DEPARTMENT OF ECONOMICS

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1 DEPARTMENT OF ECONOMICS Emsson Taxes and the Adopton of Cleaner Technologes: The Case of Envronmentally Conscous Consumers Mara José Gl-Moltó, Unversty of Lecester, UK Dmtros Varvargos, Unversty of Lecester, UK Workng Paper No. 11/49 November 011

2 Emsson Taxes and the Adopton of Cleaner Technologes: The Case of Envronmentally Conscous Consumers Mara José Gl-Moltó Unversty of Lecester, UK Dmtros Varvargos Unversty of Lecester, UK Frst Verson: 4 November 011 Abstract We model a market wth envronmentally conscous consumers and a duopoly n whch frms consder the adopton of a clean technology. We show that as polluton ncreases, consumers shft more resources to the envronmental actvtes, thereby affectng negatvely the demand faced by the duopoly. Ths effect generates ncentves for frms to adopt the clean technology even n the absence of emssons taxes. When such taxes are consdered, our results ndcate that the beneft of adoptng the clean technology s ntally ncreasng and then decreasng n the emsson tax. The range of values for whch the emsson tax ncreases ths beneft becomes narrower when the consumers envronmental awareness s stronger. Keywords: Envronmentally Conscous Consumers; Technology Choce; Envronmental Taxaton JEL Classfcaton: L13, Q55, Q58 1

3 1 Introducton Recent years have wtnessed an ncreased awareness for ssues pertanng to the mpact of economc actvty on envronmental degradaton. As a result, both polcy makers and the wder publc have ntensfed ther efforts and actons towards polluton reducton. On the one hand, polcy makers have attempted to encourage frms nvestments n envronmental R&D usng a varety of nstruments such as taxes on emssons, caps or R&D subsdes. On the other hand, envronmentally conscous consumers have not only shfted ther preferences towards goods wth envronmentally frendly attrbutes (e.g., recyclable packagng, organc produce, certfcaton of envronmentally frendly producton technques etc.) but they have also ncreased the resources they devote to general actvtes that mtgate the extent of envronmental degradaton. There are many ways through whch consumers can contrbute resources to mprove the envronment. One example s the partcpaton n carbon offsettng schemes. These schemes are supported by frms n a varety of ndustres, from avaton (Brtsh Arways, for example) to energy generaton (Eon). Through these schemes, ndvduals contrbute fnancally to the purchase of carbon credts to compensate for ther own emssons. Another example s the ndvduals donatons to certan NGOs who purchase permts from emssons tradng systems on ther behalf, thereby reducng the amount of avalable permts and therefore effectve emssons. Examples of such NGOs are the Acd Retrement Fund and the Clean Ar Conservancy Trust n the US or Sandbag n the UK. Fnally, ndvduals can take part n envronmental volunteerng, whch often nvolves not only the supply of unpad work (wth ts assocated opportunty cost) but an addtonal fnancal contrbuton. 1 So far, the lterature has contemplated the exstence of envronmentally conscous consumers n models of product dfferentaton, where consumers preferences for the envronment motvate competng frms to choose the envronmental attrbutes of ther products (e.g., Bansal and Gangopadhyay 003; Conrad 005; Deltas et al. 008; Andre et al. 009). However, such frameworks fal to capture the essental features of the arrangements 1 For example, Global Vson Internatonal s an organsaton whch runs a number of proects related to clmate change and conservaton all over the world. Volunteers pay a fnancal contrbuton and work on ther chosen proect for a certan amount of tme. These papers analyse the scope for publc nterventon even n the presence of envronmentally conscous consumers n the context of horzontal dfferentaton (Conrad 005); vertcal dfferentaton (Bansal and

4 we descrbed earler (carbon-offsettng programmes, donatons to chartes, volunteerng, etc.). In ths type of arrangements, consumers effectvely nternalse (part of) the envronmental damage and spend some of ther resources to general envronmentally frendly actvtes. The reason why the formal analyss of these ssues s mportant s because by spendng more on envronmentally frendly actvtes, consumer resources are drected away from the consumpton of goods produced by all competng frms. Thus, ths may generate an aggregate demand effect whch affects negatvely the demand faced by all frms (rather than a shft n the relatve demand between dfferent goods as n models of vertcal and horzontal dfferentaton). Ths dfferent type of envronmental conscousness therefore calls for an alternatve frame of analyss n order to study ts effects on frms behavour and ts mplcatons for envronmental polcy. In ths paper, our am s to fll the current vod n the lterature. We begn our analyss wth the descrpton of a market where consumers have preferences over the consumpton of a homogeneous good and envronmental qualty. These consumers can also devote resources towards envronmental mprovements. We show that, n response to an ncrease n polluton, consumers shft ther resources away from the consumpton of goods and towards actvtes that mtgate the extent of envronmental degradaton. Subsequently, we analyse a Cournot duopoly n whch ths negatve demand effect mpnges on both frms decsons concernng output producton and the cleanlness of the technologes they employ. The latter s charactersed by the pollutants emtted per unt of producton and ts choce may ental postve technology spllovers across frms. 3 In ths context, we derve and dscuss the mplcatons of the negatve demand effect of polluton for frms optmal choces. Furthermore, we show how the relatve strength of ths effect may mpnge on the effectveness of emsson taxes as polcy tools desgned to motvate the adopton of cleaner producton technques by frms. 4 Gangopadhyay 003; Andre et al. 009); and where two dmensons of dfferentaton, envronmental and ntrnsc characterstcs of the goods, are consdered (Deltas et al. 008). 3 There s substantal evdence on the extent technologcal spllovers across frms and/or ndustres. See Grlches (199), Buonanno et al. (001) and Clarke et al. (006). 4 In addton to the more manstream nstruments of envronmental polcy (.e., emsson taxes; subsdes to envronmental nnovaton) the use of nformatonal campagns to rase envronmental awareness as a polcy nstrument has become the focus of a number of studes (see Petraks et al. 005; Garca-Gallego and Georgantzs 009, 011). Our decson to focus on emsson taxes les on the mportance of (envronmental) technology choce n our settng. 3

