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Chapter 23

O P T I M A L P O LI CI ES F O R N AT U R A L M O N O P O L I E S

R O N A L D R. BRAEUTIGAM

Northwestern University

Contents

1. Introduction 12902. Th e natural monopoly problem: A traditional view 12913. Why regulate? 12994. Pricing alternatives: Basic con cep ts 1309

4.1. Price discri min ation differential pricing) 1 3 1

4.2. Non line ar outlay schedules nonlinear tariffs) 1311

4.3. The com mon cost problem in the multiproduct firm 13125. Peak load pricing 13166. Ramsey pricing 13207. Non linear outlay schedules 1327

7.1. Pareto impro ving nonlinear outlay schedules 13297.2. Asymm etric information 1332

7.3. Opti mal nonlinear outlay schedules 1335

8. Interservice subsidy 13379. Conc lusion 1342References 1343

The author wo ul d like to express appreciation to the two editors of this Handbook, and to JohnPanzar and Tai-Yeong Chung for a number of helpful comments and suggestions.

Handbook of I ndustri al Organi zation Volu me I Edited by R. Schmalensee and R.D.Willig Elsevier Science Publishers B.V. 1989


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1 I n t r o d u c t i o n

R R Braeutigam

Over the pas t decade the re has been subs tan t i a l r e fo rm in many indus t r i e sh i s to r i ca lly opera t ing under he avy governmenta l con t ro l, bo th in the U ni tedSta tes and abroad . In the Uni ted S ta tes , where such governmenta l con t ro ltypical ly takes the form of regula t ion of pr ivate ly owned enterpr ises whenpol icy-makers bel ieve that compet i t ion wi l l not work wel l to a l locate resources ,remarkable changes have occurred in a l l or par ts of the a i r l ine , ra i l road, motorcarr ier, te lephone, cable te levis ion, natura l gas and oi l indust r ies , among others)Many other countr ies , inc luding those in which sucl i governmental in tervent iontakes the form of nat ional iza t ion, have recent ly been reconsider ing the ro le of

such gov ernm ental in tervent ion as well. 2In many cases the bas is for regula t ion has i t se l f been a t i ssue in the pol icydeb a tes su r round ing regu la to ry refo rm, o f t en lead ing to a r emova l o f o r aredu ct ion in the extent of governm ental control of tradi t ional ly regula ted in-dus t r ie s . In o the r cases r e fo rm has had some e ffec t even when the hand o fregu la t ion has no t been re t rac ted. Fo r f irms such as local e lec tr ic and gas u ti li ties ,loca l t e l ephone opera ting com panies , and o i l and gas p ipe lines ( to nam e jus t afew) , heav y regula t ion pers is ts. S til l, regu la tory reform in these indust r ies has ledto a reassessment of the k inds of controls that might be u t i l ized under regula t ion.

The p r im ary p urpose o f th is chap te r i s to examine some o f the op t ima l po l ic i es

tha t migh t be used to con t ro l a na tu ra l m onopo ly . A t the ou t se t we m us tde f ine jus t wh a t a na tu ra l m ono poly is f rom an econom ic pe r spec t ive , and wh y itposes a p rob le m tha t migh t war ran t governm ent in te rven t ion . Sec t ion 2 beg ins byexam ining these i ssues f rom a t radi t ional perspect ive , which argues for regula t ionwhen there are pervas ive economies of scale in a market . I t then offers a morecon tem pora ry charac te ri za tion o f na tu ra l m onop oly based on the concep t o fsubaddi t iv i ty of cos ts ra ther than on economies of scale .

Sec t ion 3 re -examines the na tu ra l m ono poly p rob lem wi th a though t fu l eye onthe quest ion: To regula te or not to regula te? Al though the t radi t ional v iewsugges ts tha t go vernmen t in te rven tion and na tu ra l m onop oly go hand in hand ,eco nom ic analys is s ince the la te 1960s has suggested ra ther forceful ly that theremay be ways to in t roduce compet i t ion fo r a marke t , even i f a na tu ra l monopolys t ructure exis ts wi th in a market . Thus , one of the themes of th is chapter i s tha t

1See Weiss and Klass (1986) for a discussion of the nature and effects of regulatory reform in anumber o f these indus t r i es .

2Exam ples inc lude the poss ib le p r iva t i z a t ion o f some ra i l roads in Japan , the deba te sur roun dingthe sa le o f pa r t o f the ownersh ip o f the t e lephone sys tem to the p r iva te sec to r in Grea t Br i t a in , andthe l ibe ra l i zed ru les fo r in te rconnec t ing p r iva te ly owned eq u ipm ent to the t e lephone ne two rk in W es t

G e r m a n y, a m o n g m a n y o t h e r s .


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Ch 23: O ptimal Policies or Natural Monopolies 29

regula t ion is only one of severa l poss ible ways of deal ing wi th a natura lm ono poly. Sec t ion 3 then p rov ides an overv iew of poss ib le com pet i tive ap-

p r o a c h e s t o t h e n a t u ra l m o n o p o l y p r ob l em .As Sec t ion 3 wi l l make dea r, the re wi l l be c i rcumstances when compet i t ion as

a po l i cy tow ard na tu ra l m ono poly is no t f eas ib le o r, even if f eas ib le , m ay l ead toa market outcome which is qui te ineff ic ient . Sect ion 4 summarizes a number ofwa ys in wh ich one migh t im prove the e ffi ci ency o f r e source a l loca t ion wi thgovernment in tervent ion, inc luding external subsidies to the f i rm, and the regu-la t ion of tar iffs wi th pr ice d iscr iminat ion (or d i fferent ia l pr ic ing ) o r theint roduct ion of nonl inear out lay schedules (nonl inear tar i ffs ) . The concepts arein t roduced in the context of the s ingle product f i rm. The sect ion then discussessom e of the p rob lem s encou n te red in the case o f the mul t ip roduc t firm, inc lud ingthe common cos t p rob lem, i . e . the p rob lem of p r i c ing ind iv idua l se rv ices whenthere a re cos t s o f p roduc t ion tha t a re sha red in the p roduc t ion o f more than oneou tpu t , a nd therefore can not c lear ly be a t t r ibuted to individual services.

Th e c hap te r then tu rns to some of the major concep t s in op t ima l ( econom ica llyeff ic ient ) pr ic ing in regula ted indust r ies . T hese include pe ak loa d pr ic ing (Sect ion5) , Ramsey pr ic ing (Sect ion 6) , and nonl inear out lay schedules (Sect ion 7) .Final ly, S ect ion 8 addresses a se t of i ssues re la ted to the fa i rnes s of regula tedpr ices , o f t en d i scussed in the con tex t o f c ross subs idy o r in te rse rv ice subs idy .A f te r p resen t ing and d i scussing the impl ica t ions o f some of the poss ib le no t ions

of subs idy, the sec t ion conc ludes by re la t ing the concep t s o f subs idy f ree andeco nom ical ly eff ic ient pr ices .A chapter of th is k ind necessar i ly re l ies on ( in fac t focuses on) the work of

m any o the r r e sea rchers . An y a t t emp t to c i t e the l it e ra tu re exhaus t ive ly wo uld befu ti le , and ano the r au thor a t t empt ing the sam e t ask would no dou b t inc lude a se to f r e fe rences somewhat d i ffe ren t f rom those used he re . My hope i s tha t g la r ingomiss ions have been min imized and tha t r eaders wi l l be unders tand ing on th i spo in t . At the same t ime the au thor would l ike to acknowledge two re fe rencesespecia l ly useful in the prepara t ion of th is manuscr ip t . These are Baumol , Panzaran d W il lig (1982) and B rown an d Sibley (1986) .

2. T he natural monopoly problem: A traditional view

The cen t ra l e conom ic a rgument fo r r egu la t ion o f an indus t ry i s tha t the indus t ryi s cha rac te r i zed by na tu ra l m onopoly . The concep t o f na tu ra l m ono poly hasbeen ref ined over the years , par t icular ly dur ing the las t decade. In th is sect ion wewil l f i rs t d iscuss a ra ther t radi t ional v iew of natura l monopoly and i t s importancewi th respec t to the ro le o f r egu la t ion as i t migh t have been p resen ted be fo re the1970s . We wi l l then summarize a more recent perspect ive on these same issues .


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1292 R R Braeutigam

In his classic treatise Kahn (1971, p. 2) describes the concept of natura lmonopoly to mean th at the technology of certain industries or the character of

the service is such that the customer can be served at least cost or greatest netbenefit only by a single firm (in the extreme case) or by a limited number of'chosen instruments' ,,.3 In Kahn 's extreme case average cost declines as outputincreases throughout the range of production in the market; thus a single largefirm serving the entire market would have a lower average cost than any smallerrival. In that case it will not be possible to have more than one firm operating inthe market if the lowest possible average cost is to be achieved.

This view is also presented by Scherer (1980, p. 482) who writes: The most

traditional economic case for regulation assumes the existence of naturalmonopoly-that is-where economies of scale are so persistent that a singlefirm can serve the market at a lower unit cost than two or more firms.Reasonably clear examples include electric power and gas distribution, localtelephone service, railroading between pairs of small to medium-sized metro-politan areas, and the long-distance transportation of petroleum and gas inpipelines. '4

The traditional story thus hinges on the existence of economies of scale(orincreasing returns to scale in an industry.

Strictly speaking, of course, the concept of economies of scale is one based onthe technology of the firmJ In a single product production process with constantprices for factors of production, the notion of economies of scale means that theaverage cost schedule for the firm declines as market output increases. This canbe illustrated as in Figure 23.1. The figure represents a market being served by asingle firm producing a single, nonstorable output (or service), whose level isdenoted by y. The (inverse) demand schedule for this product is shown as p(y),where p refers to the price of the output. The firm produces any given y at the

3Fo r good re fe rences on ma ny of the top ics addressed in th i s chap te r, see Schmalensee (1978) an dCrew and Kle in dor fe r (1986), which dea l wi th a l t e rna t ives in con t ro l l ing a na tu ra l mo nopoly. See a l so

Sta te R egula t io n o f Pub l ic Ut i l it i e s and M arg ina l Cos t Pr ic ing , by L .W. W eiss , Chap te r 9 in Weissand Klass (1981, p . 263) .

4Schere r (1980 , p . 482) a l so po in t s ou t tha t r egu la t ion may be implemented in indus t r i es fo r avar ie ty o f reasons o th er than the ex i s tence o f na tu ra l monopo ly. For example , r egu la t ion migh t occureven in an e ff ic ien tly opera t ing marke t i f those who h o ld po l i t i ca l power a re d i sp leased wi th themarke t ou tcome. I t migh t a l so be imposed i f we l l o rgan ized po l i t i ca l in te res t g roups a re ab le to

ma nip u la te po l i t i ca l l evers to rea l ize po l i t ica l o r economic ga ins tha t would no t be ach ieved in anunreg u la ted m arke t . Because these reasons fo r regu la t ion a re based o n po l i t i ca l econom y ra ther tha non na tu ra l m ono poly , they a re no t t r ea ted fu r the r in th i s a r ti c le . For m ore on these top ics, see, fo rexam ple, H ugh es (1977) , Posn er (1974), an d Pe l tzman (1976).

