FORECASTING MARKET PRICES OF ELECTRIC POWER AFTER DEREGULATION IN THE U.S.: METHOD AND APPLICATION

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1 FORECASTING MARKET PRICES OF ELECTRIC POWER AFTER DEREGULATION IN THE U.S.: METHOD AND APPLICATION by Vladmr V. Starkov * West Vrgna Unversty Abstract The model developed n ths paper provdes forecast of regonal equlbrum prces of electrc power after the transton to retal competton. The nteracton among electrc utltes s assumed to be bounded by the present NERC regons wthn the U.S. The results of the Cournot model are contrasted wth Bertrand soluton and the regulated prces. It s found that Bertrand (compettve) prces are lower than average cost prces, but olgopoly prces are consderably hgher. Predcted market power vares substantally among NERC regons, due prmarly to dfferences n average costs of producers. Industry concentraton has a lesser effect on prces because of contestablty. JEL Classfcaton: D43, L13, L94 Key Words: Olgopoly, Market Power, Electrc Utlty Industry, Deregulaton Ths s a workng paper n progress. Please do not quote wthout the author s consent * West Vrgna Unversty, Department of Economcs, P.O. Box 6025, Morgantown, WV , tel.: (304) , fax: (304) , e-mal: vstarkov@wvu.edu

2 1. Introducton Under tradtonal regulaton, nvestor-owned electrc utltes generally earn an adequate rate of return. Whle some mght expect utltes to resst deregulaton that creates a more compettve and uncertan envronment, some utltes have embraced FERC Order 888 and the subsequent state-level movement toward competton n retal transactons. The support of deregulaton by some power producers may arse from the fact that certan utltes beleve they stand to gan from deregulaton because the open market prces wll be hgher than the regulated rates they charge presently. Some other producers, however, stand to lose from the transton to competton. 1 Ths study develops a method to measure the amount of market power obtanable by U.S. electrc utltes after deregulaton of the retal electrcty market. Interacton among electrc utltes s assumed to occur wthn the regons set by the North Amercan Electrc Relablty Councl (NERC). 2 Holdng companes and ndependent nvestor-owned electrc utltes are assumed to be olgopoly players, whle other producers n the regon are consdered prce-takers. The proposed method s appled n all the ten exstng NERC regons to estmate equlbrum market prces for both Cournot and Bertrand cases of olgopoly. In addton, ndexes of market power are calculated for every regon. I thank Stratford Douglas for helpful comments and gudance of my research. I am also ndebted to Russell Sobel and Kevn Forbes for ther valuable dscusson of the paper. 1 One most obvous dstncton can be drawn between hgh- and low average cost producers. 2 The reason to delneate future markets for electrcty accordng to the boundares of the NERC regons s that physcal constrants lmt transfer of power between NERC regons. Also, n some regons, such as MAAC, the frms hstorcally have operated as a common power pool. 1

3 Whle estmates of changes n market power after deregulaton usng ex post data are common n the academc lterature, measurements of such changes ex ante are far less numerous. Studes by Green and Newbery (1992) and Green (1996, 1999) utlzed a supply functon method developed by Klemperer and Meyer (1989). Those studes modeled margnal costs of producers as ether constant or lnear. On the other hand, von der Fehr and Harbord (1993) argued that cost functons of the UK electrcty producers are better represented by step functons. A stepwse functon of average varable costs was used by Rudkevch et al. (1998) to calculate nstantaneous market clearng prces assumng nteracton among n dentcal proft-maxmzng frms. Andersson and Bergman (1995) used a conjectural varaton model of olgopoly to fnd the equlbrum prce and to explore the effect of frm sze and the number of frms n the market on the prce level. The analyss, appled to Swedsh electrc ndustry, showed that n Nash equlbrum unregulated prces wll be hgher than they are under regulaton. An assessment of future market power n Calforna and New Jersey electrcty markets was made by Borensten et al. (1999a,b). Although analyss n ths paper has the same goal as that performed by Borensten et al., ths study s sgnfcantly dfferent n many aspects. My paper has a broader scope of nqury that covers the entre terrtory of the U.S. Whle Borensten et al. analyzed market power under dfferent demand condtons at several perods of the year, my study presents annual averages of prces and ndexes of market power. Lke Borensten et al., I do not attempt to model dynamc competton whch, n partcular, would nclude possbltes of entry and ext. Yet some dynamc aspects may be 2

