Green Consumers, Greenwashing and the Misperception of Environmental Quality
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Lambertini, Luca; Pignataro, Giuseppe; Tampieri, Alessandro Working Paper Green Consumers, Greenwashing and the Misperception of Environmental Quality Quaderni - Working Paper DSE, No. 958 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca; Pignataro, Giuseppe; Tampieri, Alessandro (2014) : Green Consumers, Greenwashing and the Misperception of Environmental Quality, Quaderni - Working Paper DSE, No. 958, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4062 This Version is available at: https://hdl.handle.net/10419/159797 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/
ISSN 2282-6483 Green Consumers, Greenwashing and the Misperception of Environmental Quality Luca Lambertini Giuseppe Pignataro Alessandro Tampieri Quaderni - Working Paper DSE N°958
Green Consumers, Greenwashing and the Misperception of Environmental Quality Luca Lambertini , Giuseppe Pignataroy , Alessandro Tampieriz August 4, 2014 Abstract In this paper we analyse a setup where consumers are heterogeneous in the perception of environmental quality. The equilibrium is veri…ed in a setting with horizontal and vertical (green) di¤erentiation. Pro…ts are increasing in the misperception of quality, while, the investment in green quality decreases the more the goods are substitutes. We further consider the introduction of either an emission tax or an environmental standard. The former rises the investment in environmental quality due to the higher cost of production, whereas in equilibrium quality always improves after the introduction of the latter. We show that an optimal environmental standard is an e¤ective regulatory instrument against greenwashing and that the e¢ cacy of the interventions is conditioned to the damage distribution and the aggregate level of emission. JEL codes: L13, L51, Q50. Keywords: Green quality; Misperception; Pigouvian taxation; Environmental Standard. Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy; [email protected]. yDepartment of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy; [email protected]. zFaculty of Law, Economics and Finance, University of Luxembourg, Avenue de la Faïencerie 162a, L - 1511 Luxembourg; [email protected]. 1
1 Introduction Access to knowledge and innovations in technology have led to increasing awareness of environmental issues. Several studies have shown that world-wide, consumer’s appetite for green products has increased signi…cantly in the past years (Chase and Smith, 1992; Kim and Choi, 2005; Chen, 2008, inter alia). Communities demand cleaner environments and the rise of consciousness has resulted in signi…cant environmental improvement (Reitman, 1992). More companies around the world have reacted by developing eco-friendly products (Kohl, 1991; Chang, 2011). The eco-label is, for instance, one of the practises which allows consumers to identify the quality and the environmental consequences of a production process generally unobservable. The role of information di¤usion and the quality perception have been partially underscored in studies dealing with environmental policies.1Environmental regulation in the literature is usually viewed as a form of agency issue where the polluting …rms have better information about the true level of their abatement activities than the regulator. If certain aspects of environmental quality are costly to measure, regulators may resort to proxies to infer information about environmental quality. This may allow …rms to circumvent the regulatory constraints by maximizing along those margins that are costly to measure (Bansal and Gangopadhyay, 2003). In this paper, instead, an alternative perspective is proposed. We investigate the e¤ect of environmental regulation when green consumers misperceive the quality of the products. In reality, there is a perception in the marketplace that a green package equals greater value. With little knowledge to make an informed decision, individuals seem to rely on …rms’packaging to understand the positive (or negative) impact of production. This should not come as too much of a surprise, as consumers have traditionally lacked a detailed understanding of green innovation. Part of the consumers would undertake larger green consumption