s residen'tial

class load curves for the peak weeks of 1968 and 1974. NERA made use of a technique

called the "Cubic Spline' 1 which was developed by Dale Poirie~. This technique was

also applied to the average kW load of individuals attached to common transformers

of the Co~monwealth Edison Company by Hendricks~ Koenker, and Podlasek.4 !he

technique of HKP explained the differences among the individuals by income and

explained the shape of the load curve by weather variables. NERA' s analysis used

only temperature and humidity.

Neither NERA nor HKP used price as a variable in their equations. NERA,

however~ estimated the effects of weather on the daily residential class load

curve for 1968. They then applied a change in the saturation level of air con-

ditioning to the load cuTve estimated for 1974 and compared the estimate of 1974

to the load curve that actually occurred. They found that the estimated off-peak

loads for almost every day \vere substantially larger than the loads that actually

·)ccurred. NERt\ drelv the conclusion that be~ause the price of electricity increased

between 1968 and 1974, the off-peak demand fer elect:r·icity must be more

elastic than on-peak demand for electricity. This may be an unwarranted con-

elusion. Other appliance sa'turations have changed in addition to ai.r conditioning

saturation between 1968 and 1974. Furthermore, the saturation of central air

conditioning versus window units changed in the VEPCO service area. The change

in the saturation of other appliances, since those appliances are used mainly in

the \vaking hours, could have caused the difference NERA observed. Furthermore, it

appears the terms "off-peak demand" and ''on-peak demand" are too vague to use ln

deriving a model that describes the demand for electricity~ Perhaps it would be

3Dale J. Poirier, ''Piecewise Regression Using Cubic Splines," Jout'!lfll of the American Statistical Associatio~, September, 1973~

4Roqer Koenker and Wallace Hendricks, "Estima'Lion of the Residential Demand

Cycle for Electricity," Proceedings on Forecasting ~ethodology for Time-of-Day and Seasonal Electric Utility Loads 1 EPRI SR-31, March 1976.

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better to descTibe the elasticity of demand for electricity to be a function of

time of day and weather. Thus~ one would speak of the elasticity during the

.r-;arly afternoon '"hen a eeL _cain set of temperat·tres has occurred. This is a

better description of a period than is "peak.n "Peak period" or the peak load

of an electric utility system can only be defined after it has occurred while the

preferred description of the period is more general. In addition" the claim that

there is an 11off-peak" demand curve for electricity and an "on-peak" demand curve

for electricity limits the investigator to only two periods.

NERA should be commended for moving away from an incorrect specification"

namely the demand for kilowatthours, toward an investigation of the load shape of

the utility. Task Force 2 has stated previously, that the chief concern of

electric utilities and regulatory commissions about the effect of time of day

prices is the 1mpact those prices would have on the load shape of the electric

utility. Task .Force 2 recognizes that NERA had limited data and limited time

i1~ order to investigate this impact. We also feel that NERA and otheT investi-

gators would be the first to recommend further study of the impact of price on

the load shape. This can only be done by structuring a nat~onwide or region-

wide experiment that includes enough variation in price and lasts faT a period

long enough to arrive at the correct conclusions about the effect of price and

how it varies through the time of day and year.

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APPENDIX

A Summary of Some of the Studies

This section is a series of short su~~aries of some of the studies

contained in Table 1. A more complete discussion of some of the studies can

1 2 be found in Taylor and Guth •

1. Fisher and Kazsen This is one of the most complete and ambitious stud{es

listed. Fisher and Kaysen used the following equation as the short-run mudel:

~ln Dt ~ ci + d.6ln Pt + 13 Llln y . . t Where,

the change of the logarithm of the annual Kwh's by all households

in the com.."'lU!:lity from year t-1 to year t.

6ln Yt - the ditiuge in the logarithm of the per capita personal income

from year t-1 to year t.

- the ann.ual rate of growth o~ "white goods" (appliances). •this

term appears in the intercept term and is a result of the

estimation process. However, the derivation of the equation

assumed that the stock of white goods grows exponentially.

The model was estimated using 47 states (North and South Carolina were

combined, Washington,D.C. was combined with Maryland) for the years 1946 to

1957. The model has several problems. Treating states as homogenous cmrenuni-

ties introduces aggregation bias. The assumption of a constant growth ~~te in

the stock of "white goods" is open to question because of the level. of saturation

of some appliances. The price variable is average price ~pas~, i.e. p~ice is

the revenue per Kwh sold (4.ln Pt) .

1Lester D. Taylor, "The Demand for Electricity: A St.n-vey," The Bell

Journal of Economics, Vol. 6, No. 1 (Spring, 1975), 74-110.

2 . Lou1.s A. Guth, Price Elasticity ~"'f_Remanrl for Electricity,:, Before the

Public Service Co~'Uission of New York, Case No. 26go6.

