Spot and Contract Markets in the Brazilian Wholesale Energy Market

Transcription

1 Spot a Cotact Maet te Bazla Woleale Ee Maet Paulo Couto a Aé Ro e Olvea Te pape moel te teacto betwee a cotact a a pot maet woe featue ae boowe fom te Bazla Woleale Ee Maet. Te pot maet moele a a aom mecam tat cooe quatt a pce of electct. Te cotact maet compoe of eeato, etal upple of electct a eale. Te eeato a upple ae pce tae, wle te eale ave maet powe. It ow tat, we te umbe of eeato a upple ceae, eve f tee ol a moopolt eale te maet, te cotact pce covee to te expecte pot pce. Moeove, te quatt of ee tae te cotact maet appoace te total amout of ee avalable te tem we te umbe of eale ceae wtout bou.. Itoucto It ot a ovetatemet to a tat, follow te lea of te Ute Kom, ome electct tem aou te wol ave ueoe a evoluto. Afte te Bt Electct Act of 989, a ew electct uppl ut emee te Ute Kom tat a eve a a moel fo pvatzato a etuctu of electct ecto coute le Nowa, Swee, Dema, Aeta, Ute State a moe ecetl Bazl. Uuall te etuctu tat wt eoazato tat ttute eulate commo caae tamo a tbuto, followe b te pvatzato of tate-owe etepe. Dtbuto to eetal coume tall ema a moopol mot tem, but competto uppoe to tae place eeato fom te outet. Woleale competto eque ale of electct fom eeato to tbuto compae, a coequetl tee mut ext a maet wee electct ca be tae. Due to mbalace betwee cotact amout a actual flow of ee, wc ca ol be aee we mete ae ea, tee a ee to et up a mecam to eue opeatoal effcec. I a compettve evomet, te atual coce fo uc a mecam a pot maet. Te fucto of uc pot maet a bee extevel tue te lteatue. o tace, Gee a Newbe (99), vo e e a Habo (993), Gee (996) a Wolfam (998) tu te Electct Pool Ela a Wale. Amue, Bema et al. (998) a Aeo a Bema (995) pove a aal of te Noc Powe Excae, a Mooe a Aeo (997) cu te ew aaemet te Calfoa pot a cotact maet. Depatmet of Ecoomc, Uvet of Baíla. Depatmet of Ecoomc, Uvet of Baíla.

2 I Bazl, te Woleale Ee Maet wa ceate 998, but t mplemetato a bee aual. It tate Septembe 000 a expecte to be complete b ebua 00. T maet a ome pecula featue ue to two atpcal caactetc of te Bazla tem: (a) appoxmatel 93% of eeato oelectc, a (b) ma eeato plat ae locate te ame ve ba, pouc extealte cacae. I a utell, te Bazla Woleale Maet (MAE) oaze a follow. Te Bazla Electct Reulato Aec (ANEEL) eteme te tem fm ee, wc te amout of ee tat ca be eeate b te tem wt 95% pobablt. T fm ee allocate betwee te oelectc a flexble temoelectc plat, a te fm ee allotte to a eeato cottute te cel to te quatt of electct t ca ell tou cotact. Te Natoal Stem Opeato (ONS) cae of patc, wc ceule bae o teccal fomato pove b te eeato (o a temoelectc). A optmzato alotm to wc t ame teccal fomato a etmate of ema fo electct ae fe to calculate te value of wate, wc te ba fo te etemato of te pot pce. Tu, fom te pot of vew of te aet te maet, te pot pce a aom vaable. Te ffeece betwee te quatt of ee a eeato tucte to eeate a te quatt t ol fowa value at te pot pce. T mea tat eeato ae expoe to a pot pce, wc moe evee f te ow oelectc plat, ce te ca e up pouc le ee ta te fm ee a a eult of tem optmzato. I oe to allevate t poblem, a mecam of ee eallocato wa ceate. Bacall, t a to eac eeato a facto of te actual electct eeate b oelectc plat popoto to t ae of te oelectc fm ee. Tee oe featue of te oazato of te Bazla electct maet tat of patcula teet fo te tu of cotact maet. Eve eeato wa eque to tal cotact wt tbuto compae. Tee cotact pecf fxe amout of electct to be elvee to te tbuto compae utl te ea 00. Afte 00, toe quatte wll be euce at a ate of 5% a ea. T mea tat tall te cotact maet wll ave a elatvel mall ze. Afte 00, oweve, te cotact maet oul flou, a te ceae quatt of ee avalable to be tae oul etal te appeaace of eale t maet. A a matte of fact, t alea appe, albet to a mall cale. Geeato ae ete blateal cotact wt tbuto compae to ell te ee uplu ( exce of wat pecfe te tal cotact). T pape moel te electct maet Bazl ue te aumpto tat te cotact maet matue eou to allow fo te peece of eale. Te moel pa pecal atteto to te teacto betwee te cotact a pot maet, a t oe ot t to accout fo te extece of a ee eallocato mecam. Altou t aw t ma featue fom te Bazla cae, te moel of teet t ow, ce t b ew elemet to te aal of cotact maet, le te ole plae b eale a a pot maet wee eeato ave o maet powe. Tee ae ote pape te lteatue tat alo am at expla te teface betwee pot a cotact maet. Gee (999), fo tace, vetate ow te cotact maet te UK wo. I oe to o tat, e moel te pot maet u te