5 The remanng of the paper s structures as follows. In Secton, we analyse a market n whch envronmentally conscous consumers devote resources towards envronmental mprovements and derve the mplcatons of hgher polluton for consumer demand. In Secton 3, we use these mplcatons n a Cournot duopoly model wth endogenous technology choce and derve equlbra n both the absence and the presence of emsson taxes. Secton 4 shows how the negatve demand effect from polluton affects the scope of emsson taxes as ncentve mechansms for the adopton of cleaner producton methods. Secton 5 concludes. A Market wth Envronmentally Conscous Consumers Consder a market whch conssts of a unt mass of dentcal consumers and N frms that produce and sell quanttes of a homogeneous product. The prce of ths product s denoted P. Each consumer [0,1] s endowed wth an (exogenous) ncome of y 0 and her preferences are defned over the consumpton of the homogeneous good, denoted her envronmental concerns, captured by the varable E, accordng to C, and u δ ln( C ) (1 δ)ln( E ), (1) where δ (0,1) weghts the two arguments of the consumer s utlty. We shall elaborate on the consumers preferences over the natural envronment by assumng that these are composed of two components. Frstly, we ncorporate the amenty value of mproved envronmental qualty (common to all consumers) by postulatng that polluton a by-product of frms producton actvtes entals a utlty cost for consumers. Secondly, we assume that each consumer s envronmentally actve n the sense that she s wllng to devote resources to pro-envronmental actvtes. Formally, we capture these two effects by assumng that where E e( M) x, () x denotes the amount of a consumer s endowment devoted to envronmentally frendly actvtes, M denotes polluton or total emssons, whle the functon em ( ) satsfes e( M ) Effectvely, we ntroduce a oy-of-gvng (or warm glow ) argument to provde consumers wth the motve to spend on envronmentally frendly actvtes. Snce the semnal work by Andreon (1989, 1990) there has been 4

6 Each consumer s problem s to choose subect to () and her budget constrant C and x to maxmse the utlty functon n (1) PC x y. (3) Naturally, when maxmsng her utlty, the consumer takes P, M, and her exogenous ncome y as gven. Assumng nteror solutons, we can reformulate the problem by substtutng () and (3) n (1) to wrte and * y x x arg maxδ ln (1 δ )ln[ e( M ) x ], (4) x P The frst-order condton for the problem s The second-order condton s C y x P * *. (5) U δ 1 δ x y x e( M ) x. (6) U δ 1 δ x ( y x ) [ e( M ) x ] 0. (7) Therefore, we can obtan that x by settng U / x 0 n (6). It s straghtforward to establsh * x (1 δ ) y δe( M ), (8) * where we assume that the consumer s endowment s suffcently hgh to guarantee that x * 0. Substtutng (8) n (5) we get * y e( M ) C δ. (9) P Recall that consumers n the market are assumed to be dentcal an assumpton that apples to both ther preferences and ther endowments. Thus, we have y y and we ample expermental evdence of ths behavour n publc good games (see for example, Palfrey and Prsbey 1996, 1997; and Goeree et al. 00). However, note that we can reformulate the problem to assume that consumers nternalse the benefcal effects of ther own actons for overall envronmental qualty, wthout causng any change to the qualtatve characterstcs of our subsequent results. 5

7 can use (9) to obtan the aggregate demand functon for the homogeneous consumpton good accordng to * 1 * 0 C C d δ y e( M ). (10) P Equaton (10) reveals a standard, negatvely sloped demand functon wth respect to the prce (.e., C * / P 0). Interestngly, equaton (10) also mples that polluton affects aggregate demand. The next proposton formalses ths clam. Proposton 1. An ncrease n polluton wll result, ceters parbus, n a reducton of the consumpton good s aggregate demand. Proof. Usng equaton (10), we can see that * 1 C / M P e ( M ) 0. QED The ntuton for ths result s straghtforward. The ncrease n polluton wll stmulate the consumers desre to devote resources towards envronmentally orented actvtes an effect that s manfested n the ncrease of the margnal utlty from such actvtes (see equaton 6). The equlbrum can only be restored f ths margnal utlty falls back to ts orgnal level; thus, each consumer wll optmally choose to ncrease her spendng on x. However, wth a gven amount of ncome avalable, ths shft has to materalse at the expense of consumpton. Hence, the demand for the consumpton good wll ultmately declne as, for a gven prce level, the demand curve shfts downwards (see Fgure 1). 6 6 The assumpton of a unt substtuton elastcty between C and E s nnocuous for our results. We can derve qualtatvely dentcal results f we replace (1) wth a more general CES utlty functon θ θ 1 θ 1 θ 1 θ θ (1 ) u δc δ E, θ 0. In ths case, the aggregate demand functon becomes C * y e( M ) P δ δ P θ θ θ 1 [1 (1 ) ]. 6

