THE CORPORATE SOCIAL RESPONSIBILITY PRICE PREMIUM AS AN ENABLER OF SUBSTANTIVE CSR

企业社会责任溢价作为实质性企业社会责任的助推器

LEANDRO NARDI HEC Paris LEANDRO NARDI 欧洲工商管理学院（HEC Paris）

Research on corporate social responsibility (CSR) has investigated the determinants of firms’ choices to engage in substantive, as opposed to merely symbolic, CSR. However, scholars have yet to examine the economic incentives governing these choices. In particular, the literature offers little insight into how consumers’ willingness to pay a CSR price premium affects the choice between symbolic versus substantive CSR. To address this question, this paper proposes a formal model wherein substantive CSR reduces the negative socioenvironmental externalities associated with firms’ products, while consumers vary in their ability to monitor these externalities, and in their preferences for CSR. The paper establishes conditions under which the CSR price premium functions as an enabler of substantive CSR. It also examines how monitoring intensity, product differentiation, and competitors’ CSR engagement choices moderate this enabling effect. For example, when competitors engage in symbolic CSR, higher monitoring increases the enabling effect of the CSR price premium if substantive CSR sufficiently reduces negative externalities, but decreases it otherwise. Product differentiation and competitors’ decisions to engage in substantive CSR have similarly nuanced roles. A further application of the model suggests that CSR communication costs may be instrumental in discouraging all forms of symbolic CSR, including greenwashing and social washing. 关于企业社会责任（CSR）的研究已探讨了企业选择实质性CSR而非仅仅象征性CSR的决定因素。然而，学者们尚未考察支配这些选择的经济激励因素。特别是，现有文献对消费者支付CSR价格溢价的意愿如何影响象征性CSR与实质性CSR的选择提供的见解较少。为解决这一问题，本文提出一个正式模型，其中实质性CSR可减少企业产品相关的负面社会环境外部性，而消费者在监测这些外部性的能力以及对CSR的偏好方面存在差异。本文确立了CSR价格溢价可作为实质性CSR推动因素的条件。同时，本文还考察了监测强度、产品差异化以及竞争对手的CSR参与选择如何调节这一推动效应。例如，当竞争对手进行象征性CSR时，如果实质性CSR能充分减少负面外部性，更高的监测强度会增强CSR价格溢价的推动效应，否则会削弱这一效应。产品差异化和竞争对手参与实质性CSR的决策也具有类似的微妙作用。该模型的进一步应用表明，CSR沟通成本可能有助于阻止包括漂绿和社会漂绿在内的所有形式的象征性CSR。

Research on corporate social responsibility (CSR) distinguishes between symbolic and substantive CSR (Durand, Hawn, & Ioannou, 2019; Marquis & Qian, 2014). “Symbolic CSR” is the adoption of lowcost activities intended to signal social responsibility without effectively benefiting society (Bowen, 2014; Cuypers, Koh, & Wang, 2016). In contrast, “substantive CSR” also includes resource-intensive initiatives with the potential to generate societal benefits (Delmas & Montes-Sancho, 2010)—for instance, by reducing the negative socioenvironmental externalities associated with a firm’s products (Kaul & Luo, 2019). Prior work has examined conditions under which firms are more likely to engage in substantive, as opposed to symbolic, CSR. Firms’ access to the resources required (Durand et al., 2019) and stakeholders’ monitoring activity (Campbell, 2007; Luo, Kaul, & Seo, 2018) are examples of such conditions. 关于企业社会责任（CSR）的研究区分了象征性CSR和实质性CSR（Durand, Hawn, & Ioannou, 2019；Marquis & Qian, 2014）。“象征性CSR”指的是采取低成本活动，旨在表明企业的社会责任，而非真正惠及社会（Bowen, 2014；Cuypers, Koh, & Wang, 2016）。相比之下，“实质性CSR”还包括资源密集型举措，这些举措有可能产生社会效益（Delmas & Montes-Sancho, 2010）——例如，通过减少与企业产品相关的负面社会环境外部性（Kaul & Luo, 2019）。先前的研究考察了企业更有可能从事实质性CSR而非象征性CSR的条件。企业获取所需资源（Durand et al., 2019）以及利益相关者的监督活动（Campbell, 2007；Luo, Kaul, & Seo, 2018）就是这类条件的例子。

However, the literature has yet to examine the economic incentives that may lead firms to engage in substantive or symbolic CSR. For instance, suppose there is a price premium on socially responsible products (hereafter, referred to as a “CSR price premium”). Such a premium could be an incentive for substantive CSR engagement (Hawn & Ioannou, 2016; Porter & Kramer, 2006). Yet, if the distinction between substantive and symbolic CSR is costly for consumers (Kaul & Luo, 2019), and if the former is more expensive than the latter (Durand et al., 2019), the CSR price premium could lead to symbolic CSR engagement. 然而，现有文献尚未研究可能促使企业参与实质性或象征性企业社会责任（CSR）的经济激励因素。例如，假设具有社会责任感的产品存在价格溢价（以下简称“CSR价格溢价”）。这种溢价可能会激励企业参与实质性CSR（Hawn & Ioannou，2016；Porter & Kramer，2006）。然而，如果消费者区分实质性CSR和象征性CSR的成本较高（Kaul & Luo，2019），并且前者比后者更昂贵（Durand et al.，2019），那么CSR价格溢价可能会促使企业参与象征性CSR。

This paper proposes a formal model to study conditions under which the CSR price premium increases firms’ willingness to engage in substantive, as opposed to symbolic, CSR. In this model, firms compete in a differentiated market and generate negative socioenvironmental externalities (such as pollution). They also choose either symbolic or substantive CSR. Symbolic CSR combines low-cost activities with no societal benefits and CSR communication efforts that support a CSR price premium, such as issuing CSR reports (Hawn & Ioannou, 2016). In turn, substantive CSR combines low-cost activities and CSR communication with costly initiatives that reduce the negative socioenvironmental externalities generated by the firms and improve CSR communication quality (Marquis & Qian, 2014). On the demand side, while consumers value CSR, some of them may scrutinize the quality of CSR communication, only paying the CSR price premium for substantive CSR firms. Consumers may also monitor negative externalities, reducing their willingness to pay for products associated with higher levels of these externalities. 本文提出了一个正式模型，以研究企业社会责任（CSR）价格溢价在何种条件下会提高企业参与实质性而非象征性CSR的意愿。在该模型中，企业在差异化市场中竞争并产生负面社会环境外部性（如污染）。它们还会选择象征性或实质性CSR。象征性CSR包括低成本且无社会收益的活动，以及支持CSR价格溢价的CSR沟通努力，例如发布CSR报告（Hawn & Ioannou，2016）。反过来，实质性CSR结合了低成本活动和CSR沟通，同时包含减少企业产生的负面社会环境外部性并提高CSR沟通质量的高成本举措（Marquis & Qian，2014）。在需求端，虽然消费者重视CSR，但其中一些人可能会审视CSR沟通的质量，只为实质性CSR企业支付CSR价格溢价。消费者还可能监测负面外部性，降低他们对与这些外部性水平较高相关产品的支付意愿。