4 captured by usng several dfferent demand elastctes n the analyss. Relatvely nelastc demand s characterstc of the short run, and relatvely elastc demand of the long run. Whle Borensten et al. (1999a,b) modeled cost curves of generators usng hstorcal cost and capacty data, parameters of producers margnal cost functons used n ths study are derved from estmates of translog total cost functon. Borensten et al. (1999a) forecast the prce of electrcty delvered to consumers. Such a forecast must account for the costs of transmsson and dstrbuton. They modeled those costs by addng a constant markup to the producton costs of all the generators. My analyss nstead focuses on prces at generaton stes. I do not attempt to model transmsson effects because even wth the compettve power generaton, transmsson wll most lkely reman regulated and thus transmsson charges wll be determned outsde of the market realm. Further, the papers by Borensten et al. (1999a,b) consder only the Cournot type of olgopoly. My study models both Cournot and Bertrand cases. A consderaton that supports the Bertrand outcome n the future market for electrcty s the dsncentve to rase prces above margnal cost that may come from mplementng the market structure known as poolcos. In a poolco the rght to make actual sales wll be gven to the supplers who submt the lowest prce bds. However, as several studes have shown, the possblty of exercsng market power n the poolco s also qute concevable. One strategy descrbed by Rudkevch et al. (1998) nvolves a cooperatve agreement among producers to bd above margnal cost. The other strategy outlned n Newbery (1995) and Wolak and Patrck (1997) s strategc wthholdng of low-cost unts from operaton and bddng the output of more expensve unts to drve prces up. Emprcal evdence of market power exercsed by electrcty producers n aucton 3

5 markets of England and Wales s found by Wolfram (1998). If one accepts the feasblty of exercsng market power, the Cournot model becomes a sutable tool to obtan equlbrum prces. The structure of the paper s as follows. Secton 2 outlnes the method, Secton 3 descrbes the data used for the emprcal study, Secton 4 presents the results, and Secton 5 concludes the paper. 2. Model Both Cournot and Bertrand models of olgopoly can be derved from a conjectural varaton model p*(y) + p Y 1+ Y y y = MC (y ), (1) where p* s the equlbrum prce, Y s the total market supply, y s the supply by the frm, Y - denotes total output of all frms except, and MC represents the margnal cost. Ths specfcaton (1) embodes all the classcal models of olgopoly as specal cases dependng on the value of the conjectural varaton parameter Y y. The Cournot model s obtaned when the conjectural varaton s equal to 0. The Bertrand outcome follows when the conjectural varaton s equal to -1. A compettve outcome where producers prce ther output at margnal cost can be found by usng Bertrand conjectures n the model (1). The supply condton for a sngle frm s then gven by 4

6 p*(y) = MC (y ) (2) The method of fndng the Bertrand prce used here s smlar to the compettve cost analyss descrbed by Torres (1998). Market supply s found by addng up supply curves of producers, whch are dentcal to the producers' margnal cost functons n a compettve market. Parameters of the margnal cost functon are obtaned by estmatng a translog total cost functon (see Appendx 1 for detals). Market demand s set exogenously at ts latest hstorcal level (or, alternatvely, at the level projected n the future). The market-clearng equlbrum prce p* B wll then be equal to the margnal cost of the hghest-margnal-cost producer(s) at the pont where market supply s equal to market demand. A detaled descrpton of the method used here to obtan the Bertrand prces s presented n the Appendx 2. Alternatvely, equaton (1) solved for the Cournot case produces the reacton functon of the frm 3 θ p*(y) 1+ = MC (y ), (3) α where α s the prce elastcty of market demand, and θ s the market share of frm, so that θ = 1. The aggregate market supply s obtaned by multplyng both sdes of expresson (3) by θ and summng up across all the n frms, θ θ p *( Y) 1 + = θ MC ( y ). (4) α After collectng terms and smplfyng notaton, equaton (4) can be wrtten as 3 See ths result, e.g. n Varan (1992), p