8 * C C * A A c( P, M ) M B M A C * B B c( P, M ) 0 P P Fgure 1 The precedng analyss has demonstrated a lnk between aggregate demand and polluton n an economy wth envronmentally conscous consumers. More mportantly, the mechansm we have descrbed mples that ths lnk may be pertnent to varous aspects of a frm s decson makng process. To see ths, recall that polluton s a negatve sde-effect of frms producton actvtes. Now, let us assume that each frm 1,..., N produces and supples a quantty q by accessng a technology that emts producton. In ths case polluton wll amount to N 1 unts of pollutants per unt of M q. (11) The expresson n (11), combned wth the demand functon n (10), reveals how and why the mechansm summarsed n Proposton 1 can be a crucal characterstc of frms choces concernng producton, technology adopton etc. As such, t may have sgnfcant mplcatons for polces desgned to nduce the mplementaton of envronmentally frendler producton methods by frms. Our purpose s to utlse the man pont from the precedng dscusson n order to provde a formal analyss of these mplcatons. Ths s a task we undertake n the followng sectons of the paper. 7

9 3 Emsson Taxes and Envronmental Technology Choce The precedng analyss has demonstrated a scenaro that supports an aggregate demand * functon C c( P, M ), where c, c 0. Now, let us consder an ndustry whose frms face P M such a demand functon. When dong so, we shall restrct our attenton to a duopoly, henceforth N. The equlbrum n the market where the good s sold requres that C * 1 q. Therefore, the aggregate demand functon can be wrtten as 1 q c( P, M ). (1) ( ) ( ) Our demand equaton n (1) has the same qualtatve propertes as (10), that s, t s decreasng n the prce ( P ) and the level of polluton ( M ). To smplfy matters, we shall follow the standard approach of workng under a lnear approxmaton of an aggregate demand functon that possesses the same qualtatve propertes. Hence, the remanng analyss wll be makng use of c( P, M ) a Γ( M ) P, a 0, (13) where Γ ( M ) 0. A lnear approxmaton s also employed to capture the negatve effect of polluton on the demand for the good. That s where γ 0 quantfes the relatve strength of ths negatve effect. Γ( M ) γm, (14) Snce frms produce a homogeneous product, t s helpful to thnk of them as operatng under Cournot competton. Therefore, our formal analyss wll be undertaken on the bass of an nverse demand functon whch we can get after combnng equatons (11)-(14). That s P α (1 γ ) q. (15) Each frm faces a constant margnal cost of producton m 0 1. Furthermore, t may be lable to a penalty (or tax) of τ 0 per unt of emssons. Gven that a frm emts q unts of polluton, ts varable costs are ( m τ ) q. (16) All n all, frms varable profts can be wrtten as follows: 8

10 v α (1 γ ) q q ( m τ ) q. (17) 1 Frms can choose the type of technology they employ to manufacture ther goods. In partcular, we assume that each frm can choose between two alternatve technologes ( drty or clean ) whch dffer n ther assocated emssons per unt of output and adopton costs the latter assumed to be fxed. We consder that there s a trade-off between the level of emssons and the adopton cost. That s, the drty technology entals an emsson rate and can be adopted at zero cost whle the clean technology s assocated wth a lower emsson rate but a hgher adopton cost. In what follows, we shall be assumng that holds. Ths restrcton s suffcent, albet not necessary, to ensure the stablty of the equlbrum that we wll derve after solvng the system of best response functons later n our analyss. 7 We also ntroduce the possblty of postve spllovers assocated wth the desgn and mplementaton of the cleaner producton method. That s, t s less costly for a frm to develop and adopt the clean technology f ts compettor s also usng ths clean technology. Formally, frms face a fxed cost Φ such that where φ φ. 0 f = Φ φ f, =,. (18) Gven (17) and (18), each frm s total profts, φ f, = π, are gven by π α (1 γ ) q q ( m τ ) q Φ. (19) 1 7 Notce that ths noton of stablty dffers from the one appled to varables that dsplay an explct dynamc pattern. In ths case, an equlbrum s sad to be stable f, startng from any pont n ts neghbourhood, the adustment process n whch players take turns myopcally playng a best response to each other s current strateges converges to the equlbrum. Formally, usng π to denote profts, the stablty condton s π π q q q, where {1,}. See Martn (001). 9

11 The obectve of the frm s to maxmse profts by the approprate choces of q and We assume that frms wll choose ther technologes frst. Once frms technology choces are observed, frms choose ther output levels. Thus, the game has two stages: durng the frst stage, frms choose ther technologes whereas durng the second stage frms choose ther output levels. We assume that frms choose smultaneously n each of these stages. As usual, we solve ths game by backwards nducton and use subgame perfecton as our equlbrum concept The Second Stage: Output Choces In ths stage, frms set ther output levels to maxmse profts. The frst order condton for maxmsaton s gven by π q α (1 γ ) q q (1 γ ) m τ 0. (0) 1 Notce that the second order condton for a maxmum s fulflled ( / (1 ) 0) π q γ. Thus, we can solve (19) for q to obtan the best response functon for each frm, whch s As expected, frms outputs are strategc substtutes snce [ a m τ (1 )] * q γ q. (1) (1 γ ) q * / q 0. An ncrease n the compettor s output wll put a downward pressure on the good s prce, thus reducng the frm s margnal revenue. Gven that the margnal cost of producton s unchanged, the frm wll fnd t proftable to reduce ts producton n order to restore the margnal revenue back to ts orgnal level. It s worth notng that the magntude of ths effect s renforced by the presence of the parameter γ. The ntuton for ths s that frm s output adds to the total level of emssons, trggerng a shft of the consumers demand away from the good and, as a response, a lower level of output by frm. The same ntutve mechansm more or less apples when we try to explan the nverse relaton between the frm s producton and ts own emsson rate. Notce, however, that ths adverse effect s renforced by the presence of the emsson tax whch, effectvely, adds to the cost of producton. 10

