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1 School of Economic Sciences Working Paer Series WP Profit-Enhancing Environmental Policy: Uninformed Regulation in an Entry-Deterrence Model* Ana Esínola-Arredondo and Félix Muñoz-García June 18, 015

2 Pro t-enhancing Environmental Policy: Uninformed Regulation in an Entry-Deterrence Model Ana Esínola-Arredondo y School of Economic Sciences Washington State University Pullman, WA Félix Muñoz-García z June 18, 015 Abstract This aer considers a olluting rm, subject to environmental olicy, who seeks to deter the entry of otential cometitors. We investigate under which conditions rm ro ts are enhanced by regulation. We show that, contrary to common belief, ine cient rms may lobby in favor of environmental regulation when their roduction is esecially olluting. In addition, we evaluate how this result is a ected by the regulator s information accuracy and the environmental damage from ollution. Keywords: Entry deterrence; Signaling; Environmental olicy; Informational advantage; Pro ts. JEL classification: D8, H3, L1, Q5 We would like to thank all articiants of the 13th International Industrial Organization Conference, esecially to Ramya Shankar for her insightful comments and suggestions. y Address: 111C Hulbert Hall, Washington State University, Pullman, WA anaesinola@wsu.edu. z Address: 103G Hulbert Hall, Washington State University. Pullman, WA fmunoz@wsu.edu. Phone: (509) Fax: (509)

3 1 Introduction Environmental regulation is often deemed as detrimental for rm ro ts. While this result holds under comlete information, we show that, under incomlete information, regulation can facilitate rms information transmission, and thus have a ositive e ect on ro ts. We consider a setting in which an incumbent monoolist faces entry threats from a otential newcomer, which is uninformed about the incumbent s roduction costs (e cient or ine cient). The incumbent s outut generates an environmental externality that the regulator seeks to correct with the use of ollution taxes. For comleteness, our model allows the regulator to have di erent degrees of information about the incumbent s costs (i.e., erfectly informed, artially informed, or comletely uninformed). In this incomlete information setting, the regulator must set a rst-eriod emission fee on the incumbent, who resonds by choosing an outut level. Both fee and outut are subsequently observed by the entrant, as signals it uses to infer the incumbent s e ciency level before deciding whether to join the industry. Our model is, therefore, useful to analyze industries where rms develo new roducts whose costs are di cult to assess by regulators and otential entrants. In our study, we rst show that the e cient rm increases its outut relative to comlete information in order to reveal its tye to otential entrants and thus deter entry. That is, the e cient incumbent exerts a searating e ort that cannot be ro tably mimicked by the ine cient tye of rm. We demonstrate that such e ort is ameliorated by regulation. Hence, emission fees give rise to two oosite e ects on ro ts: a negative e ect, as rms are forced to decrease their outut; and a ositive e ect, as fees reduce the incumbent s searating e ort. We show that the ositive e ect dominates when ollution is su ciently damaging, and thus fees are strict enough. In this context, the ine cient tye of rm nds it unro table to mimic the outut level of the e cient incumbent, thus allowing the latter to reveal its tye exerting a small searating e ort. As a consequence, stringent regulation can become ro t enhancing under incomlete information settings. In summary, environmental olicy hels the e cient rm more easily convey its tye otential rivals. Second, we exlore whether the ro t-enhancing e ect of emission fees is sensitive to the regulator s information accuracy. In articular, a oorly informed regulator would assign a large robability on the incumbent s costs being high when they are actually low, thus setting a lax fee on this rm. Such inaccurate information roduces two e ects on ro ts: a ositive e ect (from the less stringent fee), and a negative e ect (as the incumbent is now forced to increase its searating e ort in order to convey its tye to otential entrants). We identify under which conditions the ositive e ect dominates and, hence, ro ts monotonically increase as the regulator becomes more oorly informed. In articular, we show that such monotonicity arises when the environmental damage from ollution is relatively large. In this context, emission fees become stricter, hindering the ability of the ine cient rm to mimic the outut decision of the e cient rm, which ultimately reduces the searating e ort that the latter needs to exert to convey its tye. Finally, we study the equilibrium in which the ine cient tye of incumbent deters entry by