7 h p* 1+ α = θ MC (y ), (5) where h θ 2 by analogy wth the Herfndhal ndex of ndustry concentraton expressed n decmals. Substtutng the defnton of margnal cost, MC = TC y, and the defnton of market share, θ = y /Y nto (5), a smple rearrangement leads to where ε s the elastcty of total cost wth respect to output of frm. p* = 1 α ε TC Y α + h, (6) Equaton (6) allows us to estmate the equlbrum olgopoly prce ex ante, that s, before the actual olgopoly game begns. The values of the parameters n equaton (6) are found as follows. Market output Y s set exogenously at ts latest hstorcal level. 4 The prce elastcty of market demand α s taken to be wthn the range suggested by varous expert evaluatons. An analyss of the prce senstvty to the elastcty of demand s then conducted. The output-cost elastctes ε are computed after estmatng parameters of the translog total cost functon (see Appendx 1 for the detals on calculatng ε s). To determne the equlbrum Cournot prce p* C, a smulaton study was conducted. Reacton functons of every producer n the olgopoly were calculated as the proft-maxmzng response n output to a gven market prce. The algorthm starts wth a certan exogenous prce of electrcty common for all 6

8 producers, and frm-specfc levels of output. Every frm then chooses ts optmum output wthn ts own capacty constrants, expectng ts rvals to hold constant ther levels of producton. Summaton across the frms gves a new level of the aggregate supply. The new market prce s computed from the constant-elastcty demand functon p = Y D k 1 α where Y D s the market demand, p s the prce, α s the prce elastcty of demand, and k s a parameter. The market clearng constrant s mposed, so that Y D = y. The new prce level becomes an nput for the next teraton of the output optmzaton. The teratons are termnated when the aggregate output changes by less than 1%. The addtonal assumptons used n the method are as follows. Lke Borensten et al. (1999a,b), I assume that olgopoly supples the resdual demand after the supply of the prce-takng frms s controlled for. The value of k s found usng the assumpton that the demand curve passes through the hstorcal pont of demand. Specfyng the value of k, however, s problematc because under regulaton there was no unform market prce of electrcty, rather electrcty rates were based on average costs of generaton and regulated rates of return on captal. The problem of unform ntal prce was mtgated by senstvty study when several dfferent prce levels were used to ntalze the algorthm. The ntal prces were selected based on the average prces faced by consumers n every NERC regon reported by the Energy Informaton Admnstraton Data 4 Alternatvely, t could be set at the projected level of demand n the future. 5 Energy Informaton Admnstraton. Electrc Power Annual,

9 Because ths research ams to forecast prces of electrcty at generaton stes, the cost data used pertan to the generaton sector of electrc utltes. The data have been obtaned from the followng sources. The hstorcal cost and output data were retreved from the database on U.S. electrc utltes publshed by Utlty Data Insttute (UDI). The nformaton on utlty bond ratngs necessary for the estmaton of the cost of captal was obtaned from Moody s Electrc Utltes Manual. The hstorcal prces of utlty stocks and returns on utlty equty were found n the Compustat database. The prce elastcty of market demand for electrcty used here les wthn the range suggested by varous studes. 6 I conduct a senstvty analyss of the olgopoly equlbrum prce wth respect to the elastcty of demand. The emprcal analyss covers all ten NERC regons. The tme perod of the observatons s from 1982 to The sample conssts of all electrc producers n the U.S. classfed as ether ndependent nvestor-owned utltes or holdng companes. Throughout the sample perod the structure of the ndustry s assumed to be fxed at the state t was at the end of Utltes that were parts of holdngs at the end of 1998 were treated as such from begnnng to end of the sample perod, and companes that by the end of 1998 were formed as result of mergers were treated as aggregated throughout the sample. Electrc utltes that ceased operatons before 1998 were excluded from the sample. The total number of electrcty producng frms n the sample s 99. The panel data set therefore conssts of 1584 observatons. Ths sample s larger than most other studes have used before. Also aggregaton at the holdng company level, as opposed to the producer level, gves a new perspectve to the analyss. For 6 Several recent studes used the followng absolute values of own-prce demand elastcty. Borensten et al. (1999a): 0.1, 0.4, and 1.0; Andersson and Bergman (1995): 0.3 and 0.6; Green and Newbery (1992) values range from 0.08 to Estmates of long run demand-prce elastctes by Halvorsen (1978) vary from 1.00 to 1.21 for resdental sector 8

