The Subtraction Rule and its Effects on Pricing in the Electricity Industry

Transcription

1 Dscusson Paer No 04- The Subtracton Rule and ts Effects on Prcng n the Electrcty Industry Walter Elberfeld

2 Dscusson Paer No 04- The Subtracton Rule and ts Effects on Prcng n the Electrcty Industry Walter Elberfeld Download ths ZEW Dscusson Paer fro our ft server: ft://ftzewde/ub/zew-docs/d/d04df De Dscusson Paers denen ener öglchst schnellen Verbretung von neueren Forschungsarbeten des ZEW De eträge legen n allenger Verantwortung der utoren und stellen ncht notwendgerwese de Menung des ZEW dar Dscusson Paers are ntended to ake results of ZEW research rotly avalable to other econosts n order to encourage dscusson and suggestons for revsons The authors are solely resonsble for the contents whch do not necessarly reresent the onon of the ZEW

3 Non-Techncal Suary On rl 9 00 the cartel offces ublshed the reort fro the workng grou securty of suly n servce of the cartel offces of the federal reublc and the states about the coverage fro the nterventon nors accordng to the anttrust regulatons n nsectng the level of network access charges for ower suly usage and the relevance of the anttrust regulaton of edng behavoral atterns shown by electrcty network owners n relaton of network access The reort contans a basc stateent of the cartel offces relatng to the arorateness of the level of network access charges as well as to edng behavoral atterns of ntegrated network owners n the electrcty ndustry Of artcular ortance n ths reort s the socalled subtracton rule S-rule whch has been roosed to rove the verfcaton of roerly nflated network access charges Under ths rule the cartel offce would calculate the dfference between the network owner s rce charged to the consuers and overall argnal costs of a rval ncludng network access charges whch the coettor has to ay to the network owner If ths value s negatve t would be concluded that network access charges are roerly nflated The resent aer analyzes the roosed rule wthn a sle Hotellng-fraework Two states are coared; one state n whch the S-rule s leented and one where t s not The S-rule changes the network owner s ncentves Prcng below the rval s argnal costs would volate the S-rule trggerng a sancton y ncreasng hs rce the network owner can reduce or avod the sancton If the network owner ncreases hs rce the rval wll follow sut snce reacton functons are uward slong Indeed f the network owner s argnal costs are oderately or uch lower than those of hs rval ths s what wll haen so that the S-rule would lead both frs to charge hgher rces akng all consuers worse off However f the network owner s only slghtly ore or less effcent then the ntroducton of the S-rule does not affect frs behavor and rces wll rean unchanged

4 The subtracton rule and ts effects on rcng n the electrcty ndustry Walter Elberfeld February 004 bstract The aer deals wth the subtracton rule whch has been roosed by the workng grou securty of suly n servce of the cartel offces of the federal reublc and the states as an nstruent to dentfy roerly nflated network access charges n the electrcty ndustry We analyze frs rce resonses and adatatons to ths rule The results suggest that the ntroducton of the subtracton rule would ncrease rces regardless of whether network access charges are roerly nflated or not Keywords: Electrcty arket network access charges abuse of a donant oston JEL-Classfcaton: L4 ddress: Centre for Euroean Econoc Research ZEW Deartent of Industral Econocs and Internatonal Manageent POox Mannhe Gerany Phone: 49/6/5-79 Fax: 49/6/5-70 e-al: elberfeld@zewde I would lke to thank Professor C C von Wezsäcker for very helful coents

