Tradable Emission Permits Regulations: The Role of Product Differentiation

Transcription

1 Internatonal Journal of Busness and Eonoms, 005, Vol. 4, No. 3, 49-6 radable Emsson Permts Regulatons: he Role of Produt Dfferentaton Sang-Ho Lee * Department of Eonoms, Chonnam Natonal Unversty, Korea Sang-Ha Park Department of Soal Welfare, Naju College, Korea Abstrat hs paper examnes the role of produt dfferentaton wthn the model of Sartzetaks (997, 004) and shows that onsumer surplus may be redued under a tradable emsson permts system rather than a ommand and ontrol system when there s a hgh degree of produt dfferentaton or less ompetton between two frms. We also nvestgate omparatve stat effets of the degree of produt dfferentaton on equlbrum output and abatement levels under the two regulatory regmes. Key words: ommand and ontrol system; produt dfferentaton; tradable emsson permts system JEL lassfaton: L; L5; Q. Introduton In lght of the nreasng mportane of envronmental regulaton, the wdespread aeptane of a tradable emsson permts (EP) system generates an nterestng debate among poly makers on the effeny of EP regulaton and ts omparson wth the ommand and ontrol (CAC) regulaton. Many researhers are of the opnon that governments an promote soal welfare by mplementng a EP system, whh mnmzes abatement osts when they dffer between frms. However, even under a ompettve permts tradng market, Borensten (988) and Malueg (990), for example, ndated the possblty that a EP system may redue both onsumer surplus and soal welfare when the produt market s not perfetly ompettve. In addton, Malk (990, 00), Keeler (99), and Stranlund and Dhanda (999) ast doubt on the effeny propertes of the EP system when frms may be nonomplant. Reeved November 6, 004, revsed September 8, 005, aepted January 5, 006. * Correspondene to: Department of Eonoms, Chonnam Natonal Unversty, 300 Yongbong-dong, Bukgu, Gwangju , Korea. E-mal: sangho@honnam.a.kr. he authors are ndebted to two anonymous referees whose valuable suggestons and nsghts mproved the paper.

2 50 Internatonal Journal of Busness and Eonoms In ontrast, Sartzetaks (997) onsdered a homogeneous Cournot duopoly model under the assumpton of onstant and equal osts of produton between frms and showed that EP regulaton an nrease not only onsumer surplus but also soal welfare under ertan ondtons. However, Sartzetaks (004) demonstrated that f frms dffer n both produton and abatement tehnologes, ompetton n the emsson permts market annot always assure effeny when the produt market s duopolst. he present paper extends the analyss of Sartzetaks (997, 004) by onsderng the role of produt dfferentaton and shows that onsumer surplus mght be redued under a EP rather than a CAC system when there s a hgh degree of produt dfferentaton or less ompetton between two frms. hs result mples that the degree of produt dfferentaton s an mportant fator that needs to be taken nto aount n the desgn of EP regulatons. We also nvestgate omparatve stat effets of the degree of produt dfferentaton on equlbrum output and abatement levels under the two regulatory regmes onsdered.. he Model We examne the Cournot duopoly model where frms sell dfferentated goods and ompete by settng quanttes. Extendng reent work by Sartzetaks (997, 004), we analyze n detal the effet of produt dfferentaton on onsumer surplus and soal welfare. In lne wth Dxt (979) and Sngh and Vves (984), we postulate that there s a representatve onsumer whose preferenes for onsumpton of the two goods are desrbed by U = a ( q + q ) q + γ q q + q, () where a (>0) s a onstant measure of market sze, q s the output of the frm ( =, ), and γ ( 0,) aptures the degree of produt dfferentaton: the hgher γ, the lower the degree of produt dfferentaton. hus, a low γ orresponds to a stuaton of rather lmted ompetton and a hgher γ aptures ntensfed ompetton. he extreme ases are llustratve. As γ approahes 0, the two frms are effetvely loal monopolsts. As γ approahes, the two goods are nreasngly homogeneous. In fat, γ = orresponds to the duopoly wth homogeneous produts ase of Sartzetaks (997, 004), where two produts are perfet substtutes. hs mples that a representatve onsumer has a lnear ndfferene urve n hs preferenes spae. herefore, the preferenes wth γ ( 0,) that are defned n () represent onsumers wth onvex preferenes. hs spefaton results n a lnear demand struture wth p = a q γ q,, j =,, j, () j where p s the pre of good.

