Incentives for Price Manipulation in Emission Permit Markets with Stackelberg Competition

Transcription

1 Incentves for Prce Manpulaton n Emsson Permt Markets wth Stackelberg Competton Francsco J. André and Lus M. de Castro. Dept. of Economc Analyss. Unversdad Complutense de Madrd. Campus de Somosaguas, 83 Madrd, SPAIN. March 04 Prelmnary and ncomplete verson. Please, do not quote or dstrbute wthout authors approval. ABSTRACT It has been shown n pror research that cost effectveness n the compettve emssons permt market could be affected by tact colluson or prce manpulaton when the correspondng pollutng product market s olgopolstc. We analyze these cross market lnks usng a model ala Stackelberg to show that under reasonable assumptons, there are no ncentves to collude for lobbyng prces up. Tact colluson to manpulate prces down exsts f the permt prce s low enough. We also conclude that dstrbutng free permts among frms by means of grandfatherng ncrease the chances for prce collusons to manpulate the prce up. JEL code: D43, L3, Q58 Key words: Emssons permt market, Tact colluson, Market power.

2 Introducton In ths paper we check the exstence of olgopolstc frms ncentves to collude n order to nflate the prce of emsson permts and obtan a hgher proft when there s a leader-follower relatonshp n the output market. The use of cap-and trade (CAT) systems has become ncreasngly popular as a polcy approach to ncentvze frms to curb pollutng emssons. Important examples nclude the US SO tradng system under the framework of the Acd Ran Program of the 990 Clean Ar Act, as an early applcaton or, more recently, the European Unon Emsson Tradng System (EU ETS). The man reason why CAT programs are so attractve and popular among economsts s that they allow reducng pollutng emssons n a cost-effectve way by means of a prce system. As long as margnal abatement costs dffer across pollutng frms, ncentves for trade exst and the market can play a postve role n achevng a pre-specfed envronmental target at a mnmum cost. As t s well documented n the lterature, under the assumpton of perfect competton, cost-effectveness s guaranteed regardless of the ntal allocaton rule chosen for the permts (see Montgomery, 97, n a statc settng and Rubn, 996, n a dynamc framework). Unfortunately, the perfect-market assumpton rarely holds n practce and t turns out that the cost-effectveness of a CAT system s challenged f there s market power n ether the permts market or the assocated product market or n both. The lterature analyzng the relatonshp between mperfect competton and emsson permts can be dvded n three dfferent branches, whether market power s ntroduced n the permts market, the good market or both smultaneously. Regardng the exstence of market power n the permts market, the poneerng work s Hahn (984). Based on a statc model a la Stackelberg, he stated that the effcency loss depends on the ntal allocaton of permts, and, more specfcally, the permt prce s an ncreasng functon of the domnant frm s allocaton. As a seller, the domnant frm wll manpulate the prce upwards and vce versa to optmze ts cost, unless the ntal allocaton equals the effcent one, what requres a perfectly nformed regulator. Hagen & Westskog (998) extended the Hahn settng n a dynamc twoperod model and found a non-optmal dstrbuton of abatement n an mperfect compettve market wth bankng and borrowng.

3 A second lne of research addresses the concurrent exercse of market power n both permt and output markets. Ths topc has receved attenton, among other authors, by Msolek & Elder (989), who extended Hahn s settng to the product market and concluded that a sngle domnant frm can manpulate the permt market to drve up the frnge frm s cost n the product market. Hnterman (0) found that a domnant frm wll set the permt prce above ts margnal abatement costs and therefore costeffectveness cannot be acheved by means of the permt allocaton alone. Ths paper fts n a thrd branch that consders mperfect competton n the product market but not n the permt market. The reason to choose ths lne s twofold. Frstly, The EU-ETS prce shock n 005 generated a great deal of nterest n ssues related to market power. Intally, the prce of allowances was far n excess of expectatons, but n Aprl 006 the prce suddenly fell and reached zero n md-007. Emprcal studes have not been able to explan those too hgh prce levels when the number of permts exceeded emssons n every year of the frst phase. Then, t s natural to wonder f the reason for those prce oscllatons mght be connected to the output market rather than the permt market n the sense that permts could be used somehow obtan wndfall profts ether n the output market or the market of some mportant nput such as electrcty. Secondly, as noted by Montero (009) and Muller et al. (00), whle market power among frms s very common n output markets, the exstence of market power n emsson permts s more lkely to appear when countres rather than frms are the relevant players. When frms are the nvolved agents, typcally there s a very large number of them, whch makes t very dffcult that market power arses. Ths s clearly the case n the EU ETS, wth around,000 nstallatons nvolved and the latest steps of the European Commsson seem to be n the drecton of ncreasng the degree of competton (for example, by centralzng the allocaton of permts or movng from grandfatherng to auctonng). In ths thrd lne, some artcles have shown that perfect competton n the permts market mght not be enough to render a cost-effectve outcome f the product market s not perfectly compettve. Sartzetaks (997) assumes a homogeneous Cournot duopoly and compares the effcency of a compettve emssons market to a command- As an example, regardng Annex countres n the Kyoto Protocol, Russa receved a ffth of the permts and a thrd went to USA. Countres wth market power can easly manpulate prces up (down) through tarffs on permt exports (domestc subsdes to cleaner technologes) and also mplement polces regardng the lnkage between domestc and foregner markets. 3