12 Solvng the system of best response functons for {1, }, we fnd the equlbrum levels of output, whch are and q q a m τ( ), () * 1 1 3(1 γ1) a m τ( ). (3) * 1 3(1 γ ) Gven these results, we are now able to formalse our analyss on the equlbrum output responses, assocated wth dfferent technology choces. The followng proposton summarses the correspondng qualtatve effects. Proposton. A frm s optmal producton s, ceters parbus, decreasng n ts own emsson rate but ncreasng n ts compettor s emsson rate. The effect of the compettor s technology choce (.e., the compettor s emsson rate) on the frm s output exsts f and only f τ 0. Proof. Usng equatons (1) and (), t s straghtforward to establsh that q1 / 1, q / 0 τ 0 and q1 /, q / 1 0 ff τ 0. A few ponts mert dscusson here. On the one hand, the frm s own emsson rate has a negatve effect on ts own output through two dfferent mechansms. Frst, a hgher emsson rate means more polluton and therefore a hgher shft n demand, leadng to a reducton n output. Second, the own emsson rate wll postvely affect the effectve margnal cost of producton of frms as long as emssons are taxed ( τ 0 ). The hgher ths cost, the lower the output wll be. The compettor s emsson rate wll affect postvely the frm s own output as long as emssons are taxed. Although ths result may seem at odds wth the effects we dscussed earler, t can be explaned as follows. When a compettor chooses a more pollutng technology, there are two conflctng effects on the frm s output. The drect effect s the one we alluded to earler durng the dscusson of the characterstcs of the best response functon an effect whch s negatve. There s an ndrect effect, however, whch works n exactly the opposte drecton. In partcular, the compettor wll combne her choce of a hgher emsson rate wth a lower level of output an effect partally attrbuted to the 11

13 presence of the parameter γ, but also amplfed by the fact that the emsson tax exacerbates the overall cost of producton. It s ths latter effect that renders the ndrect mpact to the compettor s output domnant and, gven that output levels are strategc substtutes, makes t proftable for the frm to ncrease ts output. Moreover, ths s precsely why taxaton s crucal for the materalsaton of technology choce nteractons when frms determne ther output levels. Substtutng () and (3) n (19), we can wrte each frm s total profts as and π [ a m τ( )] 1 1 v1 Φ1 Φ1 9(1 γ1), (4) π [ a m τ( )] 1 v Φ Φ 9(1 γ ). (5) These expressons, together wth () and (3), reveal that, n terms of equlbrum output and, therefore, varable profts, the choce of technology across frms s subect to strategc substtutablty: other thngs beng equal, a frm s choce to mplement a cleaner technology reduces the other frm s varable profts, thus leavng fewer resources avalable for the mplementaton of the cleaner technology. Nevertheless, the technology choce entals fxed costs whose presence ntroduces a strategc complementarty accordng to (18): other thngs beng equal, a frm s decson to mplement a less pollutng technology makes t less costly for the other frm to do the same because of the postve spllover effect. Gven that the profts of each frm depend on ther own and ther compettor s technology choces, four scenaros arse: one where both frms choose the cleaner technology, (, ); another where both frms choose the drter technology, (, ); and two asymmetrc ones, where frm 1 chooses the clean technology and frm the drty one, (, ), as well as the opposte case where (, ). Thus, the varable profts n each of these scenaros can be wrtten as follows:, ( a m τ ) v, (6) 9(1 γ ), ( a m τ ) v, (7) 9(1 γ ) 1

14 Frm 1, [ a m τ( )] v 9(1 γ), [ a m τ( )] v 9(1 γ ), (8). (9) Note that n the above equatons, we use the frst superscrpt to dentfy frm s own technology choce and the second superscrpt to dentfy ts compettor s technology choce. Brngng together equatons (6) to (9) and equaton (18), we complete the matrx of payoffs n Table 1. In the next secton we wll dentfy under whch condtons each of the above mentoned four scenaros may arse as equlbrum outcomes. Frm, 1 v, v,, 1 v, v, φ, 1 v φ, v,, 1 v φ, v, φ Table 1. Payoff matrx 3. The Frst Stage: Technology Choces In ths stage, frms seek to maxmse profts through the approprate choce of technology. Our precedng analyss ndcates that frms have an ncentve to mplement a cleaner technology even n the absence of taxaton due to the effect of polluton on the aggregate demand of envronmentally conscous consumers, captured by the parameter γ. We wll start by analysng the case wthout envronmental polcy ( τ 0 ) Technology Choce wthout Emsson Taxes Let us go back to equatons (4) and (5) and set τ 0 to get 13