3 Sang-Ho Lee and Sang-Ha Park 5 Produton generates an emsson E of a pollutant. Followng the assumptons of Malueg (990) and Sartzetaks (997, 004), the emsson level s dependent on both the produton level q and the emsson abatement atvty level z. Spefally, E = ( ρ z ) q where ρ (> z >0) s the onstant emsson rate per unt of output, whh s the dental for the two frms. On the ost sde, lke Sartzetaks (997) we assume that total osts are nreasng n output and abatement: C ( q, z ) = e z q, where e represents the tehnologal dfferene between the two frms. In other words, wth the same q and z, the larger e, the greater the osts of emsson reduton. We assume that e > e > 0 so that frm () has a less (more) effent emsson reduton tehnology. Fnally, t s assumed that the government plans to redue emsson levels to E, whh s determned n the poltal arena, perhaps through nternatonal agreements on emsson redutons or foldng under the pressure of speal nterest groups. he problem that envronmental poly makers onsder s to hoose between a CAC system and a EP system to ontrol urrent polluton levels. 3. Command and Control Regulaton Under a CAC system, regulators mpose a non-tradable emsson quota on frm ( E ) and on the ndustry ( E = E + E ). Here, we onsder the symmetr ase where E = E. Frm hooses output and abatement levels n order to maxmze ts profts π = ( a q γ q ) q e z q subjet to the emsson onstrant j E ρ z q. hat s, the optmzaton problem s: ( ) L ( ) ( ( ) ) q = a q γ q j q e z q + λ E ρ z q max > { 0, z 0} > hen, the frst order Kuhn-uker ondtons for frms are as follows: L q L z = a q = e q z L = E λ ( ρ z ) = 0,. (3) γ q e q z λ j (4) + λ q = 0, (5) L λ ( ρ z ) q 0, λ 0, λ = 0. From (5), the mplt pre for the emsson quota gven q s equal to the margnal ost of emsson abatement,.e., λ q = e z q = C z > 0. hus, the emsson onstrant n (6) s bndng,.e., E ( ρ z ) q = 0. Now, substtutng λ = e zq nto (4), we obtan two output response funtons for eah frm. Solvng these two smultaneous equatons gves the followng optmal output and abatement levels for frm at equlbrum: (6)

4 5 Internatonal Journal of Busness and Eonoms ( γ ) ρ( λ γλ ) a j q =, (7) 4 γ z λ = e q = e λ ( 4 γ ) ( a( γ ) ρ( λ γλ ) j. (8) o ontnue our analyss, we alulate the sum of two produts and outputs dfferene as follows: ( λ + λ ) a ρ Q q + q = + γ, (9) ρ( λ λ ) q q =. γ (0) Note that the output dfferene depends on the mplt pre dfferene. In partular, the frm that has a lower mplt pre for emssons produes more output n equlbrum;.e., λ > λ mples q > q. Note also that from the j j bndng emsson onstrant n (6), z s proportonal to q. hs also mples that λ > λ j yelds z > z. hus, we have the followng lemma (see Appendx A for j the proof). Lemma : If e > e, then λ > λ. Proposton : Under a CAC regulaton system, a more (less) effent frm has hgher (lower) output levels and hgher (lower) emsson abatement efforts n equlbrum. (In our notaton: q > q 0 and z > z 0.) > > he proposton shows that a less (more) effent frm has a hgher (lower) mplt pre. hus, ths frm produes lower (hgher) outputs, leadng to lower (hgher) abatements. However, ths result depends on both the degree of produt dfferentaton and the emsson quota. For example, from (A) n Appendx A, we see that f the regulator redues the emsson quota for eah frm, ts pre rses: λ E < 0. Now we onsder omparatve stat of the degree of produt dfferentaton. Usng the omparatve stats of Edln and Shannon (998), we know that the optmal output level q s nreasng n the degree of produt dfferentaton f q π z q, z. hen, we obtan ( π ) s dereasng n γ at ( ) π q π z a q γq q e z q ( q, z ) = j e q z, whh s dereasng n γ. herefore, q < 0, mplyng Q < 0. hs mples that as the degree of produt dfferentaton dereases (.e., γ nreases or, equvalently, ompetton nreases), equlbrum output dereases. In addton, from the same proedure of obtanng q, we obtan z < 0. hs mples that