OSee J .C . Pan zar ' s co n t r ibu t ion in C hapte r 1 o f th i s Han dbo ok fo r an ex tens ive overv iew of theprod uc t io n and cos t concep ts we wi ll be u s ing th roug hout t i ff s chap te r.


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Ch. 23: Optimal Poficies or Natural Monopolies

PRICE p

A C ~ I - -

AC ~P

DEMAND

OUTPUT g

Figure 23.1. The classic natural mo nopo lyproblem.

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m i n i m u m p o s s i b le t o t a l c o st , C ( y ) , a n d t h e av e r ag e co s t o f p r o d u c t i o n is d e n o t e db y t h e s c h e d u l eAC y ) = C y ) / y. 6

F o r t h e m o m e n t , a s s u m e t h a t t h e f ir m re c e iv e s n o s u b s i d y f r o m e x t e r n a ls o u r c e s ( i n c l u d i n g t h e g o v e r n m e n t ) , a n d t h a t i t i s n o t - p o s s i b l e f o r t h e f i r m t op r i c e d i s c r i m i n a t e , s o t h a t a s i ng le , u n i f o r m p r i c e p re v a i ls i n t h e m a r k e t . T h ep r o d u c e r w i l l n e e d t o g e n e r a t e t o t a l r e v e n u e s t h a t a r e a t l e a s t a s l a rg e a s t o t a lc o s t s t o r e m a i n e c o n o m i c a l ly v i ab l e . T h u s , t h e p r i c e c h a rg e d b y a n y f i r m w i lln e e d t o b e a t l e a s t a s l a rg e a s t h e a v e r a g e c o s t o f p r o d u c t i o n f o r t h a t f i rm . A s i sc l e a r f r o m F i g u r e 2 3 .1 , n o f i r m c a n e n t e r a n d p r o d u c e y > YB, s i n ce t h e o u t p u tc a n n o t b e s t o r e d a n d p r o f it s w o u l d b e n e g a t i v e f o r s u c h a l ev e l O f p r o d u c t i o n .F u r t h e r m o r e , i f a n y fi rm w i t h t h e s am e t e c h n o l o g y e n t er s t h e m a r k e t a n dpr od uc es 37 < YB, an oth er f i rm co uld en ter an d pr od uc e )3, w here 37 < )3 < YB;t h is s e c o n d f i r m c o u l d c h a rg e a p r ic e p i n t h e r a n g eA C f ) < p < AC(37) , an dd r i v e t h e f ir s t f ir m f r o m t h e m a r k e t w h i l e r e m a i n i n g e c o n o m i c a l ly v ia b l e i ts e lf .T h e o n l y p r o d u c t i o n l e v el t h a t w o u l d p r e c l u d e p r o f it a b le e n t r y b y a n o t h e r f ir mcha rg ing a l owe r p r i ce is y = YB, w i th p = PB- In t he t r ad i t i ona l v i ew the mark e ti s s a i d t o b e c h a r a c t e r i z e d b y a n a t u r a l m o n o p o l y, s i n c e c o m p e t i t i o nwithin t hem a r k e t i s n o t p o s s i b l e .

T h e n a t u r a l m o n o p o l y p r o b l e m t a ke s o n a d d e d c o m p l e x i ty w h e n e n t r y a n d e x ita r e n o t c o s t l e s s a n d a t e m p o r a l d i m e n s i o n i s a d d e d t o t h e p r o b l e m . F i r m s m i g h th a v e i n c e n t i v e s t o e n t e r t h e m a r k e t , c h a rg e a p r i c e i n e x c e s s o f a v e r a g e c o s t t oe a r n s u p e r n o r m a l p r o f it s, a n d t h r e a t e n t o r e d u c e p ri c e t o a v e r y l o w l ev e l ( e v e n

6M ore com pletely, the c os t function is also a function of a vector of fac tor prices, w,C y, w).

Ho wever, factor prices will be assumed constant throughou t this chapter, so references o them w ill besuppressed to simplify notation as mu ch as possible.


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Ch. 23: Optimal P olicies or Natural Monopolies

PRICE pDEMAND

y l g a g O U T P U T

Figure 23 2 Subaddi t iv i ty wi tho u t g loba l economies o f scale

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(y{, iY 2 , ' , Yn ) p r o d u c e d b y t h e i t h f ir m . T h e n , u s i n g th e d e f i n i t i o n o f B a u m o l ,Pa nza r and W i l lig (1982 , p . 17) a cos t func t ion C ( y ) i sstrictly suba dditiveat yi f f o r a n y a n d a l l q u a n t i ti e s o f o u t p u t syX . . . y k y j ~ y, j = 1 . . . . k , s u c ht h a t

k k

E Y J = Y w e h av e C ( y ) < ~ ' . C ( y J ) . (1 )j = l j = l

As (1 ) ind ica te s , t he vec to r y r ep resen t s the indus t ry ou tpu t . The bas i c ques t ionh e r e i s w h e t h e r y c a n b e p r o d u c e d m o r e c h e a p l y b y o n e f i r m p r o d u c i n g y a lla l o n e t h a n i t w o u l d b e f o r a c o l l e c t i o n o f t w o o r m o r e f i r m s w h o s e i n d i v i d u a lo u t p u t v e c t o r s s u m t o t h e s a m e i n d u s t r y o u t p u t y.

S i n c e co s t s m a y b e s u b a d d i t i v e a t s o m e v a l u es o f y b u t n o t a t o t h e rs , t h e n e x ts t e p t o w a r d d e f i n in g a n a t u r a l m o n o p o l y i s t o e x a m i n e w h e t h e r c o s ts a r es u b a d d i t i v e at a l l o f t h e r e l e v a n t i n d u s t r y o u t p u t v e c to r s y t h a t m i g h t b e

p r o d u c e d ; t h e d e m a n d f o r e a c h o f t h e o u t p u t s w i l l h e l p t o d e f i n e t h i s r e l e v a n tr a n g e o f o u t p u t s . B a u m o l , P a n z a r a n d W i ll ig g o o n t o d e fi n e a n a t u r a l m o n o p o l y( s t il l on p . 17 ) a s fo l lows : A n indu s t ry is s a id to be a na tu ra l m on op o ly i f , ove rthe en t i r e r e l evan t r ange o f ou tpu t s , t he f i rms ' cos t func t ion i s subad d i t ive .

The example o f F igure 23 .2 i l l u s t r a t e s tha t a subadd i t ive cos t s t ruc tu re needn o t e x h i b i t e c o n o m i e s o f s ca le o v e r t h e e n t ir e re l e v an t ra n g e o f o u t p u t s . T h ee x a m p l e i s c o n s t r u c t e d s o t h a t t h e o u t p u t l ev e l a s s oc i a te d w i t h m i n i m u m c o st , y l ,i s s l igh t ly l e ss th an YB, the o u tp u t l eve l a t w h ich the de m an d schedu le in t e r sec tsthe ave rage cos t s chedu le. Th e ave rage cos t s chedu le has the typ ica l U shape ,and i t i s subadd i t ive fo r 0 < y


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In the s ingle product case i t i s c lear that economies of scale imply subaddi t iv-i ty. However, i t turns out that economies of scale need not imply subaddi t iv i ty in

the m ul t ipro du ct case; th is should not be a great surpr ise s ince, g iven the crucia lro le o f va r ious fo rms o f cos t com plementa r i ty and economies o f jo in t p rodu c t ion ,i t i s to be expected that economies of scale cannot te l l the whole s tory in them ul t ip rodu ce case . 7

A com par i son o f F igure 23 .1 wi th F igure 23.2 l eads to ano the r concep t(sustainabil i ty) which is useful in appreciat ing diff icult ies that might be associ-a ted w i th the na tu ra l m onop oly p rob lem. Le t us a ssume en t ry and ex it a recost less , tha t ent rants wi ll provide exact ly the sam e service as the incum bent , andthat a l l f i rms ( the incum ben t and a ll potent ia l ent rants) ope ra te wi th access to thesame technology, and therefore wi th the same cost funct ions . In the f i rs t graph,which dep ic t s the t r ad it iona l v iew of na tu ra l m onopoly, i t would be poss ib le fo rthe f i rm to f ind a pr ice which deters ent ry by any other f i rm seeking to take awaythe incum bent ' s ma rke t by charg ing a lower p ri ce than the incumbent . Inpar t icular, i f the extant f irm charges a pr ice P B, then any e ntrant charging alower p r i ce wi l l no t be ab le to b reak even . In o the r words , i f the incumbentcharge s PB, i t can sus ta in it s m on op oly posi t ion agains t entry.

However, Panzar and Wil l ig (1977) have pointed out that i t wi l l not a lways bethe case that a natura l monopoly can sus ta in i t se l f agains t ent ry. They show that ,con t ra ry to conven t iona l wisdom, a r egu la ted monopol i s t may be vu lne rab le to

entry, even i f the incumbent produces eff ic ient ly, earns only a normal re turn oninves tment , and i s conf ron ted by an en t ran t opera t ing wi th the same t echno logyas i t s own.

Figure 23.2 presents such a case . Suppose that in serving the whole market theincum bent charges PB. Then i t would be poss ib le fo r an en t ran t to charge a lowe rpric e (say, p = pl) , prov ide yl units of service, and avo id a deficit . This is a casein which the marke t i s uns tab le , and in which the na tu ra l m ono poly i s unsu s -t a inab le . I f the w hole marke t i s to be se rved , i t would the re fo re requ i re two o rm ore f i rms (s ince the ent rant wi ll prod uce only yl in the example) . Fur thermo re ,s ince the cos t s t ructure i s subaddi t ive in Figure 23.2 , ent ry would be socia l ly

inefficient; yet , such entry is a real possibil i ty, even though entrants mightp rov id e no new se rv ices and opera te wi th no be t t e r p roduc t ive t echn ique .