According to this model, the CSR price premium increases a firm’s willingness to engage in substantive, as opposed to symbolic, CSR if a fraction of consumers either scrutinizes the quality of CSR communication or monitors negative externalities. Yet, this enabling effect of the CSR price premium is highly heterogeneous. For example, when competitors engage in symbolic CSR, higher monitoring intensity increases the enabling effect of the CSR price premium, if substantive CSR sufficiently reduces negative externalities, but decreases otherwise. The effect also increases with product differentiation for firms competing in more differentiated markets, but decreases in less differentiated settings. When competitors engage in substantive CSR, these effects become more nuanced. Finally, the paper also examines how auditing of CSR activities, regulation of negative externalities, and CSR communication costs contribute to discouraging symbolic CSR. 根据该模型，如果部分消费者要么审视企业社会责任（CSR）沟通的质量，要么监督负面外部性，那么CSR价格溢价会增强企业开展实质性而非象征性CSR的意愿。然而，CSR价格溢价的这种促进作用高度异质。例如，当竞争对手开展象征性CSR时，如果实质性CSR能充分减少负面外部性，那么更高的监督强度会增强CSR价格溢价的促进作用，否则会降低。在产品差异化程度更高的市场中，竞争企业的产品差异化程度越高，该效应越强；而在差异化程度较低的市场中，该效应则减弱。当竞争对手开展实质性CSR时，这些效应会变得更加复杂。最后，本文还探讨了CSR活动审计、负面外部性监管以及CSR沟通成本如何抑制象征性CSR。

This work extends research on the determinants of substantive CSR (e.g., Cuypers et al., 2016; Durand et al., 2019; Marquis & Qian, 2014) by unveiling the nuanced role of the CSR price premium, which is considered a key economic driver of CSR investments (Kaul & Luo, 2018; McWilliams & Siegel, 2001). The paper also complements prior work on greenwashing (e.g., Delmas & Burbano, 2011; Lyon & Maxwell, 2011) by showing that policies on CSR communication (such as the adoption of mandatory standards for CSR reporting) may discourage symbolic engagement not only by curbing selective disclosure (Lyon & Montgomery, 2015) but also by increasing CSR communication costs. Additionally, while scholars argue that higher monitoring intensity increases incentives for substantive CSR (Campbell, 2007; Kim & Lyon, 2015), this study suggests that the opposite effect may occur when substantive CSR has a limited capacity to reduce negative externalities. Lastly, the paper establishes a non-monotonic relation between product differentiation and incentives for substantive CSR, as well as a pattern of peer effects, that contrast with prior theories (e.g., Cao, Liang, & Zhan, 2019; Flammer, 2015). 本研究通过揭示企业社会责任（CSR）价格溢价的细微作用，拓展了对实质性CSR决定因素的研究（例如Cuypers等人，2016；Durand等人，2019；Marquis & Qian，2014），而CSR价格溢价被认为是CSR投资的关键经济驱动力（Kaul & Luo，2018；McWilliams & Siegel，2001）。本文还通过表明CSR沟通政策（如采用CSR报告的强制性标准）可能通过抑制选择性披露（Lyon & Montgomery，2015）和增加CSR沟通成本，不仅阻碍象征性参与，从而补充了之前关于漂绿行为的研究（例如Delmas & Burbano，2011；Lyon & Maxwell，2011）。此外，尽管学者们认为更高的监督强度会增加实质性CSR的动力（Campbell，2007；Kim & Lyon，2015），但本研究表明，当实质性CSR在减少负外部性方面能力有限时，可能会出现相反的效果。最后，本文确立了产品差异化与实质性CSR动力之间的非单调关系，以及与优先理论（例如Cao、Liang & Zhan，2019；Flammer，2015）相矛盾的同伴效应模式。

SUBSTANTIVE VERSUS SYMBOLIC CSR AND THE CSR PRICE PREMIUM: A GAME-THEORETICAL FRAMEWORK

实质性企业社会责任与象征性企业社会责任及企业社会责任溢价：一个博弈论框架

Theoretical Background

理论背景

As management scholarship increasingly acknowledges the critical role of business organizations in addressing societal issues (Barney & Rangan, 2019; Cabral, Mahoney, McGahan, & Potoski, 2019; McGahan, Zelner, & Barney, 2013), scholars argue that CSR programs are a key channel through which corporate social and environmental action materializes (e.g., Barnett, Henriques, & Husted, 2020; Hawn & Ioannou, 2016; Kaul & Lu0, 2018; Morgan & Tumlinson, 2019). In this context, the distinction between symbolic and substantive CSR becomes crucial, as substance is seen as a necessary (though not sufficient) condition for CSR to create positive social impact (e.g., Kaul & Luo, 2019). 随着管理学科越来越多地认识到商业组织在解决社会问题方面的关键作用（Barney & Rangan, 2019; Cabral, Mahoney, McGahan, & Potoski, 2019; McGahan, Zelner, & Barney, 2013），学者们认为企业社会责任（CSR）项目是企业社会和环境行动得以实现的关键渠道（例如，Barnett, Henriques, & Husted, 2020; Hawn & Ioannou, 2016; Kaul & Lu0, 2018; Morgan & Tumlinson, 2019）。在此背景下，象征性CSR与实质性CSR之间的区别变得至关重要，因为实质性被视为CSR产生积极社会影响的必要条件（尽管不是充分条件）（例如，Kaul & Luo, 2019）。

Drawing on research on decoupling and symbolic management (e.g., Bromley & Powell, 2012; Tilcsik, 2010; Westphal & Zajac, 1997, 1998), the literature generally defines symbolic CSR as any set of activities, practices, or initiatives intended to promote a firm as a socially responsible entity while lacking more tangible socioenvironmental action (Bowen, 2014; Durand et al., 2019; Marquis & Qian, 2014). Typically, symbolic CSR combines CSR communication efforts and low-cost activities with no relevant social benefits (e.g., Durand et al., 2019; Kaul & Luo, 2019). As an example of a symbolic CSR initiative, a company may publicly announce the creation of an internal CSR committee that, although serving as a signal of social responsibility (e.g., Hawn & Ioannou, 2016), never really acts to improve the firm’s performance in social or environmental dimensions. Symbolic CSR is also often associated with greenwashing or social washing, a practice whereby firms claim to be more environmentally or socially responsible than they in fact are (Delmas & Burbano, 2011; Kim & Lyon, 2015). 基于对脱钩（decoupling）和象征性管理（symbolic management）的研究（例如，Bromley & Powell, 2012；Tilcsik, 2010；Westphal & Zajac, 1997, 1998），学术界普遍将象征性企业社会责任（CSR）定义为任何旨在将企业塑造为具有社会责任感实体的活动、实践或举措，但缺乏更具体的社会环境行动（Bowen, 2014；Durand et al., 2019；Marquis & Qian, 2014）。通常，象征性CSR结合了CSR沟通努力与低成本且无实质性社会收益的活动（例如，Durand et al., 2019；Kaul & Luo, 2019）。例如，一家公司可能公开宣布成立内部CSR委员会，尽管这作为社会责任的信号（例如，Hawn & Ioannou, 2016），但从未真正采取行动来改善企业在社会或环境方面的表现。象征性CSR还常与漂绿（greenwashing）或社会漂绿（social washing）相关联，即企业声称自己在环境或社会责任感方面比实际情况更强（Delmas & Burbano, 2011；Kim & Lyon, 2015）。