10 the defntons of varables used n the estmaton and the methods by whch they were obtaned see Appendx 3. The mean sample values for the varables used n the study are reported n Table 1. Table 1 goes about here. 4. Results At the frst step, parameters of the total cost functon are obtaned by estmatng the translog specfcaton. The results of the translog functon estmaton are presented n Table 2. Table 2 goes about here. All the parameters of the translog cost functons are statstcally sgnfcant, yet only four out of nne regonal dummes are sgnfcant at the 5% level, and two more are sgnfcant at the 10% level. Monotoncty condtons were satsfed at every observaton. Concavty condtons were not satsfed consstently, however, as noted n Thompson et al. (1996), p. 37, estmaton of scale economes or other relatonshps between output level and cost s not affected by the ncomplete satsfacton of the concavty restrctons. Although negatve sgns of coeffcents for labor and fuel are contrary to those commonly reported, calculated elastctes of total cost wth respect to labor and fuel are postve. The coeffcents of the translog cost functon were used to estmate frm-specfc elastctes of total cost wth and from 1.53 to 1.75 for ndustral and commercal sectors. Short run demand elastctes of the resdental sector le between 0.48 and 0.78, and the short run estmate for the ndustral sector s equal

11 respect to output as well as the parameters of frm-specfc margnal cost functons. Then smulatons were conducted to obtan Bertrand and Cournot prces. The results of the smulaton study are presented n the Table 3. The number of olgopoly players n every regon shows the number of producers used n smulatons. Compettve prces reported here represent those formed n an aucton when producers bd prces equal to the margnal cost of generaton, and every unt of output s sold at the market-clearng prce. The compettve prces also correspond to those formed under the Bertrand model of olgopoly. Table 3 goes about here. The Cournot prces were obtaned by the teratve procedure descrbed above. To ntalze the algorthm, two dfferent types of condtons were tested. One that used hstorcal prces and hstorcal output levels represents a smultaneous transton for all the producers from regulaton to an open market regme. (Because under regulaton generators do not sell output at a unform prce, several ntal prces were used). However, f dfferent electrc utltes face dfferent tmeframes for transton, a market power regme wll be unlkely to develop untl the transton s completed by all the producers. Then n the short run, they argued, producers wll prce ther output at margnal cost. Ths scenaro was modeled by usng Bertrand prce and output as a startng pont for teratons. The results obtaned wth both ntalzaton methods were very close. The means and standard devatons of the Cournot prces are presented n Table 3. 10

12 In general, the Cournot teraton method dsplays a robust convergence. The varance of the resultng prces was lower than the varance of the startng values n most trals. The Cournot prces were estmated for several dfferent elastctes of market demand for electrcty that le wthn the range of expert evaluatons, and tend to rse as prce elastcty of demand decreases n absolute value. Ths s because an olgopoly can mantan hgher prces n a market wth less elastc demand. In addton to demand elastcty, olgopoly prce s nfluenced by the sum of average total costs of producers. 7 The hgher the average total costs, the hgher s the equlbrum prce. Ths explans why regons wth low concentraton do not always get the lowest estmated olgopoly prces (e.g. NPCC). Table 3 also lsts the regulated prces. They were calculated accordng to the followng procedure. In smplfed terms, regulators set electrcty prces by addng a certan rate of return to producer s average total cost. Assumng away the dfference among types of electrcty consumers, and gnorng the prce markup that comes from the regulatory rate of return, producers average total cost can serve as an approxmaton of prces charged to consumers. Hence, computng an average of producers average total costs weghted by respectve market shares approxmates the average level of prces n a regon under regulaton. 7 Ths can be seen mathematcally when the defnton of total market supply Y = y s substtuted nto the α TC formula (6), whch becomes p*= ε. α+ h y 11