4 and-control regulaton n whch the emssons of each frm are legally fxed. Emssons tradng modfy the allocaton of emssons among frms and consequently ther producton choces. Sartzetaks (004) shows that welfare can decrease when emsson tradng s allowed between asymmetrc frms endowed wth dfferent abatement and producton technologes. The permt prce that clears the market s a weghted average of the value of emssons of frms under command and control and, therefore, the cost of the more neffcent frm s reduced whle the cost of the more effcent one s ncreased when permts trade s ntroduced. Meuner (0) analyzes the effcency of emsson permt tradng between two mperfectly compettve product markets and conclude that even f the frms are prce takers n the permt market, the ntegraton of permt markets can decrease welfare because of mperfect competton n product markets. Theoretcally, f markets are perfectly compettve, a unque global permt market that covers all pollutng actvtes would be effcent to allocate an aggregate emssons level. If markets are not perfect but some frm enjoys market power, several permt markets may be more effcent than an ntegrated one. Ehrhart et al. (008) show that colluson n the product market may occur even f the frms are prce takers n the permt market. Under some condtons, a permt prce ncrease leads to hgher profts due to a decrease n product quanttes whch ncreases the output prce. In the ndustral organzaton lterature ths strategy s generally known as rasng rvals costs. In the partcular case of an emsson permt market, Erhart et al (008) conclude that frms mght have ncentves to collude n order to push the prce of permts upwards. Although ths movement has the drect effect of rasng one s cost, snce t also rases the rval s, both frms could beneft by restrctng the quantty and ncreasng the prce. They argue that n EU ETS, even f there s no explct market power n the permt market there are loopholes n the tradng law that allow collusve behavor among frms to manpulate the prce of permts. Ths paper addresses the queston f frms nterests could be algned to push up the prce of permts (and, therefore, f there are ncentves to collude) under Stackelberg competton. So, we check f the colludng ncentves reported by Erhart et al. (008) stll arse n a settng that s asymmetrc n nature (Stackelberg) whereas Erhart et al. restrct to purely symmetrc settngs. We frst set a general model n whch we show that the effect of a hgher permt prce on the proft of both the leader and the follower s ambguous. So, the possblty 4

5 that frms beneft from a prce ncrease stll exsts, but the asymmetrc role of the frms ental that such a possblty happens under dfferent condtons for the leader and the follower. Then we explore a partcular case wth a separable cost functon to come up wth more accurate nsghts. As a frst central fndng, we conclude that both frms face a proft functon that s convex n the permt prce. So, when the prce s low enough, both frms wll beneft from a further prce decrease and, when t s hgh enough, both wll beneft from a prce ncrease whle, for ntermedate prces or hgh prces, only the follower benefts from a prce ncrease and t s the other way around for the leader. Therefore, there s no room for tact colluson. Ths s n contrast to Ehrhart et al. (008), who set a symmetrc model and therefore, both frms nterests are always algned. The mplcaton of ths fndng s that the exstence of leadershp n output markets reduces the room for collusve agreements n the permt market. Actually, n our specfc example wth a separable functon, we conclude that the collusve regon shrnks to the extent to dsappear. In an extenson, we consder the possblty that some permts are dstrbuted for free (by means of grandfatherng) and we conclude that ths possblty opens agan the way for collusve agreements. The remander of the paper s organzed as follows. Secton states the basc model. In Secton 3 a partcular abatement cost functon s consdered. Concludng remarks are gven n the last secton. The Model We set up a smple duopoly Stackelberg model of a pollutng ndustry sector wth tradable permts. Frm s a leader and frm s a follower n the output market whle both frms are prce takers n the related emssons permt market. For the sake of comparablty, the same as Ehrhart et al. (008), n ths secton we assume that the frms do not enjoy any ntal allocaton of permts, and so they have to buy all the permts they need n a market at a gven prce p (the possblty of a free endowment of permts s consdered as an extenson n Secton 3). The game has two stages: n the frst stage, frms decde sequentally ther output levels, x and x, a la Stackelberg facng the 5