Panzar and Wi l l ig have de f ined the concep t o f sus ta inab ih ty in a f r ameworkal lowing for mul t ip le products . Br ief ly, suppose that the monopol is t produces nd i ffe ren t p roduc t s in a p roduc t se t N , an d a l low S to be any sub se t o f tha t

7See Ban mo l , Pa nza r and W i l l ig (1982, pp . 173). Fo r exam ple , equa t ion 7C1 on p . 172 r ep rese n t s ac o s t f u n c t i o n t h a t h a s g l o b a l l y i n c r e a s i n g r e t u r n s t o s c a l e , b u t i s n o t s u b a d d i t i v e e v e r y w h e r e . T h e c o s tf u n c t i o n f o r t h a t e x a m p l e i sC y l , Y 2 ) = Y { + Y~ Y 2+ Y~, wi th 0 < a < 1 and 0 < k < 1 /2 . Se c t ions7 C - 7 E o f t h a t b o o k o u t li n e s o m e p r o p e r t e s ts o f n a t u r a l m o n o p o l y a n d s u ff ic i en t c o n d i t i o n s fo rs u b a d d i t i v i t y. S e e a l s o J. C . P a n z a r s c o n t r i b u t i o n i n C h a p t e r 1 o f t h is H a n d b o o k f o r a m o r e e x t e n s i v e

d i s c u s s i o n o f s e v e r a l i m p o r t a n t c o n c e p t s r e g a r d i n g m a r k e t s t r u c t u r e , i n c l u d i n g a m o n g o t h e r s e c o n o -m i e s o f s c a l e a n d s c o p e , t h e d e g re e s o f e c o n o m i e s o f sc a l e a n d s c o p e a n d p r o d u c t s p e c i f ic e c o n o m i e so f sca l e .


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Ch. 23: Optimal Policies o r Natura l Monopolies 1297

p ro d u c t se t (S __c_N ) . L e t p m b e a p r ic e v e c t o r c h a r g e d b y t h e m o n o p o l i s t o v e ri ts p r o d u c t s e t N , l et p ~ b e t h e p r ic e v e c t o r c h a rg e d b y a n e n t r a n t p r o v i d i n g th e

p r o d u c t s e t S , a n d l e t t h e p r i c e v e c t o r c h a rg e d b y t h e m o n o p o l i s t o v e r S a n d o v e rt h e s e r v ic e s n o t p r o v i d e d b y t h e e n t r a n t [ S ] r es p e c t iv e l y b e p ~ a n d P ~ I F i n a l ly,d e n o t e b y Q ( p m ) t h e v e c t o r o f q ua n t it ie s t h a t w o u l d b e d e m a n d e d i f o n l y t h em o n o p o l i s t s e r v e d t h e m a r k e t , a n d l e t s ep s , P ~ I ) b e t h e q u a n t i t i e s o f t h ep r o d u c t s e t S d e m a n d e d w h e n t h e e n t r a n t a p p ea r s. T h e n t h e p ri c e v e c t o r p m iss u s t a i n a b l e i f a n d o n l y i f ( i) t h e m o n o p o l i s t e a r n s n o n - n e g a t i v e p ro f i ts a t p r o, a n d( i i) p ~ . y~ - C (y ~ ) < 0 (e n t ra n ts ea rn n ega t ive prof i t s ) fo r a l l S ___N , w i t h

m s mP~ < PS , Y~ < Q Ps ,Pt s l ) an d y~ q : Q (p m ) (w h ich exc ludes t he t r iv i a l pos s i -b i l i ty t h a t t h e e n t r a n t w i ll e x a c tl y d u p l i c a t e t h e e n t i r e o p e r a t i o n o f t h e in c u m -b e n t ) . T h e n a n a t u r a l m o n o p o l y is s ai d t o b e s u s t a in a b l e i f a n d o n l y i f t h e r e is a tl e a s t o n e s u s t a i n a b l e p r i c e v e c t o r.

P a n z a r a n d Wi l li g ( 1 97 7 ) h a v e s e t f o r th a n u m b e r o f n e c e s s a ry c o n d i t i o n su n d e r w h i c h a r e g u la t e d m o n o p o l y w o u l d b e s u s t ai n a b le i n a w o r ld w i t hf r ic t i o n l e s s e n t r y a n d e x i t. A m o n g t h e s e a r e th a t t h e n a t u r a l m o n o p o l y m u s tp r o d u c e y m , t h e o u t p u t v e c t o r a s s o c i a t e d w i t h p r o , a t l e a s t c o s t , e a r n o n l y an o r m a l r e t u r n o n i t s i n v e s t m e n t , a n d o p e r a t e w i t h a p r o d u c t i o n s t r u c t u r e t h a t i ss u b a d d i t iv e . O n e f u r t h e r n e c e s s a r y c o n d i t i o n r e q u i r e s t h e f o l l o w i n g d e fi n it io n :

De fini tion undom inated pr ice vector)

L e t p = ( P l , P 2 . . . . . P n ) a n d / ~ = ( /3 1 ,/3 2 . . . . . /3 n) b e v e c t o r s y i e ld i n g z er o p r o f -i ts f o r a m o n o p o l y . T h e v e c t o r p i sundomina tedi f t he re ex i s t s n o / ~ :~ p w i th/3i < P i , V i , a n d /3i < pi fo r at least on e i .

I n t h e s i n g l e p r o d u c t e x a m p l e o f F i g u r e 2 3 . 1 t h e r e w i l l b e o n l y o n e u n -d o m i n a t e d v e c t o r ( h e r e a s c a la r ), P B- H o w e v e r, i n t h e m u l t i p r o d u c t c a s e t h e r em a y b e a n i n f in i t e n u m b e r o f s u c h v e ct o r s. T h e t w o p r o d u c t c a s e is il l u s tr a t e d i nF i g u r e 2 3 .3 . H e r e t h e v e c t o r s p t a n d p 2 a r e u n d o m i n a t e d , w h i l e p 3 is d o m i n a t e d( b y p l , f o r e x a m p l e ).

T h e p r i c e v e c t o r p m m u s t a l so b e u n d o m i n a t e d i f i t i s s u s t ai n a b le . T h e r e a r eo t h e r n e c e s s a r y c o n d i t i o n s f o r s u s t a in a b i li ty r e g a r d i n g e c o n o m i c e ff ic i en c y a n dc r o s s s u b s i d y, c o n c e p t s t h a t w i ll b e i n t r o d u c e d i n s u b s e q u e n t s e c ti o n s. W et h e r e f o r e p o s t p o n e c o m m e n t s o n t h e s e u n ti l a m o r e a p p r o p r i a t e t im e . 8

SAmong othe r conclusionsof Panza r and W illig are som e that we w ill address no further other thanto m ention the m here. First, there is no way to transform an unsustainable monopo ly into asustainable oligop oly by som e regulatory act splitting the marke t amon g a num ber of oligopolists.Second , strong dem and substitutability amo ng the products offered by the m onopo list and productspecific econo miesof scale mak e it m ore difficult or a mo nopo ly o b e sustainable. As a related point,although it is relativelyeasy to identify a num ber of necessary conditions for sustainability, it is alsorelatively difficult o find rather general sufficientconditions. Vertical integration also introduces a setof interesting problems for sustainability of a natural mo nopo ly; for an analysis of this see Panzar(1980). For another good general referenceon sustainability, see Sharkey (1981).


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z. . Z E R O

1 5 0 P R O F I T

C U RV E

l

Figure 23 .3 . Un dom ina ted p r ice vec to r.

R R Braeutigam

Recent research in the characterization of natural monopoly has yielded anumber of interesting results on the empirical front as well as theoretically. Muchempirical work utilizing modern production and econometric theory has beendirected at traditionally regulated industries in the last decade; no small part ofthis work casts doubt on whether some of the industries historically regulated inthe United States do in fact have the structural characteristics of a naturalmonopoly. 9

Finally, recent economic research has increasingly emphasized that a structureof natu ral monopoly is not sufficient as a basis for regulation. As the nextsection shows, even if an industry is characterized by natural monopoly in thesense that there is not room for competition within a market, under somecircumstances competition o r the market may succeed in allocating resourcesquite efficiently in the absence of regulation. The theoretical and empiricalresearch on natural monopoly has contributed many economic arguments insupport of deregulation and other measures of regulatory reform in a number ofAmerican industries since 1970.1

9See , fo r example Spady and Fr ied laender 1978) and Fr ied laen der and Spady 1982), wh o re jec tthe conc lus ions o f ea r f i e r s tud ies tha t show the motor ca r r i e r indus t ry to have economies o f sca le ;they show tha t , when empi r ica l s tud ies o f the cos t s o f motor ca r r i e r s con t ro l fo r the e ffec t s o fregu la t ion , the s t ruc tu re o f the indus t ry i s one w i th essen tia l ly cons tan t re tu rns to scale. See a l soCaves , Chr i s ten sen and T re theway 1983) regard ing the s t ruc tu re o f the a i r fines indus t ry. For a nexamp le o f an empi r ica l t es t o f subaddi t iv i ty as opposed to econom ies o f sca le) , see Evans an dHeckman 1984) .

1For a summary of the deve lopments in severa l r ecen t ly deregu la ted indus t r i es , see Weiss andKlass 1986) .


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3 . W hy regu la te?

1299

Regu la t ion i s a po l i t i ca l ac t . I n any pa r t i cu l a r ca se the re may be a hos t o fposs ib l e po l i t i ca l and economic answers t o t he ques t ion : Why regu la t e? Answersa re o ff e red by bo t h p os i t ive and no rm a t ive r esea rch . In th i s chap te r we wi l l focuson the l a t t e r. Th i s i s no t t o d imin i sh the impor t ance o f t he pos i t i ve ana lyses o fregula t ion ; tha t i s t rea ted e lsewhere in th is H an db ook . 11 O n the cont rary, f ro m apo l i t i ca l v i ew, pe rhaps the m os t s ign i fi can t f e a tu re o f r egu la t ion i s t ha t i tred is t r ibutes income, c rea t ing winners and losers , thereby shaping in teres t groupsand coal i t ions . Thus , i t i s not surpr i s ing tha t there i s a la rge pos i t ive l i te ra ture onregu la t ion , bo th in economics and po l i t i ca l s c i ence , add res s ing r easons fo rr egu la t ion f a r b roade r t han na tu ra l monopo ly. These wr i t i ngs dea l bo th wi th thec rea t ion o f r egu la to ry agenc ie s by Congres s and wi th the behav io r o f r egu la to rybo die s on ce they are in p lace . 12

In focus ing in s t ead on no rma t ive i~sues f rom an economic pe r spec t ive , we a ska na r rower qu es t ion in th is s ect ion : W hen sho u ld a na tu ra l m on op o ly beregula ted a t a l l? In assess ing the effec ts of regula t ion , and la te r in compar ingva r ious op t ions fo r pub l i c u t i l i t y p r i c ing , we need to employ a c l ea r measu re o feconomic bene f i t s t o consumers and p roduce r s . Whi l e such measu res do ex i s t ,they are of ten d i ff icu l t to apply g iven the k inds of market da ta tha t a re usual lyava i l ab le . Th e work o f Wi l li g 1976) has sugges ted tha t the we l l -know n m easu re

o f co nsu m er a nd p roduce r su rp lus i s an adequa te approx im a t ion in m os t c ir -cum stan ces , and tha t is the no t ion tha t i s adopte d in th is chapter, x3

11S ee t h e c h a p t e r s o f t h i s H a n d b o o k b y N o l l ( C h a p t e r 2 2) a n d b y J o s k o w a n d R o s e ( C h a p t e r 2 5 )for a d i scuss ion o f m any h ypotheses abou t the reasons fo r and e ffec ts o f regu la tion .