15 and π ( a m) 1 1 9(1 γ1) Φ, (30) π ( a m) 9(1 γ ) Φ. (31) These equatons reveal that the choce of a cleaner technology (.e., as opposed to ) wll be optmal f and only f polluton entals the type of aggregate demand effects that we dentfed n Secton. If γ 0, and n the absence of envronmental taxes, there s no ncentve by nether frm to ncur a cost for an actvty that has no beneft whatsoever. However, nsofar as γ 0, such beneft clearly exsts: a frm may be wllng to ncur the fxed cost of envronmental nnovaton, antcpatng that ths wll nduce envronmentally conscous consumers to shft ther resources towards the consumpton of goods. In fact, such motve exsts even n the absence of spllovers. Nevertheless, f spllovers exst, they wll create a further ncentve for frms to adopt the cleaner technology. Let us dscuss now the condtons under whch each combnaton of strateges may arse as an equlbrum. Note that here, the varable proft s solely a functon of the own emsson rate. Thus, the net beneft n terms of varable profts of mplementng a cleaner technology s the same rrespectvely of the compettors choce, snce,,,, v v v v. In fact, n both cases ths dfference yelds ω ( a m) γ( ) 9(1 γ )(1 γ ). (3) It s evdent from (3) that, n the absence of emsson taxes, a beneft exsts f and only f γ 0 that s, only f polluton results n aggregate demand effects. Next, we need to compare ths net beneft wth the dfference n fxed cost of adoptng each technology. 8 The result of ths comparson wll determne the equlbrum of the game. The results of ths comparson are presented n the next proposton. Proposton 3. Suppose that τ 0. Then the followng are equlbra:. (, ) f ω φ; 8 As a tebreakng rule, we assume that f a frm s ndfferent between the two technologes, t wll choose. 14

16 . (, ) and (, ) f φ ω φ ;. (, ) f ω φ. Proof. See the Appendx. Proposton 3 states that the only equlbra that arse are symmetrc (ether both frms choose the clean technology or both frms choose the drty one). In partcular, when the net beneft of choosng the clean technology s very small (too small to be proftable to adopt t even when there are spllovers), the only equlbrum s (, ). Conversely, when ths beneft s very hgh (hgh enough to make adopton proftable even wthout spllovers), the only equlbrum s (, ). For ntermedate levels, both (, ) and (, ) arse as equlbra snce adoptng the clean technology s only proftable f the compettor adopts t too; that s when there s a possblty of beneftng from spllovers. In ths case, however, ths outcome s not guaranteed as frms face a coordnaton problem due to the multplcty of equlbra. 9 For values satsfyng ω ( φ, φ ] although the postve spllovers would make t mutually advantageous for both frms to choose the clean technology, the expectaton that the compettor may not choose (hence, elmnatng the benefts emanatng from the spllover effect) may dscourage frms from a choce of. In the next secton, we analyse the frst stage n the presence of emsson taxes and try to dentfy the equlbrum outcomes that transpre n ths scenaro. 3.. Technology Choce n the Presence of Emsson Taxes For subsequent purposes, we begn ths part by defnng, [ a m τ( )], ( a m τ ) ω v v 9(1 γ ) 9(1 γ ), (33) and 9 Effectvely, the exstence of spllovers ntroduces a strategc complementarty n the choce of technology. See Cooper and John (1988) for a detaled dscusson on the mplcatons of coordnaton falures n models wth strategc complementartes. 15

17 ,, ( a m τ) [ a m τ( )] ω v v 9(1 γ) 9(1 γ ). (34) The nterpretaton of (33) and (34) s smlar to the correspondng one n equaton (3). Here, however, the ncrease n varable profts from mplementng the cleaner technology depends on whether the compettor chooses the drty or the clean technology. We label wth ω ths ncrease n the latter case and wth ω n the former. If ω s hgher than φ, a frm s best response to ts compettor choosng the drty technology s to adopt the clean technology. Analogously, f ω s hgher than φ, ts best response to the clean technology s to adopt the clean technology too. Some tedous, but straghtforward, algebra reveals that ω ω holds. In other words, the net beneft from mplementng the less pollutng technology s hgher when the compettor actually mplements the more pollutng one. Recallng that the presence of the emsson tax ntroduces some strategc substtutablty n the optmal choce of technology (as opposed to the strategc complementarty emergng from the presence of spllover effects), the ntuton behnd ths result s clear: when the compettor chooses the cleaner technology, and as long as the government taxes emssons, t becomes more compettve n the product market, as ts margnal cost s lower than t would be f t chose the drty technology. In turn, ths affects negatvely frm s output and therefore the (varable) proftablty of adoptng the cleaner technology. Wth these n mnd, we can use the two propostons that follow n order to summarse the equlbrum outcomes that materalse durng the frst stage of the competton (when τ 0 ). Proposton 4. Suppose that τ 0 and ω ω φ φ. Then, the followng are equlbra:. (, ) f 0 ω φ ω φ ;. (, ) and (, ) f ω φ 0 ω φ ;. (, ) f ω φ ω φ 0. Proof. See the Appendx. Proposton 5. Suppose that τ 0 and ω ω φ φ. Then, the followng are equlbra: 16