5 Introducton On rl Gerany leented the EU Electrcty Market Drectve fro 996 nto a new energy law the Energewrtschaftsgesetz EnWG Wth ths legal change Gerany oened ts arket fully to coetton endng the era of regonal onooles rotected by dearcaton agreeents Under the new law each consuer s allowed to choose fro a wde range of dfferent sulers However varous colants fro new sulers and consuers suggest that certan robles are stll resent Esecally colants about hgh network access charges ndcate that these ght be roerly nflated Therefore the workng cottee securty of suly n servce of the cartel offces of the federal reublc and the states rbetsauschuss Versorgungsscherhet der Kartellbehörden des undes und der Länder aonted at ts eetng on October / 000 n Manz the workng grou electrcty network utlzaton of the anttrust dvsons of the federal reublc and the states rbetgrue Netznutzung Stro der Kartellbehörden des undes und der Länder to exane the subtted rerovals and to work out a concet for coordnatng the rocedures aong the anttrust dvsons of the federaton and the federal states In ther reort dated onn rl 9 00 the workng grou suggested a certan rule the subtracton rule n the followng we wll refer to ths rule as the S-rule whch should hel to rove the verfcaton of roerly nflated network access charges The workng grou descrbes the S-rule as follows: Fro the gross-retal rce of electrcty klowatt-hour rate lus deand rate allocated to the kwh for an ntegrated electrc utlty one deducts the netuser fee and the statutory redeterned dutes electrcty tax sales tax concesson leves The reanng balance consttutes the redonantly varable costs for rocureent of electrcty and dstrbuton net-rce of electrcty The so couted costs for the acquston of electrcty and retalng can then be coared wth the arket rces for the rocureent of electrcty or the costs of rocureent for electrcty of other energy suly coanes as well as wth the retalng costs of coarable electrc utltes because a arket rce doesn t exst [ ] If the so deterned costs for rocureent and dstrbuton consderably exceed the arket rces or the average costs ncurred by other electrc utltes resectvely ths wll ndcate that the ntegrated electrc utlty knowngly charges hgh network usage fees n order to ake thrd arty access dffcult In the resence of a cobnaton of hgh network usage fees and very low assessed rocureent and retalng costs of electrcty a strong ndcaton for the narorateness of the charged network usage fee exsts lthough these fndngs alone ay not suffce for the ascertanent of narortate fees n ters of 9 aragrah 4 no 4 GW they are however sutable to suort the result of an narorate rcng found n the context of the treatent of coarsons 5f The recently decded TEG-case -45/0 deonstrates that the undeskartellat s ndeed wllng to aly the S-rule n order to fnd out whether network owners deand roerly nflated nework access charges lthough the TEG-decson s anly based on a cost enqury the cartel offce has also calculated the rce and cost eleents of the S-rule and concludes that the result onts nto the sae drecton as the result of the cost analyss see -45/0 Snce the wordng n the text s qute cautous one gets the resson that the cartel offce tself s not sure yet whehter the S-rule can serve the Reort about the coverage fro the nterventon nors accordng to the anttrust regulatons n nsectng the level of network access charges for ower suly usage and the relevance of the anttrust regulaton of edng behavoral atterns shown by electrcty network owners n relaton of network access ercht über de Rechwete der kartellrechtlchen Engrffsnoren für de Überrüfung der Höhe des Entgelts für de Nutzung der Stronetze and de kartellrechtlche Relevanz von den Netzzugang behndernden Verhaltenswesen der Stronetzbetreber The text refers to ths rule as the Subtraktons-/Verglechsethode bezüglch der Kostenbestandtele