4 concealing its costs from otential rivals. We demonstrate that emission fees lower the rm s costs of concealing information, thus roviding more incentives to ractice entry deterrence than when regulation is absent. Hence, regulators can exect suort from the most unexected ally: ine cient rms which, in addition, are esecially olluting. Our ndings, therefore, hel to exlain the recent lobbying for stringent environmental regulation by relatively olluting comanies, such as the mining comany Rio Tinto, and the oil comany BP, as art of the Pew Center on Global Climate Change. 1 Several aers analyze settings in which environmental regulation a ects ro ts under contexts of comlete information, such as Porter (1991), Porter and van der Linde (1995a,b), Farzin (003) and Schoonbeek and de Vries (009). Our aer shows that, under incomlete information, rms can still favor regulation. Seci cally, a rm favors emission fees when they facilitate its signaling ability, i.e., conveying or concealing information from otential rivals. Our study also contributes to the literature on entry-deterring models with signaling; see Milgrom and Roberts (198), Harrington (1986), and Ridley (008). This literature, however, abstracts from the regulatory contexts in which rms oerate. We demonstrate that considering such regulatory setting is crucial to understand rms incentives to suort or oose environmental olicies. That is, our results would rovide an additional motive for rms to favor emission fees, even in the absence of the standard arguments rovided by the literature, such as innovation and cororate social resonsibility. As described above, our aer builds on signaling models in which the uninformed entrant observes several signals, each of them originating from di erent agents. In articular, Schultz (1999) analyzes the ability of di erent incumbents to use their outut decisions to deter entry, and shows that a ooling equilibrium can be sustained if the incentives of these rms are relatively aligned. Similarly, Esinola-Arredondo and Munoz-Garcia EM (013, 015) examine entry decisions when the otential entrant observes one signal originating from the incumbent rm (outut) and another from the regulator (emission fee), demonstrating that a ooling equilibrium exists in which entry is deterred if the incumbent s and regulator s references are aligned, i.e., when entry is damaging for the incumbent and it can be deterred without generating large welfare losses. While EM (015) describes under which conditions the incumbent rm seeks to deter entry in a given information and regulatory context (incomlete information and emission fees), it does not evaluate rms interests towards regulation and information; our main investigation in this aer. Therefore, our results hel understand in which settings rms would actually suort the introduction of environmental regulation while racticing entry deterrence, and if a more accurately informed regulation can become ro t enhancing. 3 This result is relevant for olicymakers who evaluate the imlementation 1 Maloney and McCormick (198) emirically analyze which rms suort environmental regulation in di erent U.S. industries, such as textile mills and smelting lants for cooer, lead and zinc. Their study shows that, while these rms are subject to a costly regulation, their market share increases, otentially indicating larger ro ts. Denicolò (008) also examines a signaling model, in which a rm decides whether to acquire advanced technology in order to convey its costs of regulatory comliance to an uninformed regulator. However, rms are always active in the industry, and thus entry deterrence cannot arise. In addition, Denicolò (008) does not allow for the regulator to sustain di erent degrees of information. 3 EM (013) considers a signaling model in which the regulator erfectly observes the incumbent s costs and, as a 3

