Automatic adjustment clauses and allocative efficiency in public utilities

AutomaticAdjustmentClausesandAlloctiive Efficiency in PublicUtilities Thomas G. Cowing and RodneyE. &evenson

Thispaperprestnuofornrslamlysboftheeffkiency effects ol mtaamtic a@utmnt chues (AACs) in reguwed indus3rks. lJsio# a two-input In&t of ex ant&x

po6tinputcbiceandagmemlputty-clxytecbnotogy,we arUryucthe dative extentofaUocativedLstortiom due to each of time akmmtive mgutatory poiicks-pe&dic rate review with and without an AAC, aad an AAC

without any rate review-far the caseda reguhted firm

usingAACs in industries

alreadymbjcct30 iatemittent rate review is not unambipous, even in the fke ofsevere cost htflation, and is pirticubuiy sensqive to the mapitudeoftheprice&stkityofdpIal#foroutputaltdtbe rate and dirtction dtnput price &ages. We are forced to coaclude that the u!S of AACS in regulated iaduktries such as electric power, while originally ,justifbxt on the basis of financial viability, may well carry signifkaat

that chomm an ex post technotogy to maxhnize the present vrlue offuture pm&. Our results hwkate that the ecooomic rationale for

economic costs in the form af allecative idtktency may outweigh the benefits.

INI-RODUCIION

also influencethe input choices of the regulated firm (i.e.,they may atfect allocative efliciency).2 This paper presents a formal analysis of the efficiencyeffects of automatic adjustment clauses in regulated industries3 Specifically,we analyze the effectsof a fuel-specificAAC upon the ex ante and ex post choices of a profit-maximizingutility that is also subject to periodic rate review.Although some AACs cover nonfue! inputs as well,our analysis is general enough to include these cases. Several policy implications of our analysis are also discussed.‘J

Traditional methods of public utility regulation have involved the periodic review and adjustment of rates to influence output and constrain profits. More recently, regulatory procedures have heen amended to allow for the LWof automatic adjustment clauses (AACs) by whiclt cost increases associated with certain classes of inputs (e.g.,fuel) are allowed to be passed through in the form ot rate increaseswithout formal review.’Much of the impetus for AACs stems from the erosion of earnings encountered by utilities during inflationary periods. The use of AACs also avoids the necessityof a formal regulatory reviewand thus reduces regulatory lag, at least for those cost categories covered by the AAC. Beyond providing utilities rate reliefin inflationary periods, AACs may ‘Automatic adjustmentclausesfor public utilities data back at leastto World War 1.but during the 1950sand 196& many ftrmsdid not have accessto suchclauses,and for many of thoserim15 that did, the clauxeswere de&& to apply only IO industrialcustomers.The 1970ssaw a rapid expansionin the useof AACs and the extensionof theseclausesto residentialcustomers.By 1976, about two-thirds of all eketric utility rate adjustmentscamefrom the operationof the fuel adjustmentcktuse,while the mma:ning one-third were the result of decBkM.Ishl~alrptecnscs. lhomrrG.eowingisRdcssoritlUK~mnrtofEcollomicsat cheStpCCU~y01NewYork,Bin%amtohNewYo~.RodneyE. Stevensonis Professorin the School of Commerce, University of Whamsin, Madiin Wisconsin. Address reprint requests to Professor Thomas G. Cow@, Department of Economics, State Univ&ty of New York, Binghamton.New York 13901.

2While designedfor inflationary periods,AACs

remain equally elkctive during dellationary periods. ‘The alloeativc eBects of rate-of-return regulation have been examinedin a number of recentattic& follow-ing’tbeseminalpaper of Averch and Johnson (1%2). llwsc include analyses of statii effttiettcyby Baumol and Kkvorick (1970X Stein and Borts (1972), and Baiky(l974); the effectsofrgulatory lag by Baikyand Cokman (1971) and Davis (1973); the regulatedtirm under uncertainty by Kkvorick (1973) and Peks and Stein (1976); and the question of optimal regrlstion by Sheshinski (1971). Kkvorick (1971), and Callen. Mathewson, and Mohring (1976). 4Although this paper is written in the framework of public utility rate regulation, the analysis appliesequally well to any long-term contractwith provisionsfor automaticcost-relatedpriceadjustments and/or periodic price renegotiatton.Gtu analysiswould apply to a new Srm, a sin&-plani fbm facing the need to raplace its existing pidnt,aramultiplMtlirmlacingan~~~~ianeascinload(~, from a new subdevelopmeator industrial compkx) when capacity utilixation rates of existing plauts are not expectedto change.The analysiscan be extendedto the caseofpartialplant'replacettwnt (is, bringingon a new plant and reducingcapacity utiliiation of existing plants)as a programming problem.

317

Journalof Ewmmics and Business34.317-329 (1982) @ I%2 Tempk University

that

01~~r95/s~ul7-I3S2.75

T. G. Cowing and R. E. Stevenson

318 The

model

developed in this paper assumes a “puuy-claq” type of production technology. Ex ar,te (i.e., before the srle&on of a specific technology) rhe regulated utility is free to choose from among a

multiperiod model without and with demand growth are derived and examined in sections four and five, respectively. The fiial sections discuss implications of the anaiysis with respect to regulatory policy.

number of (long-run) technologies with alternative input

mix requirements. Each of these kchnologies is

assumed to be characteri

by fixed proportions

w!ilh respect to the single variable input.

THE

BASK

MODEL

fuel. so that once a specific technology is chosen, ir must be operated ex Cost willlout benefit of input substitution. WC also assume a capacity limitation on output

Assume a putty-clay technology with rhe ex ante technology specified in terms of a well-behaved neoclassical production function with two inputs,

determined by the amount or size of the fixed input,

Q* = QV‘. Kh

capital, so that output can be increased up to capacity using proportional changesin the

variable input. This

*.putty-clay” characterization of the production technology. at least for rhe case of electric utiliries. is rcalislic in terms of numerous engineering descriplion5 (II‘ the process ol’ electricity generation and in light 01 sc\eral recent econometric studies.” A general outline of the basic mode1is presented in

with Q@. W=Q(F,

O)=O, QF, Qh.>O.