12See also Joskow and Noll (1981) , and Noll and Owen (1983) for excel lent discussions of thepo l i t i ca l economy of regu la t ion . S t ig le r (1971) desc r ibes how regu la to ry bod ies may red i s t r ibu teinc om e wi th act iv i t ies that have effects as po werful as ta xat io n i tself . Pos ner (1974) an d St igler (1975)descr ibe how organ ized in te res t g roups may cap tu re a regu la to ry agency, e i the r by the in i t i a l des ignof the regu la to ry p rocess o r by o ther means as t ime passes . Pe l t zman (1976) cas t s the theory o fregu la t ion in to a supp ly and d em and f ramework , the supp ly o f regu la t ion be ing p rov ided by

pol i t i c ians an d agenc ies des i ring to maximize vo te marg ins , and the dem and f rom in te res t g roups wh owould benef i t under va r ious regu la to ry ou tcomes . F io r ina and Nol l (1978) beg in wi th the vo te r s 'dem and fo r Cong ress iona l fac i li t a t ion services to exp la in the congress iona l dem and fo r admin is t ra t iveac t iv i ty. G oldb erg (1976) sugges ts tha t r egu la t ion may b e v iewed as a con t rac t be twee n a regu la to ryagency (ac t ing as the agen t o f consumer g roups) and regu la ted f i rms . Owen and Braeu t igam (1978)descr ibe s t ra teg ies by which the regu la to ry p rocess may be used to a t t enua te the ra te a t which changesin market and technological forces affect individual economic agents , effect ively giving agents legalr igh t s to the s ta tu s quo . See a l so Hughes (1977) fo r an in te res t ing h i s to r ica l pe rspec t ive on theimp etus fo r and t rans i t ion o f regu la t ion f rom co lon ia l t imes in the Uni ted S ta tes (and even ea r l i er inE n g l a n d ) u n t i l t h e p r e s e n t .

13As a t echn ica l po in t , the use o f the usua l Marsha l l i an demand schedule observed f rom marke tda ta to measure consumer surp lus wi l l be an exac t measure o f the wdfare change assoc ia ted wi th apr ice ch ange fo r a n ind iv idua l i f the re a re ze ro income e ffec ts . H owever, Wi l lig (1976) h as show n th a t

even i f the re a re nonzero income e ffec t s , the measure o f consumer surp lus ob ta ined f rom aM arsh a l l i an d em an d schedule may se rve to approx imate the ac tua l we l fa re change qu i te closely.


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1300

PRICE p

PB

AC II)

. o T Io K J l

i B u E O U m U T. U

Figure 23.4. IYlrst and second best .

R.R. Braeutigam

C o n s i d e r n o w t h e c a s e o f t h e s i n g l e p r o d u c t f i r m o p e r a t i n g w i t h e c o n o m i e s o fs c a le t h r o u g h o u t t h e o p e r a t i n g r a n g e o f p r o d u c t i o n a s in F i g u r e 2 3 .4 . F o ri l l u s t r a t i ve pu rpo ses , a s sum e the co s t s t ruc tu re i s a ff ine , w i th a p os i t i ve f ixed cos tF a n d c o n s t a n t m a r g i n a l c o st m , so t h a t C ( y )= F m y. I n t h i s e x a m p l e t h eave rage cos t s ched u le dec l ines eve ryw here s ince m arg ina l cos t is le s s t han av e rage

cos t .A ssum e tha t t he f i rm mus t c ha rge a un i fo rm t a r i f f ( i. e. the s am e p r i ce ) to a l l

c u s t o m e r s , a n d t h a t w e s e ek t h a t p r ic e t h a t m a x i m i z e s n e t e c o n o m i c b e n e f it( a l t e rn a t i v e l y, t o m a x i m i z e e c o n o m i c e ff ic ie n c y) a s m e a s u r e d b y t h e s t a n d a r dc o n c e p t o f c o n s u m e r p l u s p r o d u c e r s u rp l u s. 14 S t a n d a r d e c o n o m i c p r i n c ip l e si n d i c a t e t h a t n e t e c o n o m i c b e n e fi t w i ll b e m a x i m i z e d w h e n t h e le v e l o f o u t p u tY - YE , w i th s e rv i ce p rov ided to a l l cus tom ers ( ando n l y t o t h o s e c u s t o m e r s ) w h oa re w i ll i ng to pay a t le a s t as mu ch a s t he ma rg ina l cos t o f p rodu c ing yE 15 In t ha tc a s e t h e t o t a l s u r p l u s i s r e p r e s e n t e d b y t h e a r e aA E H less th e f ixed c ost F. 16S i n c e t h is i s th e m a x i m u m s u r p lu s t h a t c a n b e g e n e r a t e d i n t h e m a r k e t , a p r i c in gpo l i cy t ha t l e ads t o t h is a l l oca t ion o f r e sou rces is t e rme d f i r s t be s t . 17

14There are a nu m be r of c lass ic references deal ing with the conn ect io n between e cono mic eff ic iencyan d regulat ion . See, am on g others , Hote l l ing 1938) , Pigou 1920), Taussig 1913) , and Turv ey 1969).More recen t work which summar izes modern deve lopments in the economic theory o f regu la t ioninclu de Brow n and Sibley 1986), Rees 1984), Sharkey 1982b) , and Za jac 1978) , a l l of whic h areexcel len t references in the f ield .

15See Tu rvey 1968, 1969) on the econo mics of margin al cost pr ic ing.X6The f ixed cos t ca n be represen ted in m any w ays in F igure 23 .4 ; one such measure i s the a rea

IBGH so tha t wi th marg ina l cos t p r ic ing the to ta l su rp lus i s r epresen ted by the a reaAEH less thea r e a 1BGH.

17In the exam ple here we have assumed tha t the f i rm mus t charge the same pr ice fo r each un i t so ld

in the m arke t . I t m ay be poss ib le to ach ieve fi r st bes t wi thou t incur r ing a de f ic i t i f the f i rm can charged i ffe ren t p r ices to d i ffe ren t use rs p r ice d i sc r imina t ion) o r i f d i ffe ren t un i t s o f ou tpu t can b e so ld a tdifferen t pr ices no nl in ear tari ffs) . Bo th of these al ternat ives will be addressed below.


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H o w e v e r, i n t h e e x a m p l e t h e f i r m w il l n o t b r e a k e v e n w i t h m a rg i n a l c o s tp r i c ing . In f ac t , g iven the a ff ine cos t func t io nC = F + my, t he p ro f i t s o f t he f i rm

are ~r = - F < 0 . Thus , i n o rde r fo r the f i rm to r ema in econo m ica l ly v i ab le , i twi l l h av e to rece ive a su bs idy o f F . 18

S ince r egu la to r s (pa r t i cu la r ly in the Un i t ed S ta te s ) a re no t t yp ica l ly end ow edw i t h t h e p o w e r s o f t a x a t io n , t h e y m a y f i n d th e m s e l ve s f a c e d w i t h a n e e d t o f i n d ap r i c ing po l i cy tha t avo ids a de f i c i t fo r t he f i rm. Wi thou t p r i ce d i sc r imina t ion o rex te rn a l subs id ie s to the f i rm, the r egu la to r mig h t a t t em pt to d i r ec t t he f i rm to se tt h a t p r i c e w h i c h m a x i m i z e s n e t e c o n o m i c b e n e f i t w h i l e a l l o w i n g t h e f i r m t orem ain v iab le . S ince p ro f it s a re nega t ive a t t he f i r st bes t p r i ce , t he re wi l l be a ne tben e f i t l o ss a s soc ia t ed wi th the need to sa t i s fy a b reakeven c ons t r a in t fo r the f i rm(i .e . ~r > 0) . An y pr ice h ighe r tha n PB wi l l redu ce to ta l surplus be low the levela t t a i n a b l e w h e n p = P B ( t h e a r e aABI . T h u s , t h e b r e a k e v e n - c o n s t r a in e d o p t i -m u m (wh ich is te rm ed sec on d bes t ) -occur s a t t he p r i ce p = pB .19 Th e we l fa reloss a s soc ia t ed wi th second bes t ( a s opposed to f i r s t bes t ) i s t he re fo re the a reaBGE in Fig ure 23 .4 . Su ch an e ff i ci ency loss is o f t en ca l led a dea dw eigh t lo s s .

T h e p o i n t o f t h i s d i s c u s s i o n i s t o s u g g e s t t h a t i n m a n y c i r c u m s t a n c e s i t m a yno t be poss ib l e to ach ieve f ir s t bes t w i th ou t gov e rnm en t in t e rven t ion ( e .g . w i th a ne x t e r n a l s u b s i d y t o t h e fi rm ) , a n d a p r o g r a m f o r g o v e r n m e n t in t e r v e n t i o n m a y b equ i t e cos t ly. Ye t , a s we sha l l show now, i t may o f t en be poss ib l e to ach ieve ane c o n o m i c p e r f o r m a n c e n ea t s e c o n d b e s t w i t h o u t g o v e r n m e n t in t e r v e n t i o n ( e v en if

c o s t s a r e s u b a d d i t i v e o v e r t h e r e l e v a n t r a n g e o f o u t p u t s s o t h a t i t m i g h t n o t b ep o s s i b l e t o h a v e m a n y f ir m s c o m p e t i n g s i m u l t a n e o u s l y w i t h i n a g i v e n m a r k e t ) .Thus, policy-makers may wish to ask whether the deadweight loss at second best islarge enough to warrant intervention, especially if some form of competition can beintroduced into the market that would lead to second best.

H o w m i g h t t h e r e b e a n a l t e rn a t iv e fo r m o f c o m p e t i t i o n f o r s u c h a m a r k e t ? O n eansw er w as sugg es ted in a c l a ss i c a r t i cl e by Dem se tz (1968). Th e focus o fD e m s e t z ' s a r t i c l e i s o n c o m p e t i t i o nfor t h e m a r k e t r a t h e r t h a nwithin t h e m a r k e t .D e m s e t z p o i n t e d o u t t h a t m u c h o f t r a d i t io n a l e c o n o m i c s i s d i r e ct e d a t t h e n o t i o no f c o m p e t i t i o n w i t h i n t h e m a r k e t p la c e , w h i c h m a y n o t b e p o s s i b le i f th e r e a r e

subs tan t i a l economies o f sca l e . He sugges t s tha t even i f compe t i t i on wi th in them ark e t i s no t poss ib l e , one migh t s t il l have com pe t i t i on fo r the r igh t to ope ra t e int h e m a r k e t . I n o t h e r w o r d s o n e c o u l d e n v is i o n b i d d i n g a m o n g p r o s p e c t iv e

1 8 If t h e s u b s i d y i s p r o v i d e d b y t h e g o v e r n m e n t , t h e n o n e m u s t t a k e i n t o a c c o u n t n o t o n l y t h ew e l f a r e e f f e c t s in t h e m a r k e t f o r y, b u t a l s o t h e p o s s i b l e w e l f a r e lo s s e s i n o t h e r m a r k e t s t h a t w i l l b et a x e d i n o r d e r t o p r o v i d e r e v e n u e s f o r t h e e x t e r n a l s u b s i d y p r o v i d e d t o k e e p t h e f i r m v ia b l e. I f t h et a x e s a r e l e v i e d i n m a r k e t s w i t h t o t a ll y i n e la s t i c d e m a n d s , t h e n t h e w e l f a r e l o s s f r o m t h e t a x w i l l b ez e r o a n d p = m i n t h e m a r k e t f o r y w i l l b e f i r st b e s t . H o w e v e r, i f w e l f a r e l o s s e s o c c u r a s a r e s u l t o ft h e t a x a t i o n , t h e n p = m m a y n o t b e o p t i m a l .