18 . (, ) f 0 ω φ ω φ ;. (, ) and (, ) f ω φ 0 ω φ ;. (, ) f ω φ ω φ 0. Proof. See the Appendx. The scenaros descrbed n Proposton 4 and Proposton 5 dffer wth respect to the relatve strength of the spllover effect φ φ whch s larger n the scenaro n Proposton 4. Nevertheless, there are some common outcomes n both scenaros. Partcularly, when the net beneft of choosng the clean technology s very small or very hgh, the equlbra are analogous to the equlbra arsng n the absence of taxes; that s, (, ) and (, ) n the latter. n the former case However, a maor dfference across scenaros arses for ntermedate values of ths beneft. In the frst scenaro, the relatvely strong spllovers make the adopton of the clean technology proftable f and only f the compettor adopts t too. If the compettor uses the drty technology, the beneft n terms of varable profts s not enough to make the adopton of the clean technology proftable. Ths s reflected n the equlbrum outcomes descrbed n Proposton 4 (); n such a case, both (, ) and (, ) are Nash equlbra. However, when the spllover effect s not so strong, t may be proftable for a frm to adopt the clean technology as a reply to the compettor s adoptng the drty technology. In such a case, the compettor s n dsadvantage n the output market due to the hgher margnal cost. For the same reason, t s optmal for the compettor to adopt the drty technology as a reply to the clean technology, as ts less compettve poston n the market and therefore lower output makes t less proftable to ncur n the hgher fxed costs of the clean technology. Thus, two asymmetrc equlbra arse, (, ) and (, ), as Proposton 5 () shows. Consequently, frms face a coordnaton problem due to the multplcty of equlbra n both scenaros for ntermedate values of the beneft of adoptng the clean technology. 17

19 4 Envronmental Polcy and Incentves for Pro-Envronment Innovaton In ths secton, our purpose s to examne the effectveness of envronmental polcy on ncreasng the ncentve of frms n adoptng the less pollutng producton method. Our prevous analyss has made clear that the emsson tax τ wll affect ths ncentve through ts mpact on varable profts. In partcular, t wll do so through the effect t has on the net beneft of ntroducng the cleaner technology. That s, the ncrease n varable profts when a frm shfts from the drty (.e., ) to the clean technology (.e., ). The prevous secton has revealed that the ncrement n varable profts from ntroducng a cleaner technology vares dependng on whether the compettor chooses to nnovate (ω ) or not (ω ). We also know that the hgher ω and ω are, the more lkely that a frm wll choose to adopt the clean technology as a reply to ts compettor respectvely adoptng the clean technology or the drty technology. Here we wll use comparatve statcs to check whether τ has a postve, negatve or non-monotonc effect on ω and ω. Ths wll allow us to establsh whether emssons taxaton makes the adopton of the clean technology more lkely to happen n equlbrum. To ths am, we shall examne ω and ω separately, begnnng wth the former. As t s evdent from our prevous analyss and dscusson, we are nterested on the effect of τ on the composte term ω n (34). Pror to undertakng the formal analyss, however, we need to mpose an upper bound on the emsson tax. Ths s necessary to ensure that varable profts are non-negatve under any possble scenaro concernng technology choce a m by the frm. A look at (34) reveals that the tax must satsfy τ 0,. Gven ths, the followng proposton summarses our result. a m Proposton 6. There exsts τ * 0, such that 18

20 ω τ 0 for τ τ * 0 for τ τ * 0 for τ τ *. Furthermore, t s τ * γ 0. Proof. See the Appendx. One mplcaton of Proposton 6 s that there s a tax rate that maxmses the ncentve to adopt a clean technology when the compettor s expected to act smlarly. Addtonally, we can see that when the negatve aggregate demand effect from polluton s more pronounced (.e., when γ s hgher) then the tax rate that maxmses the ncentve for pro-envronment R&D becomes lower. In terms of ntuton, the non-monotonc effect of the emsson tax s due to the conflctng effects on varable profts. On the one hand, the emsson tax motvates the frm to choose a cleaner technology n order to reduce ts overall tax oblgaton. On the other hand, however, excessvely hgh taxaton makes the overall tax burden so hgh and the reducton n varable profts so strong, that t elmnates any ncentve for the adopton of the cleaner technology. Naturally, the tax rate where these margnal benefts and costs are equal, s the one that wll provde the hghest ncentve for pro-envronment nnovaton. An mportant element n our analyss comes from the mpact of the negatve demand effect of polluton, as ths s captured by the parameter γ. Gven that ths effect already provdes an ncentve for the adopton of a cleaner producton method (see Secton 3..1), the parameter γ exemplfes the dstortve nature of the emsson tax, meanng that the scope for envronmental polcy to ncrease the ncentve for envronmental nnovaton becomes lmted for hgher values of γ. Consequently, t s possble that the same ncrease n taxaton that would rase the ncentve for the adopton of the cleaner technology when γ 0, may actually decrease ths ncentve for γ 0. In terms of Fgure, ths scenaro s * * depcted for values of the emsson tax that le on the nterval ( τ, τ ). γ 0 γ 0 Next, we undertake a smlar analyss for the case where the frm expects ts compettor not to adopt the cleaner producton technque that s, we focus on the composte term ω 19