(11

and the ex post technology specified in terms of a constant fuel-output ratio /jt for subcapacity levels of output:

fiF=F,/Q,.

for Q,
. . .. n

0)

the Ibllowing section. while results for a simplified !no-period model without rate review areanalyzed in ~hc third scc:ctionto understand better the basic relationships involved. More general res~Jlts using a

-_- __--- ___~.-----. - .--- ~.___ ----

--.~

_

‘A recent paper b) Kendrtck (19751 focuses on the relrttonship betweenAACs and tnozttti\c mechamsms fur producttvtty Improtements hug does not ILmk dtrectly at the Issue of allocat~e ellictency. Qutte rec. :tiy several papers

i r,d Hahorsen

hthmson

>\e?,of the

!L'iiC

thcx 1s a rare

(197&

Gallop xtd

119781 and

efictency elfects of fuel adJuslment clauses Whtle

formal analysis contat&

na~llel d~..ir?, contmuous

in the latter pAper. therr

opmniza~~on wtth respect to all mputs.

Includmg LLdxtal. The”putty-cla)”

technolop) assumed in thts .twpcr .

would appear to be a more accuratede&y&on

ut~ltt~es, especialIt “For

Karlson

habeattrmp:ed econometnc anal-

of man) regulated

electrrc uhhttes.

a summary of thrs engtneertng htcraturc tn the case 0’

con\entlonal eltr.tnc power productton. see Cowmg and Stn~th 11978) Recent econometrrc studtes of subst*tutlon possMiires

for

rlrctrlc generalIon include Fuss (1977). Petersen I 1975). and Boyes

I 19761 Strtctly

stated. the producttort prccess ofan electricity plant or

firm (asaumtng no resale market for electrx u:dity plants1 could be Je~rlbed

ah putt~~~“one-waj” semtputty. Ex ante. the firm can

chunse among destgn optlons for plants with varymg factor utput proportIons. Ex post (I.e.. after a plant has been built with a specllic dcltgn optr’!nl full tnput substltutablhtj the fum n-&t

not be able (3 substmtte other inputs (e.g., fuel) for capital sina the ~dp~tal IZ .mbedded m the purchased eqtnpment. Substiturton arc likeH]se hmrted at the firm level for multlplant ftrms.

t h po,t the lirm m‘ght be able. for example. substitute capital for fuel h:j mtihfjrng

extstutg plants or by adding and utilizing a new plant

/fuelratio

w tt h a high wpltal

and lrmiting utilization of an older plant

with a lower capital/fuel ratio. Ex post the firm cannot substitute fuel for capttal Iunlessa resale market for old facilities exists so that tbe Iii canextract thrc+tal

tt hastmested initsexistingequ~pment. For ease

of analysts we have chosen the putty-clab model as a reasonable dppro~unai~on oi

ltlr

Output capacity Q* is defined as

Q*= max {Q,!.

underlvtng production prcmxx

r=l.

. . .. II.

(3)

Ako assume a constant (over price and time) price elasticity of dc,nand for output with a neutral growth shift. so that the demand for output in period I is given by

Q, = C(I + 6)‘f’,~‘I with

Q;O. t=l,

. . .. n.

where P, is the output price in period I, q is the price elasticity of demand, and ci is the growth rate. The automatic adjustment clause procedure permits the oulpul price P, to change in each period by some frb_tion 4 of the change in average fuel costs relative to initial period costs, so that the outputpricing equation can be written as

would not be possibie. While

be able to substttute capilal for other tnputs (e.g.

through the attachment of addmonal reheat cycles). the firm would

po~bht~rr

where F,. K,. Q, are fuel and capital (assumed lixed ex post) input3 and output. respectively, in period 1.

p,=_p,+(#)

w,F,_ 55, 0,

Q, 1

0s;ss;

r=l,

. . ~g

(5)

where P, is the initial period output price, assumed given, and W,is the price of fuel in period t. The firm faces a regulatory rate review in period g (with certainty). This rate review adjusts the output price from P, to P, using period g as the teft period. Since the automatic adjustment process is continued after the review in terms of a new base period, period g, the

AutcmatkAdjustment

Clauses and Allocative Efficiency

postreview.pricing equation must be written as

t=g+l,

temporal framework the objective of the firm is to select an optimal ex post technology (i.e.,an optimal ,3,) from the ex ante production function, equation (I), to maximize the present value of future profits W.

. ..) n (6)

where the review-adjustedoutput price pg using test period data is set by the commission to allow the firm to earn a rate of return s on its invested capital. Thus p# is given by7 P,=(w$,+WQe. (7) We assume s > rp, the price of capital in period g. Equations (5)and (6)can be simplifiedby use of the ex post relationship in equation (2), yielding P,=P, +QB&v,-w,)

f=l, . ..*g

(8a)

P,=Pg+&3~w,-wJ

r=g+l,

(8b)

. . .. n.

Input prices for fuel w, and capital services r, are assumed to be given to the firm and to change over time as follows: w,=w,(I +a)’ and r,=r,(l +p)‘,

319

t=l, . . .. n,

(9) where w, and r, are (given)initial period prices,and a and ; are known parameters. Finally, the firm is assumed to maximize the present value of protits W over the given lifetime n of the investment, where W can be written as W=

i [R,-w,F,-r,KJb, (10) t-1 where R, and 6, are total revenues and the discount

factor, respectively,associated with the f th period. Thus the firm faceschanging input costs over time and an automatic adjustment procedure that permits it to change its output price to recover some or all of these intertemporal cost changes, depending on the input coverage and the specificvalue of 4 in equation (8).The firm also facesa (certain)rate reviewin period g that shifts the output price to allow the lirm to earn test period profits equal to SK.” Within this inter-

