Certification over cartelization : improving environmental sustainability

Certi cation over Cartelization

Rosa Hoogma, 10430520

rosa.hoogma@student.uva.nl

Supervisor: Prof. dr. Maarten Pieter Schinkel

9 August 2017

Abstract

The Dutch Minister from Economic A airs introduced a legislative proposal that exempts rms from the cartel prohibition if the agreements include su cient sus-tainability practices in order to increase sussus-tainability initiatives by rms. By using a vertical product di erentiation model, I show that the opposite e ect is will occur if rms invest in environmental sustainability. When consumers value environmen-tal sustainable products and when rms constantly have to invest in green technol-ogy to maintain (or increase) environmental sustainability, and then choose prices, sustainability coordination will decrease the incentive to invest in green technol-ogy. The overall level of environmental sustainability in the market decreases com-pared to quality competition. The level of sustainability is not dependent on the di erence in xed cost structures between rms while this is the case when rms face competition. Therefore, when rms compete, the government can introduce dependent on the di erence in xed cost structures, a more speci c policy, namely eco-labeling, to increase the level of sustainability in the product market.

Acknowledgement

I would like to thank Prof. dr. Maarten Pieter Schinkel for his useful comments, re-marks and support. Furhtermore, I would also like to thank Dr. Sander Onderstal for his helpful suggestions to get results of better quality.

Statement of Originality

This document is written by Rosa Hoogma who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Contents

1 Introduction . . . 5

2 Horizontal agreements . . . 8

3 Eco-Labeling . . . . . . . . 17

4 Basic model with externalities . . . 21

4.1 Competition . . . 22

4.2 Social welfare . . . 30

5 Environmental sustainability coordination . . . 37

5.1 Investment decision . . . 40

5.2 Social welfare . . . 42

6 Welfare analysis . . . 46

7 Policy implications . . . 51

1

Introduction

In today's world, it is no news that solely focussing on maximizing pro ts in the shortest run possible will contribute to many environmental issues like global warm-ing, climate change, deforestation and so on. The inverted U-shaped relationship between environmental degradation and economic growth is reality. However, the steepness of this curve is partly determined by underpricing from resources, unpaid externalities (if acknowledged), protection of the industry and policy distortions which are environmentally destructive (Panayotou, 1993). An extensive body of lit-erature suggests that competition might encourage socially irresponsible behavior (Albert, 1993; Schneiberg, 1999; Adler, 2004; Hawn & Kang 2016). Several com-petition authorities consider exemption of horizontal agreement s among rms if these agreements diminish or remove the impact of negative externalities on society

1_{. Or put di erently, approve cooperation between rms if they promote a certain}

public interest. The Commission (1999) shared this view by exempting the horizon-tal agreement in 1999 between European importers and manufacturers of washing machines to stop selling the most energy consuming washing machine models. The Commission concluded that the anticompetitive e ects would not exceed the en-vironmental bene ts2. This exemption formed the foundation for 2001 Guidelines on Horizontal agreements, which included a separate chapter for the assessment of environmental agreements (Kingston, 2012). However, this chapter was removed again in the 2010 Horizontal Guidelines. According to Kingston (2012), due to the complex structure between the Directorates Generals in the commission, di erent goals emerge, resulting in Horizontal Guidelines without a de nition of

environmen-1_{Article 101 TFEU which prohibits cartels and other agreements that could disrupt}

competi-tion, declares in paragraph 3:

`The provisions of paragraph 1 may, however, be declared inapplicable in the case of: - any agreement or category of agreements between undertakings,

- any decision or category of decisions by associations of undertakings, - any concerted practice or category of concerted practices,

which contributes to improving the production or distribution of goods or to promoting technical or economic progress, while allowing consumers a fair share of the resulting bene t, and which does not:

(a) impose on the undertakings concerned restrictions which are not indispensable to the attainment of these objectives;

(b) a ord such undertakings the possibility of eliminating competition in respect of a substan-tial part of the products in question.'

tal agreements.

Then, in February 2017, the Commission ned three companies e68 million for car battery recycling cartel. Unlike in most cartels, where companies agree to set higher prices to increase pro ts, this cartel decreased the input price from recycling batteries from their suppliers. This decision indicated that the Commission shared the vision that competition promotes sustainability. In the Netherlands, the Min-ister of Economic A airs, Henk Kamp (2016), is currently promoting sustainability initiatives by introducing a legislative proposal called `Space for Sustainability Ini-tiatives'. The goal of this legislation is that sustainability initiatives between rms can be adopted by the government as legislation. In this way, ruling shall not be a ected by European Competition Law. Firms that together promote future sus-tainability could therefore be exempted from the cartel prohibition. However, while (state) regulations could help to solve the problem, they also increase the risk of collusive behavior (Scott, 1993; Campbell, 2007). In 1999, the Advocate-General A-G Jacobs, shared the same opinion in the Albany case:

`It can be presumed that private economic actors normally act in their own and not in the public interest when they conclude agreements between themselves. Thus, the consequences of their agreements are not necessarily in the public interest.' 3

Hence, it remains the question what role competition policy should play in environ-mental protection and whether there are better alternatives. The world is currently following an unsustainable path and therefore cooperative agreements that promote sustainable initiatives could be a solution. However it is very unclear, both in aca-demic literature as in practice, if this would be an e cient government intervention and whether there are better alternatives. To the best of my knowledge no study focused on exemption of horizontal agreements among rms compared to other pol-icy instruments to promote environmental protection, in particular the legislative proposal by Henk Kamp (2016) `Space for Sustainability Initiatives'. This leads to the research question that is the following;

Is exempting horizontal agreements among rms that together promote future sus-tainability the most e cient way in order to increase sussus-tainability practices com-pared to quality competition and eco-labeling?

agreements among rms as a policy instrument for environmental protection. Sec-ond, I will analyze eco-labeling as alternative policy instrument. Third, the vertical product di erentiation model with externalities by Amacher, Koskela & Ollikainen (2004) is presented. Fourth, I will characterize the equilibrium of the model under di erent scenarios; competition with eco-labeling and sustainability coordination. Next, I will compare the equilibrium across the di erent scenarios and explain the e ect the policy has on environmental sustainability followed by a proposed alter-native, namely eco-labeling. The last section contains the conclusion and sugges-tions for further research.

The main nding is that rms underprovide environmental quality and this will be even further reduced when rms coordinate their environmental quality levels. Furthermore, the incentive to invest in green technology decreases when rms co-operate on the level of environmental quality. Environmental quality is no longer dependent on the relative cost structure from both rms, while in the case of qual-ity competition, environmental qualqual-ity is dependent on the relative e ciency in in-vestment. If the government can control the total unit cost of investment with eco-labeling a higher environmental quality can be obtained if rms are competing on environmental quality.

2

Horizontal agreements

Firstly, it is worth noticing that the extensive body of literature on regulation fo-cusses on two theories (for example, Posner, 971; Stigler, 1971; Becker 1983; Peltz-man 1989; Baldwin, Cave & Lodge, 2012). The `public interest theories of regula-tion' wherein it is assumed that regulation is the solution to market failure, and therefore aims to establish economic e ciency. The second theory is the `private interest theories of regulation' wherein the regulators can imperfectly promote the public interest and the regulatory agencies represent the interest of (political) par-ties involved. This paper will focus on the former, using regulation to overcome market failures.