5 Sang-Ho Lee and Sang-Ha Park 53 as the degree of produt dfferentaton dereases, the equlbrum abatement effort dereases. Fnally, from the equlbrum ondton n (5), we easly derve that the mplt pre λ nreases (dereases) as long as both q and z nrease (derease). herefore, f the degree of produt dfferentaton dereases or the degree of ompetton nreases, the mplt pre also dereases: λ < 0. he ntuton s as follows: sne the equlbrum output for eah frm dereases as γ nreases, the frms put a lower value on the emsson quotas relatve to the ase of a lower γ,.e., the mplt pre for the emsson quota dereases. However, the effets of the degree of produt dfferentaton on eah frm dffer. For example, from (A) n Appendx A, we obtan that ( λ ) λ < 0 when γ ( 0,),.e., λ < λ < 0. herefore, as the degree of produt dfferentaton dereases, the mplt pre of a less effent frm dereases faster than that of a more effent frm. 4. radable Emsson Permts Regulaton Under a EP system, regulators assgn an emsson quota E to eah frm and allow t to trade emsson permts at the market pre. Followng Sartzetaks (997, 004), we assume that the market pre of permts s determned by the market learng pre. hus, eah frm behaves as a pre taker n the emsson market. herefore, f we defne the net demand of frm as D = E ( ρ z ) q, total net demand of emsson permts s zero at the market equlbrum D + D = 0. Eah frm maxmzes the followng proft funton under a EP system: max π ( a q γqj) q eq z t( ( ρ z) q E) { q > 0, z > 0} =, () where t s the market learng pre of permts. he frst-order ondtons are π q = a q π = e q z + tq z γ q e q z j t ( ρ z ) q = 0, () = 0. (3) From (3), we see that the market pre for emsson permts gven q s equal to the margnal ost of the emsson abatement,.e., tq = eq z = C z > 0. Substtutng ths nto () and solvng two output response funtons for eah frm smultaneously, we an obtan the followng optmal output and abatement levels for frm at equlbrum: a tρ q =, + γ (4) t t( + γ ) z = =. e q e a tρ (5) ( )