THE MC EFFECT: A SIMPLIFIED TWOPERIOD MODEL

The general model outlined above, a multiperiod model involving both automatic rate adjustment for fuel price inflation and periodic rate review, is analytically rather complicated so that our general results are not entirely intuitive. To develop a more heuristic understanding of our general results we first analyze a simplifiedtwo-period model involving only an AAC (i.e.,without rate review).Parallel results for our general model are then presented in sections four and five. Assume a two-period model with no growth in demand and no rate review. Inflation is assumed for both input prices, as given by equation (9),and the AAC is assumed to be operative so that the price of output in the second period P, is given by equation (8a) for t = 2. The output price in the iirst period P, (and thus Q,) is assumed to be exogenous to the firm (i.e.,the firm is required to meet first-period demand Q, at a price P, set by the regulatory commission). We first note that the assumption of fuel prize inflation implies that P, v$ be an increasingfunction of time t owing to the AAC pass-through e&t from rising fuel prices.Thus capacity delined as Q* will be equal to demand in the first period Q ,and hence wi:! be exogenous to the firm.As a result,the only ex ante choice variablefor the firm is F,, which a!ong with the given Q, will determine an opt’sal ex post technology in terms of a specifx fuel-output ratio 8,. The required capital stock K can be determined from the ex ante production function equation (l), given Q, and an optimal F,. For our two-period model, the present value of profits in equation (IO)can be written as W-R,

‘Thruatdaapreshilld*Mndinperiodg,~~tQ,~~shilldrmond.in equation (7) rdlazts tbc institutional fact that regulatory commissionsact a5 if ckctricity demand were trxally rnchstic since they use test period data includingdemand data when computing the nm rate or pritx to be used by the utility. eThcinitiplpriodwtputpriceP,isaswmdtobegivmtothc~nn (“y tlu ragulalOrycomm&m)arxlbatcedacsnolrclkctagivmrace ofreturn to be allowed by thclirm on its new investment.This is likely tobe:hccPscwithcith~f~(~t~~t~ofCOM~Tin the IckFommunicPtionsindustry)or new plantsfor existingfirmssince the old rate (pria)swucturc mustgenerallyk us4 until su&imt data for the new facilityare availabk to pmnit formal regulatoryr&w. In ourmoddsucbamieartaksplaainthcgpc~~

-wtF,

-r,K

(11) +b(R,- WA -r2N where b is the discount factor associated with ithe

second period w1=(1 +a)w, and r,=(l +y)r,. Differentiatingequation (11)with respect to F, and rearranging terms, we have

aw

aF,=- WI -rtC1 +b(l +?)I l$1 JR2

+bK

-W+a)w,

aF2 a~,’

(12)

T. G. Cowing and R. E. Stevenson

320

where CK/CF, is the optimal slope of the ex ante isoquant for the lirst period (i.e., for Q,). Noting that R2=P2QL and FZ=F,Q2/Q:, we ha\e CR, QZ - = fj~,(l

Q,

?F,

rewrite Z as

Ql-Qz Q,

(1 +z) ---

Z=hc!J,

-a), and (17)

*

(13)

where 11is the price elasticity of demand defined as I - ;Q /;P)(f’/Q), andj? is the ratio of fuel costs K$, to total revenues R1 in the second period. Substituting

the expressions given in equation (13) into s:quation ( 12). setting equation (12) equal to zero. and rearrang-

mg yields c’li

+b(l +;)] ;i-

r,[l

= -(u,[ I

The caseof nc, AAC effect (i.e.. the cost-minimizing or elliclent case) can be obtained by setting #=U and solving for iii; /;F,, obtaining (151 h-cc

for 9 = 0. P, = P, and hence Q2iQ, = I. of ;Ln .4AC on allocative efiicienc> can now hc examined b> rewriting equallon (14) as The efkct

-(O,Ll +b(l -kr)]+W,h(l

+31)

Q,-Qz .-0,

From equation (I 7) it is clear that for positive values of r and 4. Q, will always exceed Qr, so that the critical parameter in analyzing the sign of Z is the elasticity of demand 9. For example, if demand is inelastic (i.e., O< tl< I) Z will be unambiguously positive. This implies allocative inelliciency in the form of an optimal technology selected by the regulated firm that has a fuel-using bias. On the other hand, the alternative case of elastic demand is not as clear-cut. Looking at equation (17). we see that some (but not all) values ofy greater than unit) will causeZ to be negative and hence will imply a capital-using bias. It is also clear that for smaller values of tl greater than unity, Z will generally be positive depending on the relative magnitudes of r. 4, ,I. and/& Thus for this simplilied two-period model we conclude that an automatic adjustment clause will result in allocative inetliciency in the form of an induced fuel-using bias if demand is either inelastic or mildly elastic. Only for highly elastic demand is there the possibility of a capital-using bias.“ Furthermore. the possibility of a nondistorting AAC’ effect (i.e., the case of Z =O) appears rather unlikely. Some additional insight into the nature of the intertemporal tradeotTbetwc_nprofits in period I and 2 can be gained from Figure 1. The profit curves shown repreent profits in either period as a function of the fuel/output ratio fi,. For the first period x1 is drawn. Then nL is drawn for the second period on the asrumption no AAC (i.e.,4 =O), while $ represents profits in the secondperiod for 4 >O. In the absenceof

of

----

nhere the lirst term on the right-hand side IS the numerator of the ratio in equation (I 5). Defining the sum of the second two RHS terms in equation (16) as i:. we note that the Ac.C will induce a fuel-usmg bias (i.e.. ;1marginal rate o,‘ technical substitution smaller in absolute sign than equation (I 5)) if and only if Z is positive. On the other hand, a capital-using bias will result if Z is negative. while if Z is identically equal to zero. the regulated firm will select an efficient input ratio. In order

to

examine these three cases further, we

~-

* II can be shown,rewrllmg equatlon 1171, thal the n&My bullic~cnt condmon for Z -z0. 1s

and

Alrhough somewhat rntractabie from an analytical point of view, numencalanalysiscan be usedand mdrales that q must be greater than 1.5 m order to prod= a negatwe2, arsunilng#kO.S& LO.2 and wherea takeson any of the value shownin Table 1. Forj, =O.J, a more reasonablevalut (seeTabk I. note 2), q must be grea@rthan 2.0 Wore Z becomes negative. Thus there are strong grounds for concludmgthat Z will usuallylx positive.This analysisalsorevealsthe analyticaldi6iity in working with an AAC-REG nuxq eval in our grosslysimplifiedtwo-period model.