Economists often make a distinction between three di erent regulatory instruments to achieve environmental objectives: direct regulation, market-based instruments (or incentive-based) and voluntary agreements. Which instrument or combination of instruments is best in any given situation depends upon the characteristics of the (political) goal. Interest in market-based instruments and voluntary environmen-tal agreements are growing, as direct regulation on its own has its imperfections (Kingston, 2012; Stavins, 2003). To name but a few: direct regulation heavily de-pends on e ective public enforcement, it is very costly, and as the EU has no envi-ronmental enforcement agency, the enforcement of envienvi-ronmental law is limited. Voluntary environmental agreements are agreements that have the objective to protect and improve the quality of the environment and are seen as a form of self-regulation on voluntary basis, either spontaneously or as a response to possible leg-islation (Kingston, 2012). The popularity of voluntary agreements (VA called here-after) have not remained unnoticed in Europe. Since the early 1990s hundreds of voluntary agreements have been made.

The Commission (1996) distinguished two types of VA between regulators and rms. One which encourages participation: by providing positive incentives as cost-sharing or subsidies. The other one encourage participation by threatening a hasher outcome if a VA is not reached. The latter is in fact not voluntary as a rm has basically nothing to choose. VA that induce participation by threatening a hasher outcome is the most successful of the two (Segerson & Miceli, 1998). Designing a pure thread economic model, Segerson and Miceli (1998) show that e cient envi-ronmental protection is reached when legislative thread is strong and the regulator

has the bargaining power in setting the level of environmental protection. Thus, when rms themselves can decide the level of environmental protection, the level of e ective protection will be much lower. An extensive body of literature compares VA with legislation (for example, Stralund, 1995; Delmas & Montes-Sacho, 2010) and nds similar results. Dubbink and van Vliet (1996) show that there is evidence that governmental involvement (co-management as a category of environmental agreements) best in practice. They empirically analyzed governance of the Dutch North Sea at shery from 1976 to 1993 to improve sustainable use of renewable natural resources. The co-management system consisted of shermen's organiza-tions, public authorities and individual shermen's whose objective was to take over some of the public responsibility. This is in stark contrast to Holy (2017), who argued that the cooperative agreements between rms and authorities too often fail their improvement targets due to the gap between business' interest (making pro t) and substantial environmental protection.

What we see more often nowadays is the partnerships between business and envi-ronmental NGO's (Holy, 2017; Arts, 2002). One explanation is that both kind of enterprises generally believe that agreements are more successful than agreements together with governments (Glasbergen & Groenenberg , 2001).

The Dutch Policy Rule

The Dutch Minister of Economic A airs, Henk Kamp, (2014) is con dent that agreements between rms would be more e cient. Companies have expertise in their industry and cooperation between them would lead to an increase in sus-tainability initiatives. Consequently, the Dutch Authority for Consumer and Mar-kets (ACM) would be one of the rst in the world to be able to accept agreements among rms if these would lead to signi cant sustainability practices. The policy rule would exempt the agreements from article 101 of the Treaty on the Function-ing of the European Union (TFEU) and Article 6(3) of competition law. Article 2 of the policy rule Competition and Sustainability states

\When applying the provisions laid down in Section 6, paragraph 3 of the Dutch Competition Act to anticompetitive arrangements that have been made for the purpose of sustainability, the Netherlands Au-thority for Consumers and Markets (ACM) takes into account in its

as-sessment of whether the criteria have been met the following aspects that are speci c to sustainability:

a. With regard to the criterion that the arrangements are to contribute to the im-provement of production or distribution, or to the promotion of technical or economic progress, the long-term bene ts for consumers are also taken into account;

b With regard to the criterion that consumers are to be allowed a fair share of the bene ts resulting from the improvement of production or distribution, or from the promotion of technical or economic progress, the long-term bene ts for consumers are also taken into account;

c. In the assessment of the criterion that the arrangements are not to impose any restrictions that are not indispensable to the attainment of the sustainability objectives, in each case, it is taken into account the fact that, if an under-taking carried out activities for the purpose of sustainability on its own, that undertaking could lose market share or lose pro ts due to increased produc-tion costs, thereby possibly taking away the incentive for that undertaking to launch sustainability initiatives;

d. In the assessment of the criterion that the arrangements are not to a ord un-dertakings the possibility of eliminating competition in respect of a substan-tial part of the products and services in question, the possibilities of su cient competition on other competition parameters than the sustainability element with regard to the product or service are taken into account."

The ACM (2014) published accordingly a document that contained an assessment of the anticompetitive e ects which possibly distort competition and thus explained to what extend the sustainability initiatives are compatible with competition law. ACM discussed the criteria on the basis of the decisional practice and Notices of the Commission on the interpretation and application of Article 101 TFEU and the European court rulings. If the criteria were ful lled, the cartel prohibition is declared inapplicable. This document basically showed that for sustainability initia-tives to comply with competition law it is rather di cult. "The Chicken of

Tomor-article 101 (3) TFEU. The bene ts for the environment and the increased costs for the consumer were not well balanced (ACM, 2015). Even though the agreement in-cluded more space and longer life for the chicken, the price for the consumer would go up too much and the ACM argued it was a cartel without exception. Another example is the Energy Agreement between energy producers in the Netherlands. The agreement involved shutting down ve coal power plants in order to reduce CO2 emission. Yet, according to the commission, this would lead to a dispropor-tionate price increase compared to pollution abatement due to limited product capacity. Therefore, this sustainability initiative was not approved by the ACM (2013). The commission (2013) saw this already coming before the policy rule was accepted and expressed their concerns about the contradictions with EU law. To overcome the tension between the competition rules and the sustainability ini-tiatives, Dutch Minister of Economic A airs, Henk Kamp adjusted the policy rule in 2016 and promised to come up with a legislative proposal in a letter to the House of Representatives dated June 23 2016. The di erence between the rst policy rule and the revised policy rule was mainly about the de nition of users. The minister of Economic A airs, Henk Kamp, (2016) explained that the revised policy rule ex-cludes the bene t for non-users and requires to include long term bene ts when as-sessing the agreement and resulted in the following revised policy rule Competition and Sustainability:

"a. . . bene ts to the society as a whole. . . "

"b. . . quantitative and qualitative bene ts for users that materialize in the long."

The de nition of users for EU competition law includes all direct and indirect sumers and again the Commission (2016) explained their concerns about the con-tradictions with EU law. Furthermore, they explain the risk of inapplicability of national law as the threshold for trade between Member States is easily met and therefore national law would not apply. Lastly, the Commission mentioned the dif-ference between regulation and competition law. If policy goals are considered to be bene cial to the society as a whole, regulation is the right tool. Competition law, however can take into account sustainability initiatives or other non-economic

goals to the extent that these are perceived as bene ts in the eyes of the consumer in the relevant market but it cannot simply replace regulation.

Paragraph 3.3 (page 9) from the explanatory notes of the revised policy rule states: \With this approach, the bene ts both to the current consumer in the future, as well as to future consumers of the product or service concerned are taken into ac-count: it is about a longer term than right here, right now, and others that do not themselves consume the product." This raises the following concern; what do we know about the future consumer (Schinkel, 2016)? For example, as long as the fu-ture generation can buy cheaper products, but not more environmental sustainable products, the policy rule will still not be e ective. Another equilibrium would of course exist when the future generation is already used to buy products with higher standard of environmental quality. Allowing for future generations in this assess-ment for cooperative sustainability would be in fact totally wrong as you can al-ways come up with a future generation that is either against it or for. The fact that the environment is increasingly damaged would not serve as an argument anymore, however the price of the products will.