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2. Routhakker and Taylor estimated the following equation:

Where,

qt = a+ Bq . + a..Xt +)<Pt t-1

qt = personal consumption expenditures for ~c:;lectricity per capita in 1958

dollars.

total personal consumption expenditures per capita in 1958 dollars.

implicit deflator for electricity/implicit deflator for personal

consumption expenditures.

Because the equation is linear (elasticity varies with price), the

elasticities shown in Table 1 are computed at the mean values of the peribd.

The estimated equation was derived assuming expenditures on electricity

are affected by either 11stocks" of appliances or habit formation, ioe. expendi-

tures increase if the 11stocks"of appliances increase or if the habit of using

electricity increases.

The empirical results confirm that the "stock" adjustment hypothesis, as

well as the income and price hypothesis,: have effects on electricity consump-

tion. The price variable used is a ratio of two price indices. This is a

different treatment of "price" than most other studies, but is a consistent

treatment given that expenditures on electricity is the dependent variable.

3. Wilson Wilson utilizes a modified Fisher and Kaysen approach but uses

typical electric bills3 rather than average price. He develops two separate

demand models, one which concentrates on energy consumption and tl-· a other on

the stock of electric appliances., H'ilson's results are in contrast to those

3Typical Electric Bills, Fed~ral Power Commission, Washington, D.C.

•

of F~~her and Kayseno His empirical results indicate that the price variable

for electricity dominates the demand equation and enters with a price elasti-

city of -~.33~ In addition) the negative income elasticity estimate causes

one to speculate that the model may not be specified correctly.

Wilson 1 s .second mode~. is a modification of the Fisher and Kaysen appli-

ance stock procedure. Wilson examines appliance saturation, which he

attempts to explain with economic and demographic variables. Wilson admits

this analysis has problems. Each equation estimates only a portion of the

ultimate demand for electricity. In addition, the data do not reflect multi-

ple holdings of specific appliances by a household, nor consider usage as a

function of the size and/or efficiency of appliances.

4~ Mount, Chapman, and Tzrr~ MGT utilize economic and demographic factors

in models designed to explain ~lectricity demand.

The issue of functional form is considered directly with three alternative

demand models being used. They consider a constant elasticity model and

two variable: elasticity models. Each model results ?..n different short-run

and long-run elasticiti~s.

The m0del ia fitted to data drawn from a cross-section time series pool.

Average price rather than marginal price i3 used because aggregation would

cause either variable to produce essentially similar results, and the lack of

unique measures of each variable preclud~s accurate differentiation between

them.

5. Anderson Anderson proceeds on the assumption that ''locked-in" customers

are totally unresponsive to changes in energy costs ~nd income in the short-run.

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However, demand varies due to the existence of "flexible11 customers.

Anderson's estimated model is a combination log linear exponential. func-

tion· that incorporates the marginal price of electricity by using a set of

simultaneous equations designed to eliminate simultaneity bias.

Taylor, in his discussion of Anderson states that "since the demand for

electricity in the long run is tantamount to the demand for energy consuming

equipment, the long run price elasticities of demand car_1 be estimated from

4 the stock equations as well as from the energy consumption equations."

However, in order to perfonn this estimation.one must assume that ap"';liance

size is not increasing~ the efficiency of appliances is unchanging, and that

demographic characteristics are unchanging. Similarly, Anderson's "locked iP11

approach takes on greater significance during periods of declining availa.,ility

of energy substitutes for electricity.

6. Lvman Lyman conside.red only t\vo functional forms a~d did not allow the

data to determine the functional for.ill. His ~.Jas a rather weak application of 5

the Box-Cox approach. A stepwise regression wa~ also used which failed to

recognize the different determinants of consumption by region. He claims

that state data are not 1.lseful because they are too aggregated. This may be trut..!

for some states such as Califor~ia, but it is conceivable that other market

ar~as would exceed the size of the state.

While in seven of the ten regions, residential demand is inelastic, this

is not true for the West coasto Here the analysis suffers from severe data

problems and yields a price elasticity of -9.78. Obviously, the problems in

aggregation of a heterogeneous region are severe as indicated by

the large elasticity coefficient.

4 't op. cJ. .

5G.E.P. Box and D.R. Cox (1964). "An Analysis of Transformat ·· ····~> J. Roy. Statist. Soc. Ser. B 26, 211-243. See also Paul Zarembka, ~·Trans:l:: .tation of Variables in Econometrics," Frontiers in Econometxics, (1974).

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7. Halvorsen Halvorsen presents an analysis of the residential d~mand for

electricity which utilizes a simultaneous equation framework to account for

supply phenomena. The system of equations includes two demand equations,

one supply price equation, and two accounting identities .