3 teo of uppl fucto equlba evelope Klempee a Mee (989). H ma cocluo tat eeato pla a Beta ame et pce equal to maal cot a cove all of te expecte output te cotact maet, wle Couot eeato ell o cotact ule te ca ea a e pemum fom ell to -avee bue. Te eco pat of t eult cotat wt Allaz a Vla (993), wo aalze te tatec l betwee te fowa a te pot maet. Te ma objectve to pove a atoale fo te extece of fowa maet te cae of cetat a pefect foet, a te ow tat fm (ot eceal eeato, ce te o t etct te aal to te electct maet) wt Couot cojectue o ell fowa pat of te poucto. T cooboate b aote moel of cotact te electct ut, pove b Powell (993). H ma f tat, we eeato collue, futue pce wll be above expecte pot pce a e wll be patal. T pape ffe fom te lteatue metoe above two ma epect. t, t oe ot allow eeato to et quatte o ubmt uppl ceule te pot maet. Te alo o t ave a cotol ove te pot pce. Seco, bot eeato a etal upple of electct ae uppoe to beave compettvel te cotact maet, cotat wt te ecet lteatue o futue a fowa maet, wc acowlee tat ma commote tae o toe maet ae ot pouce compettvel. Howeve, a wa metoe above, te eeat ecto of etuctue electct ute uppoe to be compettve afte pvatzato tae place, a tat wat t pape t to moel. All te maet powe te cotact maet belo to te eale, aote ovelt touce b t pape. Te pape oaze a follow. Secto evelop te bac famewo of aal a coe te cae of a cotact maet wt ol oe eale. Secto 3 exte te aal to te cae of ma eale pla a Couot ame. Secto 4 coclue a te Appex peet te ma poof.. Cotact maet wt oe eale Te tuato coee t ecto oe wee tee ae eeat compae (eeato) a m electct uppl compae (upple), wc ae plae bot te pot a cotact maet, a oe eale te cotact maet. A cotact ee a fowa cotact tat pecfe a ve quatt of electct to be elvee te futue fo a ceta pce. Te eeato ae exe b,,,, a te upple b,,,m. All eeato ave te ame tecolo a eac oe ae a amout of fm ee b te eulato. All upple ave te ame tecolo a eac oe a to uppl a amout of ee equal to te etal maet. Te ft aumpto mae tat R, wee R R a. T mea tat te upple wll ell all electct eeate. Te pot maet moele a a aom mecam, wc el a aom pot pce. Te cotact tae ae fowa cotact. m R 3