6 ntended urose In the resent aer we wll argue that the S-rule should not be ntroduced We wll show that the leentaton of the S-rule entals a strong tendency to ncrease rces Usng a Hotellng 99-tye duooly odel we develo ths result by coarng two states; one state n whch the S-rule s leented and one where t s not Secton contans the basc fraework and derves equlbru rces when the S-rule s not leented Secton derves equlbru rces when the S-rule s leented In Secton 4 we analyse several alternatve resonse strateges by whch network owner ay react to the ntroducton of the S-rule Fnally Secton 5 concludes ll roofs are relegated to an aendx The basc fraework Frst of all t s ortant to notce that electrcty s not a hoogenous good n the econoc sense of the word Though electrcty s a hghly standardzed roduct fro a techncal ont of vew and therefore ay be seen as a hoogeneous good n a hyscal sense t s not hoogenous n the econoc sense It already starts wth consuers references for certan tyes of rary energy usage Soe eole refer electrcty generated fro renewable energy sources nstead of nuclear ower soe desre electrcty generated fro uncal sulers and stll others refer electrcty fro newcoers n order to roote coetton In these cases we talk about deal references They are very dstnctve only wth a norty of consuers Much ore ortant s the fact that consuers ossess a dstnct reference for a relable suly Though a large art of the servces guaranteeng the relablty of suly s autoatcally covered by certan suleentary servces the erceton of the consuer s that soe sulers are ore relable than others Moreover there are soe extra servces whch are offered by soe frs and not by others In any cases the ersonnel fro the suler s retal dvson antans face-to-face contact wth larger custoers thereby nfluencng ther decson akng Therefore the sellng of electrcty concerns n all ts artculars a arket wth dfferentated roducts Consequently we wll odel the electrcty arket as a dfferentated roduct arket The foral structure of the odel s as follows There s a contnuu of consuers φ They are unforely dstrbuted n ters of tastes on a lne of otental roducts of length one eg φ [ 0 ] We assue that a consuer s references can be descrbed by U = r t φ φ φ where denotes the rce of varety φ The ter t φ φ reresents the dsutlty n oney unts whch a consuer exerences f he buys φ nstead of hs ost referred varety φ The araeter r descrbes the utlty fro consung φ In the followng we assue that r s large n the sense that every consuer wll urchase one or the other varety eg we assue that the arket s fully covered Ths assuton s very lkely to be fulflled n the electrcty arket gven observed rces and the wllngness to ay for electrcty The deand sde of the odel resuoses that deand s rce nelastc and that each consuer buys exactly one unt of electrcty The latter assuton eans that we consder a knd of standardzed custoer Ths erceton requres that a real custoer buyng only half of that quantty has to be consdered as a half custoer and a custoer buyng 00 tes ore than the standardzed custoer has to be vewed as 00 custoers Of course n ractce a large custoer wll behave dfferently than 00 sall custoers buyng the sae 4

7 aount and ndeed ths dstncton ay becoe ortant f one enters nto a detaled nvestgaton of the abuse of a donant arket oston However at our level of abstracton gnorng the dfferences between sall and large custoers s nsubstantal The noton of a standardzed custoer les that the sales of a fr concde wth the nuber of standardzed custoers There are two frs and sulyng soe regon wth electrcty The varetes offered are φ and φ resectvely wth φ φ [ 0 ] Wthout loss of generalty we assue that φ < φ Moreover we assue that φ = φ whch eans that roduct dfferentaton advantages are syetrc Ths assuton together wth the nequalty φ < φ les that φ ] 0 / [ and φ ] / [ consuer who s ndfferent between the two frs s located at φ = d where φ s obtaned by equatng utltes eg Uφ = Uφ Wth T = t φ frs resectve deands can be wrtten as j d = φ = j j = T In Gerany network owners are to a large extent vertcally ntegrated wth generaton and retal suly servces t the sae te they have to rovde transsson servces to any coetng suler ccordng to ths ownersh structure we assue that one fr fr s a new fr whch entered the arket after deregulaton whle s vertcally ntegrated and owns the dstrbuton network and ower roducng facltes Let r denote the network usage rce charged by and denote the varable constant unt costs of network usage by r Each fr s able to satsfy ts deand ether by generatng electrcty wth own ower lants or by buyng electrcty on the wholesale arket Denote s varable constant unt rocureent costs by c = Varable constant unt retal suly costs are denoted by v = Wth ths notaton frs roft functons can be exressed as j = T where = r c v are s overall argnal costs j j = The frst order condtons yeld the reacton functons 4 j T j = In equlbru fr sets the rce 5 = j T 5