Automatic Adjustment Clauses and Allocative Efficiency Profits

321 be convenient to develop the case of no demand growth first.

FUEL PRICE INFLATION WITHOUT DEMAND GROWTH

an AAC, prolits will be lower in the second period because of cost intlation, while the profit-maximizing point may be either to the left or the right of that for the first period depending on the relative inflation rates of the two inputs, fuel and capital. The IV and w* curves represent the present values of the sum of period-one and period-two prolits, assuming 4 = 0 and 4 >O, respectively. In the presence of an AAC (i.e., #>O), profits in period two will be higher than otherwise since the AK permits some of the cost increase due to higher input prices to be passed on to the consumer in the form of higher prices. Thus if we assume the fuel-using bias case, both Ir, and w* will be higher than and shifted to the right of xi and lV’, respectively. The result in this case is a fuel-output ratio, or ex post technologyfi that is larger than pF, the optimal fueloutput ratio for #=O. As we have seen, it is also possible for an AAC to result in a fuel-output ratio smaller than BiF, but the case of a fuel-using bias shown in Figure 1 clearly reveals the tradeoff between profits in period one and profits in period two that the regulated firm must consider in selecting an optimal ex post technology to operate in both periods. This tradeoH would exist in the absence of an AAC, but as Figure I demonstrates, the existence of an AAC and the proportion of the cost increase allowed to pass through (i.e.,4) influence the optimal fuel-output ratio via the relative shift in .$ With this analysis of the AAC e&t in mind, we now turn to an analysis of the more general multiperiod model outlined in section two, although it will

We now assume an n-period model with input price inflation, an AK so that fuel cost increases are automatically passed through in the next period, and periodic rate review but no growth in output demand. We can look at the combined effects of an AAC plus formal rate-of-return regulation without the additional complication of demand growth, which .is considered in section five. Given fuel price inllation and a positive 4, P, will be an increasing function of time. If we assume that the impact of the formal rate review in period g is to further reduce demand, Q, will unambiguously decline over time.!” Thus Q* will be exogenous to the firm and equal to Q,. The regulated firm can be regarded as selecting an optimal ex post technology (i.e., an optimal flF) by maximizing Win terms of F,, or equivalently, fip It is clear from equations (7) and (8) that for a given s, the time paths of P, Q, and F, are fully determined by the optimal value of /?p The required first-order conditions can be derived by maximizing W with respect to BF, yielding”

Noting from equation (8) that the impact of changes in bF on output price P,will be different as between pre- and postreview periods, equation (18) must be rewritten as

where M; and Mr refer to the general expression

M,=

2

-~,3 F

=Q, F

(I

-q+&$

F

,

-w,

1

t = 1, . . .) n (20) loTbe necessaryconditionsfor the rate review shit in periodg are developedfurtherin sectionfiveand in the appendix.They involvethe conditionthat dn,/JP, be positive.which will be Asfii ifdem Ind is either inelasticor mildly elastic. I’ OpIimization of W with respectto F, insteadof fiF woud yield identicalresellssinceQ ,is assumedgiven.The useof fiF as the choice variabk focus a@ntion on the choia of an optimal ex post technologyrather than on optimal input kvels that changeover time. This methodologyis followedthroughoutthe paper althoughin the caseof final demandcapacitydeterminationd&used in sectionfive,it is necesaq to apply an additional equilibrium condition sino2Q cannot be regardedas gAn in that case.

T.

322 and x heref; is the ratio of fuel costs to total revenuein period t. Expressions for M; and M;’ can be derived from equations (7) and (S).” Substituting these expressions into equation (19) and solving for SK /L?F,]Q,, equivalent to the slope of the ex ante isoquant for Q, at ahe initial equilibrium point, we obtain

where

\h.,wE.-r;+q/;~--H',]. G,= Q,C&~*,h, = Q,( 1 - ‘1 +

rtf;!.

t = 1, . . ., n,

.[i is the fuel cOSt share J total revenues in terms of Pg rather than P, (i.e.. H’~FJP~QJ,and p#,lP, is the rtitio

,,f preshift to postshift output price in period g.” hiterpreting equation (21). we first not; that in the case of no formal regulatory review, we have

Given the intractable nature of equation (21) and

the desire to avoid specifying a restrictive form of the ex ante production function such as CD or CES. numerical analysiswas used to examine the allocative effects of imposing an AAC on a firm subject to intermittent formal regulatory review.‘* These results are summarized in Table lA, for the case of inflation with zero growth in demand.15 Table 1A shows that the addition of an AAC mechanism to a regulated firm subject to factor price i&tion and periodic rate review (hereafter AACRIG) unambiguously reduces the magnitude of the equilibrium MRTS, equation (21), and hence induces the firm to select an ex post technolog! that is less capital-intensive than it would be in the absenceof the &4C.16 This is clearly in accord with our demonstration in the precedingstxtior. ihat the use of an AAC generally creates incentives for the adoption of relatively fuel-using technologies, and given an olktting effect(i.e., a capital-using or A-J bias) from the formal rate review. The magnitude of this (net) impact on input choice is sensitive to such parametersas the rate of inflation in fuel prices and the price elasticity of demand for output. For example. in the case of no demand growth and mild inflation (i.e.. a=O.O2) the AAC-REG firm is more efficientwith respectto input _-_..-

since the same pricing equation will apply to both periods, while the additional deletion of the AAC (I.e., 4 = 0) yields

(23) since Q, will equal Q,. This last result is clearly the intertemporal cost-minimizing or efficient solution. In the case of periodic rate review but with no AAC (i.e., 6 = O’rwe have

-~~iY Only = -

SK / ZF,lq,

i Q,M.,b,+ wy i h,b,; Q, 1-1 r-g+,

“An appendu wntaawnga moredetaikddenvaConofmany orthe theoret@ results pxnted in the paper isavailable from the authors. ’ 3Equation (2 1)representsthe slope of an tntertemporal tsocosthne and iseguvalent totheratiooftheshadow orektiveinput pricesthat the regulated Lrm fa~ps.In equ~hbrium_thts rauo will be equated to the

dope of the a.??ropnatetsoquantand hew can be denoted MRTS.

