The Strategic Adoption of Environmental Corporate Social Responsibility with Network Externalities

: Thispaperadoptsagreenmanagerialdelegationmodelinapollutingnet-work industry wherein consumers form fulﬁlled rational expectations of network externalities. We show that ﬁrms are consistently incentivized to undertake ECSR (environmental corporate social responsibility) under price competition, while positive network externalities can increase the strategic level of ECSR. We also show that product substitutability between network products can play an important role in determining a ﬁrm’s strategic level of ECSR and resulting proﬁts. Finally, ECSR is conducive to increasing environmental quality and social welfare in a high-polluting network industry. Therefore, the strategic adoption of ECSR in a network industry is Pareto-improving as environmental damage becomes serious.


Introduction
Environmental corporate social responsibility (ECSR) is growing in importance due to public pressure regarding environmental concerns about climate change. Many global corporations participate in greenhouse gas reduction programs and have issued ECSR statements and outlined related activities in their annual reports. 1 The strategic promotion of ECSR has become a top priority on the business agenda of many industries and international organizations. The encouragement of ECSR is also a key policy agenda in the USA and EU through best practice guidance and, where appropriate, intelligent regulations and fiscal incentives. For example, in 2019, the United Nations launched an environmental protection initiative called "Action for the Earth," which was responded to by Microsoft, Sony, Ubisoft, Niantic, and other ICT companies. Microsoft recently announced its ECSR plan to share the social responsibility of protecting the environment with other companies and achieve carbon negative emissions by 2030. Specifically, Microsoft will allocate US $1 billion to establish the "Climate Innovation Fund" to develop global carbon emission reduction and elimination technologies. It will also produce 825,000 Xbox consoles using carbon-neutral technology to eliminate the adverse impact of game equipment production on the environment. Apple also announced an investment of US $4.7 billion in Green Bonds, helping to develop green technology innovation, accelerating its progress toward the goal of becoming carbon neutral across its supply chain by 2030.
Many economics theorists have shown that firms can use ECSR strategically, despite its high cost, as it can improve reputation and increase profits, as it can either increase market demand or decrease compliance costs as government regulations increase. For example, Liu, Wang, and Lee (2015) and Buccella, Fanti, and Gori (2021) considered the demand-increasing effect of ECSR and showed that firms might undertake ECSR to raise profits. In the presence of emission taxes, Poyago-Theotoky and Yong (2019), Buccella, Fanti, and Gori (2022), Xu, Chen, and Lee (2022), and Park and Lee (2023) examined a green managerial delegation contract based on ECSR. They showed that firms' profits increase with the construction of an environmental incentive scheme that induces regulators to lower the emissions tax rate, reducing total tax expenditures. Finally, without considering government regulation and the demand-increasing effect of ECSR, Matsumura (2017, 2020) and Park (2019, 2021) examined voluntary ECSR under price competition. They demonstrated that firms could earn higher profits when ECSR increases market prices in which strategic complementary relationships exist.
On the other hand, literature on the information and communications technology (ICT) industry has examined the effects of positive externalities on firms' strategies for network industries such as software, mobile communications, and computer-based online products (e.g. Katz and Shapiro 1985;Shy 2001;Birke 2009). In such industries, it is natural to observe that the utility of a particular consumer increases with the number of other users. In recent years, due to the dramatic development of network industries, many scholars have studied how the presence of positive network externalities may alter the standard results under imperfect competition. For example, several recent works have examined the model of strategic delegation (Bhattacharjee and Pal 2014;Chirco and Scrimitore 2013;Choi and Lee 2021;Choi, Lee, and Lim 2020;Choi, Lee, and Lee 2022;Fanti and Buccella 2016;Hoernig 2012;Lee, Choi, and Han 2018).
However, the impact of ECSR in network industries has been largely, and surprisingly, neglected. The present work aims to fill this gap and investigates the effects of network externalities on the ECSR activities within network industries. In the presence of positive network externalities, an increase in ECSR to reduce negative externalities caused by pollution has an offset effect on output production when the firms consider both positive and negative externalities simultaneously. That is, the presence of positive network externalities can induce firms to produce more outputs while focusing on negative environmental externalities can prompt firms to produce fewer outputs and emissions. Thus, competition structure may affect prices and, therefore, the relative impacts of these contrasting externalities. In particular, if firms price competitively, they act more aggressively in the product market, which has an indirect positive effect on profits via consumer expectations, and this effect is larger with stronger network externalities.
Furthermore, if firms can choose strategic levels of ECSR under strategic complementary relationships, a higher ECSR can increase the market price through a cost pass-through effect which also has an indirect positive impact on profits. As a result, depending on the critical strength of network externalities, strategic concerns regarding ECSR under price competition can play an important role in changing the offset effect between these contrasting positive and negative externalities. Our analysis highlights the strategic role of ECSR in a polluting network industry as a profitable instrument on the business agenda.
In this paper, we adopt a green managerial delegation model wherein firms choose the level of ECSR and the prices of network products that are fully incompatible while consumers form a rational passive expectation of total demand before firms choose price and ECSR, which is correctively fulfilled at the equilibrium (Choi, Lee, and Lim 2020;Katz and Shapiro 1985). We show that firms consistently are incentivized to undertake ECSR because strategic ECSR decisions have a strategic complementary relationship under price competition. Thus, costly investment in ECSR can increase market prices and profits through the cost pass-through effect. We also show that network externalities can enhance this cost pass-through effect. However, substitutability between network products can play an important role in determining a firm's ECSR and profits. We further show that undertaking ECSR increases environmental quality and social welfare in a high-polluting network industry. Therefore, the strategic adoption of ECSR in this type of industry can create a win-win situation under price competition when environmental damage becomes serious. Finally, we extend the analysis into (i) the case of (partial) compatibility between network products and (ii) the case of commitment to the output, and discuss the robustness of our findings in an endogenous choice game of ECSR among firms.
The remainder of this paper is organized as follows: We present a basic model in Section 2 and examine the main results in Section 3. We analyze the endogenous choice of ECSR and discuss (partial) compatibility and the commitment to the output in Section 4. The final section concludes the study.