6 nverse demand functon ( ) P X, where X : = x + x and, n a second stage, they decde smultaneously ther cost-mnmzng emsson levels, e and e. The cost functon of frm (,), (, ) C x e, depends on output (x ) and net emssons (e ) and s contnuous and twce dfferentable n both arguments wth the followng propertes: C C C < 0, > 0, < 0. e e x e Ths functon ntegrates producton and abatement costs and reflects the fact that producng clean (wth low emssons) s more costly than producng drty. Every unt of emssons must be covered by a permt that can be obtaned n the market at a gven prce p. Consderng the cost of permts purchasng, total cost of frm s gven by (, ) : (, ) () TC x e = C x e + pe. () The model s solved by backward nducton. In the second stage of the game both frms decde ther emsson levels to mnmze ther total cost, (, ) TC x e, subject to e 0, whle takng as gven ther output levels and the prce of permts. If the soluton s nteror, we get the standard frst-order condton (FOC) from whch we obtan the (nverse) demand for permts of each frm: C + p = 0. (3) e Total dfferentaton of the FOC shows that optmal emssons are ncreasng n output and decreasng n the permt prce: defned as C + = 0 = > 0, (4) C C e e x de dx e e x x C e C e de dp e p C e + = 0 = < 0. (5) Usng the envelope theorem, we conclude that the mnmzed total cost functon emssons. The second order condton s always fulflled due to the convexty of C n 6

7 ( ) ( ( )) ( ) ( ) ( ) TC x, p : = TC x, e x, p = C x, e x, p + pe x, p (6) has the followng propertes: TC = e 0, p (7) TC C C e C = + + p =, x x e x x (8) C TC C C e C x e = + = x x x e x x C e, (9) C TC C e x e x p x e p C e = = > 0. (0) Now we move to the frst stage, where the frms choose ther output levels. We start analyzng the follower s behavor, who faces the followng maxmzaton problem: The FOC of ths problem s whch, solvng for (,,, ) ( ) (, ) MaxΠ x x e p = P x + x x TC x p. () P TC P ( x + x ) + x = 0 X x () x x, p. x, gves the reacton functon of the follower, ( ) Dfferentatng the FOC and operatng we conclude that the optmal follower's output s decreasng n the leader's output and the prce of permts: dx dx dp = dx < dp dx TC dx x p dp 0, (3) TC x = < 0. (4) dp TC dx x The leader takes the follower's reacton functon nto account when maxmzng ts own proft. The FOC of the correspondng problem s 7