G.Cowing ad R. E. Stevenson

~-

-

” For another recem exampk of the useof numrxal analys: m examuung the axxtomx rmpbcauon of rcguhtron. see Cdkn. Mathewson. and Mohnnp 11976). ’ ’ A morecommonnwasurcd ths welfarelosslrom rqutauon ISrhc sum of consun& and produars’ surpiuscsas usa& for cxnmpk. by Calkn. Mathewson,and Mohnng (1976i A surplusmeasureofsocxal welfarerqures thespccftcatronofa produeuonfuncltor~.L~ttxtton that we haveavordedtomatntam thegcnerahtyofourcomlusioos.On the other hand.our measurem termsof MRTS only includeswelfare losst~,due to allocatrve me&iency. Whrk thts mtght seem unSmsfactMy,cholpsin~duemwrmoddlotheind~Lplc dwdfarc(and dstoruowpaaUydomwcasurplusmCPRUT prrtrularlysomthecaacdin&stkdetnam3),esshownbyW~~968~keumingeithxmdasticorewmmildlyelasticdaMnlit~ uniikelythatasu@usnuasure dsd&ucwould@ldtcsultsqueliral-

~vclydi&rmtkomowrlmatsoawmcanePsaublcdcgradmplt ~~b6wtability m tbeenante to&&gy. We ~IEZ&PJwouldarguethat o~mQwedalbaUivce&uuqslikdytobean%mabk 2pfxoaitnationto a more compkte mmr6urcdsoctaIwel’&atkasl withrespbxto cccNl%z dlicklxy. “‘The resultsd the nurnencal anatyssrsummarued m Table 1 mvolved the followmg parameter values;w, = 1.25. rl =0.17, r-0, s=O.?~~~l.g~5,n~1O,pndd~0.10,wwhercdithedr~untra~.In addnron.o thx valuesfor rr.6, n. andf, that are nported,~, valuesof02 and 0.4 were also usd. The computatronalformulasusedrequiredan iwgned value C:/; not compktely consistentwrth the equilibnum mterpretattonattnbuted to the resultssince/,. rhro@ F,. must Lx regarded 85 an cndogenousvariabk. The resultsusmg alternative valuesfor j, did not appear very scnstuveIO this pounttal sourceof b‘as. and tre itingf, as an endogenousvariabk would have requled the spc&2a .lon of a prodwtlon function,an assumptionavoided in this analysir to mamtam the generality of the results.

Automatic Adjustment Clauses and Allocative Efficiency

TABLE 1. Analysis of Induced Input Distortion Q

.02

.07

.I2

6

r

q=O

q=o.5

r,=1.0

T)=l.5

A. INFLATION, WITH NO GROWTH 1.02 0 97 1.08 0 r1 1.08 1.02 ‘2 1.16 0.94 0.95 13 0.92 0.84 0.82 0.87 0 ‘1 1.05 0.99 ‘2 1.14 0.78 0.81 ‘3 0.74 0.68 0.66 0.69 0 ‘1 1.02 0.94 ‘2 1.14 0.64 0.66 ‘3 0.59

0.95 0.99 0.96 0.80 0.94 0.83 0.64 0.88 0.67

B. INFLATION. WITH GROWTH rl 1.09 1.04 1.02 1.19 1.09 1.03 ‘2 0.91 0.91 0.92 :: 0.86 0.94 1.02 1.19 1.11 1.05 ‘2 0.72 0.76 0.83 :; 0.67 0.84 1.03 1.17 1.20 1.14 ‘2 0.56 0.67 0.82 5: 1.13 1.06 1.03 1.25 1.12 1.04 r2 0.90 0.90 0.92 :: 0.87 0.95 1.02 1.27 1.17 1.09 ‘2 0.70 0.74 0.81 ‘3 rt 0.66 0.84 1.01 1.31 1.27 1.23 ‘2 0.64 0.53 0.78 ‘3

1.02 0.97 0.95 1.13 0.99 0.95 1.26 1.11 1.07 l.C2 0.98 0.95 1.11 1.02 0.93 1.23 1.19 1.02

.02

.05

.07

.05

.12

.05

a2

.I0

.07

.lO

.I2

.I0

Table I Notes

1. ‘1 equals the ratio of equilibrium

slope of isoc.uant for AAC-REG to that of the efficient case (i.e., no ACC and no REG). r2 and r3 are similllr ratios for the caws of REG-onIy and AAC-only, respectavely. 2. All computations are for 41 = 0.3, which is epproximotcly the ratio of total fuel costs to total electric operating revenues for class A and B privately owned electric utilities in 1978. See FPC (1978), p. 1. 3. Other paremeter values assumed are wt = 1.25, r = = 0 s = 0.22 @ = l,,q = 5. Q - 10, and B d.ISkZtLe &of 0.1.14

323 of the use of AACs to counteract the input distortion caused by periodic ratekof-return regulation (i.e., the A -J bias) if fuel price inflation is relatively weak and there is no growth in demand.” This conclusion is not supported for casesof either mderate (o(= 0.07) or strong (a = 0.12) inflation. In such cases,the addition of the AAC creates a fuelusing bias that more than compensatesfor whatever capital-using bias may have resultedfrom REG-only. This distortion appears to increaseas the rate of fuel price inflation is increased,as shown in Table lA, and createsa rather strong argument in terms ofallocative efficiency against the use of MCs in rate-regulated industries. The e!Iicacy of using AACs in industries already subject to periodic rate review is not unambiguous and is particularly sensitive to the rate of fuel primeinflation assumed. One additional result of this analysis merits comment. Although the REG-only firm is unambiguously more capital-intensive relative to the AACREG firm, it does not necessarilydisplay a capid bias in its selection of an optimal ex post technology. Comparing the REG-only case with an efficient choice, we see in Table IA that the REG-only tirm will choosea technology with a fuel bias rather than a capital bias for moderate or higher infiation rates and for elastic demand. There are even some ranges of inelastic demand where this result is also true, given a large enough rate of fuel price intlation (relative to capital price inflation). Although this result may appear to be inconsistent with the unambiguous capital-bias result of the static A -J model, it foVows from the intertemporal nature of our model and the assumption that rate review is intermittent, taking place several periods after the investment decision. Thus the input-distorting effect of rate-of-return regulation dependscrucially on the type of regulatory environment assumed, including whether or not dynamic dimensions are included, a result with obvious policy implications.’ ’ -

choice than the REG-only firm if output demand is inelastic. In Table 1 this is shown in the form of r, values. the ratio of equation (21) to equation (23), which are closer to unity than the associatedvalues of r2. the ratio of equation (24) to equation (23). for values of q lessthan 1. On the other hand, if dema Id is elastic.the REG-only firm generally selectsan ex post technology with input proportions slightly more efficient than the AAC-REG firm. If we assume that electricity demand is inelastic, as many econometric studies have indicated, a casecan be made in support