8 Note that rces ncrease wth the degree of roduct dfferentaton φ φ = φ Indeed f φ φ ncreases T ncreases lyng a hgher rce of each fr Fr s outut s gven by 6 q = j 6T T To avod corner solutons we assue that couted as < T Equlbru rofts can be 7 j T = 8T In rncle the dstrbuton network rovdes ts owner wth a tool to ractce arket foreclosure In a coletely deregulated arket the network owner could refuse to rovde access to rval sulers or equvalently ay engage n a rce squeeze eg charge the an exorbtant rce The fnal rce then would be close to the onooly level In order to revent such an outcoe the rce of network usage has to be regulated n soe way The Geran aroach to solvng the network rcng roble s based on the so-called negotated thrd arty access odel It leaves the detaled regulaton of network access and transsson rcng to be negotated by the dfferent assocatons n the electrcty ndustry The results of these talks were wrtten down n the assocatons agreeent or Verbändeverenbarung VV n May 998 Revsed versons of the frst VV were deterned n Deceber 999 and Deceber 00 s already entoned n the ntroducton however certan robles stll see to exst In artcular colants about excessve network access and transsson rces suggest that rces at least n soe cases ght be roerly nflated In order to detect excessve network usage rces the workng grou for electrcty network utlzaton has roosed to ntroduce the S-rule In ters of our notaton ths eans that the undeskartellat wants to calculate the dfference S = r c v = If ths value s negatve t s concluded that r s roerly nflated whle a nonnegatve value ndcates that r s arorate Note that S s the dfference between s fnal rce and s overall argnal costs One ght ask why nstead of S the balance s not based on the value of r c v If ths were the case the S-rule could be seen as a knd of reeda- Turner-test whch however s dffcult to leent snce the network owner could always try to shuffle costs fro the generaton and retal dvson nto the network dvson The otental advantage of the S-rule s that n rncle all deternants are observable However ths does not ean that the S-rule does not ental any robles Esecally f the retal suly and/or rocureent costs of the network owner are lower than the resectve costs of the rval t s ossble that he wll charge hs custoers a cost coverng rce whch however leads to a negatve value of S Ths s ossble even f the rce for network usage s arorately set To see ths defne r = r r c = c c and v = v v ostve r ndcates that the network usage rce ght be roerly nflated whle a r close to zero suggests that the access rce s arorate ostve c v eans that has a cost advantage wth resect to electrcty generaton retal suly whle a negatve value states that has a cost advantage 6

9 ssue that the network usage rce s arorate eg r = 0 and the network owner s ore effcent than hs rval eg c v < 0 Then the value of S s gven by 8 S = c v r = c v T where the second equalty follows fro the assuton that the network usage rce s arorate Straghtforward calculatons establsh the followng lea: Lea One has 9 S < 0 < T Lea states that the value of S s negatve f the network owner s ore effcent and the degree of roduct dfferenton s not too large Thus the lea shows that the S-rule can lead to stakes The network owner ay be accused of abusng hs donant arket oston by chargng an excessve network usage rce even f ths s not the case tye II error Of course as long as the S-rule s not leented ths has no consequences and fr behavor s not affected Prcng n resence of the subtracton rule ny anttrust enforceent nsttuton s faced wth costs n ts effort to dstngush between coettve and antcoettve behavor of frs These costs nclude the drect costs of dentfyng frs whch are consdered to volate anttrust laws However these costs are lkely to be sall snce relatvely few frs are ever subject drectly to anttrust sanctons The an costs are caused by frs resonses and adatatons to anttrust rules and the way how they affect rces costs and nnovaton; see Joskow 00 97/98 If a network owner s confronted wth the conjecture of abusng hs donant arket oston he wll antcate a ossble costly nvestgaton and the rsk of a dssuason or a serous fne Perhas he ust also act on the assuton of sufferng fro bad ress thereby forfetng hs reutaton In order to avod these nconvenences t can be exected that n any cases the network owner wll refran fro actons whch abet the conjecture of abusng a donant oston In ths secton we analyze the rcng behavor of frs under the assuton that the undeskartellat leents the S-rule and volatons are subject to sanctons We assue that the sanctons are ncreasng lnearly wth the volaton of the S-rule eg f the Kartellat observes S < 0 the enalty wll be k S wth k > 0 Note that s roft functon s not affected by the ntroducton of the S-rule It s the sae as n the stuaton where a volaton of the S-rule s not unshed eg gven by n Secton However the new rule changes the roft functon of the network owner whch now reads 7