4 It alo aume tat bot te eeato a te upple ave eatve a expoetal utlt fucto u( ) e π π, wee π poft, a tat N µ, σ. Te upple poft ve b π pr ( R ) q ( ), () wee q te pce of a ut of cotacte electct a quote b te eale to te upple, p te fxe etal pce of electct a te quatt bout fowa. Oe ca mmeatel ume tat te upple ae pce tae te cotact, pot a etal maet. Te upple eveue te amout of ee t ell tme te etal pce. It cot clue te cot of bu ee te pot maet a te cot of bu t te cotact maet. Notce tat te quatt t bu te pot maet te ffeece betwee ow muc electct t a to ell a ow muc t bu tou cotact. o mplct, o accout tae of a ote cot te upple mt cu. Te maxmzato poblem of upple ca be expee tem of te cetat equvalet meaue, el: a max pr ( R ) q Va ( pr ( R ) q, ) () wee te expecte value of te pot pce, a aveo. Te oluto to t poblem ca be eal calculate: a te upple coeffcet of q a Rσ q R, a σ A Bq a σ a σ (3) wee A R a B a σ. Notce tat A > 0 a B > 0. a σ Te eeato alo a pce tae te cotact a pot maet. Accol, poft fucto ve b: π ( ) q v, (4) wee te quatt of output ol fowa, q te ut pce of cotacte electct quote b te eale to te eeato a maal (a aveae) cot. Te eeato poblem ca te be epeete a: v te eeato (cotat) a max ( ) q v Va( ( ) q v ), (5) 4

5 wee a te eeato coeffcet of aveo. Te oluto to t poblem q a σ q C a σ a σ a σ D q, (6) wee C a D a σ. It ca be eal ee tat D > 0. a σ Te eale a moopolt te cotact maet. He quote a ell pce to te upple a a bu pce to te eeato. He eutal a tu wat to maxmze poft, ve b te pea q q tme te quatt tae. H poblem teefoe: max( q q ) t.. q q 0, (7) m wee electct. om t lat expeo, oe obta,.e., total ema equal to total uppl of cotacte A Bq C Dq, (8) wee m m m m A A R ( a ), B B ( a ), C C σ σ ( a ) a D D ( a ). σ σ Te popoto below follow fom te oluto to (7). Te ma poof ae te Appex. Popoto.: Te equlbum quatte a pce a cotact maet wee (a) eeato a upple ae pce tae, (b) te eale a moopol powe, (c) all eeato ave te ame tecolo a coeffcet of aveo a () all upple ave te ame tecolo a coeffcet of aveo, ae ve b: 5

6 aσ aσ q R, q, m σ a a R, R a m m (9) wee a a,, m a a a,,. Upo pecto, oe ca mmeatel ee tat te fowa pce of ee ol lowe ta te expecte pot pce, wle te pce of ee bout e ta te expecte pot pce. Accol, te ee cotacte b eeato le ta te fm ee a te ee cotacte b upple le ta te total etal ale. Te follow coolla a mmeate coequece of te popoto. Coolla.. Te equlbum pce a quatte ave te follow popete: (a) lm q, q a ecea fucto of m a a cea fucto of m a, R a σ (b) lm q a, a σ ;, q a cea fucto of a a ecea fucto of ; (c) lm 0, a cea fucto of a, a, a σ ; m, () lm 0, lm 0 a lm lm. m m Poof: Te ol eult tat oe t follow mmeatel fom (9) (). t otce tat lm R lm 0, ce R a ae fxe. T expla te ft two m lmt. A fo lm lm, ote tat m,.e., oe ot epe o. Smlal, R R R R R m, wc mea tat oe ot epe o ete. Acco to (a) a (b), te pce pa b te eale to te eeato cea te umbe of eeato a te pce cae to te upple ecea te umbe of upple. T a up eult, ce te eale a a moopol te cotact maet. Howeve, fo a ve volume of total fm ee (a ee ol b te upple), a ceae te umbe of eeato mea tat eac eeato vuall expoe to le, ce t a le ee to tae. Smlal, f te umbe of upple ceae, eac upple vuall face le of be expoe to te pot pce. I ote wo, te elatct of ema fo cotact ceae becaue 6