” For a recent review of a number of econometricstudiesof the demand for electricity,seeTaylor (1975).A number of thesestudies report estimatesof the priceelasticnyof demandm the rangefrom 0.2 for the short-run to 1.36 fi.lr the long-run.See esp&ally Anderson (1973) Houihakker. Verleger.and Sheehan(1973).Mount. Chapman. and Tyrrell(l973). and Halvorsen(1975). ‘+The iii’s cost of capital would include Ihe fiinclal cost of capital,economicdepreciationof equipment. and associatedproperty be equal to the lirm’s dlscmunt taxes and thus would not dly rate. lqThjs genersl result has also been derived in several precous stud& although not with respectto the use of an AAC. See. for example, Bailey and Coleman (K97lb Davis (1973). and Holthausen (1976).

T. G. Cowing and R. E. Stevenson

324 FUEL PRICE INF’LATION WITH DEMAND GROWTH

2

We demonstrated iq the last section that in the case of fuel price inflation with no growth in demand. Q, is unambzguousiy a decreasing function of time so that capacity is detcrmirned by the exogenous initial period demand Q:. Alternatively,

if we now assume some

positive rate of growth in output demand 6, it is possible given ,Asufiiciently large growth rate for such growth to aver
ofQ, to fall from

the

steadily rising output price and hence result in Q,. increasing witlz time. In such a case capacity Q* will b: determined by final period demand Q. rather than Q, snd will be endogenous to the firm sinct Q, is a finnction of P,. which is determined in p&rt by the particular ex pa>st technology selected.The firm must maximize W by simultaneously selecting both F, and Q, and hence an optimal pk. The conditions for Q, increasing rather than Jecreasing over time in the more general model that includes growth in the demand for output can be derived easily. We first note that gross profits in period f (i.e., R, - w,F,) can be written as n[r= p,Q,(l -./;I

i=l,...,n.

time and substituting the former results into the latter expression, we have

The sign of this shift effect will depend on the relative

magnitudes

of the fuel cost share of total revenues in

period g and the price elasticity of output demand. Since most econometric studies of electricity demand have indicated

.. II.

either

inelastic

or

mildly

elastic

demand and since recent data for electric utilities suggest that j; is approximately assume that the e&t

0.3. we can generally

of a shift in output price in

period g will be to change profits in the same direction. We need only know the time path of profits. equation (25). to determine the sign pf the required review4nduce.j

price shift in period g since rising

(falling) ptofits will mean that the output price must be decreased (increased) to reduce (increase) profits to their original level. Summarizing

these results in the general case of

demand growth, we note that in the case of fuel price inllation with either little or no growth in demand, II, will unambiguously

decline over time so that the

output price in period g. Pg. will have to be increased their initial period level. as shown in Figure 2A In the case of inflation

(26)

with substantial

growth,

.:, un-

ambiguously increases over iime so that a reauction in P, is required, as shown ill Figure 26. Looking at the impact

t = 1.

t)/rl.

by the regulatory commission to restore profits to

(25)

Differentiating equations (4) and (2j) with respect to

0, = Q,(6 - rq5qF,,.


determination

of this shift m output

price on the

of capacity. ‘ve note that our previous

analysis of the time path of Q, requires no further

and

amendments. In the first case, inflation with little or

,+, = P,( 1 -.I,@,

- rw.F,( 1 - 4,.

I = 1, . ., II, (27)

no growth, capacity is still determined by the initial

where i is the rate of change and ii is the rate

ofx over time (i.e.. dx /dr) ofdemand growth, assumed positive.

period demand Q,, while in the second case capacity is determined by linal period demand Q,.

In the case of fuelprice inflation Q, will increase (decrease) over tir.le if the rate of demand growth 6 is large (small) relative to the movement along a given

The difierence between the case discussed in section four, fuel price inflation with little or no growth so that capacity is determined excrgenously by the given

demand curve iilduced by the rising output price. If

Q,, and the case of inflation with substantial growth

we assume full pass-through of a11fuel cost changes

(i.e., 0, > 0). where capacity is determined endoge-

(i.e., 9 equals unity). ir, will always have the same sign as Q,.

nously by Q,, is shown in Figure 3. Equilibrium point I

The discussion

above does not take account of the shift in output price in period g due to rate review and +‘e resulting induced shift in Q,. Differentiating equation (15) l%ith respect IO P, and evaluating the result at r =,q yields Sn -2

C’PY

represents the former case at an output level of Q,. while II represents the latter case at the final period output lel,el Q.. Both isoquants represent the ex ante production function, equatiorl (1 J. The ex post time paths are straight lines since capital stock K

is

assumed fixed in the short run. while the relationship between F, and ex post output Q, is given by the

=

._ 71,. --.-. (1 -‘f+P/f,)

P,I i -.t;,

It follows that

(28)

particular value of /II selected, that is, by the specific choice of an optimal ex post technology. The lirst-order conditions for the case of fuel price inflation

with sugstantial dcnand

derived by maximizing

growth can be

IV with respect to /I,

and

taking into account that capacity is determined by Qn

325

Automatic Adjustment Ckuses and Allocative Efficiency

A. inflation

with low, or no, growth in demand:

6 < 0, k ( 0.