X 9F or m o r e o n t h e t h e o r y o f s e c o n d b e s t a n d o p t i m a l t a x a t i o n s e e A t k i n s o n a n d S t i gl i tz 1 9 80 ) ,

D i a m o n d a n d M i r l e e s 1 97 1) , M i r le e s 1 97 6) , L i p s e y a n d L a n c a s t e r 1 9 5 6 - 5 7 ) , a n d B o h m 1 96 7).S o m e o f t h e s e a r t i c l e s d e a l r a t h e r e x p li c i tl y w i t h t h e d i s t r i b u t i o n a l i s s u e s t h a t a r e c e n t r a l t o t h ep o l i t i c a l d e b a t e i n t a x a t i o n .


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entra nts for the f ranchise r ights to serve the market ; th is form of rival ry i s of tenca l l ed D em se tz com pet i tion , which m ay be poss ib le i f two cond i tions a re

sat is f ied . Fi rs t , inputs must be avai lable to a l l b idders in open markets a tcompet i t ive ly de te rmined p r i ces . Second , the cos t o f co l lus ion among b idd ingr ivals must be prohibi t ively h igh, so that compet i t ive b idding is in fac t theou tcome of the b idd ing p rocess .

Demse tz compet i t ion cou ld occur in a va r i e ty o f c i r cumstances . A re la t ive lys imple environment would be the local col lec t ion of refuse . In th is examplecompanies could bid for the r ight to col lec t refuse for a speci f ied per iod of t ime,wh ere the b i d wo uld be the p r i ce tha t the p rospec t ive f ranch isee wo uld chargecus tom ers fo r the co l l ec tion se rv ice, and the com pan y wi th the lowes t b id w ouldwin the compet i t ion . In th i s example , the munic ipa l au thor i ty need no t own thefaci l i t ies used by the refuse col lec t ion company.

A more compl ica ted scenar io migh t invo lve the r igh t to opera te a cab letelevision franchise for a specified t ime period [see Will iamson (1976)]. Here thegov ern m ent m ight ow n the fac il ity, bu t auct ion off the r ight to opera te thesys tem. The government migh t cha rge a f ee to the opera t ing company to re f l ec tthe socia l cos t of the use of the government-owned faci l i t ies .

In the s ing le p roduc t env i ronment wi th a un i fo rm pr ice , Demse tz compet i t ionwould lead to average cos t pr ic ing, s ince a l l excess prof i t s would be bid away.Suppose a l l p roducers have access to the same t echno logy and cou ld p roduce

eff ic ient ly, and that p* is the lowest pr ice that would a l low the f i rm to breakeven . One would expec t to see b ids o f p > p* , s ince a lower b id would l eave abidder wi th negat ive prof i t s . I f the number of b idders i s large enough so that thebidding process i s in fac t compet i t ive , one would expect to see a winning bid ofp* , s ince a t tha t p r i ce a p roducer w ould ea rn on ly normal p ro f it s. As no ted in theprevious sect ion, th is i s a second bes t ( ra ther than a f i rs t bes t ) outcome.

Demse tz compet i t ion i s appea l ing because i t sugges t s compet i t ion may beposs ible even where there are substant ia l economies of scale , and i t i s f ree of theusual regula tory apparatus and regula t ion-re la ted incent ives for f i rms to behavein an econ om ical ly ineff ic ient man ner. 2 How ever, the a ppro ach is not ent i re ly

free of c oncern . To begin wi th , While i t does lead to secon d bes t , there m ay s til lbe subs tant ia l welfare losses re la tive to f irs t bes t .

The ou tc om e of Dem se tz compet i t ion i s in e ffec t a con t rac t be tween afranchisor (e .g . a governmental author i ty) and a f ranchisee . Since the f ranchiseemight wel l adopt the shor t run s t ra tegy of providing the lowest qual i ty serviceposs ible once i t has won the r ight to serve , the f ranchisor may have to speci fym inim um qua l i ty s tanda rds for the service to be provided. The que st ion arises :

2See, for example, Chapter 24 by David Baron in this Handbook which deals with the design ofregulato ry inst i tut ions and incentives under various regulatory mechanisms, and C hapter 25 by Paul

Josko w and N an cy Rose) which assesses the evidence on the effects of regulat ion. See also Owen andBraeutigam 1978) and Joskow and No ll 1981).


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Ch. 23: Optimal Policies or Natural Monopolies 1303

HOW does the government set the quality standards? How such standards are setis a problem common to Demsetz competition as well as to traditional regu-

lation; neither approach resolves the problem of specification of quality.h e terms of the contract may be difficult to specify for other reasons. Since

the contract may be in force over a period of years, it may be necessary toinclude procedures to allow for adjustments in terms of service, such as price andqual ity of service, as conditions in the market change. Some of these contingen-cies may be relatively easy to incorporate in a wri tten contract, while others maybe both unknown and unknowable at the time the franchise is established, Thedifficulty in writing a contract that includes all sets of possible contingencies iswell known. In the context of Demsetz competition this means that a firm thatwins the bidding today may attempt to renegotiate its contract tomorrow. Thefranchisor may then find itself deciding whether to attempt to force compliance,renegotiate, or initia te a new bidding process to find another franchisee. None ofthese alternatives will be costless.

Another potentia l difficulty with the use of Demsetz competition arises whenthe enterprise provides more than one service to its customers. As mentionedearlier, in the single product case the winner might be chosen on the basis of thetariff that franchisee would charge to customers, and that tariff would be secondbest. However, this selection criterion does not naturally generalize to the case ofmultiple products. Demsetz competition may lead to a number of different bids

which are undominated; recall, for example, that p l and p2 in Figure 23.3 bothyield no excess profits and are undominated. Demsetz competition offers noobvious basis for choice among a number of undominated prices, even thoughsome of these may be quite inefficient relative to others.

A second way in which it may be possible to introduce competition for themarke tplace has been formalized with the concept of contestabi lity [see Baumol,Panzar and Willig (1982), and also Panzar's Chapter 1 in this Handbook].Although contestability and Demsetz competition are similar to one another,they are not identical. They key idea in contestability is that competition for themarket can lead to second best, even if the cost structure is subadditive overthe relevant range of market outputs, a s l o n g a s t h e r e a r e n o s u n k c o s ts .Theassumption that there are no sunk costs is one not required by Demsetzcompetition, but if the additional assumption is satisfied, second best may beachieved through competition for the market w i t h o u t the need for a governmentsupervised auction of the sort required in Demsetz competition.

To see how this works, consider first the notions of fixed cost and sunk cost. Asdefined by Baumol, Panzar and Willig, 21 fixed costs are those that do not varywith output a s l o n g a s o u t p u t i s p o s i t i v e .Let y and w represent respectively

21Equations (2) and (3) in the text are respectively contained in Definitions 10A1 and 10A2 ofBanmol, Panzar and Willig (1982, pp. 280-281).


16/58

1304

v e c t o r s o f o u t p u t s a n d f a c t o r p r ic e s, a n d l e tp r o d u c t i o n i n 2 ):

C L ( y , W ) ---~~ F w ) -4- V y , w ) , w i t h 8 =

R,R. Braeutigam

C L b e t h e l o n g r u n c o s t o f

0 , i f y = O ,1 , i f y > O . 2 )

Th i s de f in i t ion pe rmi t s f ixed cos t s to ex i s t even in the long run , andF w) s them a g n i t u d e o f t h a t f i x e d c o s t . F i x e d c o s t s a r enot i ncu r red i f t he f i rm ceasesp r o d u c t i o n .

As the usua l a rgument goes , t he long run i s l ong enough fo r a l l cos t s t o beavo ided i f t he f i rm ceases p roduc t ion . However, i n the shor t e r run , s ay ap r o d u c t i o n p e r i o d p r o j e c t e d s y e a r s i n t o t h e f u tu r e , a f i rm m a y h a v e t o m a k ep r e c o m m i t m e n t s t o i n c u r s o m e c os t s ev e n if p r o d u c t i o n c e as es . I f C y, w, s ) i st h e s h o r t r u n c o s t f u n c t io n g iv e n t h e p r o d u c t i o n h o r i z o n o f s y e a r s , t h e n K w, s )a re cos t s su nk fo r a t l ea s t s yea r s , i f

C y, w, s)= K w,s) + G y,w,s), withG O,w,s)=O. 3)S i n c e a s u n k c o s t c a n n o t b e e l i m i n a t e d o r a v o i d e d fo r s o m e p e r io d o f t im e , e v e ni f an en te rp r i se ceases p roduc t ion a l toge the r, du r ing tha t pe r iod sunk cos t sca nn o t be v i ewed as an op por tun i ty cos t o f t he f irm. 22

T h e i d e a b e h i n d c o n t e s t ab i l it y i n t h e s i n g le p r o d u c t c a se i s a s f ol lo w s . I f n oc o s t s a r e s u n k , t h e n f i r m s o p e r a t i n g w i t h i d e n t i c a l t e c h n o l o g i e s a n d p r o d u c t s

wo u ld b e f r ee to en te r t he mark e t a s they p lease , cha rg ing wha teve r p r i ces theywished . Any f i rm cha rg ing a p r i ce h ighe r than ave rage cos t wou ld f ind i t s e l fd r i v e n f r o m t h e m a r k e t b y a n o t h e r f i rm c h a rg in g a l o w e r p r ic e . T h e c o n s e q u e n c eo f c o m p e t i t i o n f o r t h e m a r k e t w o u l d t h u s b e a v e r ag e c o s t p r i ci n g a n d h e n c eseco nd bes t pe r fo rm ance in the m arke t ) . 23

22 In the long run , the usua l no t ion tha t no cos t s a re sunk means tha t

l im K w, s) = O.