13 Comparson of the regulated prces wth the compettve prces suggests that f the future market for retal sales of electrcty s perfectly compettve, the prces of electrcty at generaton stes wll go down n every regon except ECAR and NPCC. Secondly, comparson of the regulated prces and the Cournot prces suggests that n the case of producers exercsng market power, retal competton wll result n hgher prces to consumers, although n several regons prces may go up only by a small margn (e.g. WSCC, SPP). It s worth a remnder that the model estmated n ths study explctly assumes away trade wth other regons. Condtons that promote nter-regonal power exchange may be desrable to assure that retal prces of electrcty wll not rse sharply due to market power. Prce markups are most often represented numercally wth ndexes of market power. I provde the two most commonly used ndexes of market power, the Lerner ndex and the Prce-Cost Margn Index (PCMI). They are defned as follows Lerner Index = Actual Product Prce "Perfectly Compettve" Product Prce * 100%, (7) Actual Product Prce PCMI = Actual Product Prce "Perfectly Compettve" Product Prce * 100%, (8) " Perfectly Compettve" Product Prce where the perfectly compettve prce s equal to the margnal cost of the product. Those ndexes summarzed n Table 4 pont to the concluson that the degree of market power n dfferent regons wll vary substantally. Accordng to the Department of Justce gudelnes, a market can 12

14 be consdered compettve f prces do not exceed ther perfectly compettve level by more than 5%. 8 My results ndcate that f electrcty demand s unt-elastc, whch approxmates the long run, future prces for power may approach ther perfectly compettve level n several regons (ECAR, WSCC), but most regons wll experence a moderate degree of market power even n the long run. Table 4 goes about here. The lowest across-the-board prce markups are found n ECAR and WSCC, and the hghest ones n ERCOT. The general trend s that, gven the same prce elastcty of demand, the larger markups are observed n the regons wth smaller number of compettors. Markups are hgher the more nelastc s demand for electrcty. Observatons of the producers levels of output obtaned n smulatons suggest that after deregulaton generaton of electrc power n many regons may take a form of contestable markets. In the smulaton, the low-cost generators operatng at maxmum capacty can supply enough power to meet baseload demand, whle hgher-cost utltes sell power only at peak demand. Yet hgher-cost producers stand ready to expand ther output as soon as the low-cost 8 U.S. Department of Justce and Federal Trade Commsson, Statement Accompanyng Release of Revsed Merger Gudelnes, Aprl 2,

15 producers attempt to exercse market power. The condtons requred for contestable markets descrbed by Scherer and Ross (1990), chapter 10, ncludng neglgble sunk cost of entry and the ablty of the entrant to recover ts fxed and varable costs before ncumbents can respond, may be present n electrcty markets. In partcular, generators wth already operatonal capacty have very low sunk costs of entry; n a daly power exchange aucton ther sunk costs of entry would consst prmarly of the costs assocated wth submttng bd schedules. Daly auctons would also restrct the ablty of ncumbent frms to react to entry nstantaneously. Should the entrant s bd be accepted, the entrant wll be able to sell ts output that day wthout facng any retalaton from the ncumbents. Electrcty markets wll also be subject to another, tradtonal, form of entry when new low-cost capacty s bult. It s an open queston whch of the two possble forms of entry wll be predomnant n realty, but ther exstence wll undoubtedly form an ncentve for the ncumbent generators to keep prces low. There are several more reasons to beleve that the forecast prces calculated accordng to Cournot model reflect an upper bound of future prce rather than a mean outcome. Frst, there s broad agreement that the cost of power generaton wll go down as the ndustry s deregulated and compettve market ncentves reduce overcaptalzaton and ncrease effcency. The second reason was ponted out by Green (1999). Accordng to Green, observatons of the Englsh spot market for electrcty show that generators can rase prces well above margnal costs; however, f generators sell the entre volume of output forward, the ncentve to rase prces above margnal cost dsappears. If rsk-averse generators 14