10 f f < = S S S k wth gven n Snce S = 0 can be wrtten as k < = f f The S-rule changes the network owner s ncentves s can be seen fro equaton quotng a lower rce wll be unshed f ths leads to a volaton of the S-rule Thus settng a low rce becoes costly for The strategc effects can be best descrbed wth hel of the frs reacton functons Whle fr s reacton functon s stll gven by equaton 4 s reacton functon changes In order to calculate the latter one has to take nto account that s roft functon has a downward knk at = The knk roduces a dscrete ju of the argnal roft functon at ths ont: k < = f f Lea The network owner s reacton functon s gven by > < = T k T k kt f f f Proof see endx Wth ths result we are ready to rove the followng rooston: Prooston There exsts a unqe rce equlbru Wth 4 T k R = and T R = the followng holds: If R < then 5 T k T k 4 = The resultng balance S = s gven by T k S =

11 Frs rofts are 6 T kt T kt = 8T 8T If R R then 7 T = S = T 8 = 8 4 If R < then = = T T and S = T = = T 8T T 8T Proof see endx ccordng to Prooston three dfferent tyes of equlbru exst Whch one occurs deends on the network owner s argnal costs relatve to those of If s costs are substantally lower than s eg < R! hs rce wll be so low that the S-rule s volated; see Fgure > Fgure : rce equlbru wth S-rule beng volated 9

12 The second tye of equlbru s dected n Fgure = Fgure : rce equlbru wth S-rule beng exactly fulflled It occurs f s costs are oderately lower than s costs eg f R R s reacton curve then crosses s reacton functon n ts flat segent The network owner then chooses a rce whch exactly fulflls the S-rule The thrd tye of equlbru s shown n Fgure Fgure : rce equlbru wth S-rule beng fulflled In ths case has only a sall cost advantage or a cost dsadvantage relatve to eg R < and 's rce does not volate the S-rule Coarng the rces and rofts n 5 and 7 wth those stated n Prooston leads to the followng corollary: 0

13 Corollary If < R then the ntroducton of the S-rule wll lead both frs to ncrease ther rce Profts of both frs ncrease If R rces and rofts wll rean unchanged Proof: see endx Note that < R s equvalent to S < 0 see Lea Ths eans that n the absence of the S-rule the network owner would set hs rce below s argnal costs If the S-rule s leented however rcng below s argnal costs would volate the S-rule trggerng a sancton y ncreasng hs rce the network owner can reduce or avod the sancton When ncreases hs rce wll follow sut snce reacton functons are uward slong Indeed ths s what wll haen so that the ntroducton of the S-rule leads both frs to charge hgher rces akng all consuers worse off If R the S-rule does not affect the frs behavor Snce the network owner s rce whch revaled before the ntroducton of the S-rule does not volate t has no reason to change hs rce Snce s a best resonse to wll also contnue to charge the sae rce Note that a decrease n T ncreases the boundares R and R ; see equaton 4 Ths eans that a decrease n the degree of roduct dfferentaton enlarges the range of cost araeters where an leentaton of the S-rule affects eg ncrease frs rces n ntuton for ths result can be gven as follows Notce that S s nfluenced by T and through s rce s s both ncreasng n and T 4 a lower value of T allows a hgher value of wthout changng the sgn of S ut ths s equvalent to shftng R and R to the rght f T decreases see Fgure 4 S < 0 S = 0 S > 0 R R Fgure 4: Paraeter regons where the S-rule s volated exactly fulfllded fulflled but not exactly In the extree case of hoogeneous roducts and dentcal argnal costs each fr sets ts rce equal to argnal costs The balance S then s zero so that the S-rule s exactly fulflled In the case where the network owner s argnal costs are lower than those of hs rval he sets a rce slghty below s argnal costs n order to wn the whole arket lyng that the S-rule s slghtly volated On the other hand f has lower argnal costs wns the whole arket and the S-rule s not volated Wth hoogeneous goods the boundares R and R are dentcal and equal to The boundary R shfts to the rght f k decreases To understand ths recall that R delneates the regon where s rcng behavor trggers a sancton eg f < R fro Recall that S = 4 n ncrease n T gves ore arket ower leadng to a hgher rce