B. Inflation

with substantial

i >O, k >O.

growth indemond:

FIGURE 2. Equilibrium

rather than Q,. This yields the following result:

time-paths for P,. Q,.

and T,,

assuming dn,ldP,>Q.

FIGURE 3. Initial demand and Final demand capacity Capital

where equation (30) representsthe slope of the ex ante isoquant at Q,,. The only formal difference between equations (211and (30) is the replacement ofQ, by Q, in the denominator. The rerults for REG-only and AAC-only are given by equations (24) and (22), respectively, with Q, in the deonominator. The efkient case (i.e., with no regulatory intervention) is given by c?K EFF _= - ,c, 2F” Q,

e,w,b/ Q. i rrbr

(31)

I=1

since the a-zumption of demand growth implies that

0

I

I

I

1

i

I

I

F' 1

Fn n

F1 Fn n I

I

Fuel

T. G. Cowing and R. E. Stevenson

326 Q, is generally less than Q. even if Output Price p, is

kiency, a result that seems reasonable in terms of

constant over time. The results of using numerical analy *is to measure

offsetting input biases.’ Perhaps the most important point to be gleaned from the-seresults in addition to a general sensitivity to the specirc set of parametric values assumedis that of the two parameters,the growth rate oidemand and the rate offuel price inflation, the latter appears to be the more important in determining optimal reg~l!‘,tory policy. In addition, the magnitude of the &‘R elasticity of demand for electricity is also critical, as it was in the case of no demand growth. If we assumeat least a moderate rate of fuel price inllation and electricity demand that is somewhere between moderately inelastic to mildly elastic, probably not too far off from our recent experience, the use of an AAC in addition to periodic rate review results in the smallest degree of input distortion relative to the other two regulatory alternatives. REG-only and AAC -only, ait hough in some casesthe diflerencesare minor.2 ’

the relative inefliciency of using an AAC in the caseof fuei price inflation with positive demand growth are summarized is, Table 1B. For a moderate rate of growth in demand (i.e.,

S = 0.05) and a iow rate of fuel price inflation, :wo of the three regulatory alternatives-AAC-&ES and REG-only-generally result in at least some degree of capital bias if demand is inelastic. Of the two cases, AAC-REG

is generally the less inefficient, although

REG ~oniy does result in slightly less input distortion for mildly elastic demand. In most cases the ditferenL%s are rather small. AAC-oniy lively less input distortion

results in reia-

only for highly elastic

demand and a high rate IJf fuel price inflation (i.e., 3 =0.12). From Table inflation

1B we also see that increasing the

rate, holding

the growth

rate constant,

generally enhances the eficiency case for using an

AAC as a regulatory adjunct to periodic rate review if the elasticity of demand is approximately unity. If demand is either highly inelastic or highly elastic. a policy of REG.-only

(i.e., without an AAC

added)

induces slightly less input distortion. There are even several combinations of the rate of iuei price inflation and the elasticity of demand for which AAC-oniy

is

ICS distorting than either of the other two policies. The policy implications

with respect to allocative

efficiency appear to be very sensitive to the values of these two parameters. It is alsoclear that doubling the rate of demand growth from 5 to 10 percent has little effat on the relative desirability or the three reeulatory policies. An alternative way of interpreting tt yje results is by selecting reasonable values for the three key parameters in terms of recent experience. If we assume a reasonably low annual growth rate. say 6=0.05, inelastic demand with q=O.O5, and an annual inflation rate of either 0.07 or 0.12. the AAC-REG option exhibits a mild fuel-using bias and a slightly smaller degree of ineficiency than either of the other t&o options.‘0 in the second case (a=O.I2) both AAC

REG and REG+nly

result in about the same

OPTIMAL MC REGULATION The AAC parameter 4, the proportion of fuel cost increasesallowed by the regulatory commission to be passed on to consumers as rate increases without benelit of formal review, can also be regarded as a policy variable. at least with respect to allocative elficiency,similar to the allowed rate of return in ratec&return regulation. Although this issue is not the primary focus of this paper, we offer some tentative comments. It is clear either from equation (30), for the general case of fuel price inflation and demand growth, or from equation (16). for the simpl&d two-period model, that changes in 4 will affect the degree of allocative ineficiency. Since equation (30) is dificuit to handle anaiyt:caiiy and since on!y the results for d, = I are shown in Table 1, we focus our comments on an analysis of the simplifted model, which allows us to look at the “pure” AAC effectsof changes in d, (i.e., without the additional complications of rate regulation). A more complete analysis of this issue would involve

a more general model including both

amount of allocative inefliciency although with opposlte input biases. It is also interesting to note that the REG

only case 21~~~s displays a capital-using or

A-J bias while the AK-only case displays a fuel-using bias. The joint case of MC-REG is abvays intermediate with respect to allocative inef‘” If theassumalgowth rilir ISreduced IOzero.the policyolREG Only t%x-xm%k+.~melkent than either AACREG or AAC+nly.

” A third case,fuel priceddlntion with growth, wasalso examined but the resultsate not mcluded !wc for reasonsof brcwty. These nsults indicated thar the dlicacy af AAC-Rffi Rgulotioa in de-

lUkmarypaiodsisquatiorvbLiatarardaibativc&bucy,at least for rclatiwly smf3ll rate5 of fuel prioc dcllatio~ and awming imlastlc demand EitherREGonly orMC-only rrsuhod in B~!nalkr degra ofallccativeirMTii, with AK-only being rclatiwly more ef!icxnt in the EBSCof highly m&stk demand This last result was furIhcr rcinforad the larger the rate of fuel pfke w.