16 seek to hedge ther rsk by enterng forward contracts, prces of electrcty may converge to margnal costs. 5. Concluson Ths study descrbes the method of forecastng electrcty prces that wll preval n the future market open to retal competton. The results of both Bertrand and Cournot types of olgopoly are presented. The paper shows how the translog cost functon can be used n the Cournot model. The method s appled to estmate equlbrum prces n the markets for electrc power bounded by exstng NERC regons. The projected prces are compared wth those under regulaton. The degrees of market power are assessed for every market. Results of the emprcal study ndcate that the predcted degree of market power vares from one NERC regon to another. If the future retal market for electrcty operates as perfectly compettve, prces for electrc consumers wll go down from ther regulated level n most regons. If producers are able to exercse market power as Cournot olgopolsts, unregulated markets wll result n prces hgher than those under regulaton. In the latter case the prce markups above the compettve level vary from one regon to another. These markups are postvely correlated wth average total costs of producers and negatvely correlated wth prce elastcty of market demand for electrcty. The degree of market concentraton has a lesser effect on the Cournot prce because most regonal power pools wll take a form of contestable markets. Ths wll put downward pressure on prces of ncumbent producers. The 15

17 results of the Cournot model lkely represent the upper bound of the future electrcty prces, whle the Bertrand prces represent ther lower bound. Thus the study provdes both the best- and the worstcase scenaros of the electrcty ndustry deregulaton. 16

18 Appendx 1 Estmaton of the Translog Total Cost Functon Output cost elastctes can be obtaned by estmatng parameters of the total cost functon. The translog cost functon developed by Chrstensen and Greene (1976) has the advantage of not mposng a pror restrctons on the elastcty of substtuton between the factors of producton. I begn wth the followng specfcaton. ln TC = α 0 + β L ln p L + β F ln p F + β K ln p K + β Y ln y β LL (ln p L ) β FF (ln p F ) β KK (ln p K ) β YY (ln y) 2 + β LF ln p L ln p F +β LK ln p L ln p K +β FK ln p F ln p K + γ YL ln p L ln y + γ YF ln p F ln y + γ YK ln p K ln y (A.1.1) Here subscrpts L, F, K are used for labor, fuel and captal respectvely; p X denotes prce of the nput X; y denotes output. To obtan effcent estmates, the above specfcaton s commonly estmated smultaneously wth the nput cost share equatons. The usual restrctons of homogenety of degree one n nput prces and symmetry of nput prce cross-effects are mposed as well. Ths leads to the system of equatons ln TC p K = α 0 + β L ln p L pk + β F ln p F pk + β Y ln y 17

19 + 1 2 β LL (ln p L pk ) β FF (ln p F pk ) β YY (ln y) 2 +β LF ln p L pk ln p F pk + γ YL ln p L pk ln y + γ YF ln p F pk ln y (A.1.2.a) s L = β L + β LL ln p L pk + β LF ln p F pk + γ YL ln y (A.1.2.b) s F = β F + β FF ln p F pk + β LF ln p L pk + γ YF ln y (A.1.2.c) Equatons (A.1.2.a-c) are estmated as a seemngly unrelated system wth the usual restrctons of homogenety of degree one n nput prces and symmetry of nput prce cross-products. The elastctes of total cost wth respect to output are then calculated for each frm at the means of observatons accordng to the followng formula ε = lntc ln y p = β Y + β YY ln y + γ YL ln p L K p + γ YF ln p F K (A.1.3) 18

20 Appendx 2 The method of calculatng Bertrand prces. The method uses the addtvty of the market supply functon and the fact that margnal cost functons of producers represent ther supply curves n a compettve market. Margnal costs of producers can be obtaned usng the relatonshp establshed by formula (A.1.3) ε = lntc ln y = TC y y TC = MC, (A.2.1) ATC where ATC denotes average total cost of the frm. Substtutng the expresson for ε from (A.1.3) nto (A.2.1), margnal cost s expressed as MC (y ) = p L pf ATC β Y + βyy ln y + γyl ln + γyf ln. (A.2.2) pk pk Thus, after the coeffcents of the total cost functon (A.1.2) are estmated, margnal cost functons for every producer can be computed accordng to the formula (A.2.2), assumng that average total cost remans constant wthn the range of output consdered. In the Bertrand case, every frm wll choose to produce the amount of output at whch margnal cost s equal to the market prce. Thus, the supply curve of a frm n Bertrand olgopoly can be wrtten as ln y = 1 β YY p' ATC β Y γ YL p ln p L K γ YF p ln p F K, (A.2.3) where p' s the market prce. 19