14 the zone where s rce leads to an exact fulfllent of the S-rule eg f R < R The sancton s a cost eleent for ncreasng ts rce If the sancton becoes less severe eg f k decreases hgher values of are coatble wth a negatve value of S and ths s equvalent wth R shftng to the rght f k becoes saller see Fgure 4 If k goes to zero R aroaches R and n the lt concdes wth R The boundary R s ndeendent of k The reason s that on the araeter sets dearcated by R s rcng behavor does not volate the S-rule and therefore the fne araeter does not lay any role n these regons 4 lternatve resonse strateges In Secton we have seen that the leentaton of the S-rule changes the strategc stuaton between frs We deterned the rce equlbru n the odfed gae and showed that the network owner accets the sancton f he has substantally lower argnal costs than hs rval eg f < R see Prooston It turned out that f the S-rule affects the frs rcng eg f < R rces wll be hgher than n the stuaton where the S-rule s not leented see Prooston In ths secton we analyze several alternatve strateges by whch the network owner ght resond to the ntroducton of the S-rule The frst alternatve resonse strategy RS we wsh to consder s: RS If the S-rule s leented chooses a best resonse to s rce under the condton that the S-rule s not volated Ths strategy s based on the decson of the network owner to strctly avod a confrontaton wth the cartel offce The objectve s accolshed by ncreasng the rce f necessary such that the new balance S s no longer negatve Prooston Suose that the network owner resonds to the ntroducton of the S-rule accordng to RS- If < R then rces wll be gven by T 9 = The resultng balance S = s equal to zero Frs rofts are T 0 = 8 4 If R then rces and rofts are the sae as those gven n art of Prooston The roof s slar to that of Prooston and therefore otted Fgure 5a llustrates the frst art of the roostton Snce at the forerly revalng rce the balance S s negatve wll ncrease hs rce by = S so that s new rce s = s best resonse to s = T / Gven no further rce change wll occur Fr has no

15 ncentve to devate snce hs rce s on hs reacton curve It s straghtforward to verfy that has no ncentve to ncrease hs rce further Moreover snce acts accordng to RS- he wll not decrease hs rce because ths would volate the S-rule The second art of Prooston s shown n Fgure 5b In ths case the constrant of RS- s not bndng so that frs choose utual best resonses = Fgure 5a: rce equlbru wth S-rule beng volated Fgure 5b: rce equlbru wth S-rule beng fulflled Coarng rces and rofts stated n Prooston wth those n Prooston leads to the followng corollary: Corollary If < R then = = > and > and f R then = and Thus f has substantally lower argnal costs than eg f < R then both rces and rofts are hgher than the resectve values n 4 and 5 Indeed ths wll be the case regardless of whether the network usage fee s roerly nflated or not The reason s that under RS- overall argnal costs of fr act as a rce floor for whch s bndng f R 5 Snce s better off by resondng accordng to RS- and also s better off t should be exected that wll choose resonse strategy RS- nstead of that descrbed n Prooston Of course the network owner could acheve a non-negatve balance S also by decreasng the network usage fee r snce ths wll reduce s overall argnal costs Ths observaton leads us to the second alternatve resonse strategy we wsh to consder: RS- S < 0 then resonds to the ntroducton of the S-rule by decreasng r such that the S-rule s exactly fulflled To rce changes of the network owner chooses a best resonse under the condton that the S-rule s not volated If S 0 leaves r unchanged and contnues to lay 5 Note that s not only bndng f R < but also f R R