In contrast, substantive CSR entails significant resource mobilization (Durand et al., 2019), as it also requires the implementation of tangible, costly, and non-easily reversible actions with real potential to benefit society (Delmas & Montes-Sancho, 2010; Durand et al., 2019; Kaul & Luo, 2018; Schons & Steinmeier, 2016)—for example, by abating the negative socioenvironmental externalities generated by a firm (Kaul & Luo, 2019). Johnson & Johnson’s Earthwards program is a good example of a substantive CSR initiative. The program mobilizes substantial resources from several distinct areas, including R&D, product design, and marketing, to promote innovations aimed at reducing the environmental footprint of the company’s large product portfolio (Mazur, 2017). In line with the definitions above, Earthwards has systematically assisted Johnson & Johnson in reducing production-generated negative environmental externalities, such as pollution or damages arising from an excessive use of natural resources (Johnson & Johnson, 2019). 相比之下，实质性企业社会责任（CSR）需要大量资源调动（Durand et al., 2019），因为它还要求实施切实可行、成本高昂且不易逆转的行动，这些行动具有切实惠及社会的潜力（Delmas & Montes-Sancho, 2010; Durand et al., 2019; Kaul & Luo, 2018; Schons & Steinmeier, 2016）——例如，通过减轻企业产生的负面社会环境外部性（Kaul & Luo, 2019）。强生公司的“地球未来”（Earthwards）计划就是实质性企业社会责任举措的一个很好例子。该计划从研发、产品设计和营销等多个不同领域调动了大量资源，以推动旨在减少公司庞大产品组合环境足迹的创新（Mazur, 2017）。根据上述定义，“地球未来”计划系统地帮助强生公司减少生产过程中产生的负面环境外部性，例如污染或因过度使用自然资源而造成的损害（Johnson & Johnson, 2019）。

Given this distinction, prior work has shown that firms are more likely to engage in substantive, as opposed to symbolic, CSR when stakeholders interested in a firm’s socioenvironmental performance are more salient to the firm (e.g., Durand et al., 2019), when a company is more transparent about the negative externalities that it generates (Delmas & Burbano, 2011), and when it has access to needed resources and capabilities (Durand et al., 2019). Past studies have also emphasized the importance of stakeholders’ monitoring activity in inducing substantive socioenvironmental action (Delmas & Montes-Sancho, 2010; Lu0 et al., 2018; Marquis & Qian, 2014; Marquis, Toffel, & Zhou, 2016). Overall, a general conclusion of this line of research is that a firm’s willingness to engage in substantive, as opposed to symbolic, CSR increases with the monitoring intensity to which the firm is subject (e.g., Campbell, 2007; Delmas & Burbano, 2011; Kim & Lyon, 2015). 基于这一区别，先前的研究表明，当关注企业社会环境绩效的利益相关者对企业更为突出时（例如，Durand等人，2019）、当公司对其产生的负面外部性更为透明时（Delmas & Burbano，2011），以及当公司能够获取所需资源和能力时（Durand等人，2019），企业更有可能开展实质性而非象征性的企业社会责任（CSR）。过去的研究还强调了利益相关者监督活动在促使实质性社会环境行动方面的重要性（Delmas & Montes-Sancho，2010；Lu0等人，2018；Marquis & Qian，2014；Marquis、Toffel & Zhou，2016）。总体而言，这一系列研究的一般结论是，企业开展实质性而非象征性CSR的意愿会随着企业所面临的监督强度的增加而提高（例如，Campbell，2007；Delmas & Burbano，2011；Kim & Lyon，2015）。

In addition, the literature has also investigated the association between differentiation in the product market and firms’ willingness to undertake substantive socioenvironmental action. There have been scant theoretical development and somewhat contradictory findings in this line of research (Duanmu, Bu, & Pittman, 2018). For instance, while some studies suggest that differentiation reduces incentives for substantive action and worsens socioenvironmental performance (e.g., Fernández-Kranz & Santaló, 2010; Flammer, 2015), others have contradicted this assertion by arguing that higher differentiation may encourage substantive CSR engagement (e.g., Kaul & Luo, 2018) and improve social performance (e.g., Duanmu et al., 2018). 此外，文献还研究了产品市场差异化与企业开展实质性社会环境行动意愿之间的关联。这一研究领域的理论发展较为匮乏，且研究结果存在一定矛盾（Duanmu, Bu, & Pittman, 2018）。例如，一些研究表明差异化会降低采取实质性行动的动力，恶化社会环境绩效（如 Fernández-Kranz & Santaló, 2010；Flammer, 2015），而另一些研究则对此观点提出质疑，认为更高的差异化可能会鼓励实质性企业社会责任（CSR）参与（如 Kaul & Luo, 2018）并改善社会绩效（如 Duanmu et al., 2018）。

Although several determinants of substantive CSR engagement have been explored in this literature, as mentioned above, the role of economic incentives has received scant attention. However, much of the attractiveness of symbolic CSR can be justified on the grounds that many consumers are willing to pay a CSR price premium (Flammer, 2015; Hawn & Ioannou, 2016; Kaul & Luo, 2018; Luo & Bhattacharya, 2006; McWilliams & Siegel, 2001; Porter & Kramer, 2006) but are unable or unwilling to assess the true outcomes of these investments (Durand et al., 2019; Kaul & Luo, 2019; Luo & Kaul, 2019). The model proposed in the present paper draws on this insight to shed light on how economic incentives—and, in particular, the CSR price premium—may induce distinct forms of CSR engagement. The following subsections introduce the model and discuss the main trade-offs and economic forces that shape the theory, which will be developed later. A detailed description of the framework is presented in Appendix A, along with the analytical arguments and proofs. 尽管文献中已探讨了实质性企业社会责任（CSR）参与的若干决定因素，但如前所述，经济激励的作用却鲜受关注。然而，象征性CSR的诸多吸引力可从以下角度解释：许多消费者愿意为CSR支付价格溢价（Flammer, 2015；Hawn & Ioannou, 2016；Kaul & Luo, 2018；Luo & Bhattacharya, 2006；McWilliams & Siegel, 2001；Porter & Kramer, 2006），但他们无法或不愿评估这些投资的真实结果（Durand et al., 2019；Kaul & Luo, 2019；Luo & Kaul, 2019）。本文提出的模型借鉴这一见解，旨在阐明经济激励——尤其是CSR价格溢价——如何诱发不同形式的CSR参与。下文小节将介绍该模型，并讨论塑造该理论的主要权衡与经济力量（理论后续将进一步展开）。框架的详细说明见附录A，同时包含分析论证与证明。