if they better understood the impact that each production has on the society. Others would confuse the level of transparency when there are no speci…c criteria qualifying a product as green.2The bene…ts by appearing to be a green company come in the form of a higher stock price, more customers or favoured partnerships with green organisations (Doni and Ricchiuti, 2013). Thus paradoxically, higher prices are more easily understood by consumers with respect to other features, especially when comparing products and green investments across categories. They implicitly suggest signi…cant eco-investments of the …rms and justify payback period facilitating consumer decisions on those products. This marketing strategies in order to appear environmentally friendly, i.e., greenwashing, usually occurs when a company spends more time and money claiming green production through advertising and marketing than actually implementing business practices that minimize environmental impact.3Firms may operate in a way that is damaging 1An interesting exception relies on the signaling framework proposed by Sengupta (2012a). 2For instance most of the products that make the claim are biodegradable, phosphate and chlorine free may still derive their ingredients from petrochemicals like crude oil or natural gas (which are not renewable). https://www.gmaonline.org/downloads/research-and-reports/greenshopper09.pdf 3The tools used in greenwashing can include press releases about green projects or task forces put 2
to the environment or in an opposite manner to the goal of the announced initiatives.4 Since consumers’ evaluation is based on advertising to make decisions, greenwashing distorts their con…dence (Hamann and Kapelus, 2004) and therefore it is positively associated to confusion and perceived risk (Chen and Chang, 2013). This paper presents a model of regulation in the presence of asymmetric information of environmental quality. Our framework is characterized by the heterogeneity of consumers due to environmental awareness. We model the di¤erence in consumers’ environmental concern as a di¤erence in their level of information. Indeed, like consumer consciousness (and perhaps related to it), the stringency of public regulation may have di¤erent e¤ects according to the misperception of the market. Throughout the paper, we focus on the extent and manner in which the quality perception of conscious consumers induces di¤erent environmental performances and analyse their impacts of aggregate qualities. We treat regulation as exogenous and abstract from information problems between the regulator and …rms. The aim is to understand how changes in regulation may in‡uence the incentive of …rms to invest in green technology or realising greenwashing behaviour. In the baseline model, we evaluate the unregulated equilibrium and examine the variation in terms of under- (over-) estimation of the true quality. The equilibrium is symmetric. Pro…ts in equilibrium are increasing in the perception, while, the investment in green quality decreases the more the goods are substitutes. Indeed, a higher degree of substitutability implies higher competition. Thus …rms react by softening their investment in environmental quality. The paper considers next two government interventions. First we investigate the e¤ect of a tax on polluting emissions. This policy increases the investment in environmental quality due to changes on …rms’incentives. The idea is that a company invests in green quality not only to acquire green consumers, like in the baseline model, but also to reduce tax burdening. We investigate next the introduction of an endogenous tax. The level of optimal taxation increases with the marginal damage on emissions if the average perception of environmental quality is high. A higher perception of environmental quality implies larger demand. If the marginal damage of emission is high, at the optimum, the increase in demands needs to be compensated by higher taxation. Moreover, the optimal tax decreases with the average perception of environmental quality if the marginal damage of emission is high. When production is very polluting, the optimal tax burden is heavy, but if the perception of environmental quality is high, the demand is so large that a lower level of taxation is su¢ cient to reach the optimum. The second intervention regards the environmental standard. Despite of the downward sloping …rms’reaction functions in quality which imply negative strategic e¤ects, the impact of an environmental standard is that of increasing the perceived environmental quality even for consumers who underestimate quality. This e¤ect rises their into place, energy reduction or pollution reduction e¤orts, and rebranding of consumer products and advertising materials. 