Market failures are considered to be public interest when the government intervenes (Wetenschappelijke Raad voor het Regeringsbeleid in Loozen, 2011). When exactly the government needs to intervene is determined by democratic chosen authorities. If there is no intervention by the government it is assumed that the companies (the market) are able to solve the market failures themselves (or the market failures are not (yet) acknowledged). Loozen (2011) agrees with the fact that companies will correct market failures as long as they make pro t and as long as they comply with article 101 TFEU. Considering the rst mover disadvantages, the increased pro-duction costs, positive externalities that discourage rms to behave and invest in environmental sustainability, we can not just simply assume that rms will solve it by themselves. As article 101 TFEU does allow rms to cooperate, and recalling the opinion from the Advocate-General in the Albany case, rms will certainly not solve it together.

In May 2017, Henk Kamp agreed that the revised policy would also indeed not meet the goal of increasing sustainability initiatives. Even though the Commission did not support his previous policies, in line with the (revised) policy rule he intro-duced a legislative proposal, still being convinced that cooperation between rms will increase sustainability initiatives.

The legislative proposal 'Space for Sustainability Initiatives'

The legislative proposal considers agreements among rms as well. The ministry considers a bottom-up approach whereby rms together hand in their sustainable initiative and decide upon the level of sustainability. The degree of participation of

rms is depending on the content of the initiative. The ACM (and if requested by the minister also other agencies) serves as a counselor determining the e ect of the agreement on the market. As it is unlikely that the agreements entail full coopera-tion will be allowed4_{, I will refer to these agreements as semi collusion; cooperation}

in some stages and compete in the others (Fershtman & Gandal, 1994). According to Henk Kamp, problems that generally hinder rms to create/realize sustainability initiatives; coordination problems, free-rider problems, and competition policy are reduced if the proposal is implemented. It decreases the risk of coordination prob-lems as it connects companies and reassures the execution of the initiative. The free-rider problem is solved because the initiative will be transformed to legislation and therefore parties cannot easily leave the cooperative agreement. Furthermore, companies will no longer be hindered by article 101 TFEU. The legislative proposal allows rms to request to (partly) implement their initiatives by the minister. In this way, EU competition law would not apply.

Setting aside strong political in uences, it is important to note that the agreement must have su ciently strong incentives for the rm to participate, i.e. rms must bene t in some way to be more successful. Unfortunately, as rms' responsible be-havior tends to decrease when they face strong competition, incentive to partici-pate in an environmental agreement will decrease too (Men, Zeng, Xie & Qi, 2015; Graa and, 2016; Hawn & Kang, 2016). According to Graa and (2015) strong price competition shortens the rm's time horizon that is used in their strategic deci-sions, which again has a negative e ect on environmental performance. Meng et al. (2016) analyzed listed companies in China between 2002 and 2008. Their ndings show a relationship between industrial competition and environmental responsibil-ity; either too low or too high industrial competition will lead to lower environmen-tal responsibility. Hawn & Kang (2016) nd similar results and stress the impor-tance of market structure for corporate social responsibility (CSR) strategies. In European Law consumer welfare is based on consumer surplus (Whish & Bailey, 2015). Loozen (2015) explains that consumer surplus the only objective

ment is for consumer welfare and any expansion of consumer welfare beyond this would be politically charged. The view that the legislative proposal would be ef-fective under conditions like bene ts for the future generation and other conditions therefore is based on a political opinion and thus a subjective interpretation. The ACM is expected to rule objectively. If the ACM is expected to rule objectively, the problem how to balance the bene ts remains to exist.

Finally, even if the two previous mentioned concerns do not hold, the legislative proposal increases the risk for full cartelization, which imposes even higher costs on society. Schinkel (2017) noticed that paragraph 3.3.2. (page 9) from the explana-tory notes states that the agreement will only be approved if a signi cant part of the companies in the industry agrees with the agreement. In the process of devel-oping a sustainability agreement, companies need to have certain information from each other to ensure that the competitor will agree with the proposal. This will increase the risk of full/tacit collusion not to forget that these actions in the pre-agreement phase (considered to be necessary) are forbidden by EU law (article 101 TFEU).

Review of IO theory on cooperation

Industrial organization literature compares horizontal cooperation and competi-tion by constructing multi-stage models (Bellefamme & Peitz, 2015). In 1994, Fer-shtman and Gandal presented a two-stage model showing that semi collusion in the second stage leads to more investment then in no-cooperative settings. They analyze two scenarios, one in which rms invest in stage 1 in cost-reducing R&D and choose production levels in stage 2. In the other scenario, rms invest in stage 1 in productive capacity and then choose production levels. They consider two types of semi collusion: collusion in the 1 stage and competition in the second and the other way around. Yet rms cannot be worse o in semi collusion in the rst stage than in the non-cooperative regime. This is based on the two-stage model by D'Aspremont and Jacquemin (1987) that considers R&D cooperation in the rst stage and competition in the second stage. This seems controversial compared to the legislative proposal in which coordinated sustainability choices are potentially approved and agreements that relate to prices and quantities are generally forbid-den and fall within the scope of article 101 TFEU.

In the presence of signi cant spillovers (>0.5) R&D cooperation can be welfare enhancing (D'Aspremont & Jacquemin,1987; Katz, 1986). The cooperative R&D

leads to lower prices and more output so that pro ts are higher than in non-cooperative outcomes. Katz (1986) considers the policy approach R&D cooperation to correct market failures in a four-stage model. Firms rst decide to participate in the agree-ment, followed by a stage where rms together decide the terms of the agreements. Then, taking these rules as xed rms maximize their own pro t and nally choose their production output in the market. He shows that industry wide cooperation is welfare enhancing, when (again) spillovers are signi cant in R&D and when compe-tition is relatively weak.

Schinkel and Spiegel (2016) apply IO theory to compare sustainability levels in cooperative and competitive settings. Schinkel and Spiegel (2016) consider a two-stage duopoly model for di erentiated goods to comparing four scenarios: (1) com-petition in stage one and two; (2) coordination in the sustainability level in stage 1 and competition in the product market in stage 2 (sustainability coordination); (3) non-cooperative choice of sustainability in stage 1 and collusion in the product market (production cartel); (4) and collusion in both stages. Their ndings show that semi collusion will lead to lower output as well. Furthermore, if consumers are willing to pay more for sustainable products, sustainable coordination directly ham-pers investments and harms the consumer if rms impose negative externalities on each other. However, if spillovers are large (and positive) then investment in sus-tainability is higher than in competition in both stages and in cartel production. Moreover, they expect that this boost in sustainable investment will increase the willingness to pay by the consumer and thus increases in production. Schinkel and Spiegel (2016) support Fershtman and Gandal (1994) that rms have stronger in-centives to invest when they coordinate their output levels as they do decrease their competitive advantage by competing

The legislative proposal should boost companies to invest and behave in a more sustainable way. Whilst this proposal may provide more exible solutions and def-initely more rapid solutions than law-making, it may not encourage rms to be-have environmental responsible (Meng et al., 2015; Graa and, 2016; Hawn & Kang, 2016). Several scholars examined cooperation and competition for environmental research (Scott, 1996; Poyago-Theotoky, 2007). Scott (1996) analyzed 61 research ventures in the US in the toxic air emission sector. He found that these cooperative

agreements promote economic e ciency in this sector. Thus research is suggest-ing that horizontal agreements are e ective however, environmental improvements might be limited as rms might not be that interested in these kind of agreements when they face strong competition. Awareness by the society could increase inter-ests for rms to invest in environmental sustainability.