23In recen t years an ex tended d i scuss ion has deve loped about the meaning of con tes tab i l i ty and

the ex ten t to which i t may be appropr ia te to employ th i s concep t in connec t ion wi th rea l wor ldmarke t s . Fo r exam ple , the theory o f con tes tab i l i ty (us ing the no t io n o f sus tamabi l i ty ) focuses onpr ices as dec i s ion var iab les and mode ls po ten t ia l en t ran t s as eva lua t ing the p rof i t ab i l i ty o f en t ry a tthe inc um ben t s p re -en t ry p r ices . Some au thors have sugges ted tha t m ore compl ica ted fo rms of theg a m e b e t w e e n e n t r a n t s a n d i n c u m b e n t s m i g h t b e a p p r o p r i at e . A l t e r n a t iv e m o d e ls m i g h t i n cl u d e m o r ec o m p l i c a t e d d y n a m i c a s p e c ts o f t h e i n te r a c ti o n s a m o n g p o t e n t i a l e n t ra n t s a n d t h e i n c u m b e n t a n d t h euse o f qu ant i f ie s as wel l as pr ices as decis ion var iables . A de tai led discussion of th is l i terature is wel lbeyond the scope o f th i s chap te r. For in te res t ing fo rmula t ions o f the r iva l ry be tween an incumbentan d a poten t ia l en trant , see Brock (1983) for suggest ions of a l ternat ive possible s tra tegies , Dixi t(1982) fo r a t r ea tm ent o f the dynamics o f r iva l ry, Kuieps and Voge lsang (1982) fo r an in te rpre ta t ionof a sus ta inab le indus t ry conf igura t ion as a Ber t rand equ i l ib r ium, and B rock and Sche inkm an (1983)for a n ex tens ion o f the t rad i t iona l Sy los pos tu la te to a mu l t ip roduc t se t t ing . See a l so Baum ol (1982) ,W ei tzm an (1983), Shephard (1984), Schw ar tz and Reynolds (1984), an d B aumol , Panzar and W i l lig

(1984) fo r fu r the r d i scuss ions o f s t ra teg ic behav ior and the ro le o f f ixed and sunk cos t s as ba r r i e r s toen t ry.


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Ch 23: Optim al Policies or Natural Monopolies 1305

W hy i s a l ack o f sunk cos t s c ri ti cal i f com pet i t ion fo r the ma rke t i s to l ead tos e c o n d be st? I f a f i rm incurs sun k costs , thenK w, s) > 0 in (3) . In order for the

f i rm to be wi l l ing to enter the market , i t must charge a pr ice that genera tesrevenues tha t cover the va r iab le cos tsG y, w, s ) as wel l as the sunk costs . I f thef i rm w e r e s s u r e d of the r igh t to opera te in the marke t fo r s yea r s ( a time pe r iodlong enough to a l low i t to recover i t s sunk costs) , then i t could charge a pr icee q u a l t o a v e r a g e c o s t ( C ( y,w, s ) /y ) , and second bes t cou ld be ach ieved . Bu tunder con tes tab i l i ty the f i rm i s no t g ran ted a f r anch i se as i t would be underDemse tz compet i t ion . The f i rm does no t know how long i t wi l l be in the marke tun t i l ano the r f i rm comes a long and t r i e s to undercu t i t s own pr ice , and i tthe re fo re would have to charge a p r i ce h igher thanC y, w, s ) / y to p ro tec taga ins t the poss ib i l i ty tha t en t ry may occur be fo re s yea r s have passed . Conse-quen t ly, secon d be s t p r ic ing wi ll no t be ach ieved unde r c on tes tab i li ty if the re a resunk cos t s .

Fur the rm ore , the sunk cos t s o f the incum bent w ould be a bygon e in the even to f en t ry b y a new firm. A prospec t ive en t ran t w ould have to con tend w i th r iva l ryf rom a f i rm ( the incum bent ) w i th re la tive ly low op por tun i ty cos t s . Know ing th is ,an ent rant might not s ink i t s own costs in response to re la t ively h igh pr icesc h a rg e d b y a n i n c u m b e n t .

O ne m ight exp ect indust r ies wi th large capi ta l requirements , espe cia l ly wh erethe cap i t a l ca nno t eas i ly be mo ved f rom on e loca tion o r one use to ano the r, to

have subs tan t i a l sunk cos t s . For example , in the ra i l road indus t ry the re a resubs tan t i a l cos t s a s soc ia ted wi th way and s t ruc tu re , inc lud ing the roadbed , whichmigh t typ ica l ly be regarded as sunk . The same migh t be sa id fo r much o f thepipel ine indust ry. Indust r ies such as these are therefore not l ike ly to be contes t -able , a l thou gh one cou ld st ill conceivably in t roduc e com pet i t ion for the marke tth rough some o the r means , such as Demse tz compet i t ion .

On the o the r hand , indus t r i e s in which cap i t a l i s h igh ly mobi le may becontes table . An example is the a i r l ines indust ry. Here research has suggested thatthe re ma y be econo mies o f dens i ty, which me ans tha t ave rage cos t s wi ll dec l ineas more t raff ic i s passed through a g iven a i r l ine network [see Caves , Chr is tensen

and Tretheway (1983)] . On the Surface , th is suggests that i t may be eff ic ient foron ly on e f i rm (or a few fi rms) to op era tewithin some c i ty -pa i r marke t s. How ever,th is i s not suff ic ient to conclude that pr ices and ent ry in a i r l ine markets need beregula ted . On the contrary, i t has been argued that a i r l ine markets are contes tables ince ent ry and exi t i s qui te easy, and that there are v i r tual ly no sunk costs in theind ust ry [see , for example , Bai ley, G rah am and K apla n (1985), and Bai ley andPa nza r (1981)]. The se ar t ic les re ly on contes tabi l i ty to suggest w hy de regula t ionfor th e a i r lines w as an app ropr ia te pol icy on ec onom ic grounds . 24

24For a fu r the r d i scuss ion o f the ro le o f con tes tab i l i ty in pub l ic po l icy concern ing an t i t rus t a s we l las regulat ion, see Bai ley 1981) .


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1306 R R Braeutigam

Beyond Demse tz compet i t ion and con tes tab i l i ty, compet i t ion can a l so bein t rod uced in a th i rd way, th rough Ch amb er l in ian mo nopol i s t i c comp et i t ion [ see

Chamber l in (1962) ] . For example , in the t ranspor ta t ion sec tor o f the economym onopo l i s t ic com pet i t ion among var ious mod es o f t ranspor t i s o f ten re fe r red toas in te rm od el compet i t ion . Th is t e rm is employed to descr ibe the r iva l rybetween ra i l roads , motor carr iers , p ipel ines , and water carr iers , a l l of whomcompete for f re ight t raff ic . I f in termodal compet i t ion is s t rong enough, i t mightbe c i t ed as a bas i s fo r deregu la tion even if one o r m ore o f the m odes o f t ranspor tappears to have the s t ruc ture o f a na tura l monopo ly.

Cons ider a s imple example o f f re igh t t r anspor ta t ion be tween two po in t s .Suppose tha t a ra i l road and a compet i t ive m otor ca r r ie r indus t ry can prov ide therequ i red po in t to po in t service, an d suppose the ra i l road has the cos t s t ruc ture o fa na tu ra l m onopoly. 25 I f the in te rmoda l com pet i tion be tween the ra i l road andthe m otor ca r r ie rs i s s trong enough to -preven t the ra i l road f rom earn ing super-normal p rof i t s (even when the ra i l road ac t s as an uncons t ra ined prof i t -maxi -mizer ) , then the unregula ted marke t ou tcom e may be ve ry near ly second bes t inthe absence of regu la t ion . 26 In recen t years the move toward deregu la t ion of thera i l road indu s t ry no doubt par t i a lly resu lt s f rom pervas ive in te rmoda l compet i -t ion among the ra i l roads and o ther modes . In fac t de regu la t ion of the motorca rd er indu s t ry in 1980 has l ed to dec l in ing ra tes in th a t indus t ry, which fu r thers t reng thens the ex ten t o f the in te rmoda l compet i t ion faced by the ra i l roads [ see

M oo re (1986)].In o the r indus t r ies s imi la r types o f com pet i t ion have occur red . For example ,cab le te levis ion, a once heavi ly regulated industry, has largely been dere gulated,no doubt in par t because o f heavy compet i t ion f rom over- the-a i r b roadcas t ing .Current ly, there is much discussion over whether oi l p ipel ines should be deregu-la ted . The proponents o f de regu la t ion re ly on the a rgument tha t the re i s muchcompet i t ion f rom o ther t ranspor t modes , inc lud ing , fo r example , the ra i l roads ,tha t would keep the p ipe l ine indus t ry f rom earn ing la rge excess p rof i t s in theabsenc e o f p r ice regu la t ion .

In sum, the views of condi t ions under which i t i s appropria te to regulate (or

deregu la te ) have changed cons iderab ly dur ing the l ast two decades. A (no do ubthighly) s impl i f ied comparison of the older and newer views is shown in Figures23.5 and 23.6 . The more t radi t ional v iew is depicted in Figure 23.5; there theex is tence o f na tura l mono poly (as charac te rized by economies o f scale ) was the

25This assumption is for the sake of example in the text. A review of the lite rature on railroad costsis be yon d th e scope of the curren t chapter; suffice it t 9 say here that there is mixed evidence onwhethe r railroads operate with economies of scale, although most papers that have addressed the issueof economies of density which, for a single product railroad, mean s that average costs will decline asmor e traffic is passed through a given network) have found evidence that they exist.

26For more o n th e theory of second best with intermodal competition, see Braeutigam 1979). Of

course, if railroads have no scale economies in this example, then the unregulated outcome would befirst best instead of second best.


19/58

Ch 23: Optimal Policies or Natural Monopolies

. IIs here ~ lNo ~ 1 , ,,D on tegulateNatura l If lonopoly

(Economies

Scale?) Regulate I

Figu re 23.5. Regu lat ion of pr ices and entry: t radi t io nal econom ic just i ficat ion.

1307

cr i t ica l fac tor in determining whether an indust ry should be regula ted . Natura lm o n o p o l y w a s t a k e n t o p re c l u d e c o m p e t it io n w i th i n t h e m a r k e t, a n d t h e re w a svery l i t t le emphasis on compet i t ion for the market as an a l ternat ive to regula t ion.

Al thou gh the m ore cur ren t v iew migh t be represen ted in a numb er o f ways , thepresen ta t ion o f F igure 23 .6 a l lows a conven ien t compar i son wi th the moret rad i t iona l v iew. The ques t ion o f whe the r a na tu ra l m onop oly ex is ts is now basedon the c once p t o f subadd i t iv ity r a the r than on economies o f sca le . I f the re is nona tu ra l m on opo ly and compet i t ion wi th in the marke t is poss ib le i.e . min im umopt imal scale i s smal l re la t ive to the market demand) , then a pol icy of noregu la t ion m ay b e used to r each f ir st bes t wi thou t governmen t in te rven tion .