6 54 Internatonal Journal of Busness and Eonoms From (4), we see that eah frm has the same output levels at equlbrum. hs s due to the symmetr market assumpton haraterzed n (). From q = q, we also have e z = e z at equlbrum from (5). herefore, z > z when e > e. hs ndates that a more (less) effent frm makes hgher (lower) abatement efforts to redue emssons. Fnally, for omparson, we observe that Q q + q ( a ρt) = + γ. (6) Proposton : Under a EP system, both frms have the same output levels and a more (less) effent frm makes hgher (lower) abatement efforts n equlbrum. (In our notaton: q = q 0 and z > z 0.) > > Proposton also depends on the degree of produt dfferentaton. For omparatve stats of the degree of produt dfferentaton, onsder the equlbrum haraterzed by (4) and (5) under a EP system. Substtutng these nto the total net demand of the emsson quota, where D + D = { ( ) } = 0 = E ρ z q, and rearrangng yelds e e ( aρ ( + γ ) E ) ( + γ )( e ) + e + 4ρ ee t =. (7) One an easly hek that the market pre of permts s hgher f the regulator redues the emsson quota for eah frm,.e., t E < 0, f the degree of produt dfferentaton nreases, or f γ dereases,.e., t < 0. herefore, a hgh (low) degree of ompetton between two frms mples a lower (hgher) permts pre. From (4) and (6), we obtan that q t < 0, whh mples that Q t < 0. Also, from (5), t follows that z t > z t > 0 sne e > e. hs mples that as the permt pre nreases, frms have an nentve to redue outputs and to nrease abatements so as to derease ther need for permts. Fnally, n order to see the effet of produt dfferentaton on outputs and abatements, substtutng the equlbrum value of t from (7) nto (4) and (5) yelds q < 0 and z < 0, respetvely. herefore, as the degree of produt dfferentaton dereases or γ nreases, equlbrum output and abatements also derease under a EP system. 5. Comparng Poly Regmes We frst provde a omparson n terms of output and abatement levels under the two regulatory regmes. We summarze our fndngs n Lemma (see Appendx A for the proof.) Lemma : If e > e, then 0 λ < < λ t. < t and < ( λ + ) λ Lemma shows that when two frms trade permts n the emsson market

7 Sang-Ho Lee and Sang-Ha Park 55 under a EP system, the permt pre s determned at a level lower than the mplt pre of the emsson quota of the less effent frm and hgher than that of the more effent frm (.e., 0 < λ < t < λ ) n order to make tradng permts possble. However, the permts pre level s less than half of the total mplt pres levels (.e., t < ( λ + λ) ) that s, the average margnal abatement ost of two frms. hs mples that the more effent frm an earn hgher profts ompared to the less effent frm. Lemma 3: If e > e, then the followng relatonshps hold: ( ( λ t) + γ ( t λ ) ρ j Δq q q =, (8) 4 γ tq λ q Δ z z z =, (9) e q q ρ( λ + λ ) t ΔQ Q Q =. (0) + γ ( ) A few remarks are n order. Frst, usng Lemmas and 3, we obtan q > q and q < q from (8). hs mples that the less (more) effent frm nreases (dereases) ts output level by buyng (sellng) the emsson permts under a EP system. Usng ths result, we observe that z > z > z > z from (9). herefore, a more (less) effent frm nreases (dereases) ts abatement efforts under a EP system. Fnally, we onlude that Q > Q from (0). hs mples total outputs nrease by shftng the regulatory regmes from a CAC system to a EP system. hs s so beause the permts pre s lower than the average margnal abatement ost of the two frms. hus, the output nrement of the less effent frm overwhelms the output derement of the more effent frm. We summarze these results n Proposton 3. Proposton 3: Shftng regulatory poly from a CAC system to a EP system mples that () the less (more) effent frm nreases (dereases) ts output level, () the less (more) effent frm dereases (nreases) ts abatement efforts, and () total outputs nrease. Usng the result that total output nreases under a EP system (.e., Q > Q ), we onlude that f the two frms supply dental and perfetly substtutable produts (.e., γ = ), market pre dereases. hus, onsumer surplus neessarly nreases under a EP system, a result establshed n Sartzetaks (997). Intutvely, ths s beause the onsumer s ndfferene urve n preferenes spae s lnear. hus, the result that total output nreases mples that onsumer surplus nreases. However, from q < q = q < q, the effet of produt dfferentaton on onsumer surplus n eah market dffers when γ. Under the preferenes defned n (), when the onsumer s preferenes are onvex, onsumer surplus mght not nrease even though total output nreases. For example, onsder the extreme ase