Model: Baseline Definitions

模型：基线定义

The framework proposed in this paper focuses on markets where firms use CSR as a basis for product differentiation1 (e.g., McWilliams & Siegel, 2001; Porter & Kramer, 2006), which may allow them to command a CSR price premium (e.g., Kaul & Luo, 2018; Martin, 2019). Following past studies in CSR and non-market strategy (e.g., Baron, 2001; Kaul & Luo, 2018; Mohliver, Crilly, & Kaul, 2019), this type of market is modeled as a differentiated Cournot duopoly (e.g., Singh & Vives, 1984; Zanchettin, 2006), wherein both firms (the focal firm, denoted by $F$ ,and its competitor, denoted by $C \cup$ produce products that generate negative socioenvironmental externalities. For example, these could be negative environmental externalities, possibly generated by the use of a dirty input (Acemoglu, Aghion, Bursztyn, & Hemous, 2012). Yet, the framework is also consistent with negative social externalities, as in the case of exploitative labor conditions resulting from doing business with suppliers who violate human rights standards. 本文提出的框架聚焦于企业以企业社会责任（CSR）作为产品差异化基础的市场（例如，McWilliams & Siegel, 2001；Porter & Kramer, 2006），这可能使它们获得CSR价格溢价（例如，Kaul & Luo, 2018；Martin, 2019）。借鉴以往企业社会责任和非市场战略领域的研究（例如，Baron, 2001；Kaul & Luo, 2018；Mohliver, Crilly, & Kaul, 2019），此类市场被建模为差异化古诺双寡头模型（例如，Singh & Vives, 1984；Zanchettin, 2006），其中两家企业（核心企业用\( F \)表示，其竞争对手用\( C \)表示）生产会产生负面社会环境外部性的产品。例如，这些外部性可能是负面环境外部性，由使用肮脏投入品（Acemoglu, Aghion, Bursztyn, & Hemous, 2012）产生。然而，该框架也适用于负面社会外部性，例如与违反人权标准的供应商开展业务导致的剥削性劳动条件。

Both firms in the model undertake CSR communication efforts intended to promote them as socially responsible companies. These efforts may include issuing reports about their CSR programs or the socioenvironmental outcomes of their operations, and supporting CSR-related advertising (Hawn & Ioannou, 2016; Servaes & Tamayo, 2013). This is consistent with past research that highlighted CSR communication as a necessary condition for a CSR price premium to be supported or sustained (e.g., Hawn & Ioannou, 2016; Servaes & Tamayo, 2013). Furthermore, the assumption that both firms undertake CSR communication is also consistent with empirical evidence, as CSR communication is generally low cost and fairly common in practice (Marquis et al., 2016). For instance, in 2018, $8 6 %$ of companies in the S&P 500 Index published a minimum of one CSR or sustainability report (Ghoneim, 2019). For simplicity, the baseline model assumes that CSR communication has zero cost for companies, an assumption that is relaxed later on. 模型中的两家公司都开展企业社会责任（CSR）传播活动，旨在将自身塑造为有社会责任感的企业。这些努力可能包括发布关于其CSR项目或运营的社会环境成果的报告，并支持与CSR相关的广告（Hawn & Ioannou，2016；Servaes & Tamayo，2013）。这与以往研究一致，该研究强调CSR传播是CSR价格溢价得以支撑或持续的必要条件（例如Hawn & Ioannou，2016；Servaes & Tamayo，2013）。此外，两家公司均开展CSR传播的假设也与实证证据一致，因为CSR传播通常成本较低且在实践中相当普遍（Marquis等人，2016）。例如，2018年，标准普尔500指数中的86%的公司至少发布了一份CSR或可持续发展报告（Ghoneim，2019）。为简化起见，基准模型假设CSR传播对企业而言成本为零，这一假设在后续会被放宽。

In addition to CSR communication, the firms also support other CSR activities, leading to either substantive or symbolic engagement. As already noted, the choice of symbolic CSR engagement involves low-cost CSR practices, activities, and initiatives that, when promoted by CSR communication efforts, may signal social responsibility without effectively impacting the negative socioenvironmental externalities generated by the firm. Examples include creating and supporting committees to evaluate a firm’s social responsibility initiatives (e.g., Hawn & Ioannou, 2016) or engaging in minimal corporate philanthropy (Cuypers et al., 2016). Given the low cost of this type of activity (e.g., Durand et al., 2019; Hawn & Ioannou, 2016) and for the sake of simplicity, the model assumes that these activities have zero cost for the firms. 除了企业社会责任（CSR）传播外，这些企业还支持其他企业社会责任活动，从而产生实质性或象征性的参与。如前所述，象征性企业社会责任参与的选择涉及低成本的企业社会责任实践、活动和举措，当通过企业社会责任传播努力推广时，这些实践、活动和举措可能会表明企业的社会责任，但不会有效影响企业产生的负面社会环境外部性。例如，成立和支持委员会来评估企业的社会责任举措（例如，Hawn & Ioannou，2016），或开展最低限度的企业慈善活动（Cuypers等人，2016）。鉴于此类活动的低成本（例如，Durand等人，2019；Hawn & Ioannou，2016），并且为了简化，该模型假设这些活动对企业没有成本。

Alternatively, the firms may choose substantive CSR.2 According to the framework, substantive CSR combines zero-cost, non-impactful practices and activities with other costly initiatives that require an upfront investment of $I _ { S } > 0$ and (in line with the discussion in the previous subsection) lead to two main implications. Firstly, these costly initiatives reduce the negative socioenvironmental externalities generated by the firm (Durand et al., 2019). Secondly, they also improve the perceived quality of company-sponsored CSR communication efforts (Marquis & Qian, 2014), which then enables firms to charge a CSR price premium from consumers who value and scrutinize the quality of CSR communication.³ For example, when firm $F$ invests in substantive initiatives, it may produce higher-quality, more convincing reports on its CSR program (Hawn & Ioannou, 2016), or more legitimate CSR-related advertising efforts (Servaes & Tamayo, 2013), which may even persuade more vigilant consumers to pay a CSR price premium. Alternatively, the firms may choose substantive CSR.² According to the framework, substantive CSR combines zero-cost, non-impactful practices and activities with other costly initiatives that require an upfront investment of $I_{S} > 0$ and (in line with the discussion in the previous subsection) lead to two main implications. Firstly, these costly initiatives reduce the negative socioenvironmental externalities generated by the firm (Durand et al., 2019). Secondly, they also improve the perceived quality of company-sponsored CSR communication efforts (Marquis & Qian, 2014), which then enables firms to charge a CSR price premium from consumers who value and scrutinize the quality of CSR communication.³ For example, when firm $F$ invests in substantive initiatives, it may produce higher-quality, more convincing reports on its CSR program (Hawn & Ioannou, 2016), or more legitimate CSR-related advertising efforts (Servaes & Tamayo, 2013), which may even persuade more vigilant consumers to pay a CSR price premium.