I f a natura l monopoly exis ts , then regula t ion may s t i l l not be warranted.

Compet i t ion fo r the marke t may be poss ib le even i f compet i t ion wi th in themarke t i s no t . I f compet i t ion fo r the marke t i s no t poss ib le , then some fo rm ofgove rnm ent in te rven t ion m ay be requi red . I f compe t it ion fo r the ma rke tsposs ib le , then pe r fo rmance c lose to second bes t migh t be reached wi thou tregu la t ion th rough Dem se tz compet i t ion , con tes tab i li ty, o r some fo rm of mo -nop ol is t ic or in termod al) com pet i t ion) .

I t may a l so be poss ib le to ach ieve a l eve l o f pe r fo rmance be t t e r than secondbes t perh aps even as good as f irs t bes t ) wi th regula t ion. O ne might then com parethe deadweigh t loss a t second bes t wi th the deadweigh t loss under a r egu la to ryreg ime des igned to improve pe r fo rma nce under governm ent in te rven t ion inc lud-ing an ex te rna l subs idy, som e fo rm o f p r i ce d isc r imina t ion , o r the use o fnon l inear tari ffs ), keeping in mind the fac t tha t a prog ram of gove rnm entin te rven t ion i s no tc o s t l e s s 2 7 I f the deadweight loss a t second bes t i s in to lerablylarge and th is requires a value judg m ent on the par t of pol icy-makers) , thengove rnm ent in te rven t ion m ay be war ran ted . To re i te ra te , the main po in t o f thi sexerc i se i s to ind ica te tha t even where a na tu ra l monopoly ex i s t s , governmentin te rven t ion m ay n o t be requ i red to ach ieve econom ic e ffi ci ency fo r a num ber o freason s , in co ntras t wi th the m ore t radi tional v iew of regula tion.

27The costs of maintaining a regulatory commission and staff , together with al l of the at tendantadm inistrat ive su pport , can be qui te large, as Wiedenbau m (1978) has suggested.


20/58

1308 R R Braeutigam

PAC

yC for f i r m

MOS small relative to Mkt

i

i s there a naturnl monopoly '?(is MOS large rel ati ve to D,so that competition WITHIN themarket i s net poss ible?)

Marke t D~ [ Don't regulate; Iachieve f i r s t bes t [

Y~

No

Second Best (re lat ive toF i r s t Bes t ' ) To le rab le ' ?

FFegulate to achieve [i rs t Best (or near I

Firs t Best ' ) outcome]

Need external subsidyor

Pr ice Discr iminat ionor

Nonl inear (Mult ipar t )Tar i ff s

( to a l low f i r m toavoid a deficit andpr ice e ff i c i en t ly )

I e DWL

/

o

Examples:Motor Carr iersWater a r r i e r s

PAC [~ qk t D~ ~ C for f i rm

MOS large rel ati ve to Mkt y

ACMC Sm al l DWL

MC

Can there be competit ion

FOR the mar ke t? -- -(a) Demsetz Competit ion(b) Contestable Market(c) Monopolistic Competit ion

(Intermodal Compet i t ion)

Second Best (or near [ Introduce Competit ionSecond Be st' ) outcom e[ FOR the Mar ket

(may avoid external subsidyand nonlinear tar i ffs)

Examples:RR's, Pipelines:Intermodal Competit ionor Demsetz Competit ion

Airlines: Contestable Mkt

Figure 23.6. Policy roadmap for regulation.


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Ch 23: Optim al Policies or Natural Monopolies 1309

To th is po in t w e have addressed one face t o f the op t ima l po l i cy toward na tu ra lm ono poly, n am ely whe the r to r egu la te a t a ll o r r e ly on som e fo rm of compet i t ion

ins tead. We now turn to opt imal s t ra tegies where regula t ion is se lec ted as theapp ropr ia te po l icy. The m enu o f poss ib le r egu la to ry con t ro ls over p ri ce and en t ryis a r ich one. The balance of th is chapter wi l l d iscuss some of those controls .

4 Pricin g alternatives: Ba sic concepts

I f r egu la t ion i s under taken as a re sponse to the na tu ra l m ono poly p rob lem, the rea re severa l courses o f ac t ion tha t migh t be fo l lowed by the regu la to r wi th respec tto pr ic ing. Of course , changes in pr ices have both dis t r ibut ive and a l locat iveeffects . In th is se ct ion we wi ll focus on the la tter, tha t i s , pr ic ing pol ic ies des ignedto achieve eco nom ic efficiency.

As Figure 23.6 indicates , regula t ion might be implemented for a var ie ty ofreaso ns re la ted to econom ic eff ic iency. For exam ple , a natura l m on op oly mightbe regu la ted b ecau se no fo rm of compe t i tion fo r the marke t i s v iable ; he re p r icesm igh t b e regu la ted to r educe the deadweigh t loss a s soc ia ted wi th the unregu la tedm on op oly pr ice , perha ps to a level associa ted wi th e ither second be s t or fi rs t bes t .Or, even i f second bes t cou ld be ach ieved th rough compet i t ion fo r the marke t ,po l i cy -makers migh t de te rmine tha t the deadweigh t loss a s soc ia ted wi th second

be st i s in to lera bly large , in which case regula tion might b e in t roduc ed to increaseeff ic iency (perh aps even to reach f irs t bes t ) .Sec t ion 3 p resen ted the bas ic d i l emma of marg ina l cos t p ri c ing wi th a na tu ra l

m on op oly. In par t icular Figure 23.4 i l lus t ra ted wh y ma rginal cos t pr ic ing wi lllead to a def ic i t for a f inn opera t ing w i th econom ies of scale i f a ll uni ts o f outp utare s old a t m arginal cos t . 28 In th is case the f inn wi ll no t be rev enu e ad equ ate ,and w ould the re fo re requ ire an ex te rna l ly p rov ided su bs idy to cover the de f i c it ifi t i s to cont inue product ion. With economies of scale and a s ingle pr ice chargedfor a l l uni ts of output , one can achieve f i rs t bes t only i f an external subsidy isp rov ided , and avo id such a subs idy on ly by incur r ing a deadw eigh t loss. Th i s

t ens ion be tw een econom ic e ff ic iency and revenue adeq uacy p rov ides a focu s fo rmuch of the l i te ra ture on regula ted indust r ies .

Ho we ver, i t t u rns o u t tha t the re m ay be o the r w ays to ach ieve g rea te r e ff ic iencythan a t second bes t (pe rhaps even reach f i r s t bes t ) wi thou t an ex te rna l subs idywhen the re a re economies o f sca le th roughout the re levan t opera t ing range . Tosee th is , recal l tha t the ear l ier d iscuss ion of Figure 23.4 assumed that the sameprice i s charged for a l l uni ts of output sold in the market . Resta ted , th is means

28Here one should keep in mind the distinction between economies of scale and subadditivity. Ifnatural monop oly were characterized by a subaddifive cost structure, but not by economies of scale

over the relevant operat ing range, as in Figure 23.2, then marginal cost i.e. first best) pricing wouldallow the firm to breakeven or even to earn some extranormal profit.


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1 3 1 R R Braeutigam

t ha t (1 ) each un i t pu rchased by an ind iv idua l cus tomer i s so ld a t t he same ( i . e .un i fo rm) p r i ce and tha t (2 ) the p r i ce pe r un i t i s t he same fo r a l l cus tomers ( i . e .

t he re i s no p r i ce d i sc r imina t ion ove r cus tomers ) .

4.1. Pric e discrimination differential pricing)

T h e f o r e g o i n g d i s c u s s i o n s u g g e s t s t h a t t h e r e a r e t w o w a y s o n e m i g h t f u r t h e ri m p r o v e e c o n o m i c e f fi ci en c y b y d e p a r t i n g f r o m t h e r a t h e r r e st ri c ti v e a s s u m p t i o nt h a t t h e s a m e p r i ce i s c h a rg e d f o r al l u n i t s o f o u t p u t s o l d in t h e m a r k e t . O n e w a yw o u l d b e t o e n g a g e i n s o m e f o rm o fprice discrimination,s o m e t i m e s r e f e r r e d t oas differential pricing.As these t e rms sugges t , a r egu la to r cou ld cha rge d i ff e ren tp r i c e s t o d i f f e r e n t c u s t o m e r s i n t h e m a r k e t , e v e n i f e a c h c u s t o m e r p a y s t h e s a m ep r i c e f o r a l l o f t h e u n i t s h e p u r c h a s e . I n t h e s i m p l e s t i n s t a n c e , s u p p o s e t h a tc u s t o m e r i m u s t p a y P i f o r e v er y u n i t o f s er v ic e h e p u r c h as e s , a n d t h a t c u s t o m e rj m us t pa y p j fo r eve ry un i t o f s e rvice he pu rchases . D i ff e ren t i a l p r i c ing m eanst h a t p ,. ~ p j f o r s o m e c u s to m e r s i a n d j . P e a k l o a d p ri c in g a n d R a m s e y p ri c in gschem es f a l l i n to th i s ca t egory and wi l l be d i scussed in g rea te r de ta i l i n Sec t ions 5and 6 .

P r i ce d i sc r im ina t ion i s, o f cour se , a sub jec t t ha t has r ece ived mu ch a t t en t io n inb o t h r e g u l a t e d a n d u n r e g u l a t e d i n d u s tr i es . M u c h o f t h a t d i s c u s si o n s u r ro u n d s t h e

lega l i ty of th e prac t ice [see, for exam ple , Scherer (1980, chs . 11 and 12)] . Ad i scuss ion o f the l ega l i ty o f p r ice d i sc r im ina t ion is no t o u r focus he re . We shou ldobse rve tha t even i f r egu la to r s wi sh to a l low o r impose p r i ce d i sc r imina t ion , i ts t i l l may no t be poss ib l e fo r economic r easons . As i s we l l known, in o rde r fo rd i ff e ren t i a l p r i c ing to be f eas ib l e the se l le r mus t be ab le to ide n t i fy the p r ice eac hc u s t o m e r ( o r a t l e a s t d if f e re n t g r o u p s o f c u s t o m e r s ) w o u l d b e w i l li n g to p a y f o rthe se rv ice . Fur the rmore , r e sa l e mus t no t be poss ib l e fo r e i the r l ega l o r t echno-log ica l r easons , so tha t a cus tomer cou ld no t pu rchase the se rv ice a t a l ow p r i ceand then se l l i t t o ano the r cus tomer a t a h ighe r p r i ce . I f r e sa l e i s poss ib l e ,a rb i t r age wi l l work to e l imina te p r i ce d i sc r imina t ion so tha t a l l cus tomers wou ld

face the same p r i ce in the marke t .To see ho w d i ff e ren t ia l p r i c ing migh t be used to improv e econo m ic e ff i ci ency

whi l e a l lowing the f i rm to avo id a de f i c i t , cons ide r aga in F igure 23 .4 , where thef i rm ope ra t e s wi th the a ff ine cos t s t ruc tu reC = F + my. S u p p o s e t h e f i rm k n o w show much each consumer i s w i l l i ng to pay fo r the se rv ice , and tha t r e sa l e i simpo ss ib le . N ow le t the f i rm cha rge a p r i ce equa l t o PB to a l l cus tomers w howould be wi l l ing to pay a p r i ce g rea te r t han o r equa l t o PB, i . e . t o a l l cus tomersl o c a t e d t o t h e le f t o f p o i n t B o n t h e d e m a n d s c h e d u le . C a l l t h e se t y p e Icus tom ers . Th en l e t t he f irm cha rge a p r i ce equa l to PE to each o f the cus tomersw h o w o u l d b e w i l l i n g t o p a y a p r i c e g r e a t e r t h a n o r e q u a l t o P E , b u t n o t m o r etha n p B- Ca l l these ty pe I I cus tomers .