3

Eco-Labeling

In 2009 Environmental Policy Review the full awareness of the Europeans about the environmental impact of products bought or used was just 14%. Therefore, ed-ucation and awareness raising can be powerful supporting tools to boost sustainable investments. This is exactly what information disclosure can do. It not only allows

rms to understand their environmental performance and encourage producers and governments to increase environmental standards, it also increases the awareness of the civil society (Kingston, 2012; Amacher, Koskela & Ollikainen, 2004; Baldwin, Cave & Lodge, 2012). In this paper I consider one particular form of disclosure of information, namely eco-labeling as a market-based instrument. So called rst party eco- labeling schemes are established by the rm who produces the product, and third party eco- labeling schemes by an independent (private or public) ini-tiator (EPA, 1998). For example, an ecolabel can be set up by the state or NGO, which set up programmes like UTZ that o er certi cation for sustainable agricul-ture in the co ee sector. Some certi cations are mandatory (based on legislation) like the EU logo that shows that the product is produced organically according to the standards in the European Legislation (2092/91). Others are voluntary, like the Danish organic food label, the Red , which is controlled by national author-ities. Established in 1990, Denmark was the rst country worldwide to introduce an organic label sponsored by state agencies. In case of voluntary eco-labeling it is up to the manufacturer to participate and up to the consumer whether to buy the certi ed product. Generally, rms pay a fee and get a license for a xed period of time if they ful ll the criteria. Mandatory eco-labeling schemes can restrict import to countries where certi cation is mandatory and are always government-backed. Baksi and Bose (2007) nd that mandatory rst party eco- labeling is preferred to third-party labeling only if the government is willing to engage in costly moni-toring of the self-labels. Although this is expensive, more and more countries are promoting third party labeling to increase the credibility of the label and avoid `Greenwashing' (Kirchho , 2000). Yet, several retailers start their own eco-label (for example fashion brands). This behavior could have negative impacts on the ef-fectiveness of eco-labels in general. Empirical evidence shows that the huge amount of diversity in eco-labels confuses the consumer. For consumers it is often di cult to distinguish third party labels or self-labeling. Furthermore, words like eco- and

bio are often misunderstood (Waginger & Ruzevicius, 2007). To make it even more di cult for the consumer, various forms exists like seal-of-approval, veri cation that an environmental criterion is met, or disclose information (EPA, 1998). Accord-ing to research conducted by Grankvist, Dahlstrand and Biel (2004), consumers who have no interest in behaving environmentally responsible are not a ected by any of these labels. However, the intermediate group is more e ected by labels that indicate negative environmentally outcomes than positive labels. The group that already has strong interest is equally e ected by all labels. One could argue that the above increases the necessity for eco-labels to be enforced by third parties to be credible.

Voluntary ecolabels may serve to di erentiate a rm's product and could increase competitive advantage (Amacher et al., 2004). The e ectiveness of eco-labeling, and so the degree of product di erentiation, is determined by the extend of partic-ipation of rms and consumer's awareness of and trust in the label. If this holds, consumers are willing to pay more for labeled products (Loureiro & Lotade, 2005). Others suggest, that labeling only works if it is integrated with other environmental policy instruments, and to be part of a coherent policy-making structure' (Potter & Hinhells, cited in Kern, Kissling-N•af, Landmann, Mauch & L•o elsend, 2001). There are many potential advantages for the use of eco-labeling as a policy instrument, and at the same time the opposite is also true. An increase in supply because of increased relative prices could induce more pollution abatement (Mattoo & Sign, 1994). Furthermore, prices and other relevant information of a customer is used to select products may be distorted because of ecolabels. Therefore, the labels may also distort the allocation of resources and create ine ciencies.

Review of IO theories on Eco-labeling

Investing in characteristics of a product could serve to di erentiate a rms' prod-uct and in this way strengten its position in the market (Amacher et al., 2004). The standard vertical-product-di erentiation model is often used in the indus-trial organization literature to analyze eco-labeling. Quality competition among

rms is modelled as a stage prior to price or output competition in a multi-stage game. The models consider a higher quality product as a more sustainable prod-uct and variable costs that are dependent on the level of sustainability (Tian, 2003;

Amacher et al., 2004).

Tian (2003) constructs a two stage game whereby two rms compete on levels of sustainability and analyses the impact on trade. The model consists of one home

rm and one foreign rm. Both rms face consumers from the home country. Again, an important assumption is that consumers that care more about sustainability, have higher willingness to pay. In stage 1, rms choose the level of sustainability and incur set-up costs. They compete in prices in stage 2. Under certain condi-tions, the eco-labels may stimulate high-value exports also from poorer countries compared to the home country (Tian, 2003). His analysis reveals that one cannot presume that mandatory eco-labeling for imported goods will bene t the home country or the environment. His model abstracts from some important character-istics, (1) as eco-labels need certi cation by independent certifying organization to be credible and (2) certi cations are only for a limited period of time. Amacher et al. (2004) take the latter into account. They present a three stage model whereby

rms rst choose the level of investment, then the level of sustainability and -nally compete in prices in a duopoly setting with vertical product di erentiation. According to them, existing literature ignores an important determinant for eco-labeling, namely the investment stage. As a label is only for a temporary period (criteria are revised on average every 3 or 4 years) rms are forced to make invest-ment to keep the licensed. In Amacher's et al. (2004) model quality can be seen as environmental quality. The government can reduce excessive investments in green technology and increase quality by increasing the fee for an ecolabel. When they consider externalities related to average environmental quality in the market the excessive investments made by rms will reduce. They do however not consider the case in which externalities overrule, even though is reality. An individual's behavior namely has neglectable impact on the environment and the individual is aware of that. When the consumer purchases a product the overall state of the environment is exogenously given. Therefore, it is the aggregate behavior rather than the indi-vidual that will a ect the state of the environment. Besides, because the consumer is aware of his, he might think that he, as an individual, does not make a change and therefore is not (less) motivated and refrains from behaving responsible. IO models assume that the consumer can observe quality perfectly and rms can observe the preferences from the consumer. However, for both, this is of course

quality. Even if products are labeled, rms can cheat on quality standards by mak- ing claims of high standards when it is not true. Because it is impossible for the consumer to detect, third party labeling is necessarily to ensure the credibility of the eco-labels. In case of eco-labels that established by associations of the industry, this could give potential problems concerning article 101 TFEU and similar prob- lems will arise when accepting agreements among rms. It would be up to Commis- sion to decide if the consumers are more damaged by the increase in price than the improvement of the environment.

Baksi and Bose (2006) focus on optimal regulatory policy taking into account asym- metric information. They compare self-labeling (that can be subject to cheating) and third party-labeling. They came to the conclusion that third party labeling is more e ective, that is, it increases the production and consumption of green good. However, it imposes a higher cost on society than self-labeling as in goods that are more sustainable probably need less investment than less sustainable goods and the government has to monitor more rms. The former will increase the price of the less sustainable good more relatively to the `greener' good. Whether that is a bad thing is questionable and maybe society has to take a step back by increasing its prices to eventually take an even bigger step forward and decreasing its prices. The cost of the latter can be reduced when the government applies horizontal monitor- ing/supervising as a control system, which is for example already used in the Dutch tax authorities (Gribnau, 2007). It basically means business will be self-auditing and by meeting with the government and the industry they decide upon the criteria for the label. The government will reduce their costs as monitoring will be less in- tensive. Yet, if we still have to take into consideration the future generation, a gen- eration who's needs are unknown, it would still be a very di cult task to increase our standard of sustainability.

Next I characterize the equilibrium of the model by Amacher et al. (2004) includ- ing externalities. One in which rms compete in all the stages and the other one in which rms collude in stage 2 (sustainability coordination). Then I compare the the equilibrium across and with the social welfare optimum. Amacher et al. (2004) do not consider the potential locked-in problem for investments. As independent parties revise the eco-label, criteria become more strict. It may be expected from

rms to follow a determined path of technology. Perhaps without this predeter- mined path, rms would have developed more environmental enhancing technologies.