4Lyon and Maxwell (2011) analyse greenwashing as a game between a …rm and an activist. In their analysis, greenwashing implies that the …rm selectively discloses the positive information about their environmental or social performance without full revealing negative information. 3
willingness to pay for the goods, while increasing …rms’ pro…ts. The results explain the producers’ willingness to accept the introduction of a standard. Instead, an endogenous environmental standard bites if the overestimation of environmental quality of some consumers is very high. The overestimation is positively related to greenwashing since the investment in green advertising induces consumers to overstate the environmental quality of the product. Firms invest more in environmental quality due to an optimal environmental standard representing an e¤ective regulatory instrument in case of greenwashing. The economic literature has recently analysed the presence of green consumers. A …rst group of papers focused on the impact of a higher consumers’ consciousness on the market equilibrium and the associated social welfare (Eriksson, 2004 and Conrad, 2005). A second group dealt with the presence of green consumers interacts with the optimal environmental policy (Arora and Gangopadhyay, 1995, Cremer and Thisse, 1999, Moraga-Gonzales and Padron-Fumero, 2002, Lombardini-Riipen, 2005). Finally, the presence of green consumers has been examined in relation with socially responsible …rms (Rodriguez-Ibeas, 2007, Garcia-Gallego and Georgantzis, 2009, Doni and Ricchiuti, 2013), or in determining the validity of the Porter hypothesis (Andrè et al., 2009, Lambertini and Tampieri, 2012). The common framework of these contributions is the pure vertically di¤erentiated duopoly. Unlike these approaches, our framework considers both horizontal and vertical di¤erentiation and goods di¤er in the degree of substitutability and in (environmental) quality. The remainder of the paper is organised as follows. Section 2 introduces the model. Section 3 shows the baseline results. Section 4 consider the regulated equilibrium through two interventions, namely, the introduction of either a tax on emission or a standard of environmental quality with a simple simulation comparing their e¤ect on quality. These regulatory interventions are developed and compared in Section 4.1, 4.2 and 4.3, respectively. Concluding remarks are proposed in Section 5. 2 The model Consider an economy with two …rms, each producing one di¤erentiated good. Firms compete by choosing the environmental quality level of their products and their prices.5 There is a number of consumers with mass normalised to 1. Their representative utility function, U(x1; x2), is:6 U(x1; x2) = (+e1)x1+ (+e2)x2x2 1+ 2x1x2+x2 2 2+c0;(1) where xidenotes the representative consumer’s quantity of good i,i2 f1;2g;eirepresents the environmental quality of good i;c0is the quantity of the numeraire good; 5Note that the demand function takes into account both horizontal and vertical di¤erentiation, while, the information technology is the same between …rms. 6See Häckner (2000). 4
while, 2[0;1] denotes the degree of substitutability between the two goods, with = 0 identifying independent goods and = 1 in case of perfect substitutes.7Under symmetric information, consumers are perfectly aware of the intrinsic environmental quality of goods 1and 2.8For each i2 f1;2g, utility maximisation with respect to x1and x2gives a certain demand function: xi(pi; pj; ei; ej) = (1 )+(eiej)pi+pj 12; j 2 f1;2g; j 6=i: (2) The rise in consumers’ ecological consciousness is constrained by the fact that often they do not have su¢ cient information about the environmental quality of …rm’s production. We model this uncertainty in environmental consciousness as a case of imperfect information in detecting the environmental quality. Environmental perceptions