8 56 Internatonal Journal of Busness and Eonoms of γ = 0 where the two markets are ndependent. hen the onsumer surplus n market nreases as muh as ( q + q )( q q ), whh s postve, whle that of market dereases as muh as ( q + q ) ( q q ), whh s negatve. Hene, onsumer surplus nreases only f q > q + ( q q ) ( + k) where k = ( q + q ) ( q + q ) <. hus, the sgn of the nrement n total onsumer surplus depends on the relatve sze of equlbrum outputs n eah market. Next, we provde a omparson n terms of the onsumer surplus and soal welfare under the two regulatory regmes. Frst, the onsumer surplus s defned as q + γ q q + q CS = U p q p q =, where U s the onsumer s utlty defned n (). hen, the dfferene n onsumer surplus between the two regulatory regmes s ( Q Q )( Q + Q ) ( )( q q q q ) ΔCS CS CS = γ, () Note that both terms n () are postve. herefore, the sgn of Δ CS n general s ambguous. (From the Proposton 3, we have q + q > q + q. By squarng both sdes of ths nequalty, we have 4 q q > ( q ) + ( q ) + q q sne q = q. From ths we onlude that the seond term n () s postve sne q q q q > 0.) hs mples that the dfferene n onsumer surplus n () depends on the degree of produt dfferentaton. In partular, we have the followng relatonshp: ΔCS > 0 f γ > ( Q )( Q + Q ) ( q q q q ), () Q Note that ( Q Q )( Q + Q ) ( q q q q ) > 0, whh mples that there s a threshold for γ below whh onsumer surplus dereases under a EP system. In ontrast, the dfferene n soal welfare s the dfferene between the dfferene of onsumer utlty n () and the ost hanges: ΔSW SW = SW Q + Q ( Q Q ) a + ( γ )( q q q q ) e ( q z ) e ( q z ), = = (3) where γ =. Note that the envronmental damage s not nluded n (3) sne the emsson level, E, s the same under two dfferent poly regmes. Note also that the frst term and the seond term are postve whle the last term of [ e ( ) ( ) ] = q z e = q z mght be postve sne z > z > z > z and q < q = q < q. hus, the sgn of Δ SW n general s ambguous. herefore, the dfferene n soal welfare n (3) also depends on the degree of produt dfferentaton. We have that

9 Sang-Ho Lee and Sang-Ha Park 57 ΔSW > 0 f ( Q Q )( a ( Q + Q ) ) e ( q z ) e ( q z ) = = ( q q q q ) γ < +. (4) Note that the hange n soal welfare always nreases under a EP system by as muh as ( Q Q )( a ( Q + Q ) ) [ e ( ) ( ) ] > 0 = q z e = q z. herefore, soal welfare nreases f the hange n total output outweghs the hange n total abatement osts. As ponted out n Sartzetaks (004), the ntuton of ths result s easer to understand n the ontext of the seond best problem, where the envronmental poly maker hooses between a CAC system and a EP system. On the one hand, due to mperfet ompetton n a dfferentated produt market whh lessens ompetton between the frms, the less effent frm produes hgher output whle the more effent frm produes lower output under a EP system (.e., q < q = q < q ). On the other hand, due to non-tradable emsson quotas, the less effent frm devotes more resoures to abatement atvty whle the more effent frm takes devotes fewer resoures to abatement atvty under a CAC system (.e., z > z > z > z ). hus, allowng frms to transfer emsson permts through a ompettve market orrets the abatement msalloaton problem but ould aggravate the produton msalloaton problem n a dfferentated produt market. herefore, the hange n soal welfare depends not only on produton ost dfferenes as n Sartzetaks (004) but also on the degree of produt dfferentaton. 6. Example In ths seton, we examne a smple example for further omparatve analyss. Spefally, we onsder a numeral example wth a = 5, e = 9, e = 3, ρ =, and E =3/. We obtan results for varous values of γ as reported n ables through 3. Frst, from able, we observe the results ndated n Proposton under a CAC system. In partular, we have λ < 0, q < 0, and z < 0. As a onsequene, as the degree of produt dfferentaton dereases or ompetton nreases, proft dereases and onsumer surplus nreases but soal surplus dereases: π < 0, Π < 0, CS > 0, and SW < 0, where Π s ndustry proft at equlbrum n a CAC system. Seond, from able, the results of Proposton are verfed under a EP system. In partular, we have t < 0, q < 0, and z < 0. As the degree of produt dfferentaton dereases or ompetton nreases, proft dereases and onsumer surplus nreases but soal surplus dereases: π < 0, Π < 0, CS > 0, and SW < 0, where Π s ndustry proft at equlbrum n a EP system.

