Strategic Firm Interaction, Returns to Scale, Environmental Regulation and Ambient Charges in a Cournot Duopoly

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1 Technology and Investment, 013, 4, Publshed Onlne May 013 ( Strategc Frm Interacton, Returns to Scale, Envronmental Regulaton and Ambent Charges n a Cournot Duopoly Sudhakar Rau 1, Subhadra Gangul 1 Helzberg School of Management, Rockhurst Unversty, Kansas Cty, USA Bahran Insttute of Bankng & Fnance (BIBF), Manama, Bahran Emal: sudhakar.rau@rockhurst.edu, sgangul@bbf.com Receved January 18, 013; revsed March 14, 013; accepted March 1, 013 Copyrght 013 Sudhakar Rau, Subhadra Gangul. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. ABSTRACT Envronmental regulaton under condtons of mperfect competton n the presence of nonpont sources (NPS) of polluton has not been well analyzed n the lterature. Ths paper models strategc frm nteracton and the effect of ambent charges on total NPS polluton n an mperfectly compettve, Cournot type duopoly under constant and decreasng returns to scale (CRTS & DRTS). We dentfy two dstnct and often opposng effects. Under CRTS, the prmary effect of a hgher ambent charge s to ncrease polluton abatement (and thus decrease polluton) whle the secondary effect s to lower output. Hgher polluton abatement and lower output renforce each other so that a hgher ambent charge results n an unambguous decrease n NPS polluton. Under DRTS, a hgher ambent charge decreases output but the effect on abatement s ambguous. Moreover, the margnal effect of a change n the ambent charge s larger under CRTS than DRTS. Our results ndcate that, n general, polluton control mechansms such as ambent charges tend to be more effectve under CRTS. Keywords: Envronmental Regulaton; Nonpont Source Polluton; Ambent Charges; Cournot Duopoly; Returns to Scale; Strategc Interacton 1. Introducton The regulaton of pollutng frms by decentralzed mechansms s not only of theoretcal nterest but s also a polcy ssue that has assumed consderable sgnfcance over the last decade. Nonpont source (NPS) polluton that s, polluton from dffuse sources rather than one specfc source accounts for the maorty of present day polluton, especally water polluton. Snce NPS polluton orgnates from several sources, frm specfc emssons are vrtually mpossble to measure and are moreover consderably complcated by ssues of moral hazard 1. A central ssue n envronmental polcy s the desgn of a regulatory system to address NPS polluton. Commandand-control polces for reducng nonpont source (NPS) water polluton mandated under the Federal Water Polluton Control Act (FWPCA) have not been partcularly 1 See [1] for a dscusson of the ecologcal, envronmental and legslatve aspects of NPS polluton. Ths paper also presents case studes of pont and nonpont source polluton. successful. Ambent charges charges based on the total amount of polluton rrespectve of frm specfc orgns consttute one possble mechansm of polluton control. The use of such charges has been wdely dscussed n the lterature ([-7]). Ambent charges have several advantages over other nstruments of polluton control such as quanttatve standards, effluent taxes and tradable permts. An effluent tax requres montorng the amount of polluton generated from each source as well as an assessment of the abatement costs of the pollutng frms ([8-1]). However such frm-specfc nformaton s dffcult to gather and requres effectve montorng nvolvng substantal enforcement costs. Much of the earler work on polluton control assumed pollutng frms to be prce takers. There s some lterature on envronmental polcy under condtons of mperfect competton for pont sources of polluton (see [13,14]). In contrast, envronmental polcy under NPS polluton and mperfect competton has hardly receved much attenton n the lterature. More recently, [3] explores the Copyrght 013 ScRes.