Demand is separated into two components: (1) electricity purchases per

customeri and (2) number of customers per capita. Each component depends on

both economic and noneconomic determinants. However, since different factors

may affect each element, t separate formulations are proposed. The determin-

ants of purchases. per customer include the average real pr_l.ce for .alec tricity,

median family income, the real price for gas, a time trend to serve as a proxy

variable for the trend in appliance prices, climate, and lifestyle. Similar

economic determinants enter the number of customers per c<:5.pita specification;

noneconomic factors differ. Urbanization and a time tr.,;nd are inclu.ded to

reflect customer accessibility to electric pmver. Also, the number of houses

per l1ousehold (along with the trend variable) are added to the formulation

to refl~ct customer demand for second homes.

In order to ident"i'fy demand equation parameters, Halvorsen in...::ludes

determinants of ~he electricity price schedule in the analysis. The author

focuses on prices facing the representative customer. In part, determination

of the price of electricity depends on total sales per customer. Additionally,

supplier production and distribution costs are important factors. Production

expenses include labo! payrolls, e~penditures for fuel, and payments to capital.

The latter is approxintated by the percent of generation originati1.1g in "higher

cost 11 investor o;;.;rned utili ties. Urban population percentages and residential

sales relative to industrial sales serve as the surrogates .for transmission and

n ~IU.­flllf;

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distribution costs~ Fin~lly, a trend variable is included to allow for

increases in production efficiency over time.

The Halvorsen analys-is incorporates average price rather than marginal

price. Halvorsen justifies this approach with two arguments. First, it is

unlikely that consumers satisfy full marginal co•1ditions for utility maximi-

za.tion which jointly pertain to intensity of appliance use as well as to the

household's appliance stock. (H~lvorsen bases this conte~tion on the pro-

hibitive information costs associated with such activity.) Second, economists

.; interested in demand responses to the more theoretically appropriate marginal

price may easily derive such measures from estimated demand elasticities which

are based on average price data. To do so, Hahmrsen approximates the relation-

ship between the average price of electricity and the quantity of elect~

ricity with a double logarithmic function.

The empirical work in Halvorsen's stu.dy is based on a pooled sample of

nine annual observations (1961-1969) acr~ss 48 different states, providing

a total of 432 data points. Estimation of the s~ochastic relationshio is 4

conducted with two--stage least squares procedures. Three functional forms--

linear, hyperbolic, and double-logarithmic--are tested for each equation.

In the end, the appropriate functional form is sele.cted on the basis of

statistical fit and the agreement of coefficient signs with a oriori

expectations.

Empirical result$ suggest that the price of electricity, median family

incom2, and the price of gas, respectively, represent the do~inant demand

determinants in terms of explanatory im~ortance. A similar ranl,ing for

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supply price determinants lists sales per customer, the ratio of residential

to industrial sales, fuel costs aud percentage generation fro~ investor-owned

utility companies, respectively, as primary S!.!pply price factors. Experimenta-

tion with ordinary least squares procedures over the sam2 data provides results

that are seriously biased for the customers per capita and averag~ nominal

price equations. Additionally, the use of average pric€7 data (typical electric

bills) also produces results which are not satisfactory.

Halvorsen concludes that the long-run elasticity of demand with respect

to marginal price equals approximately -1.2. This is the sum of adjusted

elasticities in the two demand component equations. The estimated income

elasticity is less than unity (.61), while the cross-price elasticity of

electricity demand with respect to the price of gas is quite low. In subsequent

vmrk, Halvorsen makes a more significant differentiation bet·ween long ana

short-run demand elasticities6 •

6A review of work by Halvorsen and others is available in Long-Range Forecasting Properties of State-of-the-Art Models of Demand for Electric Energy, EPRI EA-221, December 1976, prepared by Charles River Associates, Inc.

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BIBLIOGR..A.PFr..:

Anderson, K.P., "Residential Demand for Electricity: for California and the United States, 11 The (R-906-NSF), January, 1972.

Econometric Estimates Rand Corporation

Anderson, K.P., "Residential Energy Use: An Econo:netric Analysis," The Rand Corporation (R-1297-NSF), October, 1973.

Anderson, K.P., "Toward Econometric Estimation of Industrial Energy Demand: An Experimental Application to the Primary Hetals Industry," The Rand Corporation (R-719-NSF), December, 1971.

Baumel, William J. and Bradford, David F., "Optimal Departures from Harginal Cost Pricing, 11 The Am2rican Economic Review. LX (Jun~, 1970), pp. 265-283.

Berman.: M.B. and Graubard, M.H .. , uA Nodel of Residential Electricity Consumption," The Rand Corporativ~, 1973.

Chalfant, Alan,. Testimony Before the Public Service Co:nmission of New York, -Case Noo 26806.

Federal Energy Administration. The Econo'!letric Regional Demand Model, Technical Report - FEA-EATR 75-18, June 26, 1.975.