16 Prooston Suose that the network owner resonds to the ntroducton of the S-rule accordng to RS- f < R then rces wll be gven by T = where s gven n 5 The resultng balance S = s equal to zero Frs rofts are = T T If R then rces and rofts are the sae as those gven n art of Prooston The roof s slar to that of Prooston and therefore otted If S < 0 the network wll decrease the network rce by r = S = whch decreases s argnal costs Wth argnal costs r s best resonse to s T / fter ths rce change no further rce change wll occur Fr has no ncentve to devate snce ts rce s on ts reacton curve Gven T / has no ncentve to ncrease hs rce above Moreover wll not decrease hs rce because ths would volate the S-rule Coarng rces and rofts descrbed n Prooston wth those n Prooston leads to the followng corollary: Corollary If < R then = = > and > and f R then = and Corollary states that fro s ont of vew and also fro s vewont resonse strategy RS- s weakly better than RS- gan ths wll be the case regardless of whether the network usage fee s roerly nflated or not Recall fro Corollary that rofts resultng fro RS- are also hgher than those arsng fro the behavor rescrbed n Prooston Thus snce s a roft axzng fr we can conclude that wll choose RS- f the Kartellat ntroduces the S-rule ccordngly n order to deterne the effects of the S-rule on the frs rcng behavor we have to coare the rces stated n Prooston wth those n 7 The followng Prooston contans the coarson of both rces and rofts Prooston 4 Suose that the Kartellat ntroduces the S-rule Then the followng holds: If < R then rces and rofts of both frs wll ncrease eg > and > If R then rces and rofts rean the sae Proof see endx Prooston 4 states that f the network owner s overall argnal costs s oderately or sgnfcantly lower than those of hs rval eg f < R then both frs wll set hgher rces than n the case where the S-rule s not leented Ths wll be the case regardless 4

17 of whether the network usage fee s roerly nflated or not Thus we arrve at a negatve judgeent of the S-rule The followng reasonng onts at a further weakness of the concet Elberfeld and von Wezsäcker 00 argue that the S-rule wll always be sleadng f the relevant cost eleents esecally the rocureent and retal suly costs are scalculated The rocureent costs cannot be sly regstered by the stock arket rce In the resence of long ter contracts the suler wll generate n any cases the ower by hself In ths case however the relevant rocureent costs are the varable average costs whch ght be lower than the stock arket rce The retal suly costs are redonantly consdered as varable by the cartel offce However the analyss of Elberfeld and von Wezsäcker 00 reveals that these costs are to a hgh degree rreversble and fxed Thus the rocedure of the cartel offce leads to an overestaton of the true and for the network owner s rcng decson relevant rocureent and retal suly costs Fnally we wsh to ont out that the obtaned results are not restrcted to the electrcty ndustry In fact they readly aly to any network based ndustry lke gas and telecouncaton 5 Concluson In order to detect excessve network usage rces the workng grou electrcty network utlzaton of the anttrust dvsons of the federal reublc and the states roosed to ntroduce the S-rule Under ths rule the cartel offce would calculate the dfference between the network owner s rce and overall argnal costs of the rval ncludng network access charges whch the coettor has to ay to the network owner If ths value s negatve t would be concluded that network access charges are roerly nflated One roble of ths rule s that the calculated value can be negatve even f the rce for network usage s arorately set Ths outcoe s ost lkely to occur f the network owner s substantally ore effcent than hs rval Snce the network owner s unshed f he volates the S-rule the ntroducton of t changes hs ncentves y ncreasng hs rce the network owner can reduce or avod the sancton If he ncreases hs rce the rval wll ncrease hs rce as well snce reacton functons are uward slong Indeed ths s what haens so that the ntroducton of the S-rule leads both frs to charge hgher rces akng all consuers worse off If the network owner has only a sall effcency advantage or s even less effcent than the rval the S-rule does not affect the behavor of the frs In ths stuaton rces wll be the sae as before the ntroducton of the S-rule References Elberfeld W and C C von Wezsäcker 00 Ist der Subtraktonstest en geegnetes Verfahren zur Erttlung ssbräuchlch überhöhter Netznutzungsentgelte? eo Unversty of Cologne Hotellng H H 99 Stablty n coetton Econoc Journal vol Joskow P00 Transacton Cost Econocs nttrust Rules and Reedes Journal of Law Econocs and Organzaton Vol 8 no