2 114 S. RAJU, S. GANGULI effectveness of ambent charges when NPS pollutng frms cooperate wth each other. Clearly, the ssue of competetve nteracton among nonpont source polluters s central to the polcy effectveness of ambent based charges. The fundamental obectve of our paper s to study the effect of ambent charges on total NPS polluton n a Cournot-type duopolstc market. Such a settng clearly brngs to the forefront the central ssues of compettve nteracton and ts effect on the optmal desgn of ambent based polluton charges. Such duopolstc nteracton s common n many ndustres. Promnent examples nclude Arbus and Boeng, Peps and Coca-Cola, Home Depot and Lowes, Canon and Nkon, Kleenex and Puffs, Fedex and UPS, Verzon and AT & T, PetroChna and Snopec, etc. Many of these companes are located n ndustres lke transportaton, transportaton equpment manufacturng, beverages, paper, petroleum, etc. that generate sgnfcant polluton and account for consderable polluton abatement operatng and captal equpment expendtures. We assume a two stage duopolstc game. In the frst stage of the game, the regulator announces an ambent charge followng whch both frms choose ther polluton abatement technologes. In the second stage after the polluton abatement technology has been chosen, the frms smultaneously choose ther optmal output levels. The model assesses strategc frm nteracton under alternatve assumptons about producton technologes (constant and decreasng returns to scale). Smulaton s used to evaluate the effect of changes n the ambent charge on total NPS polluton under dfferent technologes.. Ambent Charges, Polluton Abatement Costs and Expendtures Perodcally, the US Department of Commerce along wth the Envronmental Protecton Agency (EPA) conducts a Polluton Abatement Costs and Expendtures (PACE) survey [15] that consttutes the most comprehensve source of nformaton on captal expendtures and operatng costs assocated wth polluton abatement for about 0,000 plants n the US manufacturng Industry. The most recent PACE data was publshed n Aprl 008. The PACE survey dvdes polluton abatement costs nto two broad categores polluton abatement operatng costs and polluton abatement captal expendtures. Table 1 reports overall data for the US manufacturng sector as well as 1 of the most sgnfcant subsectors. For the entre manufacturng sector, polluton abatement operatng costs consttute roughly 78% of total abatement costs whle polluton abatement captal expendtures consttute %. Of total polluton operatng costs, polluton treatment consttutes 5%, dsposal %, preventon 17% and recyclng 8%. Ar polluton abatement makes up the maor bulk (4%) of operatng costs whle water (33%) and sold waste (6%) account for remanng costs. As far as captal expendtures are concerned, ar polluton captal expendtures makes up nearly 66% whle water (3%) and sold waste (11%) consttute the remanng expendture. Among ndustres wth the largest polluton abatement costs are transportaton, paper, petroleum, beverages and transportaton equpment manufacturng. As noted earler, several of these ndustres are characterzed by duopolstc competton. Emprcal assessments of ambent charges on polluton are farly sparse. A recent study by the economy of Estona tred to assess f ambent ar polluton permts encouraged nvestment n polluton abatement technology. Polluton s a sgnfcant problem n Estona; the economy s ecologcal footprnt s nearly 4 tmes larger than s consdered economcal and ts energy ntensty usage per capta s among the hghest n Europe. A recent study by the Natonal Audt Offce of Estona to assess the effectveness of ambent ar polluton permts revealed several problems. Current charges taxed hazardous pollutants regardless of the level of danger they represented at one and the same rate. Pollutants that were produced n large quanttes were taxed at a lower rate than others whle some pollutants were not taxed at all. In many cases polluton charges were set so low that s was far more economcal to pay the charges than ncur the cost of polluton abatement technology. The Estonan report hghlghts the many real world desgn and mplementaton problems that underle ambent charges. Ambent polluton charges are only one part of a more comprehensve envronmental regulatory system and are most effectve when supported by other legal and admnstratve measures. 3. The Model under Constant Returns to Scale (CRTS) The basc model relates to a Cournot type settng n whch two frms 1, produce output q. Market nverse demand s gven by P a bq where Q q1 q s total output. Market nverse demand, P, s postve for Q a b. For smplcty set ab1. Now assume that ths duopolstc market s subect to NPS polluton. Let for 1, be the polluton abatement technology parameter of frm. The polluton from frm s then equal to q and total polluton s gven by 1q1 q. Notce that 0 corresponds to maxmum polluton abatement (zero output polluton) for an ndvdual frm whle 1 corresponds to no polluton abatement (100% output polluton). The form of the cost functon, gven the abatement technology of each frm, s gven by: /557GetPage/3/557Year/-1/ItemId/9/amd/557/language/en-US/Default.aspx Copyrght 013 ScRes.

3 S. RAJU, S. GANGULI 115 Table 1. Polluton Abatement Captal Expendtures & Operatng Costs (mllons of dollars). Source: Polluton Abatement Costs & Expendtures (PACE): 005; Issued Aprl 008; US Dept. of Commerce, Economcs & Statstcs Admnstraton, US Census Bureau. Copyrght 013 ScRes.