21 Total market supply s found by addng up the supples of all producers. By varyng p' exogenously a pont can be found at whch the total market supply s equal to the certan level of demand set at ts hstorcal or projected value. Ths prce p* B s a market equlbrum prce n the Bertrand model. The prce p* B wll be equal to the margnal cost of the hghest-margnal-cost producer(s) n the market. In a broad enough market t wll lkely be the case that some producers wll have margnal cost lower than p* B at any level of output. In the Bertrand olgopoly those nfra-margnal (baseload) producers wll operate at full capacty, and earn an economc rent. Some other producers' margnal cost may be lower than p* B at some range of output, and exceed p* B n another range of output. Those producers wll be margnal (or peakng) producers. The output of margnal producers wll fluctuate greatly dependng on nstantaneous demand. Margnal frms wll only use a part of ther capacty at a tme. The most expensve generators of the margnal frms wll earn zero economc proft at any gven tme perod. Yet other producers may have margnal cost exceedng p* B at all levels of output. Such producers wll make economc losses and eventually wll be phased out of the market. 20

22 Appendx 3 Descrpton of Data Used to Estmate the Translog Total Cost Functon The varables for the translog cost functon estmaton were obtaned as follows. TC - Total Cost. Combned cost of operaton and mantenance, fuel, and labor, thousands of dollars per year. p L - Prce of labor. Annual salares and wages per employee, thousands of dollars. p F - Prce of fuel, dollars per BTU. y - Output, MMWhr/year p K - Prce of captal. Estmated as a weghted average of prces of debt and equty. The nomnal prce of long-term debt s taken equal to yeld on utlty bonds ssued durng the perod under consderaton. Because the overall ratng of the frm s debt affects ts cost of borrowng, ratng of newly ssued bonds was matched wth the ratng of the partcular utlty s debt. The prce of equty was obtaned accordng to the model of dvdend growth (see, e.g., Morn, 1984). The prce of equty captal at the tme perod t s expressed as p Kt = (D t+1 /p St ) + g, where D t+1 s an expected dvdend per share, D t+1 = D t (1+g), p St s current perod stock prce, g s an expected rate of dvdend growth (obtaned as an estmate from the exponental growth model based on 20-year hstorcal rates of growth). Usng the expresson for D t+1, p Kt can be presented as p Kt = D t (1+g)/p St + g, where D t /p St s the yeld n perod t. All nomnal varables were converted nto real values expressed n constant 1996 dollars. 21

23 References Andersson, B., and L. Bergman, 1995, Market Structure and the Prce of Electrcty: An Ex Ante Analyss of the Deregulated Swedsh Electrcty Market, The Energy Journal, v.16, n.2, Borensten, S., J. Bushnell, 1999a. An Emprcal Analyss of the Potental For Market Power In Calforna s Electrcty Industry, Journal of Industral Economcs, v.47, n.3, , J. Bushnell, and C.R. Knttel, 1999b. Market Power n Electrcty Markets: Beyond Concentraton Measures, Energy Journal, v.20, n.4, Chrstensen, L., and W. Greene, Economes of Scale n the U.S. Electrc Power Generaton, Journal of Poltcal Economy, v. 84, n. 4, von der Fehr, N. and D. Harbord, Spot Market Competton n the UK Electrcty Industry, The Economc Journal, 103, Green, R., 1996, Increasng Competton n the Brtsh Electrcty Spot Market, Journal of Industral Economcs, v. 44, n. 2, , The Electrcty Contract Market n England and Wales, Journal of Industral Economcs, v. 47, n. 2, and D.M. Newbery, Competton n the Brtsh Electrcty Spot Market, Journal of Poltcal Economy, v. 100, n. 5, Halvorsen, R., Econometrc Models of U.S. Energy Demand. D.C. Heath and Co., Lexngton, MA. Klemperer, P. and M. Meyer, Supply Functon Equlbra n Olgopoly Under Uncertanty, Econometrca, 57, Morn, R.A., Utltes Cost of Captal, Publc Utltes Reports. Newbery, D.M., Power Markets and Market Power, The Energy Journal, v.16, n. 3, Rudkevch, A., M. Duckworth, R. Rosen, Modelng Electrcty Prcng n a Deregulated Generaton Industry: The Potental for Olgopoly Prcng n a Poolco. The Energy Journal, v.19, n