8 P x TC P( x + x ) + x + = 0 (5) x x x and, by dfferentatng the FOC, we conclude that the leader's output supply s also decreasng n the prce of permts: dx dp TC x p P x TC + x x x = < 0. (6) Now we are ready to address the man ssue of ths paper, namely the effect of an ncrease n the prce of permts on the frms proft. The queston s: could both frms beneft smultaneously from a prce ncrease as predcted by Erhart et al (008) n a symmetrc settng? The motvaton behnd ths queston s that, f the answer happens to be postve, both frms mght have ncentves to collude or, by any means, to lobby n order to manpulate the prce of permts up. 3 By drect dfferentaton of the proft functons we conclude that the margnal effect of the prce of permts on the profts of both frms s gven by the followng expressons: Π P x = x e p, (7) X p Π P x x = x e p +. (8) X x p There are two mportant ponts to be stressed here. Frst, the sgn of both expressons s ambguous. The reason s that an ncrease n the prce of permts has two dfferent effects. On the one hand, t drves cost up, what tends to reduce frms' proft but, on the other hand, t also causes output to decrease and, therefore, the product prce to ncrease, whch can be benefcal for both frms. So, n prncple t s possble that the second effect domnates the frst and, therefore, profts ncrease wth the prce of permts. If ths happens smultaneously for both frms, there exst ncentves to collude n order to manpulate the prce up, as noted by Ehrhart et al. (008). 3 Erhart et al. (008) argue that, n the EU ETS, there are several loopholes n the tradng law that foster colluson. These loopholes consst n the exstence of some mechansms that create the possblty for a prce manpulaton even n the absence of market power. The most mportant of these mechansms are frst, the possblty to nfluence the ntal allocaton of permts (to make t more strngent), second, the 'opt-n' rule that enables ndustres not commtted to partcpate n the permts tradng system to do so voluntarly, thrd, the possblty to mplement project-based mechansms and pay more for these credts than they would at the market and, fourth, by payng addtonal emssons dutes. 8

9 Second, the condtons under whch a hgher prce s proft-enhancng are dfferent for the leader and the follower. Ths opens the door for the possblty of a dsagreement between the frms n the sense that one s nterested n a prce ncrease and the other one n a prce decrease. Ths s n contrast to Ehrhart et al. (008), where both frms are symmetrc and, therefore, ether both frms are better-off or both are worse-off after a prce ncrease. Ths asymmetry seems to reduce the scope for a prce manpulaton agreement. To get some addtonal nsght on ths ssue, n the next secton we assume a partcular abatement cost functon. 3. A Separable Functon 3.. Basc case Assume that the costs of producton and abatement are separable n the followng way. The producton cost of frm s gven by cx, so there s a constant margnal producton cost equal to c. Gross emssons of each frm are n fxed proporton to output wth a fxed coeffcent of polluton ntensty, r > 0 (thus, gross emssons of frm are gven by rx ). By dong abatement actvtes, frms can reduce ther flow of polluton. Denote as q 0 the amount of emssons abated by frm. Then, net emssons are gven by e = rx q. Followng Sarzetaks (997) we assume the followng quadratc abatement cost functon: ( ) ( ) AC q = q d + tq (9) where d and t are postve parameters. Addng up the costs of producton, abatement and permts purchasng, and usng the defnton of q, we can wrte total cost as a functon of output and emssons: (, ) ( )( ( )) TC x e = cx + rx e d + t rx e + pe. (0) Moreover, assume that the (nverse) demand functon has the lnear form P( X ) = a bx. Proceedng as n the general model, we solve frst the second stage, where both frms decde ther levels of emssons. Endowed wth our specfc analytcal expressons, now we can explctly account for nteror and corner solutons. Solvng frm 's problem usng the Kuhn-Tucker technque we get the optmal emssons of frm and pluggng that value n (8) we get the mnmzed cost functon: 9

10 d p rx f p d rtx = () 0 otherwse + + t e ( ) ( ) ( d p) x c + pr f p d + rtx TC x, p = 4t ( + ) + x c rd tr x otherwse. It s mmedate to see that, f the soluton s nteror (e > 0), margnal product cost s constant n output and ncreasng n the permt prce whereas, n a corner soluton, total cost s strctly convex n output and ndependent of the permt prce. On the other hand, as t s typcal n the Stackelberg model, we get that n equlbrum, the leader's output and emssons are always hgher than the follower's (see below) and, therefore, e cannot be zero f e s not zero. The case where the emssons of both frms are zero s unnterestng from an envronmental pont of vew, and so we rule t out by assumpton. Therefore, we are left wth two relevant cases: the frst, that we label as "nteror soluton case", nvolves e > 0, e > 0, whereas the second (labelled as "corner soluton case") nvolves e > 0, e = 0. Snce each scenaro results n a dfferent (mnmzed) costs functon for frm, we have to solve each of them separately. As shown n the Appendx, the equlbrum quanttes for the nteror soluton case are gven by and, n the corner soluton case they are gven by x = x x ( a c)( b + r t) + brd rp( b + r t) b ( b + r t) x = ( a c + rp rd )( b + r t) + rb( p d ) 4( b + r t )( b + r t) () a c rp =, (3) b a c rp = (4) 4b, (5). (6) Proposton shows the man result of ths part. 0