Fisher, F.Mo and Kaysen, C., A Study in Econometrics: The Demand for Electricitv in the United States, Amsterdam: North Holland ~ ~-----~~~~~~~~ Publishing Company, 1962 ..

Griffin, J .M., "The Effects of Higher Prices on Electricity Consumption,'' The Bell Journal of Econo:nics and Management Science, Vol. 5, No. 2 (Autumn~ 1974), pp. 515-539.

Griffin, J.M,, 11A Long-Term Forecasting Model of Electricity Demand and Fuel Requirements,jj The Bell Journal of Econo'Uics and Hanagement Science:) -Vol. 5, No. 2 (Autumn, 1974), pp. 515-539

Guth, Louis A., Pric~Elasticity of Demand for Electricity, Testimony Before the Public Service Commission of New York, Case No. 26806

Halvorsen, R., "Demand for Elec.tric Potver in the Ut1ited States," Discussion Paper No. 78-13, Institute of Econo~ic Research, University of Washington, Seattle, 1973.

Houthakker, H.S., "Electricity Tariffs in Theory and Practice, 11 Ele~t;-_~ci~z ~ in the United Sta~, Amsterdam: North Holla-nd Publishing Cc., 1962.

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Houthakker, H.Sa and Taylor, L .. D .. , Consutn£r Demand inthe United States, 2nd ed. Cambridge: Harvard UniveJ::si_ty Press, 1970.

'I

Hou thakker, H.,S. _, Verleget' I F..~K. and Sheehan, D.P., ''Dyna'Jlic Demand Analyses for Gasoline and Rc~~:dd~n.tial Electricity, 11 Lexington, Mass.: Data Resources, Inc.a LJ73.

Lyman, R.A., "Price Elc.stici tieL in the Electric Power InG.vs tl:'Y," Department of E~onomics, Universtty of Arizona, October, 1973.

Mount, T.n.~ Chapman, L.Do and Tyrrell, T.J., "E.lectricity Demand in the United States: An Econo:netric Analysis," Oak Ridge 1.,ational Laboratory (ORNL-NSF-49), Oak Ridge, Tenn.,, June, 1973.

Nelson, D.C., "A Study of thE' Elasticity of Demand for Electricity by Residential Consumers: Sample 1-Iarke ts in Nebraska, 11 Land Economics (February, 1965), pp. 92-96.

Taylo~··, Lester D., "The Demand for Ele::::tricity: A Survey, 11 The Bell Journal of Economics, VI (Spring, 1975), pp. 74-110.

Tyrrell, T.J. and Chern, ~~.S., "Forecasting Electricity Demand: A Range of Alternative Futures," Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1975~

Wilson, J. W., "Residential Demand for Electricity, !I Quarterly Review of Economics and Business, Vol. 11, No. 1 (Spring, 1971), pp. 7-22.

Woods, D. Wo, "Econo;netric Lc,ad Forecasting for the Elect:~;ic Pmver Systems: A Report to the New England Electric System," Worct~ster Polytechn:Lc Institute. Worcester, Mass., June, 1975~

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TASK FORCE 2 MEMBERS

Ernest G. Ellingson, Chairman Manager, Economic Evaluation Georgia Power Compru1y 270 Peachtree Street Atlanta, GA 30303

Alan W. Beringsmith, Vice Chairman Rate Economist Pacific Gas & Electric Company 77 Beale Street, Room 1099 San Francisco, CA 94106

James W. Boyd EPRI 3412 Hillview Avenue P.O. Box 10412 Palo Alto, CA 94303

Lois Brandenbr.rg Room 636, General Offices Detroit Edison 2000 Second Avenue Detroit, MI 48226

Joseph Cleary Director of Utilities Airco, Inc. 575 Mountain Avenue Murray Hill, NJ 07974

Frank F. Gey Rate Administrator Central Illinois Light Company 300 Libe~ty Street Peoria, IL 61602

Gary H. Grainger Rate Research Supexvisor Wisconsin Public Service Corp. P.O. Box 700 Green Bay, WI 54305

David Jacobson M:i.nn~!sota Energy Agency 740 American Center Bldg. 160 East Kellogg Blvd. St. Paul, MN 55101

Craig R. Johnson Office o£ Utilities Programs .Energy Conserv3.tion & Environment Federal Energy Administration Washington, D.C. 20461

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Stephen A. Mallard Public Service Electric & Gas Co. 80 Park Place, Room 12332 P. 0. Box 570 Newark, NJ 07101

John McCarthy Manager, P~tes & Contracts Nebraska Public Power District Columbus, NE 68601

Don Smith Staff Economist NRECA 2000 Florida Ave. N.W. Washington, D.C. 20009

Michael Viren Chief, Economic Research Missouri Public Service Comnussion Jefferson Building Je£ferson City, MO 65101

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