7 a le mpotat fo eeato a upple. I te lmt, bot pce o to te expecte pot pce. Te ote f epote (a) a (b) ae le wt te lteatue o fowa a pot maet: () Te fowa pce pa b (to) a upple (eeato) e (lowe) te moe avee t. T mae ee becaue a moe -avee aet () a moe value to le expoue to te pot maet. Te fowa pce pa b (to) a upple (eeato) e (lowe) te lae te vaace of te pot pce. T lae vaace aocate wt moe. () Te fowa pce pa b (to) a upple (eeato) e (lowe) te lae te total ee ale (fm ee). We te ema fo ee (fm ee) e, eac upple (eeato) vuall a to tae moe ee te maet, a t ceae e of expoue. Te explaato ve (), () a () ae all bae o te aumpto tat avee aet wat to ee aat. I t moel, te o tat te fowa maet, a a facto tat ceae te (of be expoe to te pot maet) o mae te aet moe avee ceae t ema fo e, affect te fowa pce accol. It alo poble to calculate te eale poft. Sce alf of te tem fm ee wll be tae te cotact maet, t ca be calculate a σ a a σ a a π m 4 m. Oe ca mmeatel cec tat te eale poft eceae wt m a, be equal to 0 te lmt. T exactl wat oe woul expect afte te cuo above, a t alo aee wt te beavo of te eale pea,, a epote (c). Te fact tat te pea ceae wt te eee of aveo of eeato a upple, wt te vaace of te pot pce a wt te tem fm ee a coequece of te beavo of q a q. Peap eve moe tatl ta te eult (a) a (b) ae te oe plae (). Te ft oe ol appaetl quet. Te fact tat te quatt of ee ee b eac eeato aw ea to zeo, a mlal fo te upple, wle te total amout of ee tae te cotact maet oe t cae, ea to expla: te umbe of eeato a upple o to ft. Wat tub tat te ze of te cotact maet oe't cae we te fowa pce to te eeato cea a te fowa pce to te upple ecea at te ame tme (acco to (a) a (b)). Ue omal coto, t woul lea to a ceae te total amout of ee tae fowa. Te explaato fo t appaet paaox tat, we te umbe of eeato a upple ceae, te pot maet become moe attactve. Eac eeato a upple vuall expoe to le a, b ta te pot maet, et a bette pce ta tat offee b te eale. Teefoe te ze of te pot maet oe ot m. I ote wo, te eale oe ave a competto, amel te pot maet. Te ext ecto cue a moel wee tee moe ta oe eale. 7

8 3. Cotact maet wt moe ta oe eale Acco to Popoto., fo a ve umbe of eeato a upple, te eale wll obta a potve pea a, coequetl, potve poft tou t opeato te fowa maet. T oul etce ote fm to ete te maet a eale. Te tuato wee tee ae ma eale te maet wll be te focu of t ecto. Tee ae ow H eale, wc pla a Couot ame. Deale poft fucto π ( q q ), wee te quatt of ee tae b eale. Deale a to olve te follow poblem, wee : H max ( q q ) t.. A Bq C Dq (0) T poblem equvalet to A C max B D () wee te etcto a alea bee clue te objectve fucto. Popoto.: Te equlbum quatte a pce a cotact maet wee (a) eeato a upple ae pce tae, (b) tee ae ma eale wo pla a Couot ame, (c) all eeato ave te ame tecolo a coeffcet of aveo a () all upple ave te ame tecolo a coeffcet of aveo, ae ve b: R aσ aσ q, q, H m H σ a a R, R, H m m( H ), a H H ( ) H H () Pce a quatte cotacte b eeato a upple pla te ame popete te plae Popoto.. Te total amout of electct tae tou fowa cotact le ta te total amout of fm ee avalable. T popoto accompae b te follow coolla. 8