5 of environmental olicy on olluting industries facing entry threats. The following section describes the model. Section 3 (4) analyzes the searating (ooling) equilibrium, while section 5 discusses our results. Model Consider an incomlete information model whereby an incumbent rm, facing an inverse demand P (q) = 1 q, rivately observes its roduction costs, c K, either high or low, i.e., K = fh; Lg, where 1 > c H > c L > 0. A otential entrant does not observe the incumbent s costs, but knows that they are high with robability (0; 1) and low otherwise. The costs of the entrant are high, c H, and under comlete information it would only enter when the incumbent s costs are also high. 4 The roduction of all rms generates ollution that the regulator addresses setting emission fees in both eriods. The social welfare function considers consumer and roducer surlus, tax revenues, and environmental damage from ollution, ED(q) dq, where d > 1= guarantees that emission fees are ositive under all information contexts. (Emission fees are, hence, revenue neutral.) The regulator can be erfectly informed about the incumbent s costs, as oorly informed as the entrant is, or artially informed. In articular, the regulator assigns a belief to the incumbent s costs being high, where arameter [0; +1) re ects the regulator s degree of information accuracy. 5 This allows for cases in which = 0, and thus the regulator is certain about facing a high-cost incumbent, i.e., = 1; that where = 1, imlying that he is as oorly uninformed as the entrant is; and that in which! 1, entailing that he is sure about facing a low-cost incumbent, i.e., = 0. In the second stage of the game, rms comete a la Cournot if entry occurs; otherwise, the incumbent maintains its monoolistic osition. The time structure of the game is as follows: (1) the incumbent rivately observes its roduction costs, c K, where K = fh; Lg; () the regulator sets an emission fee t 1 on the incumbent s outut; (3) the K-tye incumbent resonds to fee t 1 by choosing an outut level q K (t 1 ); (4) the entrant observes two signals (emission fee and outut level), udates its rior beliefs about the incumbent s tye, and decides whether to enter; (5) the regulator sets emission fees either on the incumbent alone (under no entry) or on both rms (under entry); and (6) rm/s resond by selecting their outut level. 6 consequence, the only uninformed agent is the otential entrant. In contrast, EM (015) extends that model to allow for the regulator to have access to di erent degrees of information (e.g., being as oorly informed as the entrant, or having access to better information about the incumbent s real costs). Such extended model shows that the regulator may actually be willing to facilitate the incumbent s entry-deterring ractices under larger conditions when he is oorly informed than when his information is more accurate. 4 This is a common assumtion in the literature of entry-deterrence without regulation, often justi ed by the lack of exerience of the otential entrant in the industry. When environmental regulation is resent, this assumtion can be rationalized on the basis of the newcomer s inexerience in comlying with the administrative and legal details of the olicy. 5 For instance, the regulator could receive a non-ublic reort from other government agencies, such as the IRS, heling him assess the incumbent s costs. 6 The otential entrant does not observe the value of at the beginning of the game, but sustains a rior that assigns full robability to = 1, i.e., =. After observing the regulator s emission fee and the incumbent s outut 4

6 Under comlete information, the K tye incumbent solves max q0 (1 q)q (c K + t 1 ) q K = 1 c K 1+d which yields an outut function q K (t 1 ) = 1 c K t 1. The regulator seeks to induce the socially otimal outut that maximizes social welfare, q SO. In articular, anticiating the incumbent s outut function q K (t 1 ), the regulator sets an emission fee t K 1 = (d 1) 1 c K 1+d which solves 1 c K t 1. In the second eriod, a similar analysis alies if no entry ensues, where = 1 c L 1+d the same fee is still otimal. If, instead, rms comete a la Cournot, every rm i roduces qi K(t ) = 1 c i+c j t 3 where j 6= i. In this context, the regulator induces qk SO that solves qi K(t ) + qj K(t ) = qk SO (013). by setting a fee. For more details on comlete information strategies, see EM The next sections analyze the searating equilibrium (SE) and ooling equilibrium (PE). In the SE (PE), we examine the outut and ro ts for the low-cost (high-cost) incumbent since the high-cost (low-cost, resectively) rm behaves as under comlete information. 3 Searating equilibrium In a context in which regulation is absent, as in standard entry-deterrence games, the low-cost rm increases its outut (relative to comlete information) in order to convey its tye to the otential entrant and thus deter entry; see Milgrom and Roberts (198). When regulation is resent, the incumbent similarly increases its roduction in order to signal its e cient cost structure to otential rivals, but such additional roduction generates more ollution. sets more stringent emission fees in order to curb such additional externality. In this context, the regulator In articular, as shown in EM (013, 015), a searating equilibrium can be sustained where the low-cost rm increases its outut function, from q L (t 1 ) = 1 c L t 1 under comlete information to q A (t 1 ) = (1 c H )(1+d) 3 1+d t 1, where denotes the discount factor. The regulator, anticiating outut function q A (t 1 ), sets an emission fee t 1 = h d 1 + (1 + d)(1 ) + (3 + d) 3 3 (1 + d) i c H + (1 )c L which yields an outut level q A (t 1 ) = + 3 (+ 3)c H (1 )c L (1+d) in equilibrium. Hence, the outut di erence q A (t 1 ) ) can be interreted as the low-cost rm s searating e ort. The ql (t L 1 next lemma examines how such e ort is a ected by the regulator s information accuracy,. Lemma 1. Searating e ort q A (t 1 ) ql (t L 1 ) = [ 3(1 c H ) (c H c L )] (1+d) is decreasing in, and level, the entrant s beliefs are udated. In the searating equilibrium, the two signals hel the entrant assign full robability on the incumbent s costs being low and thus! 1. In contrast, in the ooling equilibrium, the two signals leave the entrant s rior beliefs of the incumbents costs and of the value of una ected. For a more detailed discussion of belief udating when the otential entrant observes two signals, see EM (015). 5