4 116 S. RAJU, S. GANGULI C q 1 ;, 1,; where 0 1 and s a postve constant less than 1. Note that Cq, Cqq 0 (mplyng constant margnal cost and constant returns to scale) and C 0, C. The cost functon mples that pollu 0 ton abatement s costly and s assumed to be separable n output and abatement technology. In response to NPS polluton, the regulator mposes an ambent polluton standard, and a unform ambent charge, t. If total polluton s greater than the ambent standard each frm pays a fne equal to t. On the other hand, f total polluton from both frms s less than the ambent standard, each frm receves a unform subsdy equal to t. The prmary advantage of the ambent charge over other nstruments of polluton control s that unlke other nstruments where moral hazard s an endemc problem, the ambent charge obvates the need to montor the frms constantly. The proft functon,, n a duopoly settng under these assumptons s gven by: 1q q q q 1 t ; (), 1,; The frst order condtons for proft maxmzaton mply that: 1 q q t 0;, 1,; q (3) Solvng smultaneously for the output reacton functons results n (4) below. The reacton functons capture the effect of one frm s decsons on another and thus capture the nteractve element of decson makng. 1 t t q ;, 1,; (4) 3 Now assume a two stage game. In the frst stage of the game, the regulator announces an ambent polluton standard n response to whch frms choose ther polluton abatement technology parameters gven the cost and ambent charge parameters of the model. After the polluton abatement parameters are determned n the frst stage, the frms subsequently choose the optmal level of output n the second stage of the game. Now consder the frst stage of the game wheren both frms choose the optmal polluton abatement technologes. Substtutng the values of q and q nto the proft functon yelds,,,, t, 1 q 1 q q q t q t q t;, 1,; The soluton for the optmal polluton abatement technologes s gven by dfferentatng (5) wth respect (1) (5) to. Thus q q 1q q t q t (6) 1 tq 0;, 1,; Usng the frst order condtons from (3), the above mples that 18 4t 1 7t ;, 1,; (7) 18 8t Let 18 8t, the denomnator of (7). Next note that that s a functon of. Solvng and smultaneously gves the polluton reacton functons,. Thus 18 7t 4t 1 7t 1 7t 7t, 1,; (8) Note that (8) depends on the ambent charge t as well as the margnal cost, of both frms. Suppose we assume that the margnal cost structure of both frms n the duopolstc market s smlar mplyng that. Then (8) reduces to the smpler form gven by: 18 4t 1 (9) 18 t Once the optmal polluton technology s determned, the optmal level of output can be determned n the second stage of the game by substtutng (9) nto (4). Thus 1 t q q q (10) 3 The total polluton at the equlbrum s then gven by:, t q q 1 t q (11) 3 Ths polluton functon s dependent on both margnal cost and the unform ambent charge. The manner n whch the polluton functon responds to both these varables s consdered n the next secton. 4. The Optmal Polluton Functon Ths secton derves the optmal polluton functon whch s useful n developng some underlyng ntuton of the comparatve statcs of the model. Holdng margnal cost constant, an ncrease n the ambent charge, t, on α, q and s gven by: 4 t 1 (1) t 18 t Copyrght 013 ScRes.

5 S. RAJU, S. GANGULI 117 t q t 1 3 t t 1t 3 t (13) (14) These comparatve sgns are dffcult to sgn unambguously and are therefore smulated for dfferent values of the ambent charge and margnal cost 3. The comparatve statcs consder 3 dstnct effects the effect of a change n the ambent charge (t) on the abatement parameter α, on optmal output q and on the level of polluton,. Frst, consder the effect on the abatement parameter of a change n the ambent charge. The smulated values of (1) are negatve mplyng that at gven levels of margnal cost, an ncrease n the ambent charge decreases α. Snce a lower value of α mples that more polluton s abated, an ncrease n the ambent charge has the expected outcome of decreasng the quantty of polluton. Equaton (13) mples that the ncrease n the ambent charge has a secondary mpact a hgher ambent charge decreases output. The combned effect of hgher polluton abatement and lower output s captured by (14) and the smulated results of (14) are reported n Table and depcted n Fgure 1. The negatve slope of the polluton functon s gven by (14). It s clear from both Table and the equlbrum polluton functon depcted n Fgure 1 that an ncrease n the ambent charge (whle holdng constant margnal cost) unambguously lowers total NPS polluton under CRTS. Next, consder the comparatve statcs of a change n margnal cost on the abatement parameter, output and polluton whle holdng constant the ambent charge, t. 4t 0 (15) 18 t q 131t 0 (16) 1t (17) 3 The frst result, (15), s unambguously postve and mples that an ncrease n margnal cost, holdng constant the ambent charge, ncreases α. Snce a hgher value of α mples that less polluton s abated, an ncrease n margnal cost has the effect of ncreasng polluton. The ntuton here s that snce polluton abatement s costly, the frm responds to an ncrease n margnal cost by decreasng