Furthermore, as suggested above, a key aspect of the model is that, although consumers value CSR, their preferences are heterogeneous. These heterogeneities will now be described in more detail. Note that the description that follows focuses on the case in which the competitor $\left( \mathrm { f i r m ~ } C \right)$ chooses symbolic CSR. Therefore, it covers the case in which firm $F$ chooses between substantive and symbolic CSR engagement, while firm $C \boldsymbol s$ choice is fixed. 此外，如前所述，该模型的一个关键方面是，尽管消费者重视企业社会责任（CSR），但他们的偏好存在异质性。这些异质性将在下文更详细地描述。需要注意的是，接下来的描述聚焦于竞争对手（企业C）选择象征性CSR的情形。因此，它涵盖了企业F在实质性CSR和象征性CSR参与之间进行选择，而企业C的选择是固定的这一情况。

In line with previous studies on differentiated Cournot duopolies (e.g., Baron, 2001; Kaul & Luo, 2018; Singh & Vives, 1984; Zanchettin, 2006), the model assumes the following functional form for the utility function representing consumers’ preferences: 与先前关于差异化古诺双头垄断的研究（例如，Baron, 2001；Kaul & Luo, 2018；Singh & Vives, 1984；Zanchettin, 2006）一致，该模型对代表消费者偏好的效用函数采用以下函数形式：

\begin{array} { l } { { { \cal U } = { \cal A } ( q _ { \cal F } + q _ { \cal C } ) + q _ { \cal F } \tau _ { \cal F } \Delta + q _ { \cal C } \tau \Delta - \displaystyle \frac { 1 } { 2 } \left( q _ { \cal F } ^ { 2 } + q _ { \cal C } ^ { 2 } + 2 \gamma q _ { \cal F } q _ { \cal C } \right) } } \ { { ~ - \displaystyle \frac { p \varphi } { a _ { \cal F } } q _ { \cal F } - p \varphi q _ { \cal C } + m , } } \end{array}

where $A > 0$ represents the utility that consumers derive from a product’s regular attributes (for simplicity, assumed to be equal for both firms, independent of CSR),4 $q _ { i }$ is the quantity produced by firm i, and $m$ is a numeraire good. The parameter $\gamma ( 0 \leq$ $\gamma \geq 1$ )describes the differentiation (or substitutability) between the firms’ products (Kaul & Luo, 2018; Zanchettin, 2006). Accordingly, if $\gamma = 1$ , the firms’ products are perfect substitutes, a condition that mirrors low-differentiation, highly competitive industries (Kaul & Luo, 2018; Syverson, 2004a). On the other hand, $\gamma = 0$ implies independent products, meaning that each firm produces a completely differentiated product (Zanchettin, 2006). This second condition is consistent with high-differentiation, low-competition settings (Kaul & Luo, 2018; Syverson, 2004b). Moreover, all of these parameters are analogously defined in other differentiated duopoly models (e.g., see Baron, 2001; Kaul & Luo, 2018; Mohliver et al., 2019; Singh & Vives, 1984; Zanchettin, 2006). 其中 \( A > 0 \) 表示消费者从产品常规属性中获得的效用（为简化起见，假设两家企业的该效用相等，且与企业社会责任（CSR）无关），\( q_i \) 是企业 \( i \) 生产的数量，\( m \) 是计价物商品。参数 \( \gamma (0 \leq \gamma \geq 1) \) 描述了企业产品之间的差异化（或替代性）（Kaul & Luo, 2018；Zanchettin, 2006）。相应地，若 \( \gamma = 1 \)，则企业产品为完全替代品，这一条件反映了低差异化、高度竞争的行业（Kaul & Luo, 2018；Syverson, 2004a）。另一方面，\( \gamma = 0 \) 意味着产品相互独立，即每家企业生产完全差异化的产品（Zanchettin, 2006）。这第二种情况与高差异化、低竞争的环境一致（Kaul & Luo, 2018；Syverson, 2004b）。此外，所有这些参数在其他差异化双头垄断模型中也有类似定义（例如，见 Baron, 2001；Kaul & Luo, 2018；Mohliver et al., 2019；Singh & Vives, 1984；Zanchettin, 2006）。

Given this basic structure, the other terms of Equation (1) describe consumer preferences for CSR and socioenvironmental outcomes. Accordingly, $\Delta > 0$ represents the CSR price premium, while the parameter $\tau ( 0 < \tau < 1 )$ captures heterogeneity in consumers’ preferences for CSR communication. More specifically, $\tau$ denotes the proportion of consumers in the market who do not scrutinize the quality of CSR communication. These individuals pay the same CSR price premium irrespective of the quality of the CSR communication efforts undertaken by the firms. On the other hand, $_ { 1 - \tau }$ represents the fraction of consumers who value and scrutinize the quality of CSR communication. This segment of the consumer market may perceive low-quality CSR communication as an insufficient (or non-credible) commitment to social responsibility. Thus, they are only willing to pay the CSR price premium $\left( \Delta \right)$ when the quality of CSR communication is high—that is, only when firms engage in substantive CSR—otherwise paying zero. Therefore, when firm $F$ invests in substantive CSR initiatives, $\tau _ { F } = 1$ , meaning that all consumers agree to pay the CSR price premium. In contrast, $\tau _ { F } = \tau < 1$ if the firm undertakes symbolic CSR, which indicates that only segment $\tau$ pays the CSR price premium in this case. Given this basic structure, the other terms of Equation (1) describe consumer preferences for CSR and socioenvironmental outcomes. Accordingly, $\Delta > 0$ represents the CSR price premium, while the parameter $\tau ( 0 < \tau < 1 )$ captures heterogeneity in consumers’ preferences for CSR communication. More specifically, $\tau$ denotes the proportion of consumers in the market who do not scrutinize the quality of CSR communication. These individuals pay the same CSR price premium irrespective of the quality of the CSR communication efforts undertaken by the firms. On the other hand, $_ { 1 - \tau }$ represents the fraction of consumers who value and scrutinize the quality of CSR communication. This segment of the consumer market may perceive low-quality CSR communication as an insufficient (or non-credible) commitment to social responsibility. Thus, they are only willing to pay the CSR price premium $\left( \Delta \right)$ when the quality of CSR communication is high—that is, only when firms engage in substantive CSR—otherwise paying zero. Therefore, when firm $F$ invests in substantive CSR initiatives, $\tau _ { F } = 1$ , meaning that all consumers agree to pay the CSR price premium. In contrast, $\tau _ { F } = \tau < 1$ if the firm undertakes symbolic CSR, which indicates that only segment $\tau$ pays the CSR price premium in this case.