7 becomes nil when! 1 (i.e.,! 0). The searating e ort, deicted in gure 1, is nil when the regulator is erfectly informed. 7 When his information becomes less accurate, however, he assigns a ositive robability to the incumbent s costs being high, thus setting a less stringent fee. Such a fee makes the outut decision of the lowcost rm easier to mimic by the high-cost tye and, hence, forces the former to increase its outut in order to signal its tye. This result is illustrated by leftward movements in gure 1 (lower ) for a given damage d. Figure 1 also deicts the e ect of more olluting outut on the searating e ort of the e cient rm. In articular, as d increases emission fees become more stringent, thus hindering the ability of the ine cient incumbent to imitate its roduction decision. As a consequence, the e cient rm does not need to exert such a large searating e ort when ollution is damaging, e.g., d = 1:5, than when it is not, e.g., d = 0:51, which shrinks the di erence between outut levels q A (t A 1 ) and ql (t L 1 ). (Recall that emission fees become zero for all d < 1=, imlying that the searating e ort when d = 0:51 closely resembles that in standard entry-deterrence models in which the regulator is absent.) Fig 1. Searating e ort as a function of and d. The above results suggest that a less informed regulator gives rise to two oosite e ects on ro ts: a ositive e ect, as he sets less stringent fees; and a negative e ect, since such a fee forces the rm to increase its searating e ort. The next lemma comares these two e ects. Lemma. The equilibrium ro ts of the low-cost incumbent in the SE, L;R SE (), increase in for all < 1, but decrease otherwise; where cuto 1 1 ln ln (1 d)(1 c L ) 4. In addition, 3(1 c L ) c L 1 > 0 for all d < d 1 1 3(1 c L ) c H +c L (1 c L ), and 1 decreases in d. Figure a deicts equilibrium ro ts of the low-cost incumbent as a function of the regulator s 7 For simlicity, gure 1 considers costs c H = 1=3, c L = 1=4, and no discounting. These cost arameters allow for the searating equilibrium to arise, i.e., c H < 3+(1+d)cL 3+(1+d). For our numerical examle such inequality becomes 1 < 4 3+(1+d) 3 4, which holds for all d > 1. Other arameter combinations yield similar results and can be rovided 3+4(1+d) by the authors uon request. 6

8 information accuracy,, illustrating their non-monotonicity. 8 In words, the incumbent obtains a larger ro t with a regulator who is artially informed about its tye ( = 1 in gure a) than with a erfectly informed (! 1) or a comletely uninformed ( = 0) regulator. When > 1, the regulator sets stringent fees, and thus a artially informed regulator entails an overall ositive e ect on ro ts. In contrast, when < 1, fees become lax, and further reductions in hel the high-cost rm to easily mimic the low-cost incumbent, reducing the ro ts of the latter. Fig a. Pro ts in the SE when d = 0:75: Fig b. Pro ts in the SE for di erent values of d. Figure b deicts the e ect of environmental damage on ro ts. When d is low (e.g., d = 0:51), the emission fee is lax and attracts the high-cost rm to mimic, ultimately requiring a large searating e ort from the low-cost incumbent; a behavior that is emhasized when the regulator becomes more uninformed (leftward movement in gure b). Hence, in this case equilibrium ro ts monotonically decrease. The oosite argument alies when d is high (d = 1:5), and thus emission fees are stringent. In this context, the outut level of the low-cost rm is more di cult to mimic, heling it obtain larger ro ts as the regulator becomes more uninformed. We next examine whether regulation leads e cient rms to obtain higher ro ts under the SE than in comlete information (). Proosition 1. Pro ts satisfy L;R SE () L;R if and only if, where 1 and 0 for all d d (+ 3)(1 c H ) 4(1 c L ) : ln ln (1 d) 4 3(1 c H ) 3(1 c L ) Figure 3 deicts the di erence between the ro ts in the SE and, L;R SE () L;R. Let us rst consider this di erence when d = 0:75. Starting from! 1 where L;R SE () = L;R, a marginal decrease in entails a ositive e ect on ro ts (laxer fees) that dominates its negative e ect (easier 8 In order to facilitate comarisons, gure a (and all subsequent gures) use the same arameter values as in gure 1., 7