10 58 Internatonal Journal of Busness and Eonoms able. CAC System γ λ λ q q Q z z π π π s sw able. EP System γ t q q Q z z π π π s sw

11 Sang-Ho Lee and Sang-Ha Park 59 able 3. Comparson between CAC System and EP System γ ΔQ Δπ Δπ Δπ Δs Δsw Fnally, we ompare the two regulatory poles by onsderng able 3, whh provdes some nterestng results as the regulatory regme shfts from a CAC system to a EP system. Frst, we have ΔQ < 0, whh mples that the effets of the regulatory poly hange on the nrement of total output dereases as ompetton nreases. hs s beause the tradng of permts s lmted under severe ompetton. Seond, we have Δπ < 0 < Δπ and ΔΠ < 0. hat s, as ompetton nreases, the proft nrement of the less (more) effent frm s nreasng (dereasng), but the nrement of ndustry proft s dereasng. hs mples that the effet of the proft nrement of the more effent frm on ndustry proft s larger than that of the less effent frm. hs s so beause a more effent frm an earn greater proft ompared to a less effent frm by partpatng n permts tradng. (Reall that the permt pre level s less than half of the total mplt pre level (.e., t < ( λ ) + λ ) that s, the average margnal abatement ost of the two frms.) Fnally, we have ΔCS > 0 and ΔSW < 0 : as ompetton between the two produts nreases, the nrement of total output nreases. hus, the nrement of onsumer surplus also nreases but soal welfare dereases. wo remarks are noteworthy. Frst, the nrement of onsumer surplus mght be negatve when the degree of produt dfferentaton s hgh. In partular, ths ours when γ 0. n ths numeral example. hs mples that the Pareto effeny of tradng permts s restrted under a hgh degree of produt dfferentaton. Seond, the nrement of soal welfare s always postve rrespetve of the degree of produt dfferentaton. In partular, sne ΔSW < 0 and ΔSW > 0 when γ =, ths ours for all degrees of produt dfferentaton n ths numeral example. hese two observatons mply that as the degree of produt dfferentaton dereases, the net gan n aggregate profts drops faster than the gan n onsumer surplus nreases.