Furthermore, the parameter $\varphi > 0$ describes the disutility caused by the negative socioenvironmental externalities generated by each product unit. In line with the discussion above, when firm $F$ engages in symbolic CSR (similarly to $\mathrm { f i r m } \ C )$ , $a _ { F } = 1$ , thereby indicating that the products produced by both firms generate the same level of negative externalities. On the other hand, when firm $F$ invests in substantive CSR, $a _ { F } = a > 1$ , meaning that the negative externalities generated by $F$ are reduced. The parameter $p$ ,in turn, captures heterogeneities in consumers’ willingness to actively monitor these negative externalities. In this sense, the model assumes that information on the effective level of (negative) externalities generated by each firm is costly to acquire (Durand et al., 2019; Luo & Kaul, 2019). Hence, only a segment $p$ $( 0 < p < 1 )$ of consumers in the market is willing to bear these costs and effectively verify how harmful the firms’ products are to society. Importantly, note that $p$ proxies for the monitoring intensity to which the firms are subject. For example, very intense monitoring implies that a substantial amount of information and data can be made available to the public at a lower cost (Delmas & Burbano, 2011), thereby increasing the fraction of consumers who are willing to bear the necessary costs and acquire information about the negative externalities generated by the firms. In other words, $p$ is larger under more intensive monitoring and lower otherwise. 此外，参数 $\varphi > 0$ 描述了每个产品单位产生的负面社会环境外部性带来的负效用。与上述讨论一致，当企业 $F$ 开展象征性企业社会责任（CSR）时（与企业 $C$ 类似），$a_F = 1$，这表明两家企业生产的产品产生的负面外部性水平相同。另一方面，当企业 $F$ 投入实质性企业社会责任时，$a_F = a > 1$，这意味着企业 $F$ 产生的负面外部性有所减少。参数 $p$ 则捕捉了消费者主动监测这些负面外部性的意愿异质性。从这个意义上说，该模型假设获取每家企业产生的（负面）外部性实际水平的信息成本高昂（Durand et al., 2019；Luo & Kaul, 2019）。因此，市场中只有一部分消费者（比例为 $p$，且 $0 < p < 1$）愿意承担这些成本，并有效核实企业产品对社会的危害程度。重要的是，请注意 $p$ 代表了企业所面临的监测强度。例如，非常严格的监测意味着可以以更低的成本向公众提供大量信息和数据（Delmas & Burbano, 2011），从而增加愿意承担必要成本并获取企业产生的负面外部性信息的消费者比例。换句话说，监测越严格，$p$ 的值越大；反之则越小。

Given the definitions above, note that, by varying the relative sizes of the terms containing $\tau$ and $p$ , it is possible to represent distinct patterns of consumer preference for socioenvironmental responsibility. For example, consumers may be “activists” who are unwilling to reward symbolism (low $\tau$ but actively scrutinize the socioenvironmental consequences of firms’ actions (high $p \mathrm { \Pi }$ . In turn, the opposite case may be associated with a market in which consumers derive high utility from a trending image of social responsibility but, in reality, refrain from evaluating the quality of firms’ CSR communication efforts (high $\tau )$ , or their socioenvironmental performance (low $p ]$ . Certainly, there is a continuum of possible profiles between these extremes, which is captured by the flexible functional format of Equation (1). For instance, in specific markets, CSR reports may be tailored particularly for investors (e.g., Lock & Seele, 2015), rendering most consumers largely unable to assess the relative quality of these reports. This would be consistent with a high t. However, a consumer segment in this same market may still scrutinize the social and environmental outcomes of firms’ operations (e.g., by following the lead of activists, NGOs, and other third-party organizations that monitor socioenvironmental issues), which is consistent with a higher $p$ . 根据上述定义，需要注意的是，通过改变包含 $\tau$ 和 $p$ 的术语的相对大小，可以表示消费者对社会环境责任的不同偏好模式。例如，消费者可能是“活动家”，他们不愿意为象征性的行为买单（低 $\tau$），但会积极审视企业行动的社会环境后果（高 $p$）。反过来，相反的情况可能与这样一个市场相关：消费者从企业社会责任的流行形象中获得高效用，但实际上却不愿评估企业的 CSR 沟通努力的质量（高 $\tau$）或其社会环境绩效（低 $p$）。当然，在这两个极端之间存在着一系列可能的消费者画像，这可以通过方程 (1) 的灵活函数形式来捕捉。例如，在特定市场中，企业社会责任报告可能特别针对投资者定制（例如 Lock & Seele, 2015），这使得大多数消费者在很大程度上无法评估这些报告的相对质量。这与高 $\tau$ 一致。然而，同一市场中的某个消费者群体可能仍然会审视企业运营的社会和环境结果（例如，效仿活动家、非政府组织和其他监测社会环境问题的第三方组织的做法），这与较高的 $p$ 一致。

In addition to the assumptions and definitions presented above, two technical assumptions are made to restrict the parameter space and avoid purely mathematical concerns. These assumptions are detailed in Appendix A. The first assumption requires $A$ (the parameter describing the utility derived from the regular attributes of the product) to be sufficiently high vis-à-vis the other parameters. By fixing a minimum level for this parameter, Assumption 1 guarantees that both firms produce positive quantities, irrespective of firm $F s$ CSR engagement choices (see Martin, 2019). The second assumption establishes a maximum level for $A$ , thereby restricting the parameter region of interest (see Zanchettin, 2006). 除上述假设和定义外，还做了两项技术假设以限制参数空间并避免纯粹的数学问题。这些假设有详细说明详见附录A。第一个假设要求参数\( A \)（描述产品常规属性带来的效用的参数）相对于其他参数足够高。通过为该参数设定最低水平，假设1确保无论企业\( F \)的企业社会责任（CSR）参与选择如何，两家企业都能生产正产量（见Martin, 2019）。第二个假设为\( A \)设定最高水平，从而限制了相关参数区域（见Zanchettin, 2006）。

Model: Timeline and Equilibrium

模型：时间线与平衡

The model has two stages. At the initial stage $\left( t = 0 \right)$ , both firms $F$ and $C$ implement zero-cost CSR activities and practices with no impact on production-generated negative socioenvironmental externalities. Firm $F$ then decides whether or not to engage in substantive CSR. If $F$ chooses substantive CSR, then it invests $I _ { S }$ and implements the activities and initiatives that reduce negative externalities; otherwise, only the zero-cost, non-impactful CSR activities are undertaken. At the second stage $\left( t = 1 \right)$ , both firms implement their CSR communication efforts and decide on their optimal product quantities (for simplicity, a zero discount rate is assumed). Thus, in this stage, both firms use CSR communication to promote an image of social responsibility by informing stakeholders about the CSR activities that have already been implemented. 该模型分为两个阶段。在初始阶段（\( t = 0 \)），企业 \( F \) 和 \( C \) 均开展零成本的企业社会责任（CSR）活动与实践，且对生产产生的负面社会环境外部性无影响。随后，企业 \( F \) 决定是否开展实质性 CSR。若 \( F \) 选择实质性 CSR，则会投入 \( I_S \) 并实施能减少负面外部性的活动与举措；否则，仅开展零成本、无影响的 CSR 活动。在第二阶段（\( t = 1 \)），两家企业均开展 CSR 传播工作，并决定最优产品数量（为简化分析，假设贴现率为零）。因此，在该阶段，两家企业通过向利益相关者告知已实施的 CSR 活动，利用 CSR 传播塑造社会责任形象。