polluton abatement and thereby n- 3 Equatons (10) and (11) requre that (1 η) > t α for both equlbrum output (q ) and equlbrum polluton to be postve under CRTS. Equaton 1 s unambguously negatve f a more strngent restrcton of the form (1 η) > (1/) t α s mposed on the comparatve statcs results. The subsequent results assume these restrctons. creasng total polluton. Equaton (16) s unambguously negatve mplyng that an ncrease n margnal cost decreases output whch consequently leads to lower polluton. Equatons (15) and (16) thus mply that an ncrease n margnal cost results n two countervalng effects. Whle lower polluton abatement serves to ncrease total polluton, the decrease n output works n the opposte drecton to decreases total polluton. Equaton (17) s smulated for dfferent values of the ambent charge and margnal cost (see Table 3). Table 3 mples that even though (15) and (16) work n opposte drecton, the net effect of an ncrease n margnal cost s to decrease total NPS polluton under CRTS. Ths result s also depcted n Fgure 1. The equlbrum polluton functon s shown n Fgure 1 for two specfc values of margnal cost (η = 0.10, η = 0.0). Holdng constant margnal cost along each polluton curve, t s evdent that as the ambent charge ncreases, equlbrum NPS polluton decreases. Holdng constant the ambent charge, a hgher (lower) margnal cost shfts the polluton functon downwards (upwards). In essence, for a gven ambent charge, a hgher margnal cost decreases total NPS polluton under CRTS. The extent to whch these results can be generalzed depends on several factors. The assumpton of a Cournot duopoly clearly mposes a partcular type of frm structure. A prevous paper by us [16] consders questons smlar to those n ths paper but under a Bertrand duopoly. In addton to frm structure, the results are affected by the assumed cost structure. In the next secton, we extend the results of ths secton to the case of decreasng returns to scale. 5. The Model under Decreasng Returns to Scale (DRTS) Now suppose the cost functon s gven by: C q 1 ;, 1,; (18) where Cq q 0, Cq, q 0 (mplyng ncreasng margnal cost and decreasng returns to scale) and C 0. Assumng that the margnal cost structures of both frms are smlar (.e. ), the frst order condton for maxmzaton under DRTS s gven by: 1q1q t 0, 1,; (19) q Solvng for both outputs smultaneously yelds the reacton functons: 1t t 1 q, 1,; (0) where Dfferentatng,,,, wth respect to α results n t Copyrght 013 ScRes.

6 118 S. RAJU, S. GANGULI q 1q 1 q t q q t 1 tq 0 Utlzng the frst order condtons gven by (19), the optmal values of α are gven by: t t t , 1,; Let D t 11 (1), the denomnator of (1). Substtutng for n the expresson above and after consderable smplfcaton 4, the optmal polluton abatement technologes (polluton reacton functons) as a functon of the parameters η and t are gven by:, 1,; where 1 t1 Dt 1 ; () Substtutng nto (0) gves: 1 q q q 1 1 t The level of total NPS polluton under DRTS s then gven by: q 11 t (3) The comparatve statcs of a change n the ambent charge on the abatement parameter, output and polluton s gven by: D 11 t t q t t 1 (4) 1 t (5) t q q t t t where t (6) D Snce the sgn of (4) t 4 A useful result n smplfyng (15) to arrve at the form gven by (16) s to recognze that D t 1 Dt 1 Dt 1. cannot be unambguously determned, we smulated (4)-(6) for dfferent ambent charge (t) and margnal cost (η) values. The results ndcate that whle the effect of change n the ambent charge on the abatement parameter s ambguous under DRTS, the effect of a change n the ambent charge on output s unambguously negatve. Equaton (6) ndcates that the effect of a change n the ambent charge on NPS polluton s composed of two effects the effect on the abatement parameter and the effect on output. The frst of these effects s ambguous but the second s unambguously negatve. The net effect of a change n the ambent charge on total NPS polluton s reported n Table 4. These are however all negatve n effect, the declne n output resultng from an ncrease n the ambent charge overwhelms the ambguous effect on polluton abatement. The net effect s to reduce NPS polluton under DRTS. Whle an ncrease n the ambent charge reduces total polluton under both CRTS and DRTS, the margnal effect of a change n the ambent charge s larger under CRTS. (Ths s apparent from a comparson of the values n Tables and 4). The reason for the more pronounced mpact under CRTS s due to the fact that an ncrease n the ambent charge leads to more polluton abatement under CRTS whle ths effect s ambguous under DRTS. The same noton s hghlghted n Fgure 1. The polluton functons under both CRTS and DRTS are downward slopng ndcatng that an ncrease n the ambent charge leads to a declne n total NPS polluton. The polluton functons under CRTS le on a lower plan than DRTS ndcatng that for smlar values of margnal cost, total NPS polluton under CRTS s less than DRTS. Fnally, consder the mpact of a change n margnal cost whle holdng constant the ambent charge. The comparatve statcs of a change n η are gven below: t t D t q 1 t t 1t 1 (7) (8) Copyrght 013 ScRes.