12 60 Internatonal Journal of Busness and Eonoms 7. Conludng Remarks In ths paper, we onsder the ase of a duopoly produng a dfferentated produt and dentfy the extent of produt dfferentaton as the drvng fore of our results under the spefed envronmental poles. In partular, we show that a CAC system gves a greater onsumer surplus rather than a EP system when there s a hgh degree of produt dfferentaton or less ompetton between the two frms. We also nvestgate omparatve stat effets of the degree of produt dfferentaton on equlbrum output and abatement levels under the two regulatory regmes. hese results show that produt dfferentaton an play a sgnfant role n the desgn and mplementaton of regulatory poly. Future researh may address the role of produt dfferentaton n a number of alternatve settngs to hek the robustness of our results. Appendx A A. Proof of Lemma Substtutng q n (7) and E = ( ρ z ) q n (6) yelds e ρa λ = hs mples that λ 3 ( γ ) + 4ρ e e a 4e e γρ E ( 4 γ ) j j j 4( ρ e + )( ρ e + ) γ ( ) ( e e )( γ ) aρ E( + γ ) 4 γ + 4ρ ( e + e ) + 4ρ e e z n (8) nto the bndng equaton j e E 8e e E ρ j. (A) ( E ) ( 4 γ )( e e ) aρ ( + λ) 4 4 γ + 4ρ ( e + e ) + 4ρ ee λ = =. (A) 4 Sne the denomnator n (A) s postve, the sgn of λ λ s determned by the sgn of the last term n the numerator, aρ ( + γ ) E, when e > e. Sne q + q = ( a ρ ( λ + λ )) ( + γ ) n (9) and λ s postve, we know that ρ ( q + q ) < aρ ( + γ ). hen, sne z s postve, we have ρ q > E from (6). hus, ρ ( q + q ) > E. herefore, ombnng these two nequaltes leads to E < ρ ( q + q ) < aρ ( + ). γ A. Proof of Lemma Frst we know that the total emsson quota, E, under a EP system s the same as that under a CAC system, n whh E = E + E = ( ρ z ) q + ( ρ z ) q at equlbrum. Substtutng the equlbrum haraterzed n (7) and (8) under a CAC system nto E and rewrtng (7) yelds t e ( e ρ + ( + γ )) λ + e ( e ρ + ( + γ )) ( + γ )( e ) + e + 4ρ ee =. (A3) λ

13 Sang-Ho Lee and Sang-Ha Park 6 Lettng B e e ρ + e ( + ), we an rewrte (A3) as t = γ B B + B = λ + λ. (A4) B B + B hs ndates that the emsson permt pre t s a lnear ombnaton of mplt pres, λ and λ. From Lemma, where λ > λ when e > e, we have 0 < λ < t < λ. Note also that f e > e, then B > B. hus, B ( B + B) > /. hs mples that the weght for λ s smaller than that for λ,.e., t < ( λ + λ). Referenes Borensten, S., (988), On the Effeny of Compettve Markets for Operatng Lenses, Quarterly Journal of Eonoms, 03, Dxt, A., (979), A Model of Duopoly Suggestng a heory of Entry Barrers, Bell Journal of Eonoms, 0, 0-3. Edln, A. S. and C. Shannon, (998), Strt Monotonty n Comparatve Stats, Journal of Eonom heory, 8, 0-9. Hung, N. M. and E. S. Sartzetaks, (998), Cross-Industry Emsson Permts radng, Journal of Regulatory Eonoms, 3, Keeler, A., (99), Nonomplant Frms n ransferable Dsharge Permt Markets: Some Extensons, Journal of Envronmental Eonoms and Management,, Malk, A. S., (990), Markets for Polluton Control when Frms are Nonomplant, Journal of Envronmental Eonoms and Management, 8, Malk, A. S., (00), Further Results on Permt Markets wth Market Power and Cheatng, Journal of Envronmental Eonoms and Management, 44, Malueg, D. A., (990), Welfare Consequenes of Emsson Credt radng Programs, Journal of Envronmental Eonoms and Management, 8, Sartzetaks, E. S., (997), radeable Emsson Permts Regulatons n the Presene of Imperfetly Compettve Produt Markets: Welfare Implatons, Envronmental and Resoure Eonoms, 9, Sartzetaks, E. S., (004), On the Effeny of Compettve Markets for Emsson Permts, Evronmental and Resoure Eonoms, 7(), -9. Sngh, N. and X. Vves, (984), Pre and Quantty Competton n a Dfferentated Duopoly, RAND Journal of Eonoms, 5, Stranlund, J. K. and K. K. Dhanda, (999), Endogenous Montorng and Enforement of a ransferable Emssons Permt System, Journal of Envronmental Eonoms and Management, 38, Vves, X., (999), Olgopoly Prng: Old Ideas and New ools, he MI Press. Xepapadeas, A., (997), Advaned Prnples n Envronmental Poly, Edward Elgar.