Two distinct equilibria are possible in this baseline model. If firm $F$ does not invest in substantive CSR initiatives, there is a purely symbolic equilibrium: both firms undertake CSR communication and non-impactful CSR activities, but neither effectively invests in socially beneficial initiatives. Conversely, the equilibrium in which $F$ invests in substantive CSR is “partially responsible” in the sense that $F$ does engage in CSR activities that benefit society by reducing negative socioenvironmental externalities, while firm $C$ maintains a symbolic positioning Further on in the paper, an alternative scenario is considered, where firm $C$ engages in substantive CSR. Additionally, in an extension to the baseline model (also described below), the case in which both firms can simultaneously choose between symbolic and substantive CSR is also discussed. 在这个基准模型中，可能存在两种不同的均衡状态。如果企业F不投入实质性的企业社会责任（CSR）举措，就会出现一种纯粹象征性的均衡：两家企业都会开展CSR沟通和无实际影响的CSR活动，但都不会有效投入于具有社会益处的举措。相反，在企业F投入实质性CSR的均衡状态中，从某种意义上说，F确实开展了通过减少负面社会环境外部性来造福社会的CSR活动，而企业C则保持象征性定位。本文后续还将探讨另一种情景，即企业C也参与实质性CSR。此外，在基准模型的扩展（如下所述）中，还将讨论两家企业同时选择象征性和实质性CSR的情况。

In order to solve the model, a standard backward induction approach is applied. At $t = 1$ , the optimal quantities produced under each choice of firm $F$ are determined, assuming that both firms choose their quantities simultaneously. In this stage, firm $F$ obtains $\bar { \pi } _ { F ^ { * } } S$ in the presence of substantive CSR investments and $\pi _ { F ^ { * } } N$ in their absence. Moving to the initial stage, firm $F s$ payoffs for each choice are $\pi _ { F ^ { * } } { } ^ { S } - I _ { S }$ , if firm $F$ engages in substantive CSR, or $\pi _ { F ^ { * } } N$ , if $F$ engages in symbolic CSR. 为解决该模型，采用了标准的逆向归纳法。在 \( t = 1 \) 时，假设两家企业同时选择产量，确定了企业 \( F \) 在每种选择下的最优产量。在此阶段，企业 \( F \) 在存在实质性企业社会责任（CSR）投资时获得 \( \bar{\pi}_{F^*} S \)，在不存在此类投资时获得 \( \pi_{F^*} N \)。进入初始阶段，若企业 \( F \) 开展实质性 CSR 活动，其每种选择的收益为 \( \pi_{F^*}^S - I_S \)；若仅开展象征性 CSR 活动，则收益为 \( \pi_{F^*} N \)。

By comparing these two payoffs, the firm’s willingness to engage in substantive CSR is determined as the maximum level of investment where investment is preferred to no investment: that is, $I _ { S } \leq$ $\pi _ { F ^ { * } } { } ^ { S } - \pi _ { F ^ { * } } { } ^ { N } \equiv \bar { I _ { S } }$ . Using the analytical expressions developed in Appendix A, the paper examines how the CSR price premium affects the firm’s willingness to choose substantive CSR engagement, by looking at how changes in the CSR price premium affect $\bar { I _ { S } }$ (via comparative statics). The same idea is applied to analyze how monitoring intensity and product differentiation impact the effect of the CSR price premium on $\bar { I _ { S } }$ . 通过比较这两个收益，企业参与实质性企业社会责任（CSR）的意愿被确定为投资优于不投资的最大投资水平：即 \( I_S \leq \pi_{F^*}^S - \pi_{F^*}^N \equiv \bar{I_S} \)。利用附录A中推导的分析表达式，本文通过比较静态分析，考察企业社会责任价格溢价如何通过影响 \( \bar{I_S} \) 来改变企业选择实质性企业社会责任参与的意愿。同样的思路被用于分析监督强度和产品差异化如何影响企业社会责任价格溢价对 \( \bar{I_S} \) 的作用。

Model: Main Economic Forces

模型：主要经济力量

When deciding whether or not to invest in substantive CSR, firm $F$ must consider a series of opposing economic forces and trade-offs. On the one hand, substantive CSR reduces negative socioenvironmental externalities and, therefore, the penalties imposed by consumers who monitor these externalities. These investments also improve the quality of firms’ CSR communication efforts, enabling them to charge a CSR price premium from consumers who value and scrutinize the quality of these efforts. Both of these conditions have a positive effect on productivity. On the other hand, apart from requiring an upfront investment, substantive CSR may not generate high returns—for example, if the fraction of consumers who actively monitor externalities is too small. Similarly, substantive CSR may also be less attractive due to an inherently low capacity to reduce negative externalities. 在决定是否对实质性企业社会责任（CSR）进行投资时，企业F必须考虑一系列相互对立的经济力量和权衡。一方面，实质性CSR减少了负面的社会环境外部性，因此也减少了因消费者监督这些外部性而施加的惩罚。这些投资还能提升企业CSR沟通工作的质量，使企业能够向重视并审视这些努力质量的消费者收取CSR价格溢价。这两种情况都对生产率有积极影响。另一方面，除了需要前期投资外，实质性CSR可能不会产生高回报——例如，如果积极监督外部性的消费者比例过小。同样，由于实质性CSR本身减少负面外部性的能力有限，它也可能不那么有吸引力。

Therefore, the firm’s choice is affected by a fundamental trade-off between productivity gains and reductions in negative externalities. As noted above, substantive CSR reduces but does not completely eliminate negative socioenvironmental externalities. In other words, in the model, productivity gains are never externality free; they are always followed by increases in negative externalities. Consequently, the differential productivity gains implied by the CSR price premium in tandem with substantive CSR may generate additional negative externalities that lead to reductions in consumers’ willingness to pay, thereby offsetting, at least in part, the initial gains obtained by the firm. Of course, this trade-off becomes more relevant as the reductions in negative externalities generated by substantive CSR become smaller. 因此，企业的选择受到生产率提升与负外部性减少之间基本权衡的影响。如前所述，实质性企业社会责任（CSR）会减少但不会完全消除负面社会环境外部性。换句话说，在该模型中，生产率提升从来都不是无外部性的；它们总是伴随着负外部性的增加。因此，企业社会责任价格溢价所隐含的差异化生产率提升与实质性企业社会责任相结合，可能会产生额外的负外部性，从而降低消费者的支付意愿，至少部分抵消企业最初获得的收益。当然，随着实质性企业社会责任产生的负外部性减少，这种权衡变得更加重要。

Product differentiation may also give rise to another important trade-off. In essence, differentiation in the product market affects the interdependence between the firms’ production choices and profits (Duanmu et al., 2018; Singh & Vives, 1984). All else being equal, differentiation not only has a direct impact on profits, but also an indirect effect via increases in the market share of less efficient firms. Zanchettin (2006: 1000) referred to this indirect impact as a “selection effect [that] gets stronger when either the degree of asymmetry [between the firms] increases or products become closer substitutes.” Thus, while product differentiation may have a positive (and more direct) impact on profits via higher prices (e.g., Zanchettin, 2006), it may also create a negative (and rather indirect) effect by diminishing the selection effect described above, which limits a firm’s capacity to benefit from lower market shares of competitors. As detailed below, this trade-off helps to explain how product differentiation influences the effect of the CSR price premium. 产品差异化还可能带来另一个重要的权衡。本质上，产品市场上的差异化会影响企业生产决策与利润之间的相互依赖关系（Duanmu等人，2018；Singh & Vives，1984）。在其他条件相同的情况下，差异化不仅会直接影响利润，还会通过提高效率较低企业的市场份额产生间接影响。Zanchettin（2006：1000）将这种间接影响称为“选择效应[随着企业间的不对称程度增加或产品变得更接近替代品而增强]”。因此，尽管产品差异化可能通过更高的价格对利润产生积极（且更直接）的影响（例如，Zanchettin，2006），但它也可能通过削弱上述选择效应产生负面（且较为间接）的影响，而选择效应会限制企业从竞争对手较低的市场份额中获益的能力。如下所述，这种权衡有助于解释产品差异化如何影响企业社会责任（CSR）价格溢价的效果。