Automatic Adjustnmt Clnuses and Allocative Efficiency

AAC and rate regulation, but such an analysis must

be deferred to a separate paper. The aliocative effects of changes in Urin the case of our simplified model can be seen from equation (17). Unfortunately these effects are not transparent since changes in 4 will have both direct and indirect eEfects on thedegree of allocative inefficiency,the latter arising from changes via Q3 (through changes in P2) and f2. To explore these effects further, we again resorted to numerical analysis. Our results are summarized in three basic conclusions. The first conclusion is that setting 4 =0 results in the etkient case,since Z will always equal zero as can be seen from equation (17). Second, Z is always positive forf; LO.2 and r~I 1.5, and assumthree ing the alternative inflation (0.02, 0.07, and 0.12) used in Table I. Since Z >O implies a fuel-using bias. AAC regulation will generuily induce a fueking bias if demand is either inelastic or mildly elastic, This result is independent of the value of # between zero and unity. The third and most important conclusion is that increases in (b always increase the absolute magnitude of Z whether Z be positive or negative. In cases where Z is positive, $I could presumably be adjusted to give any desired degree of fuel-using ineficiency, for example, to o&et any A-J bias resultmg from rate-of-return regulation. Also 4 appears to have a significant impact or fuel-biased inefficiency since increasing 4 from 0.5 to 1.0 generally results in the absolute magni!ude of Z more than doubling. Although we cannot say to what extent these results for the simplified model are generalizable to our more general model, we anticipate that #could be used as a policy instrument to reduce the allocative inefficiency resulting from any given allowed rate of retum.2Z If this conclusion should prove correct, it suggests that regulatory commissions that use AACs as par. of their regulatory procedures have a second potentially useful policy variable at hand. Optimal regulatory policy should be viewed in terms of the simultaneous setting of these two instruments, 4 and s. Such an approach should also result in more effective regulation sinu the twin goals of a welfaremaximizing output level and allocative ellkiency could then be pursued with two independent policy variables rather than one. It seemc clear that 4 should

zzJIMmaybetrue only w!wrean s IS urqidthat results in a capitalusing or A-J bias and where2 is positive,TXPthat the two biasesare offsetting It has beenshown,for example.in thecontextofmultiperiod modelsof rate-of-returnregulationthat an s mayexistgrealerthan the cost of capital which inducesno A-J efTect.See Bailey and Coleman (1971)and Holthausen(1976).

327

be regarded as XI independent policy instrument along with the allowed rate of return and that a number of related issues need to be examined further. CONCLUSION This paper has examined the implications with respect to allocative efficiency of using automatic adjustment clauses in regulated industries. Using a two-input model of ex antelex post input choice and a general putty-clay technology, we have analyzed the relative extent of input distortion resulting from three alternative regulatory policies--periodic rate review with and without an MC, and an AAC without any rate review-for the case of a regulated firm that chooses an ex post technology to maximize the present value of future profits. Our results indicate that the economic rationale for using AACs in industries already subject to intermittent rate review is not unambiguous even in the face of severe cost inflation and is particularly sensitive to the magnitude of the price elasticity ofdemand for output and the rate and direction of input price changes assumed. It appears that the input distortion induced by the AAC-REG policy is smaller for low rates of fuel price inflation when there is no demand growth and demand is mildly elastic. The AAC-REG input distortion is greater for higher rates of inllation when there is positive demand growth and mildly inelastic demand. This suggests two conclusions: 1) allocative ineficiency created by the ACC-REG option is related to the relative rather than the absolute magnitudes of the rates of inflation and demand growth, and 2) in a number of situations the use of an AAC to supplement rate regulation increases rather than decreases the resulting distortion in input choice. We are forced to conclude that the use of AACs in regulated industries such as electric power. while originally justified on the basis of financial viability, may carry significant economic costs in the form of allocative ineficiency that may outweigh the benefits, especially if the difference between the rates of fuel price inflation and demand growth is increasing over time or if fuel prices are actually falling. This latter result implies the desirability of an asymmetrical use of .&K’s as regulatory instruments, that is, possible use during periods of input price inflation but not during deflationary periods, assuming inelastic demand. There is also a need for more flexible regulatory policies since changes in such variables as the rate of change in fuel prices and the rate of growth in demand for electricity appear to affect the type of regulatory approach that is desirable, at least with respect to allocative effkiency. Finally, a more precise

T. G. G~,v+ng and I?. E. Stevenson

328

fix on the magnitude

of the elasticity Of Ourput

demand is necessary if optimal regulatory policy is to pursued since the relative desirability

be successfuI]y

of the three alternatives examined

The authors would like to, thank the referee for his helpful comments

and Jeffrey

Small

for hts computational

asststance.

in this paper

depends crucially on the extent of assumed price elasticity. Although analyzing

this paper has made a beginning at tiie eficiency elfects of using AACS

in

regulated industries. much remains to be done. It

wou!d be useful to relate the regutntion-inducti distortion+ in factor proportions to changes in the level of costs so that a more complete welfare measure could be computed. This would require the specification of a production function. an assumption we have avoided to preserve the generality of the results, since such cost changes are sensitive to the extent of substitutton pas!-ibilities lnd scale effects assumed.

Further

work

alternative

vould

a!so be desirable

in using

welfare measures and in extending the

dynamic dimensions of our model, particularly in the direction of including dynamic interactions and the role of uncertainty in the investment decisions of regulated firms. A

second area for additional

research is the

question of an optimal pass-:hrough proportion Cp*. either for a given allowed rate of return or in terms of the simultaneous determination of optimal values for the two

regulatory

instruments.

Since the AAC

process IS inherently intertemporal. the proper framework for sush an analysis should be a dynamic model that incorporates both AAC and rate-of-return reguIauon. A related question is that with the use of a second policy instrumem in the form of 4. regulatory commissions may be better able simultaneously to pursue the twin efficiency goals of regulation, forcing the regutated maxtmizing

monopoly

to

produce

a welfare-

output level and inducing the firm to

r: lnimize the cost of producing the correct output. A third broad area for future research related to this paper is suggested in a paper by Joskow (1974). who sugge<.ts that 119th static and dynamic A-J models of rate-of-return satisfactory frameworks

regulation

may be un-

for analyzing

the actual

practice of regulatory control. He outlines an alternative model in which inflation plays a major role and

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in terms of responses to periods of rising versus fallmg

Houthakker, H. S.. Verleger.

average costs. Since the use of an UC instrument regulation

is cl:*sely related during

inflationary

as a regulatory

10 the problem

of

periods and since

Joskow’s evidence strongly suggests that the

A-J

model may be incorrect, >is model appears to be a particularly

fruitful

framework

within

which

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to

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Accepted 4 December I98 I