7 S. RAJU, S. GANGULI 119 Table. The margnal effect of a change n the ambent charge on NPS polluton under CRTS (for gven levels of margnal cost). t = 0.10 t = 0.0 t = 0.30 t = 0.40 t = 0.50 t = 0.60 t = 0.70 t = 0.80 t = 0.90 t = 1.00 η = η = η = η = η = η = η = η = η = η = Table 3. The margnal effect of a change n margnal cost on NPS polluton under CRTS (for gven levels of the ambent charge). t = 0.10 t = 0.0 t = 0.30 t = 0.40 t = 0.50 t = 0.60 t = 0.70 t = 0.80 t = 0.90 t = 1.0 η = η = η = η = η = η = η = η = η = η = Table 4. The margnal effect of a change n the ambent charge on NPS polluton under DRTS (for gven levels of margnal cost). t = 0.10 t = 0.0 t = 0.30 t = 0.40 t = 0.50 t = 0.60 t = 0.70 t = 0.80 t = 0.90 t = 1.0 η = η = η = η = η = η = η = η = η = η = Copyrght 013 ScRes.

8 10 S. RAJU, S. GANGULI Fgure 1. Polluton functon under CRTS and DRTS. q q where Dt 1; 81 ; (9) D 4 t 1 t 1 The sgns of these comparatve statcs are not obvous. The smulated value of (7) ndcates that an ncrease n margnal cost leads to an ncrease n the value of the abatement parameter. Snce a hgher value of the abatement parameter ndcates a lower level of polluton abatement, total polluton ncreases. In essence, when margnal cost goes up costly polluton abatement s scaled back, leadng to more polluton. Equaton (8) ndcates that when margnal cost ncreases, output falls whch consequently leads to less polluton. Even though both these effects work n opposte drectons, the net effect of an ncrease n margnal cost on polluton gven by (9) s unambguously negatve. The smulated effect of an ncrease n margnal cost on polluton s reported n Table 5. It s clear from a comparson of Tables 3 and 5 that ths effect s more pronounced under CRTS than under DRTS. Fgure 1 renforces the same noton. Holdng constant the ambent charge, a hgher (lower) margnal cost under both CRTS and DRTS shfts the polluton functon downwards (upwards). In essence, for a gven ambent charge, a hgher margnal cost decreases total NPS polluton under CRTS and DRTS. The results for decreasng returns to scale above can be extended to the case of ncreasng returns to scale (IRTS). Under IRTS, the cost structure s gven by: C q q 1 ;, 1,; (30) where 0; 0. Thus, Cq q 0 f q and C 0 q, q mplyng that margnal cost s postve but ncreases at a dmnshng rate. The results for IRTS are not reported here but can be easly derved n a manner smlar to the CRTS and DRTS cases consdered above. 6. Conclusons Envronmental regulaton under condtons of mperfect competton for pont sources of polluton has been well analyzed n the lterature. In contrast, envronmental polcy under condtons of mperfect competton for nonpont sources of polluton has receved far less attenton n the lterature. Copyrght 013 ScRes.