4

Basic model with externalities

The vertical product di erentiation model by Amacher et al. (2004) with exter-nalities is considered. The model is extended by assuming that exterexter-nalities have great impact on optimal levels. In period 1, rms decide how much to invest in green technology, then in period 2 rms decide upon their investment, the level of environmental sustainability and in period 3 they compete by choosing prices. The utility function is given by

u = sk pk+ sa (1)

where sk and pk are the environmental quality (level of environmental

sustainabil-ity) and price of a good of quality k respectively. Each consumer is assumed to buy one unit of the vertically di erentiated good. Sustainable products are contribut-ing to greater environment improvements compared to less sustainable products. Of course, some consumers care less about the environment than others and therefore it assumed that consumers are heterogonous about their valuation for environmen-tal sustainability. The preference parameter captures this heterogeneity and rep-resents the marginal willingness to pay (or 'taste') for environmental quality. Con-sumers are uniformly distributed between on [ l, h]. A higher value of represents

a consumer who cares more about the environment.

k represents two type of qualities which are produced by two di erent rms. One rm produces high environmental quality goods (h) and the other rm produces low environmental quality goods (l). Furthermore, suppose that the consumers know the qualities of the corresponding goods of the two rms. This is for exampe realised when products are eco-labeled by independent agencies. There is no con-fusion about the ecolabels and therefore consumers can interpret labels perfectly.

sa denotes the externality of average environmental sustainability in the product

market and the weighted quality average is sa = (sh+s₂ l): The rationale behind this

is that one single consumer is unlikely to have impact on the environmental qual-ity by their behavior. Thus, as an individual's purchase will have an insigni cant impact on the average quality, the externality is treated as a constant in every con-sumer optimization problem, except when determining the social optimum. The preference parameter for the indi erent consumer equals ^ = ph pl

sh sl and demand for high and low environmentally quality goods are respectively given by h ^ and

^

l under the assumption of full market coverage.

More space and a longer life time for chickens is an example for an increase in en-vironmental quality. Besides, lower levels of pollution could also refer to increase in environmental quality. The increase in quality can entail variable and xed costs (Dixit, 1980). Variable costs could be thought of as the ongoing e ort to reduce en-vironmental impact by rms. For xed costs, think about investment in technology to reduce pollution or investing in a bigger plant so chickens have more space. The marginal cost function is therefore denoted by

c(sk; Ik) =

1 2bs

2

k+ k(Ik) k = H; L (2)

Investment in green technology can reduce marginal costs 0

k(Ik) < 0. Please note

that investment can not reduce the marginal cost for environmental sustainability in this model. The exact reduction is dependig on the e ciency rate of investment of the rm. Under the assumption of linear costs of output production, the follow-ing pro t function holds

k = [pk ck(sk; Ik)]dk (3)

Subgame perfect equilibria are based on each rm's choice of investments and sus-tainability levels.

4.1

Competition

As mentioned above and by Amacher et al. (2004), the externality is considered as a constant. The externality cancels out as it is symmetric. Using backward in-duction, rms choose prices subject to environmental sustainability and investment levels. The resulting Nash equilibrium price levels are

p_l = 1 3(( h 2 l)(sh sl) + ( 1 2b)(s 2 h+ 2s 2 l) + ( h + 2 l)); (4)

p_h = 1 3((2 h l)(sh sl) + ( 1 2b)(2s 2 h+ s 2 l) + (2 h+ l)) (5) p_l p_h = 1 3( 1 2b(s 2 h s2l) + ( h+ l)(sh sl) + x)

where x is the di erence between the e ciency level of each rm h(Ih) l(Il):

Amacher et al. (2004) call this the di erence in cost structure between the two rms. Looking at formula (6) it can be shown that the price di erence is i.e. de-pending on the di erence in cost structure. A negative value for x refers to a high-quality rm having a larger xed component compared to the low-high-quality rm. The opposite is true when the value of x is positive.

Environmental sustainability decision

Next, Nash equilibrium output price levels are substituted in the pro t function and the pro t functions are maximized with respect to sustainability levels sl and

sh. @ l @sl ((sh sl)( p_h p_l sh sl l)2) = 0; @ 2 @s2 ((sh sl)( h p_h p_l sh sl )2) = 0 (7)

Solving the two conditions under competition in stage 2 and rearraning gives the following s_l = 5 h 4b + 2x(Ih; Il) 3( h l) ; s_h = 5 h l 4b + 2x(Ih; Il) 3( h l) (8) s_h s_l = 3( h l) 2b (9)

The rst component of the Nash equilibrium sustainability outcomes are similar to other product di erentiation models; depending on spread of consumer taste. The second component includes investment, indicating that sustainability levels are increasing when x is positive. As mentioned before, x is positive when the xed

component of the rm that is producing low-quality products is larger than the xed component of the rm that is producing high-quality products. It is worth noticing that quality dispersion in the market is not a ected by a rms di erence in cost structure. This is because xed costs only in uence marginal costs and not the marginal costs related to the level of environmental quality. Substituting the optimal sustainability and price levels (obtained from (4), (5), (6) and (8)) in the pro t function and rearranging results in

~l= 1 6b( h l)[ 3 2( h l)+ 4x(Ih; Il)b 3( h l) ]2; ~h = 1 6b( h l)[ 3 2( h l) 4x(Ih; Il)b 3( h l) ] (10) Pro t is dependent on quality dispersion in the market, marginal cost of producing environmental quality and on the di erence in cost structures. If x is positive the low-quality rm is making more pro t then the high-quality rm. Again, x is only positive when the xed component of the rm that is producing low-quality prod-ucts is larger than the xed component of the rm that is producing high-quality products. If x is negative, the high-quality rm's pro t is larger and has a larger

xed component. Firms ' pro ts are equal when x equals zero. Investment decision

Using the solutions obtained in (10) to analyze the investment stage, where rms set their levels of investment under competition. Investment is not free. This costs, the total unit of investment cost, consists of two components; a unit cost of invest-ment ^v for both rms equal under the assumption of competitive capital markets and that includes i.e. auditing costs and fees for eco-labels. Another interpreta-tion of is an environmental taxation. can be either positive or negative, which is an adjustment to the model by Amacher et al. (2004). They assume that is strictly positive. A negative value of could be interpreted as a subsidy by the government. For example, in this model it could be the case that the government subsidizes eco-labels. Firms will only invest in green technology when pro ts are above zero,

Vl = ~l vIl; Vh = ~h vIh (11)

Amacher et al. (2004) consider the investment given by the following condition

Vl = 2 3( h l) 16b 27( h l) x 0_l(Il) v = 0 (12) Vh = 2 3( h l) + 16b 27( h l) x 0_h(Il) v = 0 (13)

Amacher et al. (2004) rewrite the previous conditions by sustituting 2₃( h l) by

A and ₂₇₍16b

h l) by B

Vl = ( A Bx) 0_l(Il) v = 0 (12')

Vh = ( A + Bx) 0_h(Ih) v = 0 (13')

Amacher et al. (2004) show that this equilibrium is unique and stable. They prove that an increase in a rm's investment level is o set by the other rm's investment level (strategic substitutes). In (12') and (13') it is very clear that the di erence is dependent on the sign of x again. The low-quality rm decides to invest if the

rst component ( A Bx) is negative (recall that 0_k(Ik) < 0). For this to be

the case, x has to be positive. The high-quality rm invests if the rst component ( A + Bx) is negative, this is the case when x is either negative or positive. How-ever, if x is strictly positive the high-quality rm will decide not to invest (resulting in a corner solution). If x equals zero, both rms invest.