11 PROPOSITION There exsts one threshold value for the permt prce, p, such that f p < p, a prce decrease would ncrease the proft of each agent. If p > p, a prce ncrease wll decrease the leader s proft and ncrease the follower s proft. The consequence of Proposton s that, n our example, there s a range where both frms are nterested n decreasng the prce but, unlke the symmetrc case developed by Ehrhart el al. (008), t s never the case that both frms smultaneously proft from a prce ncrease, and therefore they never have ncentves to lobby n order to press the prce up. The ntuton behnd the proof s the followng. Under nteror soluton, the proft of functon of frm s strctly convex n p wth a mnmum at p (=, ), wth p < p. So, when p < p both frms are n the decreasng part of the proft functon and ther proft would by hgher wth a lower prce. If p < p < p, the follower s n the ncreasng part (and so he would beneft from a prce ncrease) whereas the leader s stll n the decreasng part (and, therefore, he would stll prefer the prce to decrease). Fnally, f p > p the leader reaches the mnmum of the proft functon, but t s the case that p s precsely the value of the threshold value for the prce that makes the follower choose a corner soluton (.e., e = 0 for any p p ) and so, n ths thrd regon the shape of the proft functons change. Snce frm does not pollute n ths range, ts cost s not drectly affected by the prce of permts, whle the leader s s. As a consequence, n ths range the leader s output, and consequently ts proft are decreasng (n the prce) whle the follower s output and proft are ncreasng. In ths example we have llustrated how the asymmetry between the frms (n the sense of a leader-follower relatonshp) reduces the chances for collusve behavor to the extreme to make them dsappear. In the next subsecton we show a generalzaton of ths example where the result s not so extreme n the sense that the chances for collusve agreements decrease but they do not dsappear.

12 3.. Grandfatherng In the prevous secton, for comparablty wth Erhart et al. (008) we have assumed that the frms do not have any ntal allocaton of permts and, therefore, they have to buy all the permts they need n the market. We now extend ths settng to consder the possblty that some permts are ntally dstrbuted wth no cost for the frms by a grandfatherng scheme. So, the frms only need to buy the permts requrements that exceed ther ntal allocaton and, moreover, they have the opton to sell permts f they pollute less than ther ntal allocaton. Consder that both frms receve an equal allocaton of free permts, S, and denote as y the amount of permts that any frm buys (y > 0) or sells (y > 0) n the market, whch can be calculated as the dfference between net emssons and the allocaton of permts, y = e S = rx q S, (7) from where we get e = y + S,.e., the net emssons of a frm must be covered by permts that ether come from her free allocaton or are bought n the market. Therefore frm s total cost functon s now gven by the equaton: (, ) ( )( ( )) TC x y = c x + r x y S d + t r x y S + py, (8) whch can be expressed n terms of output and net emssons as (, ) ( )( ( )) ( ) TC x e = c x + r x e d + t r x e + p e S. (9) As we wll show mmedately, now the nteror soluton case covers all the relevant regons and so, we can now restrct to nteror solutons wthout any mportant lose of generalty. Proceedng as we dd n the prevous subsecton we get the optmal traded permts and the correspondng mnmzed cost functon: d p y = + rx S, (30) t (, ) ( ) ( d p) TC x p = x c + pr ps. (3) 4t It s mmedate to see that margnal product cost s constant n output and ncreasng (decreasng) n permt prce when the frm s a net buyer (seller) of permts. Note that the partal dervatve of the total cost wth respect to the permt prce s precsely e.