The Basic Model
We consider a duopoly market where two firms (firms 1 and 2) provide differentiated network products that are fully incompatible and compete for prices. Following Fanti and Buccella (2017), we assume the following inverse demand function: where p i (q i ) is the price (output) of product i, z i is consumers' expectation of the total sales of firm i, n (0 < n < 1) is the strength of network effects and b is the degree of product substitutability. Using (1), we obtain the following demand function: The production process of firms brings about polluting emissions. We assume that one unit of output produces one unit of pollution. Firm i realizes the emission reduction of y i by bearing the abatement cost I i = r y 2 i 2 where r is a positive parameter and is assumed to be one (r = 1) for analytic simplicity. 2 Then, the emissions of firm i are determined through e i = q i − y i under the end-of-pipe technology.
2 Note that r (r > 0) measures the abatement efficiency (the smaller r, the higher the abatement efficiency) while this treatment does not affect the validity of the analysis. ECSR with network externalities -5 The corresponding environmental damage is D i = d(q i − y i ), where d denotes the marginal damage. The profit function of firm i is: 3 where c (0 < c < a) denotes the marginal production cost. Social welfare is defined as the sum of profits and consumer surplus (CS = 1 ) minus the total environmental damage (D = D 1 + D 2 ): We consider a green managerial delegation model where the owner of firm i chooses a strategic level of ECSR to maximize its profit ( i ) while the manager of firm i determines the abatement level (y i ) and the price (p i ) to maximize the following objective function: The timing of the game is as follows. In stage 1, consumers form fulfilled expectations about the sizes of the networks that each firm is associated. In stage 2, the firms' owners choose h i . In stage 3, the managers decide the price (p i ) and emission reduction level (y i ).

Analysis
In the third stage, manager i decides the price and abatement level. The first-order conditions are: where = a − c. The second-order conditions are satisfied because (6) gives the equilibrium price and abatement level: Note that one firm's equilibrium price is increasing in its level of ECSR and consumers' expected network size for this firm. Also, both firms engage in abatement activities if the ECSR degree is positive (h i > 0).
In the second stage, owner i chooses the optimal h i to maximize its profit. Sub- (8), we obtain the best-reaction function Note that the strategic level of ECSR has a strategic complementary relationship under price competition, that is, Thus, the optimal level of ECSR for firm i is: (9) Combining (7), (9), and (2), we derive: (10) In the first stage, consumers form fulfilled expectations about the sizes of the network that each firm is associated. Thus, z i = q i , i = 1, 2. We obtain: Submitting (11) into (9) gives: Proposition 1 (i) states that firms are incentivized to undertake ECSR in a polluting network industry. This is because the strategic level of ECSR has strategic complementary relationship under price competition which causes a cost pass-through effect. That is, as ECSR increases, the equilibrium price increases, which supports firm profits. Proposition 1 (ii) states that the stronger the network effect, the larger the optimal level of ECSR for firms. This implies that network externalities can enhance the cost pass-through effect of ECSR. That is, firms will commit more to ECSR to mitigate competition if the network externalities are stronger. This finding can strengthen the results of Matsumura (2017, 2020) and Lee and Park (2019), who examined voluntary ECSR in the absence of network externalities.