9 to mimic outut), thus yielding L;R SE () > L;R. Further reductions in, however, entail a less stringent emission fee, and a easier to mimic roduction, ultimately generating the oosite ro t ranking. Fig 3. Pro t di erence L;R SE () L;R : L;R Figure 3 also shows that, as the environmental damage increases, the ro t ranking L;R SE () holds under a wider range of. Intuitively, when ollution is very damaging the regulator sets stringent emission fees, which the high-cost rm cannot ro tably mimic. Hence, when regulation is resent the e cient rm can be better o under incomlete than comlete information; a result contrasting that when regulation is absent; see Milgrom and Roberts (198). 9 4 Pooling equilibrium EM (015) show that a ooling equilibrium (PE) can be sustained in which the high-cost incumbent mimics the outut function of the low-cost rm. If the regulator suorts such concealing strategy, he increases the emission fee from t H 1 under to tl 1 under the PE. As a consequence, this rm s outut level increases from q H (t H 1 ) = 1 c H 1+d to ql (t L 1 ) = 1 c L 1+d, and its mimicking e ort is given by the di erence q L (t L 1 ) qh (t H 1 ) = c H c L 1+d.10 Let us next evaluate the equilibrium ro ts of the high-cost rm. Lemma 3. The equilibrium ro t of the high-cost incumbent in the PE, H;R, is constant in. In addition, H;R increases in d if and only if d < d 4; where d 4 1+(1+c H )+c H(1 c L )+c L (c L 3) (1 c H )(1+ c H c L ). First, the ro ts of the high-cost incumbent do not deend on, since in the PE the regulator 9 When d = 0:51 emission fees are close to zero. Figure 3 shows that our results redict that L;R SE () < L;R for all values of, resembling that in standard entry-deterring models without regulation. 10 In articular, for the PE to arise: (1) the high-cost incumbent must be su ciently symmetric to the low-cost rm, since otherwise its mimicking e ort would be too costly; and () the e ciency loss that the regulator generates by overtaxing the high-cost incumbent must be small. 8

10 mimics the emission fee he would set on the e cient rm, t L 1, and the incumbent resonds by mimicking its outut function, q L (t 1 ), thus yielding an outut level q L (t L 1 ) which is indeendent on. 11 In addition, lemma 3 identi es that ro ts are non-monotonic in d. This roerty arises because an increase in d yields two oosite e ects on ro ts: a negative e ect from a more stringent fee; and a ositive e ect, since such strict fee reduces the mimicking outut q L (t L 1 ). In articular, the mimicking e ort q L (t L 1 ) qh (t H 1 ) = c H c L 1+d decreases in d at a decreasing rate. Hence, the ositive e ect of an increase in d on ro ts is large when d < d 4, thus dominating its negative e ect, but it becomes small otherwise; as illustrated in gure 4. Fig 4. Pro ts H;R as a function of d. While ro ts under the PE are ositive, we still need to determine whether they are larger than under, as evaluated in Proosition. Proosition. Pro ts satisfy H;R H;R only if d < d 5 ; where d 5 ( )c H +6c L 4c L c H(3 c L ) (1 c H )[( )c H +c L ].. In addition, H;R H;R increases in d if and Our results, hence, go in line with those in standard entry-deterrence models without regulation, which redict that ro ts are larger in the PE than in. The ro t di erence BDE R H;R H;R can then be interreted as the bene t from deterring entry (BDE). Such a bene t is increasing in d if d < d 5, since the ositive e ect of more stringent regulation (easier to mimic roduction) outweighs its negative e ect. We next analyze whether the bene t of deterring entry is a ected by regulation. Corollary 1. BDE R BDE NR for all d (d 6 ; d 0 6 ). (See aendix for cuto s d 6 and d 0 6.) As deicted in gure 5, BDE is larger without than with regulation when environmental damages 11 The regulator s information accuracy,, a ects however his willingness to suort the high-cost incumbent in its concealing strategy. In articular, the regulator behaves as rescribed in this PE if the savings in entry costs arising from deterring entry exceed the (exected) ine ciencies from setting a stringent fee t L 1 on a rm which could ossibly have high roduction costs. 9