9 Coolla.. Te equlbum pce a quatte ave te follow popete: (a) lm q lm q, q a ecea fucto of m a H a a m H cea fucto of a, R a σ ; (b) lm q lm q, q a cea fucto of a H a a H ecea fucto of a, a σ ; (e) lm 0 a lm. (c) lm lm 0, a cea fucto of a, a, a σ ; m, H H () a ae cea fucto of H, lm 0, lm a lm H 0, lm ; H Poof: ollow mmeatel fom (). m H It ol wot commet o te eult fom te coolla tat ae ato to te aal of te pevou ecto. Nevetele, t mut be pote out tat, a oe woul expect, te eult of Popoto. bol ow to te eult of Popoto. we we et H. Rea (a), te ew f tat te fowa pce to te upple a ecea fucto of te umbe of eale. Tat exactl wat a Couot moel oul el: te moe eale tee ae te toe te competto betwee tem, a t ve te pce te cae te upple ow. I te lmt, te ca cae o moe ta te expecte pot pce. A mla eao apple to (b), wc a tat te fowa pce te eeato face cea te umbe of eale. T alo a coequece of te eace competto betwee eale. I te lmt, oce aa te expecte pot pce aceve. Tat te pea wll o to zeo a te umbe of eale ceae wtout bou, a tate (c), a ect coequece of (a) a (b). Te ew pat () efe to te beavo of te cotact el b eeato a upple a te umbe of eale ceae. We tat appe, te pce pa b upple eceae a te pce eceve b eeato ceae, appoac te expecte pot pce te lmt (a wa ee (a) a (b)). T tu mae t moe attactve fo eeato a upple to ee te cotact maet, a coequetl te cotacte ee appoace te fm ee (eeato) a ee ale (upple). Lat but ot leat, pat (e) ow tat, a te umbe of eale ceae wtout bou, te ze of te potfolo of eac vual eale to zeo a te total amout of ee tae te cotact maet move towa te total amout of fm ee te tem. T atual, ce bot eeato a upple ae vuall ta almot all te ee te ave o ee te cotact maet. I ote wo, te pot maet become le of a competto to te eale, ce eeato a upple ae expoe to te ame pot pce but ow et bette pce fom tem. T eem to cate tat te ole plae b te pot maet te to m ue to cea competto betwee eale. It wot te t lat eult: we te umbe of eale ceae, te teec fo te pot maet to. T a eou R 9