18 endx Proof of Lea We roceed n three stes If ly that < then the equatons and = T k Solvng = 0 for gves k T = = kt wth gven n 4 s s reacton functon as long as < Snce ths nequalty s equvalent to < k T t follows that = kt s s reacton functon f nequalty holds In a slar way one shows that f > = s s reacton functon f < It reans to be shown that = f 4 k T We show that for all satsfyng the nequaltes n 4 and for all 5 > 0 If < and ly that whle = T = k T It follows that 5 holds f and only f > k T Ths nequalty s satsfed snce by assuton < and > k T If > then 5 s equvalent to < Ths nequalty s holds because > and < Proof of Prooston The equlbru s deterned by the ntersecton of s reacton functon gven n 4 wth s reacton functon n Snce s reacton functon s flatter than the nverse of s and starts wth hgher values t s clear that at ost one equlbru 6

19 can exst crosses the secton of wth values saller than f and only f < k T see also Fgure Snce = T / the nequalty s equvalent to < k T Solvng s reacton functon for leads to = T The soluton of k T = = T gves the equlbru rce = / k T It follows that s equlbru rce s = / 4/ k T ntersects the constant art of = f and only f k T T s equlbru rce s the soluton of = = T whch s = / T crosses the art of wth values larger than f and only f T < s equlbru rce s the soluton of T = = T = / T whch s = / T It follows that s equlbru rce s Proof of Corollary Suose that < R Then t s easly checked that for = n 5 s greater than n 5 snce k > 0 lso coarng the rofts n 7 wth those n 6 edately shows that > and < ssue that R R Coarng rces n 5 wth those n 7 shows that both < and < are equvalent to < R Next observe that 7

20 / / = T 8T < T 8 = < / T = R where the latter nequalty s fulflled by assuton Thus s rofts wll be hgher after the ntroducton of the S-rule The sae holds for s rofts To see ths observe that T 6 = 8T 4 s decreasng n Thus the dfference s negatve for all < / T = R f t negatve for = / T or equvalently for = / T Substtutng ths value nto 6 gves = / 8 9 / 8 < T T 0 If R the rces and rofts descrbed n Prooston are the sae as those gven n Prooston Proof of Corollary Suose that < R Coarng rces n 5 wth those n 9 shows that both < and < are equvalent to < R The latter nequalty s fulflled snce < R and R < R Coarng rofts n 6 wth those n 0 reveals that < s equvalent to < R where the latter nequalty s satsfed by assuton To rove that < t suffces to show that < because < ; s gven n 7 It can be easly checked that the nequalty < s equvalent to / T 6T 7 < 0 8T Note that T < 6 les T < les that 6 T < Thus 7 holds f and only f / T < 0 or equvalenty f < R The latter nequalty s fulflled because < R by assuton and R < R by defnton If R the rces and rofts gven n Prooston and are the sae Proof of Corollary Suose that < R Coarng rces n 9 wth those n shows that both < and < are equvalent to < R Slarly one has that < = s equvalent to < R If R the rces and rofts the rces and rofts gven n Prooston and are dentcal Proof of Prooston 4 Suose that < R Coarng rces n 5 wth those n 9 shows that both < and < are equvalent to < R Slarly one has that > s equvalent to < R Thus s rofts wll be hgher after the ntroducton of the S-rule The sae holds for s rofts To see ths observe that T 8 = 8T 4 6 The nequalty holds because we have assued that both frs roduce ostve quanttes n equlbru 8

21 s decreasng n negatve for Thus the dfference s negatve for all < / T = R f t = / T or equvalently for = / T Substtutng ths value = / 8 T 9 / 8 T < nto 6 gves 0 If R the rces and rofts descrbed n Prooston are the sae as those gven n Prooston In the roof of Corollary we showed that > If R the rces and rofts stated n 5 and 7 are the sae as those stated n art of Prooston 4 9