21 n (33). In order to ensure that varable profts reman non-negatve n ths case, we use equaton (33) to dentfy a proper range of values for the emssons tax whch turns out to be τ 0, a m. The followng proposton summarses our result. Proposton 7. There exsts * 0, a m τ ω τ such that 0 for τ τ * 0 for τ τ * 0 for τ τ *. Furthermore, t s τ * γ 0. Proof. See the Appendx. As we can see, the possblty of non-monotonc effects from envronmental polcy emerges n ths scenaro as well as does the mpact of the preference parameter γ on the tax rate that maxmses the ncentve to use the clean technology. Consequently, the ntuton for these results s exactly the same wth the one dscussed n the analyss of Proposton 6. Gven that both ω and ω are nverted U-shapes n τ, t s clear that the lkelhood that a frm adopts the clean technology n equlbrum s ntally ncreasng n the tax rate but wll eventually turn decreasng. The turnng pont wll take place earler,.e. for a lower level of the tax rate, f consumers have some preference for the envronment whch makes them shft resources from consumpton to envronmental actvtes, as llustrated n Fgure. Before concludng ths secton, t s worth dscussng the role of the tax rate n determnng whch combnaton of strateges arses n equlbrum. Thus, we need to consder ontly the effects that τ has on both ω and ω. Fgure 3 provdes an llustraton of ω and ω for arbtrary levels of fxed costs and spllovers. One can see that fve regons emerge wth lead to dfferent equlbrum outcomes. In the frst regon (between 0 and τ 1 ), the best reply to both and s. Ths mples that the arsng equlbrum wll be (, ). If the tax rate s set at a hgher level (n the regon between τ 1 and τ ), the best response to s 0

22 and to s. Thus, t may occur that ether (, ) or (, ) arse n equlbrum. In contrast, f the tax rate was set n the thrd regon (between τ and τ 3 ), the only equlbrum would be (, ), as s the best reply to both and. Increasng the tax even further to be n the fourth regon (between τ 3 and τ 4 ) reduces the proftablty of adoptng the clean technology and may nduce asymmetrc equlbra where only one of the frms adopts the clean technology, that s (, ) or (, ), snce the best reply to s and vce versa. Increasng the tax rate even further (to be hgher than τ 4 ) wll lead to an equlbrum where the two frms adopt the pollutng technology (, ). Thus, settng the tax rate to be n the ntermedate regon (between τ and τ 3 ) would be the only way n whch the polcy maker can warrant an outcome where both frms adopt the clean technology n equlbrum. 10 Some mportant mplcatons for polcy makng can be drawn from the above results. The frst and perhaps counterntutve mplcaton s that ncreasng the tax rate on emssons does not necessarly create further ncentves for the adopton of clean technologes. In fact, a hgher tax rate may actually reduce the ncentves to adopt the clean technology and therefore reduce the lkelhood of ths adopton n equlbrum, partcularly f the orgnal tax rate on emsson s already relatvely hgh. Secondly, the polcy maker should be partcularly weary of such an effect n stuatons where consumers are envronmentally conscous as n such stuatons, the beneft of adoptng the clean technology turns decreasng n the emssons tax rate for lower levels of taxaton. Thus, the polcy maker should take nto account the behavour of consumers when desgnng ts envronmental polcy. For example, f carbon offsettng schemes are ntroduced n a gven ndustry and consumers are actvely partcpatng n them, t may be optmal for the government to reduce ts level of emssons taxaton n that ndustry, especally f ths level s ntally hgh; otherwse, the ncentves of frms n that gven ndustry to adopt clean methods of producton may be damaged. 10 Note that Fgure 3 s presented as an llustratve example only. We could n fact fnd that the second and the fourth regons are swtched over, or even that they do not arse. Ths would depend on the specfc combnaton of parameters n each case. What s generally true s that as τ ncreases, there s a transton from less adopton of clean technologes to more adopton of clean technologes and then agan to less adopton of clean technologes. 1

23 ωω, γ 0 γ 0 0 * τ γ 0 * τ γ 0 τ Fgure ω, ω, φ, φ φ φ ω ω 0 τ τ 1 τ 3 τ 4 τ Fgure 3

24 4 Conclusons We have analysed how the exstence of envronmentally conscous consumers affects frms adopton of cleaner manufacturng technologes. Although, n recent years the lterature has ntroduced the presence of envronmentally conscous consumers n models of product dfferentaton, such models are not sutable for the analyss of stuatons where consumers are nvolved n envronmental actvtes such as partcpaton n carbon offsettng schemes, envronmental volunteerng, donatons etc. In ths paper we propose a framework of analyss for ths alternatve type of envronmental conscous consumers. In partcular, we have assumed that consumers utlty s a functon of both ther level of consumpton of a good, the qualty of the envronment and the warm glow derved from takng part n the envronmental actvtes. As for the technology choce, we have assumed that frms have two technologes at ther dsposal whch dffer n ther assocated emssons per unt of output rato and fxed costs. We have shown that followng an ncrease n polluton, consumers wll channel resources away from the consumpton to envronmental actvtes, thereby reducng the demand for the good whch frms face and the subsequent levels of output produced by frms n equlbrum. Ths reducton n demand due to consumers envronmental conscence generates ncentves for frms to adopt the clean technology even n the absence of emssons taxes or technology spllovers. Our results also ndcate that ncreasng the tax rate on emssons does not necessarly lead to the adopton of clean technologes. In fact, the beneft of adoptng the clean technology follows an nverted U-shape n the tax rate, whch mples that after a threshold value of the emsson tax rate, further tax ncreases make less lkely the adopton of the clean technology n equlbrum. Ths counterntutve effect s more prevalent n stuatons where consumers are envronmentally conscous. Although our results have been derved n a streamlned duopolstc model, we conecture that they wll hold even under a more general settng due to the clear-cut manner of the mechansm that generates them; that s, the negatve effect on the demand caused by shftng resources away from the consumpton of the good. Consequently, the man polcy lesson that can be extracted from our model s that any envronmental polcy amed at mprovng the technologcal profle of frms should take nto account the behavour of envronmentally conscous consumers where relevant (for example, n markets where envronmental actvtes 3