10 coequece fo a eulato cocee about ett up o oveee te opeato of a electct maet. 4. Coclu Rema Te ft ma cocluo of te pape tat te pce a upple pa fo eac ut of electct bout fom a eale te cotact maet eceae a te umbe of upple ceae. Smlal, te pce a eeato pa b a eale fo a ut of electct ol te cotact maet oe up a te umbe of eeato ceae. I te lmt, bot pce move towa te expecte pot pce. T a otaa eult, ce te eale a moopol powe. It ca be explae f oe ealze tat oe of te ma eao aet ete cotact to ee aat, t cae te of be expoe to te pot pce. We te umbe of eeato a upple ceae, ve te total amout of ee avalable te tem, eac vual eeato a upple a le electct to tae, a teefoe le potetal expoue to te pot maet. T, tu, mea tat a become le mpotat to tem, a eale ave to face competto fom te pot maet, lut te maet powe. T a ue tat, epte of t mpotace to etuctue electct tem, wee uppoel eeato compettve, ot aee te lteatue. o tace, Gee (999), Allaz a Vla (993) a Powell (993), all moel te eeat ecto a a uopol. A fo te ema e of te cotact maet, Gee (999) uppoe tat te bue eteme te maet-clea pce, Powell (993), tat te et quatte, a Allaz a Vla (993) moel tem a peculato. Te eco ma cocluo tat te ze of te cotact maet oe t cae we fowa pce cae a wa tat favo eeato a upple. Nomall tee woul be a ceae te total amout of ee tae fowa, but ee te cae fowa pce a coequece of te ceae te umbe of eeato a upple, ma te pot maet moe attactve. To be moe pece, a te total umbe of eeato a upple ceae, eac oe become le expoe to a, b ta te pot maet, et a bette pce ta tat offee b te eale. T mea tat te eale a to face a eou competto, amel te pot maet, a t expla w te cotact maet oe t expa. all, te total amout of ee tae te cotact maet appoace te tem fm ee we te umbe of eale ceae wtout bou. T a coequece of te fact tat eeato a upple ae expoe to te ame pot pce but ow et bette pce te cotact maet. T mea tat pobl te pot maet become le mpotat we tee ceae competto betwee eale. T omet te eulato oul be cocee wt. Te ext tep towa a full caactezato of te Bazla Woleale Ee Maet to allow fo aet to tae tetempoall. T a mpotat featue ce te tetempoal cout ate of te Natoal Stem Opeato ma be ffeet fom tat of a eeato. Howeve, a attempt tat ecto wll ave to face te callee of eep te tetempoal atue of te moel wle atf te etcto tat te total amout of cotacte ee caot excee te eeato fm ee, a eque b te Bazla maet ule. 0

11 5. Appex Poof of Popoto.: Coto (8) ca be ue to ewte te eale poblem (7) a A C D max q q ( C Dq ) B B t.. q q 0 (3) Te poblem wll be ft olve wtout ta to accout te etcto. Next t wll be ow tat te etcto atfe at te optmum. t of all, t ca be eal ee tat te objectve fucto cocave. I fact, A C D ( A C) C q ( ) q q ( C Dq ) B B B ( A C) D DC D q q ( q ) Cq D( q ), B B B a, ce D > 0, B > 0, q B B B ( A C) D DC D q C Dq ( q ) D D < 0. B Tu te ft oe coto bot ecea a uffcet fo a maxmum. Te ft oe coto fo t poblem ve b D A C D ( C Dq ) q q D 0 B B B DC D q AD CD D q C Dq Dq 0 B B B B Dq DC BC AD DC Dq 0 B B D DC BC AD q Dq 0 B B

12 T equato ca be olve to obta a DC BC AD AD C( D B) q D DD ( B) B D B A C DAD C( D B) A C AD C( D B) q B B D( D B) B B( D B) ( A C)( D B) AD C( D B) AD AB BC BD ( B) BD ( B) AD B( A C) BD ( B) (4) (5) Te coto q q atfe f AD C( D B) AD B( A C) DD ( B) BD ( B) Sce B > 0 a D > 0, t equvalet to [ AD C( D B) ] B [ AD B( A C) ] D ABD BCD CB < AD ABD BCD > ABD BCD AD CB 0, Now te mplf aumpto tat all eeato ave te ame coeffcet of aveo,.e. a a,,, a tat all upple alo ave te ame coeffcet of aveo,.e. m m A R, B a σ a σ,, C D a σ a σ a a,, m, wll be ae. Te a, u R,

13 m m m m m R R aσ aσ aσ aσ m m m m R a σ a σ a σ a σ a σ a σ a σ a σ ABD CBD AD CB R a σ a σ a σ a σ a σ a σ m m R R R 0 aσ aσ > aσ aσ m m m R R aσ aσ aσ aσ aσ aσ Teefoe, te etcto atfe at te optmum. Coto (4) ca ow be expee a q m m R aσ aσ aσ aσ aσ m aσ aσ aσ R m m m σ aa σ σ a aa ( σ ) ( σ ) ( σ ) a a a m a σ aσ aσ m m aσ aσ aa ( σ) a ( σ) m aσ aσ aσ m m a σ a σ aσ aσ aσ m m aσ aσ aσ aσ aσ aσ aσ (6) 3