are independent draws. The consumer’s signal about the quality of good iis i,i2 f1;2g. Only a proportion 2(0;1) of the population recognises the true quality. In this case they (i) are aware that the environmental damage are harmful for them and (ii) perceive the correct quality of the good i, i.e., i=ei. A partial environmentally aware agents may instead capture interesting aspects. For instance companies use their ads and marketing campaigns to mislead consumers, by overstating claims of their environmental performance.9For i2 f1;2g, a proportion of 1consumers do not recognise the true environmental quality. It is equiprobable that they expect low quality i=e0or high quality i=em> e0. The symmetry in the probabilities of the events is for the sake of simplicity. It has the advantage of keeping the analysis tractable to examine the impact of wrong perception of goods. The interpretation of a consumer with uncertain perception is therefore: i=e0< ei: the consumer might underestimate the environmental quality of good i; i=em> ei: the consumer might overestimate the environmental quality of good i. Let us de…ne e0and emas the underestimation and the overestimation of environmental quality, respectively. In particular, emcan be interpreted as a measure of green washing. It implicitly infers the …rm’s practise of making unwarranted or overblown claims of sustainability or environmental friendliness in an attempt to gain market share. The higher the signal em, the larger the consumers’overperception of the environmental quality of the good. The (expected) proportion of consumers that receive the correct information about the environmental quality of both goods is 2. Then, a proportion of (1 )2of consumers are expected to receive wrong information about both goods, 7A similar procedure is proposed by Garella and Petrakis (2008). They analyse the e¤ect of introducing a minimum quality standard when consumers are not perfectly informed of goods’quality. 8Note that quality enters in the intercept of the utility function. Symeonidis (2003) considers the alternative approach in which qualities alter the slope of the demand functions. 9See Delmas and Lessen (2014) for a …eld experiment on this issue. 5
whereas 2(1 )are expected to perceive wrong information about at most one of the goods. Furthermore, there are four equiprobable realisations of perceptions pairs (e0; e0);(em; em);(e0;em)and (em; e0), for individuals misperceiving the quality of both goods. There are two equiprobable realisations for consumers with perception of good 1, namely (e0;e2);and (em; e2). Similar results for good 2. According to the perceived di¤erences on quality, the demand for good 1by N= 1 ex-ante identical consumers is given by: q1=2x1(e1; e2) + (3) (1 ) 2[x1(e1; em) + x1(e0; e2) + x1(e1; e0) + x1(em; e2)] + (1 )2 4[x1(e0; e0) + x1(em; e0) + x1(e0; em) + x1(em; em)] : We thus represent nine types of consumers: one group of fully aware consumers, four groups of partially aware ones and the last four groups of wrongly aware consumers. Substituting in (3), the demand qiis: qi(pi; pj; ei; ej) = (1 )+1 2(em+e0)+(eiej)pi+pj 12:(4) The role of information di¤usion and absorption is crucial in this analysis. The demand function of …rm ialways increases with the average value of quality misperception, i.e., e=1 2(em+e0). Intuitively, consumers’appetite for green products leads …rms to put forward the better ecological quality of a given product. As discussed above, the ecolabels, for instance, are some of the instruments used by …rms to win market shares thanks to a di¤erentiation strategy sur…ng the wave of consumers’ecological awareness. Since the environmental consequences of the production and the consumption of a product are generally unobservable, the eco-label appears as one of the way for consumers to collect such information. The higher the average misperception in quality induced by …rms, the larger the demand for that good. Consider next the supply side. Each …rm produces one of the two goods. We normalise marginal costs of production to zero, while …xed costs are increasing in quality: C1=e2 1; C2=e2 2:(5) Thus the pro…t of …rm iis: i=piqi(pi; pj)Ci:(6) In the spirit of Arora and Gangopadhyay (1995), emission in the industry is regulated such that each …rm is required to reduce emission at an endogenous quality level ei, i2 f1;2g. Production goes along with pollutant at the level E. Here quality in emission is a proxy for any kind of reduction on environmental damage. The net level of emission is therefore E=E(e1+e2), where E > 0. This assumption rules out the unrealistic case in which investing in green quality more than o¤set pollution. Indeed although new technologies and cleaner fuel can help cut down emissions of pollutants into the 6