24 Scherer, F.M. and D. Ross, Industral Market Structure and Economc Performance, 3rd ed., Houghton Mffln Company, Boston, MA. Thompson, H.G., D.A. Hovde, L. Irwn, wth M. Islam, and K. Rose, Economes of Scale and Vertcal Integraton n the Investor-Owned Electrc Utlty Industry, The Natonal Regulatory Research Insttute, Columbus, OH. Torres T.F., Compettve Cost Analyss n the Mneral Industres, Resources Polcy, v.24, n Varan, H.R., Mcroeconomc Analyss, 3rd ed., W.W. Norton & Co., Inc., New York, NY. Wolak, F., and R. Patrck, The Impact of Market Rules and Market Structure on the Prce Determnaton Process n the England and Wales Electrcty Market. Presentaton at the 18th Annual North Amercan Conference of the USAEE/IAEE. San Francsco, CA. Wolfram, C.D., Strategc Bddng In a Multunt Aucton: An Emprcal Analyss of Bds to Supply Electrcty In England and Wales, RAND Journal of Economcs, v.29, n

25 Table 1. Mean Sample Values for the Varables Used n the Study a. Varable Mean Value Total Cost of Generaton ($ 000) 1,740,427 Net Generaton (MWhr) 20,103,520 Prce of Labor ($ 000) Prce of Fuel ($/MMBTU) Prce of Captal (%) 6.26 a. All cost data are n constant 1996 dollars. 24

26 Table 2. Coeffcents of the Translog Cost Functon. a, b α * ECAR (0.382) (0.025) β L * ERCOT 0.349* (0.028) (0.039) β F * FRCC (0.027) (0.043) β Y 0.393* MAAC 0.053** (0.054) (0.028) β LL 0.608* MAIN * (0.002) (0.027) β FF 0.568* MAPP ** (0.002) (0.029) β YY 0.031* NPCC 0.494* (0.004) (0.024) β LF 0.418* SERC (0.001) (0.036) γ YL * SPP 0.087* (0.002) (0.028) γ YF 0.013* (0.002) * Sgnfcant at 5% level. ** Sgnfcant at 10% level. a. Standard errors n parentheses. b. In addton to the results presented, three other specfcatons were estmated. One of them contaned dummes for the frms that generate 10 or more percent of ther total output usng hydro power. Another had a tme trend to account for techncal change. The thrd specfcaton had no dummy varables. The coeffcents of the translog functon obtaned n all the four cases have the same sgns, wth the excepton of one coeffcent, and most are very close n magntude. The excepton s the second-order coeffcent of generaton, β YY, whch s nsgnfcant n the model wth the dummes for hydro power and n the model wth the tme trend. The coeffcent of β YY changes to negatve, and sgnfcant n the model that has no dummes. The present specfcaton s chosen because t renders an ncreasng margnal cost functon. A complete set of estmates s avalable from the author upon request. 25

27 Table 3. Projected Prces of Electrcty a. NERC Regon Number of Olgopoly Players Compettve Prce b, $/MWhr Regulated Prce c, $/MWhr Cournot Prce, $/MWhr Prce Elastcty of Demand ECAR (2.83) (3.83) (2.02) (9.98) ERCOT d (1.14) (2.07) (59.26) FRCC d (9.99) (0.66) (1.22) MAAC (3.29) (2.69) (3.48) (14.62) MAIN (3.84) (6.31) (10.41) (8.43) MAPP (3.25) (2.71) (5.52) (14.86) NPCC (0.35) (10.13) (10.43) (21.89) SERC (2.10) (5.19) (9.15) (16.25) SPP (1.45) (2.96) (1.33) (4.99) WSCC (2.44) (2.85) (9.81) (16.13) a. Standard errors n parentheses. b. Computed accordng to the Bertrand model of olgopoly. c. Computed as the means of producers average total costs weghted by producers market shares. d. At these values of elastcty prces grow explosvely. 26

28 Table 4. Projected Prce Markups. NERC Prce Elastcty of Demand Prce Elastcty of Demand Regon Lerner Index PCMI ECAR ERCOT a a FRCC a a MAAC MAIN MAPP NPCC SERC SPP WSCC a. Omtted because at these values of elastcty concentraton ndexes grow explosvely. 27