14 Smlal, (5) ca be expee a q m m m R R aσ aσ aσ aσ aσ m m aσ aσ aσ a m m m m σ aa a aa ( σ ) a σ ( σ ) ( σ ) m m aσ aσ aσ m m m a σ a σ a σ a σ a σ aσ (7) m m m m m aσ aσ aσ aσ aσ aσ Te combato of (3) wt (7) a (6) wt (6) el: a aσ R R aσ aσ m R R aσ aσ m R R m aσ aσ aσ a σ a σ 4

15 all, te pea ca be calculate a q q m aσ a σ σ a a m If te eeato ae mmetc, tat, te. R R R R Smlal, f te upple ae mmetc,.e. R, te. m m m m Poof of Popoto.: Poblem () ca be expee a AD BC ( D B) max BD (8) Te ft oe coto fo t poblem : ( D B) AD BC ( D B) 0 BD BD ( D B) AD BC ( D B) ( D B) 0 ( ( D B) ) AD BC ( D B) AD BC j ( D B) j j j j j (9) Sce te eale ae mmetc, ( H ) a j. Teefoe H H j 5

16 AD BC ( H ) ( D B) H HAD ( BC) HH ( ) ( D B) H ( H ) H( AD BC) ( D B) HAD ( BC) HAD ( BC ) ( D B) H ( H )( D B) AD BC a ( H )( D B) (0) A wa oe te poof of Popoto., A, B, C a D ca be ubttute fo (0), eeat m m R aσ aσ aσ aσ m ( H ) aσ aσ R m m m a m ( H ) aσ aσ ( σ ) a σ aa ( σ ) σ aa m a σ a σ H a, m H H ( H ) a σ aσ () wee te fact tat R wa ue. Te ext tep to calculate te pce: q m H R A a σ H B m a σ Raσ H aσ aσ m H m m H () 6

17 a q H C H aσ D a σ aσ H aσ H a σ (3) Te pea ca ow be eal obtae: aσ a σ q q m H H σ a a H m Now (3), (6), () a (3) ca be ue to et a aσ aσ aσ H aσ aσ H ( ) H ( ) aσ R R aσ aσ m H R R R R aσ aσ mh ( ) mh ( ) (4) (5) all, ca be calculate tee ffeet wa: 7

18 H H ( ) H H m m H H R R H R R mh ( ) H H R H H H 6. Refeece Allaz, B. a J. L. Vla (993). Couot competto, fowa maet a effcec. Joual of Ecoomc Teo 59(): -6. Amue, E. S., L. Bema, et al. (998). Competto a pce o te eme Noc electct maet. Wo Pape See Ecoomc a ace, Stocolm Scool of Ecoomc(7). Aeo, B. a L. Bema (995). Maet tuctue a te pce of electct: A ex ate aal of te eeulate we electct maet. Ee Joual 6(). Gee, R. (996). Icea competto te Bt electct pot maet. Joual of Iutal Ecoomc 44: Gee, R. (999). Te electct cotact maet Ela a Wale. Te Joual of Iutal Ecoomc 47(): Gee, R. J. a D. M. Newbe (99). Competto te Bt electct pot maet. Joual of Poltcal Ecoom 0(5): Klempee, P. D. a M. A. Mee (989). Suppl fucto equlba olopol ue ucetat. Ecoometca 57(6): Mooe, I. a J. H. Aeo (997). Itoucto to te ew Calfoa powe maet. Dcuo Pape, Calfoa Powe Excae. Powell, A. (993). Ta fowa a mpefect maet: Te cae of electct Bta. Te Ecoomc Joual 03(Mac): vo e e, N.-H. M. a D. Habo (993). Spot maet competto te UK electct ut. Te Ecoomc Joual 03(Ma):

19 Wolfam, C. D. (998). Statec b a multut aucto: A empcal Aal of b to uppl electct Ela a Wale. RAND Joual of Ecoomc 9: