Title: Unintended Impacts of Multiple Instruments. on Technology Adoption

Transcription

1 WORKING PPERS IN ECONOMICS No 344 Title: Uiteded Impats of Multiple Istrumets o Tehology doptio uthor: Jessia Coria February, 009 ISSN (prit) ISSN (olie) Istitutioe för atioalekoomi med statistik Hadelshögskola vid Göteborgs uiversitet Vasagata, Box 640, SE Göteborg , (fax) wwwhadelsguse ifo@hadelsguse

2 / 44 Uiteded Impats of Multiple Istrumets o Tehology doptio Jessia Coria Uiversity of Gotheburg bstrat There are may situatios where evirometal authorities use a mix of evirometal poliy istrumets, rather tha oe sigle istrumet, to address evirometal oers For example, oe istrumet may be used to redue overall emissios of a pollutat while aother is used to address speifi seasoal oers Very little work has bee doe o the eoomi impats of the appliatio of multiple istrumets This paper ivestigates the uiteded impats of the iteratio of a tradable permits sheme with diret seasoal regulatios o the rate of adoptio of advaed abatemet tehologies Key Words: Tehology adoptio, evirometal poliy, tradable permits, emissio stadards, iteratio of poliies JEL CODES: O33, Q53, Q55 y Q58 Jessia Coria, Gotheburg Uiversity, Departmet of Eoomis, PO Box 640, SE Gotheburg, Swede; ( ) jessiaoria@eoomisguse; (tel) I am grateful to Thomas Sterer, Jua Pablo Motero, ad Jiege Wei for useful ommets

3 3 / 44 I INTRODUCTION I some ases, the damages aused by emissios of pollutats deped almost exlusively o their magitude ad o the umber of persos whose loatio makes them vulerable to the effets However, uder may other irumstaes, the effets of a give disharge deped o variables beyod the otrol of those diretly ivolved For example, amout of water ad speed of flow are ritial determiats of a river s assimilative apaity Similarly, emissio levels that are aeptable ad rather harmless uder usual oditios a beome itolerable uder some meteorologial oditios This is the ase i some ities like Mexio City ad Satiago, Chile, where temperature iversio may prevet air pollutio from leavig the atmosphere durig witer moths, ausig oasioal evirometal rises that prompt the impositio of emergey measures to improve air quality to a satisfatory level Typially, these rises aot be predited far i advae or with ay degree of ertaity we a oly be ertai that at some uforesee time they will reur I most ases, it is virtually impossible to hage evirometal regulatios o short otie Thus, if oe poliy is used as the oly meas of otrol, it would have to be set at a level that is high eough to maitai the pollutio at aeptable levels durig emergey periods I ertai irumstaes, suh a poliy may be uaeptably ostly to soiety Bawa (975) showed that the pollutio otrol poliy that miimizes total soial osts (statioary soial osts plus short-term emergey osts) is a mixed poliy i whih market-based istrumets are used to otrol the log-ru equilibrium level of pollutio

4 4 / 44 ad diret otrols are used to maitai the pollutio below some predetermied threshold durig short-term emergeies If eforemet is effetive, diret otrols a idue, with little uertaity, the presribed alteratios i pollutio ativities, while the use of market-based poliies leads firms to use leaer tehologies i the log ru Oe importat disadvatage of diret otrols is their poor dyami properties I fat, the theory of evirometal regulatio suggests that sie eoomi istrumets idue firms to re-optimize their levels of abatemet, they reate more effetive tehology adoptio ietives tha ovetioal regulatory stadards Thus, it is worth askig whether or ot iteratio of poliies alters the eoomi ietives provided through market-based istrumets, espeially if the iidee of evirometal rises ad the relative use of diret otrols withi the mix vary The preset paper aalyzes the uiteded impats of the iteratio betwee tradable permits ad short-term emissio stadards o the rate of adoptio of advaed abatemet tehologies Uder this settig, adoptio beefits a be deomposed ito a et abatemet effet ad a permit prie effet The et abatemet effet aouts for the ireased adoptio savigs resultig from the additioal abatemet idued by a situatio of evirometal distress The permit prie effet aouts for the egative effet of ireased availability of tehology o the permit prie, whih eourages tradig ad disourages adoptio The, both effets set agaist themselves ad the fial rate of adoptio depeds o the extet to whih eah effet offsets the other ad o the iidee of evirometal rises

5 5 / 44 If the iidee of evirometal rises is exogeous, the a mix of market-based poliies ad emissio stadards does ot maximize soial welfare Ideed, if the iidee of evirometal rises is low, the a mix of tradable permits ad emissio stadards leads to a ieffiietly large prie effet ad to a rate of adoptio that is lower tha the optimal Similarly, if the iidee is high, the the mix idues a ieffiietly small prie effet, leadig firms to overivest However, if the iidee is low ad it a be redued eve further through adoptio of ew tehology, the the previous results do ot hold ad the mixed poliy ould offer a higher level of soial welfare tha alterative approahes This paper is orgaized as follows The ext setio itrodues the adoptio model Setio 3 aalyzes the adoptio ietives uder diret regulatios ad market-based poliies separately ad uder mixed poliies Setio 4 ompares the total welfare idued by mixed approahes whe the iidee of evirometal emergeies is exogeous Setio 5 ompares the total welfare whe the iidee of evirometal emergeies a be affeted by the rate of adoptio Setio 6 presets a umerial example to illustrate the mai results Setio 7 oludes the paper II THE MODEL Cosider a ompetitive idustry osistig of a otiuum of firms of mass ggregate emissios without evirometal regulatio are ormalized to uity Normally, the evirometal authority autios off [ q ] emissios, where q represets the desired

6 6 / 44 level of abatemet Eah firm must deide whether to buy permits at the market learig prie x to over its emissios, or to abate them Due to meteorologial oditios, ritial episodes of bad air quality are delared with exogeous probability µ, where µ orrespods to the rate of ritial episodes per uit of time To avoid the egative impats of suh episodes, the evirometal authority implemets a more demadig diret regulatio durig these evirometal emergeies, ompellig firms to further derease their levels of emissios The diret regulatio takes the form of a uiform emissio stadard equal to[ q ], with [ q > q ] Curret abatemet osts are homogeeous with total abatemet osts equal to q i, where q i represets firm i s abatemet Firms a ivest i a advaed tehology, leadig to lower abatemet osts [ < ] Buyig ad istallig the ew tehology auses a q i fixed ost k i U [0,] B Let π ad π deote the firms profit flows before ad after tehology adoptio Firms will adopt ew tehology as log as the adoptio beefits (ie, the differee i profits assoiated with the dereased abatemet osts) offset the adoptio osts The, the followig arbitrage oditio must hold for the margial adopter: B () π π = π = Defie λ as the rate of firms adoptig the ew tehology: B π () λ = = - F( ) = F( π π ) = = π k

7 7 / 44 Notie that sie firm profits strogly deped o the hoie ad strigey of evirometal poliies, the rate of firms adoptig the ew tehology is edogeous III INTERCTION OF ENVIRONMENTL POLICIES ND THE RTE OF DOPTION 3 doptio Ietives Uder Diret Regulatios ad utioed Tradable Permits Several researhers have foud that the ietive to adopt ew tehologies is greater uder market-based istrumets tha uder diret regulatios [See Millima ad Prie (989); Jug, Krutilla ad Boyd (996); Keohae (999); ad Nelisse ad Requate (004)] This superiority of market-based poliies relies o the fat that firms re-optimize their abatemet levels oe ew tehology is available, whih leads to larger savigs attributable to the adoptio deisio If diret regulatios are used, firms will ejoy a lower abatemet ost oly for the emissios they were abatig iitially Thus, i this settig, the ost savigs resultig from usig ew tehology whe firms are restrited to emit o more tha q uits of emissios are give by the differee i total abatemet ost due to makig a emissio redutio to that level: (3) EE EE π = ( λ) = ( )( q)

8 8 / 44 Let us ompare with the ietives provided by market-based poliies Let x deote the equilibrium permit prie of emissios Whe adopters make abatemet deisios, they solve the followig problem: L q x q, q (4) mi { = ( ) + ( )} where q is the level of emissios abated ad L is the miimized sum of abatemet osts ad paymets for o-redued emissios The first order oditio (FOC) is give by: (5) ( q ) = x That is, adopters redue emissios util the margial abatemet ost of the ew tehology equals the prie of emissios No-adopters fae a similar problem, but with a higher margial abatemet ost: N N (6) mi { N N ( ) ( )} L = q + x q q The first order oditio (FOC) is give by: N (7) ( q ) = x Thereby, o-adopters optimal level of abatemet q N is lower tha that of adopters beause of higher margial abatemet osts Substitutig the FOCs ito the miimizatio problem, the adoptio profits ad the rate of adoptio are give by: (8) TP TP π = λ = x α,

9 9 / 44 with α = > ad x α > ( )( q) If the idustry is regulated by permits, the market learig o the permit market requires: N q ( x) q ( x) ( x) q ( x) (9) = λ + [ λ ] Substitutig (5) ad (7) ito (9) ad differetiatig (9) with respet to x ad λ yields: dx α x (0) = < 0 dλ λα + 4 The the permit prie will drop with adoptio sie the diffusio of the ost-reduig tehology lowers the aggregate margial abatemet osts This prie effet idues more effiiet adoptio deisios ad prevets overivestig sie firms with higher osts of adoptio have the opportuity to buy heaper permits istead of ivestig i ew tehology 3 doptio Ietives Uder Mixed Sheme of Tradable Permits ad Diret Regulatios Lets us ow ompare the adoptio ietives whe mixed poliies are used It is assumed that evirometal emergeies our with probability µ ad that firms are ompelled to abate q uits of emissios durig these periods The the adopters problem I lie with most of the literature o the subjet, I assume parameters suh that for the same level of strigey, the ost savigs provided by tradable permits are larger tha those provided by emissio stadards This prie effet teds to also support the use of taxes istead of tradable permits to speed up the diffusio of ew tehology The fat that the emissios prie is fixed by the regulator uder the tax while it depeds o the firm behavior uder permits reates a wedge betwee the tax ad the permit systems ad betwee the differet rates of adoptio they idue

10 0 / 44 is to miimize the sum of () abatemet osts ad paymets for o-redued emissios durig ormal days ad () the abatemet osts of ahievig the emergey stadard () mi L = ( µ ){ ( q ) + x( q )} + µ ( q) + x( q) } where q, x deotes the equilibrium permit prie of emissios whe both poliies are { applied ad q q The first order oditio (FOC) for the optimal level of emissio redutio is give by: () ( q ) = x Notie that the FOC does ot hage due to the iteratio of poliy istrumets That is, adopters abate emissios util the margial abatemet ost of the ew tehology equals the prie of emissios gai, o-adopters fae a similar problem, but with a higher margial abatemet ost: N N N (3) mi N ( µ ){ ( ) ( )} µ ( ) ( ) } N (4) ( q ) = x L = q + x q + q + x q, q Substitutig the FOC ito the miimizatio problem, the adoptio profits ad the rate of adoptio λ beome: { (5) x q π = λ = ( µ )( ) α + µ Differetiatig λ with respet to µ ad re-orgaizig terms yields:

11 / 44 x (6) = q [ α ( x) ( µ )( x) α µ + µ doptiosavigs doptiosavigs Uder UderNormalDays PrieEffet EvirometalEmergeies NetbatemetEffet I (6), the term i brakets o the right-had side represets the et effet of the more striget diret regulatio uder evirometal emergeies o the adoptio savigs, ie, et abatemet effet, while the seod term o the right-had side of (5) gives aout of the effets of the implemetatio of the diret regulatio o the permit prie, ie, permit prie effet 3 Market learig i the permit market requires total abatemet to be equal to the weighted abatemet doe by adopters ad o-adopters The, substitutig the optimal rate of adoptio ito the market-learig oditio, we a solve for the market prie the effet of evirometal emergeies o the permit prie N q ( x, ) q ( x) ( x, ) q ( x) (7) = λ µ + [ λ µ ] Substitutig (5) ito (7), differetiatig with respet to x ad µ ad solvig for x ad for dx / dµ, yields [see ppedix ]: (8) αx [ α( x ) q dx = dµ 3( µ )( x) α + µ ( )( q) α + 4 > 0 3 ( x) ( x) = µ µ

12 / 44 Sie the deomiator is positive, the sig of dx depeds o the et adoptio savigs dµ Substitutig (8) ito (6) yields: (9) = q [ α ( x) µ doptiosavigs doptiosavigs Uder UderNormalDays EvirometalEmergeies NetbatemetEffet [ α ( x ) q + ( µ )( x ) α 3( µ )( x ) α + µ ( )( q ) α + 4 PrieEffet Thereby, if the adoptio savigs uder the emissio stadard are larger tha those firms realize uder tradig permits, the the et abatemet effet is positive while the permit prie effet is egative Similarly, if the savigs uder tradable permits are larger tha those uder the emissio stadard, the the permit prie effet is positive while the et abatemet effet is egative The the ompariso betwee adoptio savigs uder emissio stadards ad permits ritially depeds o the relative strigey of the diret regulatio If the emergey emissio stadard is the most demadig poliy, the adoptio savigs uder evirometal emergeies are larger tha those uder ormal days, ad the et abatemet effet is positive while the permit prie effet is egative So, the permit prie effet partially offsets the et abatemet effet, reduig the rate of adoptio The prie effet is egative sie the higher rate of adoptio idued by more

13 3 / 44 striget diret regulatio lowers the aggregate margial abatemet ost ad therefore lowers the permit prie This derease i the permit prie redues the rate of adoptio sie i order to ahieve the evirometal regulatio, firms prefer to buy heaper permits istead of buyig the ew tehology The more striget the emissio stadard, the larger the derease i the permit prie ad the larger the impat o the rate of adoptio Clearly, the magitude of the permit prie effet also depeds o the probability of evirometal emergeies ourrig If µ ireases, the relative importae of the permit prie effet dereases sie the haes of usig permits istead of buyig the ew tehology are very low Propositio : The rate of adoptio uder the mix of tradable permits ad emissio stadards ireases with the iidee of evirometal emergeies at a ireasig rate Proof: Let β 0 deote the et abatemet effet ad β ( ) α = x ad the β = ( q ) adoptio savigs uder permits ad uder the emissio stadard, respetively The µ a be re-writte as:

14 4 / 44 βα (0) = β 0 = 0, µ 3βα β µα + + ( µ ) 4 βα where > 0 3βα β µα + + ( µ ) 4 Thus, the effet of the iidee of evirometal emergeies is expressed as a futio of the et abatemet effet times less the permit prie effet Notie that whe µ, the permit prie effet teds to zero ad µ β0 Thus, if the probability µ of a evirometal emergey ourrig is high, the the degree of substitutio betwee the use of permits ad the purhase of ew tehology is small sie it is ot profitable to purhase permits tha a t be used regularly doptig abatemet tehology is therefore the oly alterative available to meet the evirometal regulatio, ad the adoptio savigs are the largest O the other had, whe µ 0, the degree of substitutio betwee the use of permits ad the purhase of ew tehology is high, ad so is the permit prie effet The βα µ 0 β0 β0 µ < Thus, if the probability of a evirometal 3βα + 4 emergey ourrig dereases, the the degree of substitutio betwee the use of

15 5 / 44 permits ad the purhase of the tehology ireases, ad so does the egative impat of the permit prie effet o the rate of adoptio The ituitio behid this result is straightforward The et abatemet effet is positive ad overomes the egative permit prie effet Sie the permit prie effet dereases with the iidee of evirometal emergeies, the total effet ireases at a ireasig rate 33 doptio Ietives Uder a System of Differetiated Tradable Permits Let us assume that istead of applyig a diret regulatio to otrol ritial episodes, the evirometal authority uses differetiated tradable permits regular tradig program is iteded to eourage a emissios redutio equal to q durig ormal days, while a emergey tradable permit program is iteded to eourage a redutio equal to q durig evirometal emergeies The adopters problem beomes to miimize the sum of abatemet osts ad paymets for o-redued emissios durig ormal days plus the sum of abatemet osts ad paymets for o-redued emissios durig evirometal emergeies () mi L3 = ( µ ){ ( q ) + x( q )} + µ ( q ) + xs( q )} q, q, where x is the permit prie of emissios durig ormal days ad x s orrespods to the { equilibrium permit prie of emissios durig evirometal emergeies The FOCs for the optimal level of emissios redutio uder the regular ad the

16 6 / 44 emergey program are give by: () ( q ) = x ( q ) = x s That is, i eah state, the margial abatemet ost of the ew tehology equals the prie of emissios s usual, o-adopters fae a similar problem but with a higher margial abatemet ost, leadig to the usual FOCs: N (3) ( q ) = x, N ( q ) = x s Usig the FOC for the optimal level of emissios redutio, we a solve for the adoptio profits ad the rate of adoptio: (4) TPP π = λ = ( µ )( x) + µ ( xs) α Differetiatig (4) with respet to µ ad re-orgaizig terms yields:

17 7 / 44 (5) λ µ TPP ( xs) α ( x) α µα ( xs ) = + doptiosavigs doptiosavigs Uder UderNormalDays EvirometalEmergeies ( xs ) µ NetbatemetEffet PrieEffet Uder EvirometalEmergeies ( x ) + ( µα ) ( x ) µ PrieEffet UderNormalDays The first term i brakets o the right-had side of (5) represets the et effet of the evirometal emergey regulatio o the adoptio savigs, or the et abatemet effet, while the seod term o the right-had side of (6) gives aout of the idiret effet of evirometal emergeies o the permit prie durig evirometal emergeies ad ormal days The market learig i the permit markets requires total abatemet to be equal to the weighted abatemet doe by adopters ad o adopters i eah state: (6) (7) TPP TPP N q = λ ( xs, µ ) q ( xs) + λ ( xs, µ ) q ( xs), TPP TPP N q = λ ( x, µ ) q ( x) + λ ( x, µ ) q ( x) d sie the required emissios redutio is larger uder evirometal emergeies q < q ], the permit prie that lears the market of evirometal emergeies is [ larger, leadig to a positive et abatemet effet

18 8 / 44 TPP Substitutig λ ito (6) ad differetiatig with respet to x S ad µ, we obtai a solutio for dxs / dµ By aalogy, substitutig TPP λ ito (7) ad differetiatig with respet to x ad µ, we obtai a solutio for dx / dµ (see ppedix B): (8) µ TPP = ( xs) α ( x) α NetbatemetEffet α( x ) s ( xs) α ( x) α α( x ) ( xs) α ( x) α µα ( xs ) + ( µ ) α ( x ) 3 µ ( xs) α + ( µ )( x) α + 3( µ )( x) α µ ( xs) α PrieEffet PrieEffet Uder UderNormalDays EvirometalEmergeies Therefore, sie the adoptio savigs are larger durig evirometal emergeies tha durig ormal days, the et abatemet effet is positive while the permit prie effets durig evirometal emergeies ad ormal days are egative ad offset the et abatemet effet gai, permit prie effets are egative sie permit pries drop whe tehology is adopted The lower prie stimulates additioal permit tradig ad less adoptio sie firms prefer to buy permits istead of ivestig i tehology Notie that the permit prie effet durig evirometal emergeies is larger sie a more striget poliy idues larger adoptio savigs, therefore iduig a higher adoptio rate ad a larger redutio of the permit prie

19 9 / 44 Propositio : The rate of adoptio uder differetiated tradable permits ireases with the iidee of evirometal emergeies at a dereasig rate Proof: Let γ 0 deote the et abatemet effet ad γ ( ) = x α ad γ ( ) = x S α the adoptio savigs durig ormal days ad evirometal emergeies, respetively The µ λ TPP a be re-writte as: (9) TTP αγ αγ = γ 0, µ 3 αγ ( µ ) αγ 3αγ µαγ + µ ( µ ) 4 αγ where 3 αγ + ( µ ) αγ µ + 4 > 0 αγ ad > 0 3αγ + µαγ + ( µ ) 4 Thus, the effet of the iidee of evirometal emergeies is expressed as a futio of the et abatemet effet times less the permit prie effet durig evirometal emergeies ad durig ormal days

20 0 / 44 Notie that whe µ, the permit prie effet durig ormal days teds to zero, while durig days of evirometal emergeies it is at a maximum ad µ TPP αγ µ γ 0 3αγ + 4 O the other had, whe µ 0, the permit prie effet durig evirometal emergeies teds to zero, while durig ormal days it is at a maximum ad µ TPP αγ µ 0 γ 0 3αγ + 4 Notie that the prie effet durig evirometal emergeies is larger tha durig ormal days sie the adoptio savigs durig evirometal emergeies are larger γ > γ ]That is, the larger adoptio savigs idue a higher adoptio rate ad a larger [ redutio of the permit prie, whih offsets the et abatemet effet The positive effet of the iidee of evirometal emergeies o the rate of adoptio is therefore higher whe µ 0, or TPP TPP > µ µ µ 0 µ Fially, otie that TPP TPP > µ µ µ 0 µ 0 That is, µ 0, the total prie effet (the weighted additio of the prie effet durig evirometal emergeies ad ormal days) is larger tha the prie effet durig ormal days, whih implies that the rate of adoptio ireases with the iidee of evirometal emergeies the most whe µ 0

21 / 44 Thus, the rate of adoptio ireases with the iidee of evirometal emergeies, but at a dereasig rate Propositio 3: The rate of adoptio uder a mix of tradable permits ad emissio stadards is lower/higher tha or the same as the rate of adoptio uder a mix of tradable permit programs If µ < µ, the rate of adoptio uder a mix of tradable permits ad emissio stadards is lower tha the rate of adoptio uder a mix of tradable permit programs The reverse holds if µ > µ Proof: Let us ompare the rates of adoptio i (5) ad (4): x q, λ = ( µ )( ) α + µ λ = ( µ )( x ) α + µ ( x ) α TPP S Durig ormal days, the adoptio ietives provided by a mixed system of tradable permits are smaller tha those provided by a mix of tradable permits ad emissio stadards The reverse holds durig evirometal emergeies That is, ( x ) α > ( )( q ) ad ( x ) α < ( x ) α µ 0 S N There is therefore a ritial value of µ determiig whih mix of poliies idues the larger adoptio savigs ad the higher rate of adoptio:

22 / 44 (30) α ( x) ( x ) µ * = > 0 α ( x) ( x) ( )( q) ( xs) α > 0 < 0 If µ < µ, the larger adoptio savigs provided by a mix of tradable permits ad emissio stadard durig ormal days offset the smaller savigs uder evirometal emergeies, ad this mixed poliy idues a higher rate of adoptio The reverse holds if µ > µ Notie that whe µ 0, the egative impat of the prie effet is larger uder a mix of tradable permits ad emissio stadards That is, TPP > x µ 0 µ 0 x Sie the et abatemet effet is smaller uder this mix, the respose of the rate of adoptio to the iidee of evirometal emergeies is also smaller, TPP < µ µ µ 0 µ 0 (see ppedix C) But as µ ireases, the prie effet disappears i the ase of a mix of tradable permits ad emissio stadards, while it ireases i the ase of a mixed system of tradable permits Therefore, λ ireases at a ireasig rate with the iidee of TPP evirometal emergeies, while λ ireases at a dereasig rate Figure N skethes propositio # 3 The ituitio behid this result is as follows I the absee of episodes of evirometal distress, the ietives provided by the mixed poliies oiide; as do the rates of adoptio If µ < µ, the larger adoptio savigs idued by a mix of tradable permits ad emissio stadards produe a larger permit prie effet, whih offsets the savigs ad redues the rate of adoptio But as µ ireases, the permit prie effet teds to zero, leadig the adoptio rate to irease O the other had,

23 3 / 44 the total prie effet ireases with µ whe a mixed system of tradable permits is implemeted The larger prie effet ireasigly offsets the et adoptio savigs, leadig the adoptio rate to derease with µ Figure N : doptio Rate Compariso λ Tradable Permits - Emissio Stadards Tradable Permits -Tradable Permits µ µ Fially, otie that the umerator i (30) gives aout of the extra adoptio savigs idued by a mix of tradable permits ad emissio stadards (TPP-EE) durig ormal days, while the deomiator gives aout of the total extra adoptio savigs idued by a mix of TPP-EE (that is, durig ormal ad emergey days) The the larger the extra adoptio savigs idued by TPP-EE durig ormal days, the higher the ritial value of µ

24 4 / 44 IV WELFRE COMPRISON It is worth askig whih mix produes the maximum soial welfare, osiderig abatemet beefits, abatemet osts, as well as the ivestmet ost related to the use of ew tehology Let us assume that the abatemet beefits durig evirometal emergeies ad ormal days are give by B ( q) = γ *( q) γ *( q) 0 ad B ( q ) = β *( q) β *( q), with γ 0 γ*( q) > β0 β*( q) ; ( B ( q))' 0; 0 ( B ( q))' 0; ( B ( q))'' 0 ad ( B ( q))'' 0 Soial welfare is the give by: N N N W = µ γ0[ λq + ( λ) q ] γ[ λq + ( λ) q ] λ ( q ) ( λ) ( q ) (3) λ N N N + [ µ ] β0[ λq + ( λ) q ] β[ λq + ( λ) q ] λ ( q) ( λ) ( q ) kdk N N Miimizig (3) with respet to[ q, q, q, q λ ], we obtai the followig FOCs: N (3) q : γ0 γ λq + ( λ) q = ( q ), 0 N N N (33) q : γ0 γ λq + ( λ) q = ( q ), N (34) q : β0 β λq + ( λ) q = ( q ), N N N (35) q : β0 β λq + ( λ) q = ( q ), (36) N N N λ: λ = µ γ0[ q q ] γ[ q q ] + ( q ) ( q ), N N N + [ µ ] β0[ q q ] βb[ q q ] + ( q ) ( q )

25 5 / 44 with = λq + ( λ) q ad B= λq + ( λ) q N N beig the total abatemet durig evirometal emergeies beig the total abatemet durig ormal days Thus, from 3-33 ad we observe that soial welfare is maximized whe adopters margial abatemet osts are the same as the o-adopters i eah state, ad that this is exatly the outome produed by a mix of tradable permit programs From (36) we observe that the optimal rate of adoptio equates the margial ost of adoptio with the margial expeted beefit i terms of ireasig abatemet aross firms durig evirometal emergeies ad ormal days ad of reduig the abatemet osts Thus, the optimal rate of adoptio depeds o the parameters of the abatemet beefit futio ad o the abatemet osts The flatter the abatemet beefit futios, the larger the expeted beefit of abatemet ad the higher the optimal rate of adoptio I terms of abatemet osts, the lower the abatemet osts of a ew tehology, the higher the optimal rate of adoptio Propositio 4: Soial welfare is maximized whe a mix of tradable permit programs is implemeted Proof: Substitutig 3-35 ito (36) we obtai the followig expressio for the optimal rate of adoptio (see ppedix D):

26 6 / 44 (37) * λ = µ ( x) + ( µ )( x) α That is, the optimal rate of adoptio oiides with the rate of adoptio idued by a mix of tradable permit programs The a mixed system of tradable permit programs idues a rate of adoptio that maximizes welfare The ituitio behid this result is as follows Uder tradable permits, diffusio of the ost-reduig tehology lowers the aggregate margial abatemet osts ad therefore lowers the permit prie This prie sigal prevets firms from overivestig i abatemet tehology if heaper permits are available, eouragig a solutio suh that the margial ost of adoptio equals the margial expeted soial et beefit If a mixed sheme of tradable permits ad emissio stadards is employed, the prie sigals are distorted If µ < µ, the larger prie effet idued by this mix leads to a rate of adoptio that is lower tha the optimal O the other had, if µ > µ, the ieffiietly smaller prie effet idued by this mix leads firms to overivest V OPTIML DOPTION RTE DURING ENDOGENOUS ENVIRONMENTL EMERGENCIES I the previous aalysis, the iidee of evirometal emergeies is exogeous However, if a sigifiat fratio of firms adopt more evirometally friedly tehologies, it is possible that the probability of evirometal rises dereases with the rate of adoptio The the soially optimal poliy i a stati settig (ie, the poliy that miimizes total abatemet osts) ould o loger be optimal To aalyze this ase, let us

27 7 / 44 assume that the probability of evirometal emergeies ourrig depeds o the rate of adoptio aordig to futio µ ( λ ), with µ '( λ ) < 0 ad µ ''( λ ) < 0 That is, the iidee of evirometal emergeies dereases with the rate of adoptio at a dereasig rate The rate of adoptio that maximizes soial welfare solves the followig problem: (38) N N N MaxW λ = µλ ( ) γ0[ λq + ( λ) q ] γ[ λq + ( λ) q ] λq ( ) ( λ) q ( ) [ ] λ N N N µλ ( ) β[ λq + ( λ) q ] β[ λq + ( λ) q ] λq ( ) ( λ) q ( ) kdk N N While the FOC for [ q, q, q, q ] remais uhaged, the FOC for the optimal rate of adoptio solves: (39) * TPP λ = λ + N N N N γ0[ λq + ( λ) q ] γ[ λq + ( λ) q ] β0[ λq + ( λ) q ] + β[ λq + ( λ) q ] Beefit ofireasedbatemet µ '( λ) N λq ( ) 0 + [ λ] q ( ) λq N ( N) + [ λ] q ( < N ) Cost ofireasedbatemet > 0 The seod term i brakets o the right-had side of (39) aouts for the effet of the adoptio rate o the iidee of evirometal emergeies, ad is equal to the margial produtivity of adoptio i terms of reduig suh iidee times the et beefit of the ireased abatemet Thus, if the et beefit of the ireased abatemet is

28 8 / 44 positive, the the optimal rate of adoptio is lower tha the rate idued by a mixed system of tradable permits Propositio 5: If the probability of evirometal emergeies dereases with the rate of adoptio, the the optimal rate of adoptio is lower tha the rate of adoptio idued by a system of tradig programs Proof: From (39) it is straightforward that the optimal rate of adoptio is lower tha the rate of adoptio idued by a system of tradable permits isofar as µ '( λ ) < 0 ad the et beefit of the ireased abatemet is positive The larger the effet of adoptio i terms of dereasig the probability of emergeies, the larger the disrepay betwee the optimal rate of adoptio ad the rate of adoptio idued by a system of tradable permits By aalogy, the larger the et beefit of ireased abatemet, the larger the disrepay betwee the optimal rate of adoptio ad the rate of adoptio idued by a mixed poliy The ituitio behid this result is as follows: The optimal rate of adoptio ireases with the expeted beefits of abatemet Sie the abatemet beefits durig ormal days are smaller ad sie the adoptio rate ireases the iidee of ormal days, the optimal rate dereases i order to offset the redued expeted abatemet beefits Propositio 6: If the probability of evirometal emergeies dereases with the rate of adoptio ad if the iidee of evirometal emergeies is low, the total welfare

29 9 / 44 uder a mixed system of tradable permits is lower/higher tha or the same as uder a mix of tradable permits ad emissio stadards Proof: Let us ompute total welfare uder a mix of tradable permits ad emissio stadards Substitutig () ad (4) ito (38), we obtai: (40) W = µλ ( ) γ0[ q] γ[ q] + λ ( )( q) ( q) ( x ) λ 0 q q x + µλ ( ) β[ ] β[ ] λ ( ) α + 4 By aalogy, substitutig () ad (3) ito (38), we obtai total welfare uder a mixed system of tradable permits: (4) TPP TPP TPP ( xs ) W = µλ ( ) γ0[ q] γ[ q] λ ( xs) α + 4 TPP TPP TPP ( x ) λ 0 q q x + µλ ( ) β[ ] β[ ] λ ( ) α + 4 * Let us assume that µ < µ That is, the rate of adoptio idued by a mix of tradable permits ad emissio stadards is lower tha that idued by a mixed system of tradable TPP permits s stated i equatio (4), sie µλ ( ) > µλ ( ), the iremetal welfare idued by a mix of tradable permits ad emissio stadards W is positive isofar as the larger expeted abatemet beefits ad the lower ivestmet osts offset the higher abatemet osts

30 30 / 44 Thus, the sig of TPP W = µλ ( ) µλ ( ) γ0( q) γ( q) β0( q) β( q) W ExpetedBeefitsof Im provedevirometalquality TPP TPP ( x ) µλ ( ) λ ( x ) s s α + µλ ( ) λ( )( q) + ( q) 4 TPP TPP ( x ) ( x ) + ( ) ( ) µλ λ x α µλ ( ) λ( x) α TPP λ λ + IvestmetSavigs ExpetedbatemetCosts of Im proved EvirometalQuality strogly depeds o the parameters of the damage futio ad o the resposiveess of the iidee of evirometal emergeies to hages i the rate of adoptio The larger the abatemet beefits durig evirometal emergeies, the ) (4 larger the W By aalogy, the larger the effet of the rate of adoptio reduig the probability of evirometal emergeies, the larger the W VI NUMERICL EXMPLE I order to illustrate the results, the followig umerial example ompares the rate of adoptio ad total welfare uder a mix of tradable permits ad emissio stadards ad a mixed system of tradable permits Parameters are hose to esure a iterior solutio ie, adoptio savigs rage i the iterval[ 0, ] The value of the parameters is preseted i Table N

31 3 / 44 Table N : Simulatio Parameters batemet beefits ormal days B ( q) = 3* q q batemet beefits emergey days B ( q) = 5* q 005* q No-adopters abatemet ost dopters abatemet ost Emissio redutio durig ormal days Emissio redutio durig emergey days 5*q *q q = 05 q = 05 Notie that the abatemet beefit futio durig evirometal emergeies is flatter tha that durig ormal days, leadig to a higher level of required abatemet Thus, 5% of total emissios must be redued durig ormal days ad 50% durig otigeies Figure N skethes the rate of adoptio uder both mixes whe the probability of evirometal emergeies is exogeous s expeted, there is a ritial value of the iidee of evirometal emergeies that determies whih mix of poliies idues the highest rate of adoptio If µ < 38%, the rate of adoptio uder the mix of tradable permits ad emissio stadards is lower; the reverse holds whe µ > 38%

32 3 / 44 Figure N : doptio Rate uder Differet Mixes of Poliies doptio Rate Iidee of Evirometal Emergeies TPP-EE* TPP-TPP** (*)TPP-EE: Mix of tradable permits ad emissio stadards (**) TPP-TPP: Mixed system of tradable permits Figure N 3 skethes total welfare uder both mixes of poliies s expeted, a mix of tradable permit programs maximizes total welfare, sie less abatemet osts ad ivestmet osts are required to ahieve the same aggregate emissio redutio

33 33 / 44 Figure N 3: Welfare uder Differet Mixes of Poliies Welfare Iidee of Evirometal Emergeies TPP-EE* TPP-TPP** (*)TPP-EE: Mix of tradable permits ad emissio stadards (**) TPP-TPP: Mixed system of tradable permits Fially, N 4 skethes total welfare uder both mixes of poliies whe the iidee of evirometal emergeies is edogeous I assume that the iidee of evirometal emergeies dereases with the rate of adoptio aordig to the futio µ ( λ ) = µ *( 0 λ ) Thus, µ '( λ ) < 0 ad µ ''( λ ) < 0 For the seleted parameters, the mixed system of tradable permits produes the largest soial welfare

34 34 / 44 Figure N 4: Welfare uder Differet Mixes of Poliies Whe the Iidee of Evirometal Emergeies is Edogeous Welfare Iidee of Evirometal Emergeies TPP-EE TPP-TPP VII CONCLUSIONS ND FURTHER RESERCH This paper aalyzes the uiteded impats of the iteratio of tradable permits with seasoal diret regulatios o the rate of adoptio of advaed abatemet tehologies It is show that if the iidee of evirometal emergeies is exogeous, the mixig diret regulatios with tradable permits idues a ieffiiet rate of adoptio, while the use of a system of tradable permits maximizes soial welfare O the other had, if the iidee of evirometal emergeies is edogeous, the the mix of tradable permits ad emissio stadards ould evetually offer a higher level of soial welfare tha the

35 35 / 44 alterative approah The results rely o the assumptio that trasatio ad moitorig ad eforemet osts are similar i differet mixed poliies If this is true, soial welfare depeds o the ompariso betwee et abatemet beefits ad ivestmet osts However, if a higher availability of a ew tehology ould redue the osts of moitorig ad eforig, soial welfare maximizatio ould require a higher rate of adoptio O the other had, if implemetig a evirometal emergey market is too ostly, the the effiiey gais of implemetig a mixed system of tradable permits should be disregarded This paper addresses the effets of the iteratio betwee emissio stadards ad tradable permit poliies Both are quatity poliies that assure that a fixed level of abatemet will be attaied i the ed, regardless of the total abatemet osts required for that purpose If prie poliies were used istead, the the emissio prie would be fixed by the regulator from the begiig ad would ot deped o firms adoptio deisios The lak of a egative prie effet would therefore idue a higher rate of adoptio, whih ould be sub-optimal I olusio, it is ot obvious that a additioal poliy istrumet would preserve the effiiey properties of the existet poliy The best omplemetary poliy should preserve the beefits of the existig poliy to the greatest possible extet ad should be admiistratively feasible at a reasoable ost Further researh is required to larify the ompatibility amog poliy istrumets ad what mix of istrumets is optimal whe dealig with situatios that require the use of more tha oe poliy

36 36 / 44 VIII REFERENCES Bawa, Vijay (975): O Optimal Pollutio Cotrol Poliies, Maagemet Siee, Vol, No 9 Baumol, W ad Oates, W (998): The Theory of Evirometal Poliy, Cambridge Uiversity Press Jug, C, K Krutilla ad R Boyd (996) Ietives for dvaed Pollutio batemet Tehology at the Idustry Level: Evaluatio of Poliy lteratives Joural of Evirometal Eoomis ad Maagemet, Vol 0, No, pp 95- Keohae, Nathaiel (999):"Poliy Istrumets ad the Diffusio of Pollutio batemet Tehology", mimeo, Harvard Uiversity Millima, SR ad R Prie (989) Firm Ietives to Promote Tehologial Chage i Pollutio Cotrol, Joural of Evirometal Eoomis ad Maagemet, Vol 7, No 3, pp Nelisse, Dagmar ad Requate, Till (004): "Pollutio-Reduig ad Resoure- Savig Tehologial Progress", Eoomis Workig Paper No , Christia- ibrehts- Uversität Kiel Requate, T ad Uold, W (00): O the Ietives Created by Poliy Istrumets to dopt dvaed batemet Tehology If Firms are symmetri, Joural of Istitutioal ad Theoretial Eoomis

37 37 / 44 ppedix The rate of adoptio uder a mix of tradable permits ad diret regulatios is give by: () x q π = λ = ( µ )( ) α + µ Differetiatig λ with respet to µ ad re-orgaizig terms yields: x () = q [ α ( x) ( µ )( αx) µ + µ doptiosavigs doptiosavigs Uder UderNormalDays PrieEffet EvirometalEmergeies NetbatemetEffet O the other had, market learig i the permit market requires total abatemet to be equal to the weighted abatemet doe by adopters ad o-adopters: N q ( x, ) q ( x) ( x, ) q ( x), (3) = λ µ + [ λ µ ] with q ( x ) ( x) = ad q N ( x ) ( x) = N Substitutig λ, q ( x ), ad q ( x ) ito (3), we obtai: (4) x q ( µ )( x) α µ q = + + x ( µ )( x) α µ q + Differetiatig with respet to x ad µ ad solvig for dx / dµ yields:

38 38 / 44 (5) αx [ α( x ) q dx = dµ 3( µ )( x) α + µ ( )( q) α + 4 > 0 ppedix B The rate of adoptio uder a mix of differetiated tradable permits ad diret regulatios is give by: (B) TPP π = λ = ( µ )( x) + µ ( xs) α Differetiatig (B) with respet to µ ad re-orgaizig terms yields: (B) TPP = ( xs) α ( x) α + µ doptiosavigs doptiosavigs Uder UderNormalDays EvirometalEmergeies NetbatemetEffet ( xs ) ( x ) µ ( xs ) + ( µ )( x ) α µ µ PrieEffet PrieEffet Uder UderNormalDays EvirometalEmergeies O the other had, market learig i the permit markets requires total abatemet to be equal to the weighted abatemet doe by adopters ad o-adopters i eah state: (B3) TPP TPP N q = λ ( x, µ ) q ( x) + λ ( x, µ ) q ( x),

39 39 / 44 (B4) TPP TPP N q = λ ( xs, µ ) q ( xs) + λ ( xs, µ ) q ( xs), with q ( x ) ( x) = ; N ( x ) q ( x) = ; q ( xs ) ( xs) = ad N ( xs ) q ( xs) = TPP N Substitutig λ, q ( x ) ad q ( x ) ito (B3), we obtai: (B5) x q = µ ( xs) α + ( µ )( x) α + x µ ( xs) α + ( µ )( x) α Differetiatig with respet to x ad µ, ad solvig for dx / dµ yields: (B6) dx αx ( xs) α ( x) α = < 0 dµ µ ( xs) α + 6( µ )( x) α + TPP N Substitutig λ, q ( x ), ad q ( x ) ito (B3), we obtai: s s (B7) xs q = µ ( xs) α + ( µ )( x) α + x s µ ( xs) α + ( µ )( x) α Differetiatig with respet to x s ad µ, ad solvig for dxs / dµ yields: (B8) dx αx s ( xs) α ( x) α s = < 0 dµ ( µ )( x) α + 6 µ ( xs) α + Substitutig (B6) ad (B8) ito (B) yields:

40 40 / 44 (B9) µ TPP = ( xs) α ( x) α NetbatemetEffet α( x ) s ( xs) α ( x) α α( x) ( xs) α ( x) α µα ( xs ) ( µ ) α ( x ) + 3 µ ( xs) α + ( µ )( x) α + 3( µ )( x) α + µ ( xs ) α PrieEffet PrieEffet UderCotigeies UderNormalDays ppedix C The effet of hages i the iidee of evirometal emergeies o the rate of adoptio is give by: ( µ )( x ) α [ α( x ) q = µ + 3( µ )( x ) α + µ ( )( q ) α + NetbametEffet 4 λ (C) { q [ α ( x) } PrieEffet Let β 0 deote the et abatemet effet ad β ( ) = x α ad the β = ( q ) adoptio savigs uder permits ad uder the emissio stadard, respetively The, (C) a be re-writte as: βα (C) = β 0 = 0 µ 3βα β µα + + ( µ ) 4

41 4 / 44 Computig (C) whe µ 0 yields: βα (C3) µ = 0 β0 µ 3βα + 4 O the other had, if a mixed system of tradable permits is used, this effet is give by: (C4) µ TPP = ( xs) α ( x) α NetbatemetEffet µα ( x ) s ( xs) α ( x) α ( µ ) α ( x) ( xs) α ( x) α + 3 µ ( xs) α + ( µ )( x) α + 3( µ )( x) α + µ ( xs ) α PrieEffet PrieEffet EvirometalEmergeies NormalDays Let γ 0 deote the et abatemet effet ad γ ( ) = x α ad γ ( ) = x S α the adoptio savigs durig ormal days ad durig evirometal emergeies, respetively The µ λ TPP a be re-writte as: (C5) TTP αγ αγ = γ 0 µ 3 αγ ( µ ) αγ 3αγ µαγ µ 4 ( µ ) 4 Computig (C5) whe µ 0 yields:

42 4 / 44 (C6) µ TPP αγ µ = 0 γ 0 3αγ + 4 Let us ompare (C3) ad (C6) Sie β > γ, the absolute value of the prie effet uder a mix of tradable permits ad emissio stadards is higher: βα αγ (C7) > 3βα + 3αγ+ 4 4 O the other had, γ 0 > β0 sie ( x) ( x) ad ( )( q) < ( xs) The: βα αγ (C8) β0 γ0 < 3βα + 3αγ+ 4 4 I other words, the effet of hages i the iidee of evirometal emergeies o the rate of adoptio is higher uder the mixed system of tradable permits whe µ 0; ie, TPP < µ µ µ 0 µ 0

43 43 / 44 ppedix D Soial welfare is give by the followig expressio: N N N W = µ γ0[ λq + ( λ) q ] γ[ λq + ( λ) q ] λ ( q ) ( λ) ( q ) (D) λ N N N + [ µ ] β0[ λq + ( λ) q ] β[ λq + ( λ) q ] λ ( q ) ( λ) ( q ) kdk N N Maximizig (D) with respet to[ q, q, q, q λ ], we obtai the followig FOCs: N (D) q : γ0 γ λq + ( λ) q = ( q ), 0 N N N (D3) q : γ0 γ λq + ( λ) q = ( q ), N (D4) q : β0 β λq + ( λ) q = ( q ), N N N (D5) q : β0 β λq + ( λ) q = ( q ), (D6) N N N λ: λ = µ γ0[ q q ] γ[ q q ] + ( q ) ( q ), N N N + [ µ ] β0[ q q ] βb[ q q ] + ( q ) ( q ) N where = λq + ( λ) q ad B= λq + ( λ) q N are the total level of abatemet durig evirometal emergeies ad ormal days, respetively From (D) ad (D3) we have that: N (D7) ( q ) = ( q ) = δ

44 44 / 44 Substitutig (C7) ito (C) we have that: (D8) γ 0 γ = δ From (D4) ad (D5) we have that: N (D9) ( q ) = ( q ) = δ Substitutig (D9) ito (D4) we have that: (D0) β0 βb = δ Substitutig (D8) ad (D0) ito (D6) we have that: λ = µ δ [ N ] ( N ) ( ) [ N ] ( N ) ( q q + q q + µ δ q q + q q ) (D) [ ] Fially, substitutig (D7) ad (D9) ito (D) we have that: (D) λ = µδ ( ) + ( µ )( δ) α, ad sie δ = x ad δ = x, (D3) λ = µ ( x) + ( µ )( x) α as it is stated i equatio (4)