(2004) de ne k(Ik) further into k(Ik) = eakIk where ak < 0. They approximate

eakIk _{by 1 + a}

kIk so that the rst derivative equals ak(1 + akIk) < 0 and the second

equals a2_k > 0. Substituting k(Ik) = eakIk in the (120) and (130) and solve for

investment Il and Ih is given by

Il= Aal(1 + alIl) Bal(ahIh alIl) v = 0 (12")

Ih = Aah(1 + alIh) + Bah(ahIh alIl) v = 0 (13")

Now consider two di erent scenarios where x = 0 and x_{6= 0. Firstly, x = 0 so rms} are considered to be identical in terms of xed costs components

I_ljx=0 = 1 al v Aa2 l ; I_hjx=0 = 1 ah v Aa2 h (14) [I_h I_l]_jx=0 = ah al ahal 1 + v(ah+ al) Aahal (15)

(15) is non-zero when ah > al (recall that ak < 0). Or put di erentlyjahj < jalj

meaning that the low-quality rm is more e cient in investing. The opposite is true when ah < al (or jahj > jalj). In the latter case, the high-quality rm is

more e cient in investing. It is assumed that rms cannot reduce their costs by more than 50% and therefore ah al

ahal 4. Amacher et al. (2004) also normalize

l = 1 in A so the term between brackets is clearly negative. The outcome of

(15) is of course zero if besides equal xed costs components, the rms also have similar e ciency rates.

I_ljx6=0 = 1 al 1 + v [Aah B (ah+ al)] Aahal(A 2B) ; (16) I_hjx6=0 = 1 ah 1 + v [Aal B (ah+ al)] Aahal(A 2B) x = v(ah al) ahal(A 2B) (16 ')

Amacher et al. (2004) assume A 2B > 0 so x > 0 if ah > al. It can also be

the case that x < 0 if ah < al. The di erence in between the optimal investments

levels can be characterized as follows

[I_h I_l]_jx6=0 = (ah al) ahal (1 + v(ah+ al) Aahal (A B) (A 2B)) (17)

where _{A 2B}A B > _1. If ah < al and thus x < 0 the di erence between initial

invest-ments is postive. If ah > al and thus x > 0 an interior solution exists for both

rms which is proved by Amacher et al. (2004). Several outcomes can also be dis-tinguished when changing the sign and size of v. The above solutions can be sum-marized as follows

Proposition 1 At the interior solution for investment levels, the equilibrium is unique and stable. Furthermore, investments of the rms are strategic substitutes. The level of investment depends on the relative e ciency in the xed costs for qual-ity provision of both rms. The following outcomes evolve

(a) if x < 0, then I_h > 0 but I_l = 0 is possible if the unit cost of investment is positive and large.

(b) if x = 0, then I_h > 0 but I_l > 0 is possible if the unit cost of investment is negative or small and positive.

(c) if x > 0, then I_l > 0 but I_h = 0 is possible if the unit cost of investment is positive and large.

Proof. To derive the result in (a) note that if ah < al and implementing this in

(16'), gives the following di erence in the xed cost component x = v(ah al)

ahal(A 2B) < 0. This is the same as h(Ih) l(Il) < 0: Either h(Ih) < l(Il) or l(Il) = 0

for h(Ih) l(Il) to be negative. From (16), it is clear that a positive and large

v allows for a possible corner solution where the high-quality rm invests and the low-quality rm will not invest.

To derive the result in (b) note that x = 0 can imply (Ih) (Il) < 0, then h l>

0:

Or (Ih) (Il) > 0, then h l < 0

Or (Ih) (Il) = 0 implying that both rms invest. From (16), it is clear that a

negative or small and positive v can lead to both rms to invest.

To derive the result in (c) note that if ah > al and implementing this in (16') gives

the following di erence in xed cost component x = v(ah al)

ahal(A 2B) > 0:

This is the same as h(Ih) l(Il) > 0: For this to be negative, either h(Ih) >

l(Il) or h(Ih) = 0:Everything else equal and using (16), implies that a positive

and large v allows for a possible corner solution where the high-quality rm will not invest and the low-quality rm will invest.

Using the optimal investment levels, the levels of sustainability can be expressed as foll s_l = 5 l h 4b + 2v(ah al) 3( h l)(A 2B)ahal ; (8') s_h = 5 h l 4b + 2v(ah al) 3( h l)(A 2B)ahal

As corner solutions will essentially lead to same qualitative results Amacher et al. (2004) focus only on interior solutions where both rms invest. Several outcomes exist:

1. x = 0

Consider ah al = 0, the last component from 8' equals out as this term is

zero.

Consider the case where Ih Il< 0, meaning that the initial investment of the

Consider the case where Ih Il< 0, meaning that the initial investment of the

low quality rm is larger. For x to be zero, ah has to be smaller than al and

thus will the level of environmental quality decrease according to 8'. 2. x _{6= 0}

Consider the case where x < 0. This implies that the high-quality rm is more e cient in investing and environmental quality will be lower.

Consider the case where x > 0. This implies that the low-quality rm is more e cient in investing and environmental quality will be higher.

From these outcomes Amacher et al. (2004) draw the conclusion that the high-quality rm will mitigate competition by providing higher high-quality products when the high-quality rm is less e cient at investment.

Proposition 2 When rms maximize their pro ts, environmental quality provi-sion in the market is the highest when the low-quality rm is the most e cient at investment compared to the level of environmental quality when rms are equally e cient. The environmental quality provision in the market is the lowest when the high-quality rm is the most e cient at investing.

Proof. First note that when ah < al and thus ah al < 0 the second term will be

substracted from the rst term and when ah > al and thus ah al < 0 the second

term will be added to the rst term.

s_ljah<al = 5 l h 4b + 2v(ah al) 3( h l)(A 2B)ahal = s_ljah>al = 5 l h 4b + 2v(ah al) 3( h l)(A 2B)ahal > s_hjah<al = 5 h l 4b + 2v(ah al) 3( h l)(A 2B)ahal = s_hjah>al = 5 h l 4b + 2v(ah al) 3( h l)(A 2B)ahal >

will be in between is s_ljx=0 = 5 l h 4b s_hjx=0 = 5 h l 4b

4.2

Social welfare

So far environmental quality is considered and investment choices from pro t max-imization decisions by rms. This will be compared to the social optimal qualities and investment determined by a social planner. The outcomes are used as a bench-mark. According to Cremer and Thisse (1994), it is socially optimal to produce both qualities, because variable costs related to quality is non-zero. Therefore the following welfare function is considered consisting of consumer and producer sur-plus SW = (~ l) ~ + l 2 sl cl(sl) ! +( h ~) h+ ~ 2 sh ch(sh) ! v(Ih+Il) ( h l) h+ l 2 sa (18)

Environmental sustainability decision

Amacher et al. (2004) argue that quality provision in the market is dependent on the structures of rms and taking externalities into account increases the possibility of under provision. Interestingly, they pay no attention to the scenario in which ex-ternalities from ine cient average quality provided by the market are so large that it leads to underprovision of quality unquestionably. By taking this as a starting point socially optimal levels are analyzed. To nd the social optimal sustainability levels to maximize the social welfare function with respect to sl and sh, where the

@SW @sl = 3 l h 4 bsl+ ( h+ l) 2b = 0; (19) @SW @sh = 3 h l 4 bsl+ ( h+ l) 2b = 0

Solving these for sl and sh

sW_l = 3 l+ h+ 2 ( h+ l)

4b ; (20)

sW_h = 3 h+ l+ 2 ( h l)

4b (21)

The quality dispersion on the market is (again) not a ected by the investments or by the externality (recall that the externality are symmetric)

3 h+ l+ 2 ( h+ l) 4b ( 3 l+ h+ 2 ( h+ l) 4b ) = h l 2b (22)

Next, I will compare social optimal qualities with pro t maximizing qualities to ex-amine the conditions for under- or overprovision of environmental quality provision in the market. Two scenarios are analyzed, one in which x = 0 and one in which x is non-zero. The comparison is obtained from (8'), (20), and (21).