-M. Xing and S.-H. Lee
We obtain the following equilibrium results: 6 Proposition 2 implies that the substitutability between network products can play an important role in determining firm profit. When product substitutability is high, undertaking ECSR increases firm profits in a polluting network industry. However, when substitutability is low, and product competition is weak, undertaking ECSR benefits firms only when network effects are weak. Otherwise, the price-increasing effect caused by strategic ECSR will be outweighed by the quantity-increasing impact of network externalities.
Proposition 3 implies that undertaking ECSR decreases environmental damage and increases social welfare in a high-polluting network industry. Thus, the strategic adoption of ECSR under price competition with network externalities can increase industry profits and environmental qualities, especially when environmental damage is severe, which can eventually increase social welfare in a high-polluting network industry. Therefore, the strategic adoption of ECSR in a network industry is Paretoimproving as environmental damage becomes serious.
6 To guarantee the non-negative equilibrium results, we assume that the following is satisfied: .

Compatibility Between Network Products
In this extension, we consider that the two networks, one formed around the product of each firm, are (partially) imperfectly compatible with each other.
In (19) k denotes the degree of network compatibility. Following Naskar and Pal (2020) and Choi, Lee, and Lee (2022), we assume that the degree of network compatibility is given by the degree of product differentiation: k = b.
Using a similar procedure to Section 3, we can obtain the equilibrium results. When both firms undertake ECSR, they are: 8 8 To guarantee the non-negative equilibrium results, we assume that the following is satisfied: In addition, when both firms do not undertake ECSR, they are: 9 Proposition 1 ′ resembles Proposition 1, wherein firms are incentivized to undertake ECSR, but it further states that the compatibility of network products enhances the degree of ECSR. That is, the strategic complementary relationships among ECSR activities are stronger with compatibility between network products.
Proposition 2 ′ resembles Proposition 2. That is, the substitutability between network products can play an important role in determining firm profit. However, the proposition further states that the compatibility of network products can increase firm profits, as the degree of ECSR is higher under compatibility between network products, which enhances the cost pass-through effect of ECSR.

No ECSR ECSR
that is, D I > D * and SW I > SW * . Thus, higher network externalities caused by full compatibility between two competing network products might not be desirable for improving environmental quality. It also implies that there might be an appropriate degree of partial compatibility between the two network products.

The Endogenous Choice of ECSR
In the previous analysis in Section 3, we considered two symmetric situations regarding whether both firms undertake ECSR. In this extension, we examine the robustness of our findings in an endogenous choice game of ECSR. Then, we can consider the following four possible situations in Table 1, including an asymmetric situation where one firm undertakes ECSR while the other does not. Using a similar procedure to Section 3, we can obtain the following equilibrium profits if firm 1 undertakes ECSR and firm 2 does not (YN), or symmetrically, if firm 2 undertakes ECSR and firm 1 does not (NY): 12 The mathematical analysis is complicated; thus, we find an equilibrium of an endogenous choice of ECSR by numerical simulations and illustrate the results in [ Figure 1] where = 1, b = 0.8 and d = 0.5. In Figure 1, one can identify three regions for n, delimited by two thresholds, let us define them as n ′ (n ′ ≈ 0.068) and n ′′ (n ′′ ≈ 0.092). It can be easily shown that, given the payoff structures in each region, we have that: (i) for 0 < n < n ′ , ECSR is the dominant strategy, and the equilibrium is pareto-efficient (from the firms' perspective); (ii) for n ′ < n < n ′′ , there are multiple equilibria with the ECSR equilibrium payoff dominant; (iii) for n ′′ < n, no ECSR is the dominant strategy and the equilibrium is pareto-inefficient. This result shows that both firms undertake ECSR in equilibrium if the strength of the network effects is not sufficiently high. This guarantees our main findings in the main context.

Commitment to the Output
We consider an alternative assumption made in the literature on network industry: firms can commit to announced level of output. In this situation, the inverse demand function is given by: In order to ensure that the impact of each firm's output on its product price is higher than that of its competitors, we assume that n < 1 − b in this section.
Using a similar procedure to Section 3, we can obtain the equilibrium results. When both firms undertake ECSR, they are: 13 13 To guarantee the non-negative equilibrium results, we assume that the following is satisfied: 14 -M. Xing and S.-H. Lee In addition, when both firms do not undertake ECSR, they are: 14 Comparing the equilibrium outcomes shows that our main findings in the basic model are still robust in the following Propositions with some modifications.

Appendix
Proof of Proposition 1.