9 S. RAJU, S. GANGULI 11 Table 5. The margnal effect of a change n margnal cost on NPS polluton under DRTS (for gven levels of ambent charge). t = 0.10 t = 0.0 t = 0.30 t = 0.40 t = 0.50 t = 0.60 t = 0.70 t = 0.80 t = 0.90 t = 1.0 η = η = η = η = η = η = η = η = η = η = In ths paper, we model the mposton of ambent charges as a mechansm of polluton control n a Cournot duopoly. The model assesses strategc frm nteracton under two alternatve assumptons about returns to scale. Under CRTS, an ncrease n the ambent charge results n two dstnct effects. The prmary effect of a hgher ambent charge s to ncrease polluton abatement (and thus decrease polluton) whle the secondary effect s to lower output. The effect of hgher polluton abatement and lower output renforce each other so that an ncrease n the ambent charge results n an unambguous decrease n total polluton under CRTS. Under DRTS, a hgher ambent charge decreases output but the effect on abatement s ambguous. However, the net effect s to decrease polluton though the mpact of an ambent charge on polluton reducton s lower under DRTS than CRTS. Our model also ndcates that for a gven ambent charge, an ncrease n margnal cost results n two countervalng effects. A hgher margnal cost decreases polluton abatement (and thus ncreases polluton) whle also reducng output whch results n lower polluton. The net effect of hgher margnal cost s to reduce polluton but ths effect s more pronounced under CRTS than DRTS. The mplcaton s that NPS polluton mechansms lke ambent charges tend to be more effectve under CRTS than DRTS. REFERENCES [1] K. Loague and D. L.Corwn, Pont and Nonpont Source Polluton, John Wley & Sons, Hoboken, 005, pp [] J. Suter, C. Vossler, G. Poe and K. Segerson, Experments on Damage-Based Ambent Taxes for Nonpont Source Polluters, Amercan Journal of Agrcultural Economcs, Vol. 90, No. 1, 008, pp do: / x [3] G. Poe, W. Schulze, K. Segerson, J. Suter and C. Vossler, Explorng the Performance of Ambent Based Polcy Instruments when Nonpont Source Polluters Can Cooperate, Amercan Journal of Agrcultural Economcs, Vol. 86, No. 5, 004, pp do: / x [4] K. Segerson, Uncertanty and Incentves for Non-Pont Polluton Control, Journal of Envronmental Economcs and Management, Vol. 15, No. 1, 1988, pp [5] A. P. Xepapadeas, Envronmental Polcy under Imperfect Informaton: Incentves and Moral Hazard, Journal of Envronmental Economcs and Management, Vol. 0, No., 1991, pp [6] A. P. Xepapadeas, Envronmental Polcy Desgn and Dynamc Non-Pont Source Polluton, Journal of Envronmental Economcs and Management, Vol. 3, No. 1, 199, pp [7] A. P. Xepapadeas, Observablty and Choce of Instrument Mx n the Control of Externaltes, Journal of Publc Economcs, Vol. 56, No. 3, 1995, pp [8] W. Baumol and W. Oates, The Use of Standards and Prces for Protecton of the Envronment, Swedsh Journal of Economcs, Vol. 73, No. 1, 1971, pp do:10.307/ [9] W. Baumol, On Taxaton and the Control of Externaltes, Amercan Economc Revew, Vol. 6, No. 3, 197, pp [10] M. Wetzman, Prces vs. Quanttes, Revew of Economc Studes, Vol. 41, No. 4, 1994, pp do:10.307/96698 [11] J. Harford, Frm Behavor under Imperfectly Enforceable Polluton Standards and Taxes, Journal of Envronmental Economcs and Management, Vol. 5, No. 1, 1978, pp do: / (78) [1] M. Stmmng, Captal Accumulaton Games under Envronmental Regulaton and Duopolstc Competton, Journal of Economcs, Vol. 69, No. 3, 1999, pp do: /bf Copyrght 013 ScRes.

10 1 S. RAJU, S. GANGULI [13] T. Requate, Polluton Control under Imperfect Competton: Asymmetrc Bertrand Duopoly wth Lnear Technologes, Journal of Insttutonal and Theoretcal Economcs, Vol. 149, No., 1993, pp [14] T. Requate, Polluton Control n a Cournot Duopoly va Taxes or Permts, Journal of Economcs, Vol. 58, No. 3, 1993, pp do: /bf [15] US Department of Commerce, Polluton Abatement Costs and Expendtures (PACE): 005, US Department of Commerce, Economcs and Statstcs Admnstraton, US Census Bureau, 008. [16] S. Gangul and S. Rau, Perverse Envronmental Effects of Ambent Charges n a Bertrand Duopoly, Journal of Envronmental Economcs and Polcy, Vol. 1, No. 3, 01, pp Copyrght 013 ScRes.