(sW_l s_l)_jah=al = h l 2b + ( h+ l) 2b (23) (sW_h s_h)_jah=al = h l 2b + ( h+ l) 2b

What can be concluded from this is that a large spread of consumer taste and pos-itive externalities could lead to under provision of quality in the market. The e ect on the level of quality produced by the high-quality rm is ambiguous. However the externality and the spread of consumer taste will de nitely decrease the quality produced by the low-quality rm.

When x is non-zero the di erence between the social optimal quality level and Nash equilibrium levels is

(sW_l s_l)_jah6=al = h l 2b + ( h+ l) 2b 2v(ah al) 3( l)(A 2B)ahal ; (24) (sW_h s_h)_jah6=al = h l 2b + ( h+ l) 2b 2v(ah al) 3( l)(A 2B)ahal

In the case x > 0, ah al > 0 and thus the low-quality rm is more e cient at

investing, the low-quality rm provides higher quality compared to when rms not invest or have the same e ciency rate at investment. The low-quality underprovide quality because of the externality. The government could increase the quality pro-vided by the rm by setting higher eco-label fees and therefore increasing v: The high-quality rm is motivated to provide higher quality when it is less e cient at investing compared to equal e ciency or no investing. The rationale behind this is that the rm is mitigating competition by setting a higher quality. If the opposite holds; x < 0, ah al < 0 and thus the high-quality rm is more e cient at

invest-ing, the market underprovides quality. The government could in this case promote sustainability by subsidizing eco-labels.

Proposition 3 In the presence of externalities the market underprovides quality. This underprovision will be less when the low-quality rm is more e cient invest-ing then in the absence of investment or equally e ciency rates. The economic in-tuition is that the high-quality rm will mitigate price competition by o ering bet-ter quality products. A raise in the rm's e ective unit cost of investment could reduce the underprovision even further. However, in the reversed case, when the high-quality rm is more e cient at investing will the market provide lower qual-ities than in the absence of investment or equal e ciency rates. A negative total

Proof. Note that the last term will be added to the rst two terms when the ah <

al (and thus ah al < 0) and substracted from the rst two terms if ah > al (and

thus ah al > 0)

Investment decision

Finally, the investment choice is considered. Amacher et al. (2004) nd the follow-ing investment socially optimal levels of investment.

I_lW = 1 al v 1 2( h l)a 2 l ; (25) I_hW = 1 ah v 1 2( h l)a 2 h I_hW I_lW = ah al ahal 1 + ₁ v(ah+ al) 2( h l)alah (26)

Note that the rst term in the socially optimal levels of investment has a larger absolute value then the second term. It is worth noticing that as the rms indepen-dently choose investment levels in this scenario, the levels are independent of each other. Furthermore, investments can be reduced and even be brought to zero by an increase in the unit cost of investment. In the reversed case, a negative unit cost of investment will increase optimal investment levels. To get a better understand-ing in under- or overinvestement, levels from pro t maximization decisions by rms are compared with the socially optimal levels. Using equation (14) and (25) for the scenario in which x = 0 the di erence can be characterized as follows.

I_lW I_ljah=al = 1 al v 1 2( h l)a 2 l 1 al v 2 3( h l)a 2 l (27) = v 3a2 lA I_hW I_hjah=al = 1 ah v 1 2( h l)a 2 h 1 ah v 2 3( h l)a 2 h = v 3a2 hA

I_lW I_ljah=al = 1 al v 3 4Aa 2 l 1 al v Aa2 l = v 3a2 lA (28) I_hW I_hjah=al = 1 ah v 3 4Aa 2 h 1 ah v Aa2 h = v 3a2 hA

Under or over investment is dependent on the e ciency rate, unit cost of invest-ment and the spread of consumers taste. In case of equal e ciency there is over-investment and underprovision of quality. A small but positive v will reduce the overinvestment.

In case of di erent e ciency rates at investment, x_{6= 0, using (25) and (16) yields}

I_lw I_ljah6=al = 1 al v 3 4Aa 2 l 1 al (1 + v(Aah B (ah+ al)) Aahal(A 2B) ) (29) = v Aa2 l B (ah + al) Aah ah(A 2B) +4 3 I_hW I_hjah6=al = 1 ah v 3 4Aa 2 h 1 ah (1 + v(Aal B (ah+ al)) Aahal(A 2B) ) = v Aa2 h B (ah+ al) Aal al(A 2B) +4 3

The condition for the high-quality rm to overinvest is B (ah+ al) 5 Aah (and for

low-quality rm is B (ah+ al) 5 Aal) if v is positive. In the case of B (ah+ al) >

Aah (and for low quality rm is B (ah+ al) > Aal) the outcome is ambiguous. If

v is negative, the opposite is true, i.e. the high-quality rm is underinvesting when B (ah+ al) 5 Aah (and for low-quality rm when B (ah+ al) 5 Aal). In the case

of B (ah+ al) > Aah (and for low quality rm is B (ah+ al) > Aal) the outcome is

again ambiguous. Please note that these conditions are su cient but not necessary. Proposition 4 The relationship between the socially optimal and pro t-maximizing investment levels are as follows

(a) Socially optimal levels of investment are dependent on e ciencies at invest-ment and the value of the total unit cost of investinvest-ment.

(b) For x = 0, both rms overinvest in green technology when v>0 and uderinvest-ment in green technology when v<0

(c) For x_{6= 0, overinvestment by both rms is likely to occur when v>0 and} under-investment is likely to occur when v<0

Proof. To nd the socially optimal levels of investment, the social welfare function with optimal levels of sustainability are di erentiated with respect to Ik

@SW @Ik = ( 1 2 h 1 2 l) ( ak)(1 + akIk) v:

Setting this equal to zero and solve to Ik gives the following

IW k = 1 ak v 1 2( h l)a2k

This shows that socially optimal levels of investment are dependent on e ciencies at investment (ak) and the value of the total unit cost of investment (v)

Next, note that over-and underinvestment for x = 0 is analyzed by the following equation I_lW I_ljah=al = 1 al v 1 2( h l)a 2 l 1 al v 2 3( h l)a 2 l = v 3a2 lA I_hW I_hjah=al = 1 ah v 1 2( h l)a 2 h 1 ah v 2 3( h l)a 2 h = v 3a2 hA

I_kW I_kjah=al < 0 indicates overinvestment as rms invest more than the social optimum. For this to be smaller than zero, _3a2v

kA

< 0, v has to be positive. IW

k Ikjah=al > 0 indicates underinvestment as rms invest less than the social optimum. For this to be smaller than zero, v

3a2 kA

> 0, v has to be negative.