atmosphere, they are not replacing the non-green conventional production eliminating de…nitively the environmental damage. The damage value is assumed as a quadratic function of emissions, D=dE2;where drelies on the marginal damage of emissions.10 Consumer surplus, CS, is computed as the weighted average of the aggregate utility of all consumers’types. For instance, the utility of the consumers who are fully aware of goods 1and 2quality is given by: U(x1; x2) = (+e 1)x1+ (+e 2)x2(x2 1+x2 2+ 2x1x2) 2p 1x1p 2x2:(7) Similar for the other groups.11 Thus social welfare in the society is given by: SW =X1;2 ii+CS D: The timing of the game is as follows. In the …rst stage, …rms choose the level of environmental quality. In the second stage, …rms compete in prices. The equilibrium concept is the subgame perfect equilibrium by backward induction. 3 Baseline results Begin by the market stage. Each …rm imaximises pro…ts with respect to pi. The equilibrium price is p i(ei; ej) = 22[+e(1 )] + ei22ej 42;(8) where p 1=p 2if and only if e1=e2. The equilibrium price of …rm iis decreasing in the quality level chosen by its rival, ej. Intuitively, a rise in consumers’consciousness increases their willingness to pay for environmental quality and re‡ects a higher consumer’s marginal utility when they buy a green product. When a rival’s quality increases, the premium commanded by one’s own quality level at equilibrium is monotonically reduced. Indeed, the whole demand function to …rm iis shifted down. This negative e¤ect is higher the larger the degree of the substitutability between the two goods, . The positive effect of perceived environmental quality eon higher prices supports the idea that green consumers are in favour of an eco-friendly progress and pay more attention to prices for those products. Equilibrium quantities are consequently given by: q ip i(ei; ej); p j(ei; ej)=p i 12:(9) Thus they have the same properties of prices with respect to ejand e. In the …rst stage, each …rm imaximises its pro…t with respect to its environmental quality ei: 10 For simplicity, we abstract away from spillovers in the industry. 11 See the appendix for the computation of consumer surplus. 7
for d < b d.22 Eq. (22) suggests that if the environmental damage in the industry is relative low, the overestimation of the environmental quality of the green consumers has a positive e¤ect on the optimal level of lower bound. Thus in case of uncertain qualities, greenwashing behaviour drives a rise in the optimal endogenous standard of the …rms and guarantees an e¤ective policy by the government. In other words, whether the relative dirty types partially imitate the clean ones, this ensures bene…cial impact in terms of pro…ts due to environmental consciousness. This is possible only if the emissions are not so harmful or relatively limited over time. Otherwise, the presence of greenwashing reduces the endogenous threshold motivated by lower expected returns. The next question is whether or not the introduction of an optimal environmental standard would bite, i.e., if it indeed a¤ect the level of investment in environmental quality of the …rm or not. Comparing bewith e i, i.e., the equilibrium quality in the unregulated case yields: e 0e i>0; for em>eem;(23) where eemis de…ned in the appendix. Hence Proposition 6 An optimal environmental standard bites only if the overestimation of the environmental quality emis su¢ ciently high. P roof. See the Appendix Proposition 6 shows how the perception of environmental quality may a¤ect the effectiveness of a policy based on environmental standards. In particular, when consumers’ overestimation, em, is high, demands increase even in case of low perception. Indeed, …rms are willing to invest less in environmental quality since consumers overestimate it considerably. In this case, the introduction of an optimal environmental standard induce …rms to invest more in quality, and therefore, it is an e¤ective regulatory tool in industries where greenwashing is adopted. Notice that there is no trade-o¤ between consumer surplus and damage function. This is due to the fact that the quality is green and consumers internalise it in their utility function, so that incentives are aligned. This e¤ect does not emerge in situations where quality is hedonic. In this case, an increase in consumer surplus would imply higher emissions (Lambertini and Tampieri, 2012 and Ecchia et al., 2013). 