11 are small, d < d 6. Intuitively, emission fees are less stringent, imlying that the high-cost incumbent must exert a large mimicking e ort. Hence, the ositive e ect of regulation is o set by its negative e ect. However, when ollution is more damaging, d > d 6, emission fees become stringent, thus reducing the incumbent s mimicking e ort. In this case, BDE is larger with than without regulation. Fig 5. BDE R and BDE NR. 5 Discussion and Conclusions Is ollution good for ro ts? We demonstrate that ro ts are not necessarily decreasing in d; a result that holds both in the SE and PE. Under the SE, if the regulator is artially informed, the ro ts of the low-cost rm are larger when ollution becomes more damaging. Intuitively, regulation hinders the mimicking ability of the high-cost rm. Hence, an incumbent facing an uninformed regulator and oerating in olluting (not-so-olluting) industries would favor (oose) regulation since it facilitates (hinders) its entry-deterring ractices. Firms do not necessarily refer uninformed regulators. At rst glance, one may susect that an uninformed regulator is bene cial for a low-cost incumbent, since he assigns a large robability on its costs being high, setting less stringent emission fees. Such a result undoubtedly holds when the incumbent faces no entry threats. However, under entry threats, the ro ts of the low-cost rm are not necessarily monotonic in the regulator s information, since laxer emission fees facilitate the mimicking e ort of the high-cost rm, thus hindering its ro ts. Ine cient rms favoring stringent emission fees? We also show that, when damages are significant, the bene ts from deterring entry are actually larger when regulation is resent than absent; see Corollary 1. This yields a rather unexected rediction: the high-cost rm would actually favor environmental regulation when ollution is damaging, since such a regulation ameliorates its mimicking e ort. Further research. Our model considers a single incumbent facing the threat of entry. However, in some industries several rms face such a threat. When regulation is absent, Harrington (1987) shows that, in a context of homogeneous roducts, rms behavior under the searating equilib- 10

12 rium coincides with that under comlete information, and that the ooling equilibrium cannot be sustained. However, when roduct di erentiation is allowed, Schultz (1999) demonstrates that such equilibrium can be suorted whereby incumbents coordinate their roduction decisions to deter entry. The literature has, nonetheless, overlooked the e ect of regulation on these equilibrium results, i.e., whether it facilitates entry-deterring ractices (as shown in our model) or, instead, hinders them. In addition, our setting can be extended in several other dimensions: rst, considering that rms environmental damage is a function of their roduction costs; and second, allowing for emission fees to a ect rms abatement decisions, where abatement costs are tye-deendent. 6 Aendix 6.1 Proof of Lemma 1 The outut di erence q A (t 1 ) ql (t L 1 ) is ositive if c H < at c H = A > cL 3+ A, a cuto that originates 3+ when c L = 0 and reaches c H = 1 when c L = 1. In addition, cuto A satis es 3+(1+d)cL 3+(1+d) since 1 originates at c H = 3 3+(1+d) and reaches c H = 1 when c L = 1, and their vertical intercets satisfy 3 3+(1+d) < 3 3+ since d > 1=. Hence, for all arameter values in which the SE exists, < 1, the outut di erence q A (t 1 ) ql (t L 1 ) is ositive: Finally, the outut di erence decreases in, reaches its highest value, 3(1 ch ) (c H c L ) (1+d), when = 0; and collases to zero when! Proof of Lemma First-eriod ro ts in the SE are 1 q A (t 1 ) q A (t 1 ) c L q A (t 1 ), and rearranging yields 8d(1 c L ) (d 1)(1 c L ) + 4(1 + d) where (c H c L ) 3(1 ch ). Di erentiating with resect to, yields ln [(d 1)(c L 1) ] (1+d) which is zero if = 1 ln ln (1 d)(1 c L ) 4 3(1 c L ) c 1. In addition, cuto 1 satis es 1 > 0 for all L d < d 1 1 3(1 c L ) c H +c L (1 c L ), and 1 decreases in d = ln (1 6.3 Proof of Proosition 1 Pro ts in the SE, L;R SE (), are d) < 0: L;R SE () 1 qa (t 1) q A (t 1) c L q A (t 1) + 1 x L inc(t L 1 ) x L inc(t L 1 ) c L x L inc(t L 1 ) ; since x L inc (tl 1 ) = 1 c L 1+d, L;R SE () simli es 11