13 PROPOSITION When both frms are ntally endowed wth a free allocaton of permts, there exst two thresholds values for the permts prce, ˆp, ˆp, wth ˆp < ˆp, where ˆp < p, ˆp < p, such that f p < ˆp both frms get better off when p decreases, f ˆp < p < ˆp, the leader gets better off when p decreases and the follower gets better off when p ncreases and, fnally, f p > ˆp, both frms get better off when p ncreases. The consequences of Proposton are the followng. The proft of both frms s stll strctly convex n the prce of permts, wth a mnmum at prce p ˆ, =,. When grandfatherng s ntroduced, the values of the permt prce at whch the mnmum s reached shft to the left, what mples that there s wder range of the prces such that both frms are better-off when the prce of permts ncreases. The reason s that the exstence of free permts makes permt purchasng less costly for frms and, moreover, t opens the way from gettng postve revenues by sellng some permts More mportantly, when grandfatherng s ncluded, we have three regons nstead of two. In the new regon, to the rght of ˆp, both frms proft from a prce ncrease, whle the soluton s stll nteror (e, e > 0). Techncally, the reason why ths new regon arses s that, now, t s easer for the frms to proft n the permt market. Specfcally, ˆp s the prce at whch frm starts beng a net permt buyer and turns nto a net permt buyer. The polcy mplcaton of ths fact s that the free dstrbuton of permts ncreases the ncentves of the frms to collude n order to push the prce up. 4 Conclusons We have explored the possbltes that two frms competng a la Stackleberg n the output market and are subject to a cap and trade system could have ncentves to manpulate the prce of permts up. We do so n a framework smlar to the one by Erhart el al (008) wth the dfference that they restrct to symmetrc stuatons whereas we explore a stuaton that s asymmetrc n nature. The man research queston s f the ncentves for ths type of collusve behavour, that have been prevously reported for symmetrc models, stll exst n a model that s asymmetrc n nature, such as the Stackelberg model. 3

14 In a general model, we have shown that the sgn of the effect of a permt prce ncrease on the frms' proft s ambguous. Ths opens the way for the frms to beneft from a prce ncrease and the possblty to make collusve agreements n order to manpulate the prce up. Nevertheless, the asymmetrc role of each frm causes that the condtons under whch a prce s proft-enhancng are dfferent for them. Under a separable cost functon we show, frst, that the proft functons are convex n the permt prce wth a mnmum, and second the the mnma are dfferent for both frms, whch creates a regon of dsagreement where the leader prefers that the prce goes down whereas the follower prefers that the prce goes. Ths stuaton s ruled out n Erhart et al. (008) by constructon. Actually, n the basc case n whch there are no free permts dstrbuted between the frms, the regon where there ncentves to collude dsappears. Then man polcy mplcaton of ths fndng s that leader-follower relatonshps n the product market can prevent the exstence of ncentves for colluson n the permts market. Another polcy mplcaton s that dstrbutng some permts for free (by means of grandfatherng) opens agan the way for collusve agreements. Ths s an argument n favor of movng from a grandfatherng scheme to another ways to dstrbute the permts, such as auctonng. References Ehrhart, KM Hoppe, C Löschel, R (008) Abuse of EU Emssons Tradng for Tact Colluson Envronmental and Resource Economcs, 4: Hagen, C and Westskog, H. (998) The desgn of a Dynamc Tradeable Quota System under Market Imperfectons Journal of Envronmental Economcs and Management 36: Hahn, R. (984) Market power and transferable property rghts Quarterly Journal of Economcs 99: Hntermann, B. (0) Market Power, Permt Allocaton and Effcency n Emsson Permt Markets Envron Resource Econ

15 Meuner, G. (0) Emsson Permt Tradng Between Imperfectly Compettve Product Markets Envronmental and Resource Economcs, 50: Msolek, W. and Elder, H. (989) Exclusonary manpulaton of markets for polluton rghts Journal of Envronmental Economcs and Management 6: Montero, J.P. (009) Market Power n Polluton Permt Markets. The Energy Journal 30 (specal ssue ): 5-4. Muller, R. A., S. Mestelman, J. Spraggon and R. Godby (00) Can Double Auctons Control Monopoly and Monopsony Power n Emssons Tradng Markets? Journal of Envronmental Economcs and Management 44: Montgomery, WD (97) Markets n Lcences and Effcent Polluton Control Programs Journal of Economc Theory 5 (3): Rubn, J. (996) A model of ntertemporal emsson tradng, bankng and borrowng Journal of Envronmental Economcs and Management 3: Sartzetaks, ES (997) Tradeable Emsson Permts Regulatons n the Presence of Imperfectly Compettve Product Markets: Welfare Implcatons Envronmental and Resource Economcs 9: Sartzetaks, ES (004) On the Effcency of Compettve Markets for Emsson Permts Envronmental and Resource Economcs, 7: -9. 5