25 such as the ones descrbed above take place); otherwse, the polcy may have undesrable effects on frms decsons to nvest n cleaner technologes. Appendx Proof to Proposton 3 From Table 1 and equaton (3), we know that that frm 1 s best response to frm choosng s ( ) f ω ( ) φ. Lkewse, ts best response to frm choosng s ( ) f ω ( ) φ. Recall that φ φ. Thus, f ω φ, frm 1 has a domnant strategy whch s. Moreover, f ω φ, ts domnant strategy s nstead. As the game s symmetrc, the same apples to frm. Hence, (, ) and (, ) are the equlbra n domnant strateges f ω φ and ω φ respectvely. Now assume that φ ω φ. In such a case, frm 1 s best response to frm choosng s whereas ts best response to frm s choce of s. Agan, due to symmetry, the same apples to frm. Thus, f φ ω φ, two Nash equlbra arse: (, ) and (, ). QED. Proof to Proposton 4 Consder the scenaro where τ 0 and ω ω φ φ or ω φ ω φ after rewrtng. From Table 1 and equatons (33) and (34) we know that that frm 1 s best response to s ( ) f ω φ ( ) 0 and to s ( ) ω φ ( ) 0. Due to symmetry, the same apples to frm. Gven these condtons and ω ω φ φ, three cases may emerge: () ω φ 0 and ω φ 0 ; () ω φ 0 and ω φ 0 ; () ω φ 0 and ω φ 0. In case () both frms have a domnant strategy n (t s ther best response n both and ). Thus, (, ) s an equlbrum n domnant strateges. In case () both frms have a domnant strategy n (t s ther best response n both and ). Therefore, (, ) s an 4

26 equlbrum n domnant strateges. In case (), frm 1 s best response to s ( ) f ω φ ( ) 0 and to s ( ) ω φ ( ) 0. Of course, the same apples to frm due to symmetry. Thus, two Nash equlbra emerge n ths case; that s, (, ) and (, ). To complete the proof, note that the condtons n (), (), and () can be wrtten respectvely as and 0 ω φ ω φ, ω φ 0 ω φ and ω φ ω φ 0 snce ω φ ω φ apples n ths scenaro. QED. Proof to Proposton 5 Consder the scenaro where τ 0 and ω ω φ φ or ω φ ω φ after rewrtng. From Table 1 and equatons (33) and (34) we know that that frm 1 s best response to s ( ) f ω φ ( ) 0. Due to symmetry, the same apples to frm. Gven these condtons and ω ω φ φ, three cases may emerge: () ω φ 0 and ω φ 0 ; () ω φ 0 and ω φ 0 ; () ω φ 0 and ω φ 0. In case () both frms have a domnant strategy n (t s ther best response n both and ). Thus, n ths case (, ) s an equlbrum n domnant strateges. In case () both frms have a domnant strategy n (t s ther best response n both and ). Therefore, (, ) s an equlbrum n domnant strateges. In case (), frm 1 s best response to s and ts best response to s. Of course, the same apples to frm due to symmetry. Thus, two Nash equlbra emerge n ths case; that s, (, ) and (, ). To complete the proof, note that the condtons n (), (), and () can be wrtten respectvely as and 0 ω φ ω φ, ω φ 0 ω φ and ω φ ω φ 0 snce ω φ ω φ apples n ths scenaro. QED. Proof to Proposton 6 Usng the expresson n (34), we can calculate the frst dervatve as 5

27 ω ( a m τ ) [ a m τ( )]( ) τ 9 (1 γ ) 9(1 γ ). (A1) Obvously, the sgn of (A1) wll be dctated by the sgn of the expresson ncsed brackets. After some tedous algebra, we can reduce ths expresson to J( τ ) ( ){( a m τ ) γ[ a m τ(4 )]}. (A) We can use (A) to check that J(0) ( )( γ)( a m ) 0 and a m 4 J ( )( a m) 1 γ 1 0. Now, we can use (A1) to calculate the second dervatve. Ths s ω τ ( )[ 4 γ (4 )] 0. (A3) 9 a m Thus, we verfy that there s a unque τ * 0, that maxmses ω and can be found by settng J( τ *) 0 n (A). Eventually, ths leads to τ * ( a m)( γ ) 4 γ(4 ). (A4) To complete the proof, we use (A4) to calculate τ * ( a m)( ) γ [4 γ(4 )] 0. (A5) QED. Proof to Proposton 7 The expresson n (33) allow us to derve ω ( a m τ ) [ a m τ( )]( ) τ 9 (1 γ ) 9(1 γ ). (A6) The sgn of (A6) depends on the sgn of the expresson ncsed brackets. Ths expresson can be reduced to J( τ ) ( ){( a m τ ) γ[ a m τ(4 )]}. (A7) 6

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