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Ch. 23: O ptimal Policies or Natural Monopolies 1311

What would be the consequences of such a schedule? The revenues generatedby the type I customers would cover not only the variable costs of producing YB

units, but also all of the fixed costs F. [Observe that PB---- C Y B ) / Y B ,whichmeans that YnPB = F + myn . ] Th erevenues generated by the type II customerswould then cover just the variable costs from providing (YE- YB) units ofservice. Therefore, one consequence of the suggested schedule is tha t total costswould then cover total revenues, and there would be no need for an externalsubsidy to keep the firm viable. Also note that every customer who is willing topay an amount at least equal to the marginal cost of producing the servicereceives it, while service is not provided to customers who are not willing to payat least the marginal cost of production. Thus, a second consequence of thesuggested schedule is that it is firs t best or economically efficient. It should alsobe noted that the proposed schedule leaves the firm with no extranormal profits(producer surplus), since total revenues exactly equal total costs in the example,while consumer surplus would be equal to the sum of the areas A B I and B G E .

One could envision many other possible discriminatory tariff schedules thatwould accomplish the same objectives (achieving first best without an externalsubsidy). As a simple example, suppose each customer desires only one unit, andsuppose the firm is allowed and able to price discriminate perfectly so that itcharges each customer a price equal to the maximum amount that customer iswilling to pay for the uni t purchased. Consumer surplus is zero under this pricing

schedule since each consumer is paying the maximum amount he is wilting to payin order to get the service. In the example of Figure 23.4, the firm's revenueswould then equal the area represented by A E J O , while the costs of productionwould be the sum of the areas I B K O a n d G E J K .Again, the finn remains viable(and in fact earns a producer surplus equal to the sum of the areas A B I andB G E ) . Thus, total surplus (the sum of consumer and producer surplus) is as greatas it was under the imperfectly discriminating tariff schedule that charged PB totype I customers and PE to type II customers, and once again first best isachieved for the same reasons as given in that earlier example. Of course, thedivision of the total surplus is strikingly different under the two schedules, withconsumers receiving it all in the first example and producers receiving it all in thesecond. With still other forms of price discrimination it would be possible toachieve other distributions of the total surplus under a first best pricing structure.

4.2. N on lin ea r outlay schedules nonlinear tariffs)

The second way of departing from the assumption that the same price is chargedfor all units of output sold would be to charge an individual customer an amountper unit purchased that varies with the total quantity he purchases. This kind ofpricing is often referred to as a nonlinear outlay schedule,or sometimes a


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1312 R R Braeutigam

nonl inear ta r i ff . The difference between a linear and a nonlinear outlay schedulecan be illustrated easily. Suppose that customer i must pay p; for every unit of

service he purchases, and that he purchases Yi units. His total outlay (expendi-ture) is P~Yi, so that the average out lay per uni t purchases i s cons tan t .By directanalogy, a nonl inear out lay scheduleis one in which the average out lay is notcons tan t as the n um ber of un i t s purc hased var ies . 29

One might suspect that there are many possible ways of structuring nonlineartariff schedules. Indeed this is so, as will be discussed in greater length in Section7. For now we offer only a simple example of such a tariff. Consider the so-calledtwo-par t tariff; as the name suggests, the tariff has two parts here, a fixed and a

variable component. Suppose, for example, there are N identical consumers inthe market, and that the finn operates with the affine cost structure C = F + my.One could envision a tariff structure that would assess each customer a fixedcharge e (per month), where e = F / N is to be paid regardless of the number ofunits actually purchased. In addition customers would be required to pay avariable charge equal to m for each unit actually purchased. Thus, the totalexpenditure by a customer would be e + m y, which is an affine tariff schedule.First best is achieved since each additional unit consumed is priced at marginalcost. In addi tion the firm would remain financially viable since the total revenueswould be N e + m y ) = F + N m y.

The reader may (correctly) suspect that income effects may introduce complex-

ities in the way such tariffs are structured if economic efficiency is to be achieved;we address these effects in Section 7. In fact, nonlinear tariffs may involve morethan two parts as in the previous example. The main point of the examples in thissection is to illustrate that nonlinear tariff structures can be useful as a means ofachieving greater efficiency without external subsidies. 3

4.3 . Th e com mo n cos t problem in the mul t iproduct f i rm

We have now suggested several ways in which one might improve economic

efficiency by departing from a single price for all units of output sold in themarket. The problems discussed thus far are simplified in one very importantrespect: the firm has been assumed to produce only one product. The problem ofpricing becomes even more difficult when there is more than one output producedby the firm.

2 9 O n e p o s s i b l e s o u r c e o f c o n f u s i o n i n t h e t a x o n o m y h e r e s h o u l d b e p o i n t e d o u t . S i n c e a l i n e a ro u t l a y s c h e d u l e i s d e f i n e d a s o n e i n w h i c h a v e r a g e o u t l a y i s c o n s t a n t , i t f o l l o w s t r i v i a l l y t h a t t o t a lo u t l a y i s l i n e a r i n o u t p u t . H o w e v e r, a n o n l i n e a r o u t l a y s t r u c t u r e m a y a l s o b e l i n e a r i n o u t p u t ; i np a r t i c u l a r , w i t h t h e a f f in e s t r u c t u r e r e f e re n c e d i n t h e t e x t e x p e n d i t u r e s a r e li n e a r i n o u t p u t . T h ei m p o r t a n t p o i n t i s t h a taverage n o t t o t a l ) o u t l y i s n o t c o n s t a n t w i t h r e s p e c t t o o u t p u t p u r c h a s e d .

3 A s w i l l b e i n d i c a t e d i n S e c t i o n 7, n o n l i n e a r t a r i f fs m a y n o t a l w a y s l e a d t o f i rs t b e s t , b u t n o n l i n e a rt a r i ff s c a n b e u s e d t o i n c r e a s e e c o n o m i c e f f ic i e n c y r e l a ti v e t o s e c o n d b e s t e v e n w h e n f ir s t b e s t i s n o ta c h i e v e d .


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Ch. 23: Optim al Policies or N atural Monopolies 1313

T o s e e th i s c o n s i d e r a f i rm w h i c h p r o d u c e s t w o p r o d u c t s w h o s e le v el s o f o u t p u ta re r e sp ec t ive ly Yl an d Y2. Le t t he marg ina l co s t s o f p rod uc t io n fo r the se rv ices

b e c o n s t a n t a n d r e s p ec t iv e l y m 1 a n d m 2 , a n d s u p p o s e t h e re i s a f ix e d c o s t o fp r o d u c t i o n F. T h i s d e s c ri b es a s i m p l e m u l t i p r o d u c t a f f in e c o s t f u n c t i o n w h e r e t h eto ta l cos t s a reC = F + r e l y 1 + m 2 y 2 .

T h e f i x e d c o s t is s a i d t o b e c o m m o n t o b o t h s er vi ce s. I n o t h e r w o r d s , i t i s ac o s t s h a r e d i n t h e p r o d u c t i o n o f Y l a n d Y2. T h e p r e s e n c e o f s u c h a c o m m o n c o s tpose s a pa r t i cu la r ly d i f fi cu lt p rob lem fo r r egu la to r s t ry ing to se t p r i ces so tha t t hef i r m c a n b r e a k e v e n . A s s u m e t h a t t h e f ir m m u s t p r ic e e a c h s e r vi ce u n i f o r m l y, sotha t pu rc hase r s o f se rv ice i w i l l a l l pa y a p r i ce pe r un i t equa l t o P i fo r tha tse rv ice . As in the s ing le p ro duc t a ff ine cos t case, i t i s c lea r tha t t he f i rm cann o tb r e a k e v e n w i t h m a rg i n a l c o s t p r ic i n g. I f P l = m l a n d P 2 = m 2 , t h e p r o f it s o f t h ef i rm wi l l be n ega t ive ( in f ac t , p ro f i t s a re ~ r = - F ) .

T h e q u e s t i o n t h e n b e c o m e s : H o w m i g h t t h e r e g u l a t o r s e t r a te s s o t h a t t h e f i rmb r e a k s e v e n ? T h i s i s a n a g e - o l d q u e s t i o n t h a t h a s b e e n e x a m i n e d i n m a n ycon tex t s in the economic l i t e r a tu re a s we l l a s in r egu la to ry p roceed ings [ see , fo rexample , Tauss ig (1913) , P igou (1920) and C la rk (1923) fo r exce l l en t ea r lyt rea t i se s on th is subjec t ] . 31

F o r m a n y y e a r s r e g u la t o rs h a d r e la t iv e l y l it t le i n t e r m s o f e c o n o m i c t h e o r y t og u i d e t h e i r d e c i s i o n s i n r a t e m a k i n g i n t h e f a c e o f c o m m o n c o s t s . I n p r a c t i c er e g u l a t o r y a u t h o r i t i e s s u c h a s t h e I n t e r s t a t e C o m m e r c e C o m m i s s i o n a n d t h e

F e d e r a l C o m m u n i c a t i o n s C o m m i s s i o n h i s t o ri c a ll y h a v e d e t e r m i n e d t a r if f s ( r at e s)us in g so -ca l l ed fu l ly d i s t r ibu ted ( fu l ly a lloca ted ) cos ts , wh ich w e sha l l r e fe r t oh e r e a s F D C p r ic i ng . W e d i s cu s s t h is b r ie f ly h e r e t o c o n t r a s t t h i s o f t e n u s e dr e g u l a t o r y a p p r o a c h w i t h t h o s e b a s e d o n e c o n o m i c ef f ic i en c y t o b e d i s c u ss e d i ns u b s e q u e n t s e c t i o n s .

U n d e r F D C p r i c i n g , a s a f i r s t s t e p r e g u l a t o r s d o ( s o m e h o w ) a l l o c a t e t h ecommon cos t s among the

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