4.3 Emission tax vs environmental standard We now propose a simple simulation to investigate the impact of the two policies on quality levels. Unlike the case of perfect information, where the e¤ect on qualities is analogous between the two interventions (Holland, 2012), we show that the misperception 22 See the appendix for eq. (22) and the de…nition of b dde…ned in (27). 14
in qualities determines a di¤erent e¤ect of the emission tax and the standard. The results entirely depend on the value of emissions produced by the …rms. First, it is worth to point out that introducing the emission standard does not change the ranking in qualities whenever the value of greenwashing is relatively low as demonstrated by Proposition 6. The only alternative in this case is to apply a tax per unit of emission costs. Hence in the simulation we set the conditions on emsuch that the environmental standard is biting (see the appendix). Whether the misperception is high, instead, the quality levels determined by the two policies depend on the level of emissions generated by the …rms. We assume generic values of the parameters of the model: the proportion of green consumers able to perceive the true quality, , is equal to 0:1; the substitutability among goods, , is assumed to be 0:3; while, the constant coe¢ cient is 1. Figure 1summarises the results. For lower level of damage, d, the environmental standard with misperception ensures higher level of quality. This supports the idea that, for limited levels of emission, the impact of greenwashing is still higher under the standard than under the tax. A similar e¤ect occurs from the underestimation. The results are not con…rmed for higher value of damages, where a tax on emission guarantees higher level of environmental quality. This shift occurs since an emission tax imposes a higher unit of production cost and its impact expands for higher level of emissions rising the abatement costs has shown above. Figure 1: Emission tax vs environmental standard As a general perspective this implies that an environmental standard accompanied by greenwashing behaviour increases the e¤ective marginal cost more than the tax for lower amount of damages. Both interventions increase the e¤ective marginal cost of production, exert an ongoing pressure on price competition and reduce the output of the not eco-friendly products. However a lower quality of the green products is ensured under the standard whenever the polluting amount is high and is not overcompensated by potential misperception. The welfare realisations for consumers between the two policies might in principle depend on the relative change in consumption due to environmental awareness. The e¤ect could be even higher with asymmetric technology among …rms. The idea is that the 15
importance of environmental perception is reduced whenever one …rm is more e¢ cient than the competitor. This proxies the market power of the e¢ cient …rm with higher pro…ts as quality increases. Accordingly, the weight of overestimation (and in turn greenwashing) in determining prices is relatively lower than in the symmetric case, since pro…ts for the e¢ cient …rm grow more than its less e¢ cient competitor. By the same token, the level of ehas a lower weight for the e¢ cient …rm than for the ine¢ cient one. It is higher in the presence of an environmental standard rather than with a tax on emission, since the former policy does not a¤ect production costs. These impacts could be so large under the standard relative to the tax that outweighs the reduction in the environmental quality of the products. Other analysis on this point could be left for future research. 