I_lw I_ljah6=al = 1 al v 3 4Aa 2 l 1 al (1 + v(Aah B (ah+ al)) Aahal(A 2B) ) = v Aa2 l B (ah + al) Aah ah(A 2B) +4 3 I_hW I_hjah6=al = 1 ah v 3 4Aa 2 h 1 ah (1 + v(Aal B (ah+ al)) Aahal(A 2B) ) = v Aa2 h B (ah+ al) Aal al(A 2B) +4 3 Again, IW

k Ikjah6=al < 0 indicates overinvestment as rms invest more than the social optimum. For this to be greater than zero, _Aav2

k

< 0, v has to be positive together with B (ah+ al) 5 Aak. In the case of B (ah+ al) > Aak the e ect is ambiguous

and overinvestment will only occur when 4₃ < B(ah+al) Aak

ak(A 2B) in absolute value and underinvestment when 4₃ > B(ah+al) Aak

al(A 2B) in absolute value. Therefore the possibility for overinvestment is likely to occur when v is positive.

IW

k Ikjah6=al > 0 indicates underinvestment as rms invest less than the social optimum. For this to be greater than zero, _Aav2

k

< 0, v has to be negative together with B (ah+ al) 5 Aak. In the case of B (ah+ al) > Aak the e ect is ambiguous

and underinvestment will only occur when 4₃ < B(ah+al) Aak

ak(A 2B) in absolute value and overinvestment when 4₃ > B(ah+al) Aak

al(A 2B) in absolute value. Therefore the possibility for underinvestment is likely to occur when v is negative.

5

Environmental sustainability coordination

This section is devoted to the analysis of collusion in the second stage. Firms opti-mally choose environmental quality together after having set the level of investment independently in the previous stage. In the last, third, stage rms compete again in prices. As usual, the solution is obtained through backward induction. Hence, recall from (4) (5) and (6) the equilibrium prices. By di erentiating the joint pro t functions (7) with respect to sustainability levels, yields FOCs

@ l+ @ 2

@sl

= 0; @ l+ @ 2 @sl

= 0 (30)

Substituting these expressions and obtaining environmental qualities cannot be solved analytically. For simplicity, I ignore phase 1 by assuming that the marginal costs from both rms are known. The model by Amacher et al. (2004) assumes that the marginal costs of production depends on environmental quality (1₂bs2

k).

In-dicating that if the rms increase quality, the cost of providing quantity increases and therefore quantity is reduced and vice versa. Hence, rms can decide together that the low-quality rm will not produce any environmental quality products sl =

0. From the pro t function (7) it is very clear that pro ts are dependent on the quality di erences. If both rms choose the same quality levels both rms will not make any pro t. Hence, the option to provide high quality by the high-quality rm and the low-quality providing zero quality could be potentially an equilibrium. By substituting sl = 0 into the best response function of the high quality rm, the

sustainability level of the high-quality rm is obtained.

sh = 1 3b 2 h l+ q 4 2_h+ 2_l + b2_s2 l 4 h l+ 6bx 4b hsl+ 2b lsl+ 2bsl (31) sSC_l = 0 (32) sSC_h = 2 h l 3b + q (2 h l) 2 + 6bx 3b (33)

is larger than the xed cost component of the high-quality rm. Though it can be assumed that the low-quality rm is not investing, (2) shows that if a rm remains to invest when the level of environmental quality is reduced to zero, marginal costs will be negative. Hence, x consists only of h(Ih) and is therefore strictly negative

(or zero when the high-quality rm is not investing). Thus, looking at (33) without any investment the high quality rm is already producing environmental quality above zero. Both rms are making pro t as there is a di erence in environmental quality. (32) and (33) is indeed an equilibrium if pro ts are non-zero and larger than the pro ts each rm could achieve by choosing a quality which drives the de-mand faced by the other rm to zero. The point where the dede-mand faced by one

rm goes to zero, the other one also achieves zero pro ts (Cremer & Thisse, 1994). Furthermore, the level of investment is limited by the increase in environmental quality. Let's consider the scenario in which it is assumed that the high quality rm is investing, a more e cient investing low-quality rm (or has larger initial investment) will increase the level of sustainability. This is similar to Nash equilib-rium outcomes by Amacher et al. (2004). They show that when the high-quality

rm is more e cient in investing (or has larger initial investment) the environmen-tal quality will be lower. The economic intuition for this could be that when there is stronger competition, the high-quality rm is relaxing price competition by sell-ing higher environmental quality products. In reversed case, when rms face weak competition, the high-quality rm is the only rm investing in environmental qual-ity, this will decrease the motivation from the high-quality rm to produce environ-mental quality products. With regard to the consumer taste parameters, the level of environmental quality is dependent on the spread again. Logically, its focus is on the upper bound of the taste parameter.

The ndings are summarized as follows

Proposition 5 When rms choose together the level of environmental quality, the low-quality rm will not be motivated to produce environmental quality as marginal costs are associated with environmental quality. The high-quality rm is producing environmental quality above zero, but will this will decrease when the rm start to invest in green technology.

qual-ity levels for both rms. @ l+ @ h @sl = 0 = x + (sh sl) ( h 2 l) + 1 2b(s 2 h bs 2 l) (x (sh sl) ( h 2 l) + 1 2b (sh 3sl) (sh sl) + x + (sh sl) (2 h l) + ₂1b (sh 3sl) (sh sl) x (sh sl) (2 h l) + 1₂b(s2h s2l) @ l+ @ h @sl = 0 = x (sh sl) ( h 2 l) + 1 2b(s 2 h s 2 l) ( x + (sh sl) ( h 2 l) + b (sh sl) (3sh sl)) + x (sh sl) (2 h l) + 1 2b(s 2 h s 2 l) x 2 (sh sl) (2 h l) + 1 2b (sh sl) (3sh sl)

This cannot be solved analytically.

Next, note that when ignoring the investment stage,

1

2b > 0 formulates a trade-o between quality and quantity as marginal cost of

production increases with environmental quality. Then the equilibrium pro ts at stage 2 are:

l= ₃₆1 (sh sl) (2 h 4 l+ bsh+ bsl)2 h = ₃₆1 (sh sl) (2 l 4 h+ bsh+ bsl)

2

The quality choice follows from the fact that both pro ts increase with the quality di erence (sh sl) :

Hence, sl = 0 as costs are also associated with the level of environmental quality

Substituting this in the best response function for the high-quality the following level of environmental quality is obtained,

sSC_h = 2 h l

3b +

q

(2 h l)2+ 6bx

3b

Then, note that x < 0 as the xed cost component of high-quality rm is larger than the xed cost component of the low-quality rm and (2 h l)

2

+ 6bx 0: Normalizing h l = 1 allows for 6bx 4 and implying that every investment made

by the high-quality rm will decrease its level of environmental quality (s). Hence, the highest possible value of s is obtained when x = 0 and is 2 h l

3b +

p

(2 h l)2

3b :

5.1

Investment decision

Recall from (2) that environmental quality is reached by the ongoing e ort (vari-able cost component) and technology investments ( xed cost component). So when the low-quality rm is producing no environmental quality, sl = 0, the marginal

cost function will be negative. Therefore, it is assumed that the low-quality rm is not investing: Il = 0. Hence, the high-quality rm will only invest in sustainability.

The level of investment for the high quality rm is obtained by maximizing the fol-lowing function with respect to Ih: Amacher et al. (2004) try to understand the

investment behavior by rms better by specifying h(Ih) by eahIh (1 + ahIh) and

therefore this is substituted in the following function

Vh = SC vIh

Again, unfortunately this result can not be solved analytically.

In this model, if a rm invest, they invest in green technologies reducing their marginal costs and to some extend in (31) raises environmental quality. From (33) it may be expected that 6bx 45_{. As a consequence it could be assumed that a rm's e}

ec-tive investment ( h(Ih)) is higher when the marginal cost of environmental quality

is low, and the opposite holds. Even though this model does not take into account this relationship, in practice there could be a positive correlation between being