13 8d(1 + )(1 c L ) h3(1 c H ) + 4(c H c L ) (c H c L ) 4(1 + d) 3(1 ch )i (d 1)(1 c L ) Under, ro ts L;R = (1 + ) d(1 c L). Hence, the ro t di erence L;R SE () h (1+d) L;R 3(cH i i h3(1 c H ) + 4(c H c L ) 1) + (c H c L ) + (d 1)(c L 1) which becomes zero for all, where 1 for all d d (+ 3)(1 c H ) 4(1 c L ). 6.4 Proof of Lemma 3 Pro ts in the PE are 4(1 + d) ln ln (1 d) 4 3(1 c H ) 3(1 c L ) H;R = 1 q L (t L 1 ) q L (t L 1 ) c H q L (t L 1 ) + 1 q H (t H 1 ) q H (t H 1 ) c H q H (t H 1 ). In addition, cuto is ositive is Plugging outut levels q L (t L 1 ) and qh (t H 1 ) into H;R yields H;R = d(1 + ) + dc H c L (c L + d 1) + c H [(1 d)c L 1 d(1 + )] (1 + d) Di erentiating H;R 6.5 Proof of Proosition Pro t H;R with resect to d, and solving for d, we obtain d (1 + c H ) c H( c L ) + c L (c L 3) : ( 1 + c H )( 1 + c H + c L ) is in the roof of Lemma 3, and L;R = ( + ) d(1 c H) (1 + d) : Hence, H;R H;R for all d < d 5 ; where d 5 (c H c L )(1 c L ) (1 c H )[+( )c H c L ]. In addition, H;R H;R = d d( )c H c L (d 1 + c L ) + c H (d(1 ) 1 + (1 + d)c L ) (1 + d) 1

14 Di erentiating with resect to d, and solving for d yields d = ( )c H + 6c L 4c L c H (3 c L ) (1 c H ) [( )c H + c L ] d 5 : 6.6 Proof of Corollary 1 Pro t di erence H;R H;R is given in the roof of Proosition. Since and H;NR = (1 c H) 4 + (1 c H) 9, then H;NR 1 q L q L c H q L + (1 c H) 4 = 1 + (1 + c H c H (1 + c L ) c L ) 4 H;NR H;NR = 1 + (1 + c H c H (1 + c L ) c L ) "(1 c H ) 4 4 # + (1 c H) 9 Hence, H;R H;R H;NR H;NR for all d [d 6 ; d 0 6 ], where and d 6 d 0 6 D ' + 1 ' D ' + 1 ' 4 + (4 9) (ch )c H + 9(c L )c L ) (' )E 1= 4 + (4 9) (ch )c H + 9(c L )c L ) (' )E 1= where ' = 5 + (5 9)c H, = c H(5 9c L ) + 9c L, D 9(c H c L )(c H + c L ) 4(1 c H ), and E ' + 9c L (3c L 4) c H (9c L ). References [1] Denicolò, V. (008) A signaling model of environmental overcomliance, Journal of Economic Behavior and Organization 68, [] Esinola-Arredondo, A. and F. Munoz-Garcia (013) When Does Environmental Regulation Facilitate Entry-Deterring Practices? Journal of Environmental Economics and Management 65(1), [3] Esinola-Arredondo, A. and F. Munoz-Garcia (015) Can Poorly Informed Regulators Hinder Cometition? Environmental and Resource Economics, 61(3), [4] Farzin, Y. H. (003) The e ects of emission standards on industry, Journal of Regulatory Economics, 4,

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