5 Concluding remarks The misperception in environmental quality and the potential greenwashing behaviour of …rms are arguably one of the most important e¤ects able to in‡uence the market size. In a world of asymmetric information where green consumers misperceive the environmental quality of the product and the consequent damage caused by …rm’s production, we have analysed the e¤ect of regulatory intervention as well as the incentive to invest in cleaner process according to the aggregate emission level. Our framework evaluates a two-stage game where companies …rst maximise their pro…ts, while, in the second stage, …rms set prices according to the individual perception on quality. We show that consumers have di¤erent perceptions on quality, they are not able to observe both the investment decision of the …rm and the realised performance in terms of innovation process and total emission. The heterogeneity of information that agents can receive guarantees higher pro…ts for …rms and the e¤ect is higher, the larger is the impact of greenwashing in the market due to the overestimation of the signal. 16
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6 Appendix 6.1 Consumer surplus By evaluating the sum of utilities, consumer surplus is: CS =1 122p2 1+p2 2+e2 m+ 4(1 ) (+em+e0)2p 2(2+em+e0) (1 ) + (e0+em)22p 2(2e 2(em+e0) (1 )2e1) + 2((em+e0e 1e 2) (em+e0e 1e 2(2+em+e0)2)) + 2(em+e02e 1) (em+e02e 2) 2p 1((em+e0) (1 ) (1 ) + 2 (+p 2+e 1 e 2))] : 6.2 Proof of Lemma 1 The second order conditions of iwith respect to eiyields: @2i @e2 i =22222 422122<0; for 2<b 242212 222:(24) Thus the problem admits a maximum when the group of fully aware consumers is not too large. Note also that b 2(1) = 0, implying that the equilibrium requires some substitutability among goods. Condition (24) implies the positivity of best reply (10) and is su¢ cient condition in order to get substitutability in quality investments. 6.3 Proof of Lemma 2 Di¤erentiating e iwith respect to yields: @e i @ =8822+ 83+425[(em+e0) (1 )=2+2] 28+43+42226222<0:(25) 20
6.4 Characterization of the Endogenous Tax The …rst order condition of the Social Welfare Function SW with respect to tyields the optimal level of taxation: t=A+eB; where A=4de 2 + 2222+ 2 1224d22+ 22222de 12+ 23 2 (1 + 2d)2 + 2222(2 )2(1 + ) (2 + ) + 2(1 + ) (2 + ) [1 + (1 )] B=2(1 )6 + 4d232+42+(5 (4 + (2 ))) 2 (1 + 2d)2 + 2222(2 )2(1 + ) (2 + ) + 2(1 + ) (2 + ) [1 + (1 )] 6.5 Proof of Proposition 3 Begin by examining the variation of the optimal tax to a change in the marginal damage of emissions. Di¤erentiating twith respect to dyields: @t @d /8 (1 )1 + 2(1 )8+43+422262e+ 4(1 )8+43+4222622 35+ 22+ e8+83244+2+26 + +2+842>0; if and only if e>ee where ee4(1 )8+43+4222622 35+ 22 8 (1 )1 + 2(1 )8+43+422262 +e8+83244+2+26 + +2+842 8 (1 )1 + 2(1 )8+43+422262 Next, we investigate how a change in the perception of environmental quality would in‡uence the optimal level of taxation. By di¤erentiating twith respect to the average perception of environmental quality, it yields: 21
@t @e =2(1 )6+4d232+4+ 2(5 (4 + (2 ))) h(2 )22[1 (1 )]i(1 + ) (2 + )2 (1 + 2d)2 + 2222<0 if and only if, d > e d[4 (4 + (1 + ))] 4 (2 )2121 2 The cross derivative of twith respect to eand dcon…rms the results above: @t @e@d /(2 )2(1 + ) (2 + )222>0 6.6 Proof of eq. (19) Di¤erentiating twith respect to emyields: @t @em =(1 )6+4d232+42+(5 (4 + 2(2 ) + )) (1 + ) (2 + )h(2 )22(1 + (1 ))i2 (1 + 2d)2 + 2222>0 6.7 Characterization of the Endogenous Standard The …rst order condition of SW with respect to tyields the optimal level of taxation: e 0=C+emF; (26) such that C=2 22 and F=1 22z where variables ,,,,zrespectively indicating, = 2de (1 )22(2 + )2 + 2222(2 )2(1 ) (1 + )2(2 + )2(3 2) = 2(1 + )2212 + 4d(1 )22(8 (4 3))32222de 13 =22(1 + )18 + 2d(1 )22(10 (5 3))(1 + )2[7 3(3 ) + (1 + (1 ))] = 3322+ 4d12+4 z= 22(1 + 2d) (2 )212(1 )h(2 )2(1 + )2(2 + )2(1 + (1 ))i3222 22
6.8 Proof of eq. (22): Given eq. (26), it can be easily shown that @e 0 @em=F. This is positive if and only if: d < b d(2 )2(1 + )2(2 + )2[7 3(3 ) + (1 + (1 ))] 4222212(1 )+(27) +332222222(1 + )22[18 (10 + (5 3))] 4222212(1 ) 6.9 Proof of Proposition 6 It is enough to prove that em>eem+ %+#(28) where now all the variables , ,%,#respectively indicating, = 2(1 ) (1 + ) (3 2)422+(2 )2(2 + )22+ 4de 12 =2222d(e+ 4) (1 )22+[16 (12 (6 5))]2de3(1 )222 %=1 + 234222(2 )2(2 + ) [4 + (5 (1 (2 + )))] #=22212 + 4d(1 )22[8 (4 3)]23(1 + 2d) (1 )222 23