Lastly, on the demand side, consumers choose their demanded quantities by balancing between the utility derived from the regular attributes of the firms’ products and that from CSR and firms’ socioenvironmental performance. The paper now proceeds to assess how all of these forces interact and determine the effect of the CSR price premium on firms’ willingness to invest in substantive, as opposed to symbolic, CSR. The next section focuses on the first case, in which competitors only engage in symbolic CSR. Then, the case in which competitors invest in substantive CSR is considered. Finally, the last section applies the model to examine potential approaches to discourage symbolic CSR engagement. 最后，在需求端，消费者通过权衡从企业产品常规属性中获得的效用与从企业社会责任（CSR）和企业社会环境绩效中获得的效用，来选择其需求数量。本文接下来将评估所有这些力量如何相互作用，并确定企业社会责任价格溢价对企业在实质性（而非象征性）企业社会责任方面投资意愿的影响。下一部分将聚焦第一种情况，即竞争对手仅开展象征性企业社会责任活动。然后，考虑竞争对手投资于实质性企业社会责任的情况。最后，最后一节运用该模型，探讨阻止象征性企业社会责任参与的潜在方法。

THE ENABLING EFFECT OF THE CSR PRICE PREMIUM WHEN COMPETITORS ENGAGE IN SYMBOLIC CSR

竞争对手开展象征性企业社会责任时，企业社会责任价格溢价的促进作用

The differences in consumer preferences for CSR communication are a key channel linking the CSR price premium to the type of CSR investment that a firm selects. In this paper, these differences reflect consumer preferences for quality. Some customers are willing and able to scrutinize firms’ CSR communication efforts, distinguishing between low- and high-quality efforts. Thus, since substantive CSR increases the quality of CSR communication (e.g., Marquis & Qian, 2014), and quality matters to these consumers, they are only willing to pay a CSR price premium when CSR communication efforts are combined with substantive CSR. 消费者对企业社会责任（CSR）沟通的偏好差异是将CSR价格溢价与企业选择的CSR投资类型联系起来的关键渠道。在本文中，这些差异反映了消费者对质量的偏好。一些客户愿意且能够仔细审视企业的CSR沟通努力，区分低质量和高质量的努力。因此，由于实质性CSR会提高CSR沟通的质量（例如，Marquis & Qian，2014），并且质量对这些消费者很重要，因此只有当CSR沟通努力与实质性CSR相结合时，他们才愿意为CSR支付溢价。

Hence, when choosing whether or not to invest in substantive CSR, a profit-oriented firm should consider the differential benefits enabled by higherquality CSR communication. The additional gains from being able to serve consumers who scrutinize CSR communication quality increase the relative value of substantive CSR (and decrease the relative value of symbolic CSR), irrespective of any other benefits potentially generated by substantive CSR— such as improvements in socioenvironmental outcomes. Therefore: 因此，在决定是否投资实质性企业社会责任（CSR）时，以盈利为导向的企业应考虑高质量CSR沟通带来的差异化收益。能够服务于关注CSR沟通质量的消费者所获得的额外收益，会提高实质性CSR的相对价值（并降低象征性CSR的相对价值），无论实质性CSR可能产生的其他收益（例如社会环境成果的改善）如何。因此：

Proposition 1a. When competitors engage in symbolic CSR, if a segment of consumers scrutinizes and values the quality of CSR communication, an increase in the CSR price premium leads to a higher willingness to engage in substantive, as opposed to symbolic, CSR. 命题1a。当竞争对手开展象征性企业社会责任（CSR）活动时，如果部分消费者会审视并重视CSR沟通的质量，那么CSR价格溢价的提高会带来更高的实质性CSR参与意愿，而非象征性CSR。

Proof: See Appendix A.

证明：见附录A。

While Proposition 1a highlights the benefits of consumers valuing and scrutinizing the quality of CSR communication, in certain contexts, this may correspond to a small or negligible segment of the consumer market.6 For instance, in line with the example described above, this can be the case of an industry wherein firms tailor their CSR reports to specific audiences, such as governments or investors (Lock & Seele, 2015), rendering the general public (i.e., most consumers) unable to judge the quality of these reports. What is the role of the CSR price premium in such contexts? The short answer is that it depends on monitoring intensity. 虽然命题1a强调了消费者重视和审视企业社会责任（CSR）沟通质量的好处，但在某些情况下，这可能只对应消费者市场中一个很小或可忽略不计的部分。6例如，与上述例子一致，在某些行业中，企业会针对特定受众（如政府或投资者）定制其CSR报告（Lock & Seele，2015），这使得普通公众（即大多数消费者）无法判断这些报告的质量。在这种情况下，CSR价格溢价的作用是什么？简短的答案是，这取决于监督强度。

As discussed in previous sections, monitoring intensity is a key driver of socioenvironmental action (Delmas & Burbano, 2011; Durand et al., 2019; Kim & Lyon, 2015; Lyon & Montgomery, 2015; Marquis & Qian, 2014). When a firm is monitored and scrutinized by some fraction of its customers, the improvements in socioenvironmental outcomes generated by substantive CSR become valuable. Interestingly, these improvements can also amplify the productivity gains generated by the CSR price premium. 如前几节所述，监测强度是社会环境行动的关键驱动因素（Delmas & Burbano, 2011; Durand et al., 2019; Kim & Lyon, 2015; Lyon & Montgomery, 2015; Marquis & Qian, 2014）。当企业受到部分客户的监督和审视时，实质性企业社会责任（CSR）带来的社会环境成果改善就变得有价值。有趣的是，这些改善还能放大CSR价格溢价带来的生产率提升。

Indeed, given the trade-off between the productivity gains and reduction of negative externalities (discussed above), in the absence of substantive CSR, the productivity gains from an increase in the CSR price premium are partially offset by relevant penalties (i.e., reductions in willingness to pay) imposed by consumers who monitor negative externalities, as a considerable level of these externalities is generated in a highly productive process. However, if the company invests in substantive CSR, for the same level of productivity gains, both the (negative) externalities and the implied penalties will be lower in magnitude. Therefore, when negative externalities are monitored by a segment of the consumer market, the CSR price premium positively impacts a firm’s willingness to engage in substantive CSR. 事实上，考虑到生产率提升与负面外部性减少之间的权衡（如前所述），在缺乏实质性企业社会责任（CSR）的情况下，CSR价格溢价带来的生产率提升会被消费者因监测到负面外部性而施加的相关惩罚（即支付意愿降低）部分抵消，因为相当一部分负面外部性是在高生产率的生产过程中产生的。然而，如果企业投入实质性的CSR，在相同的生产率提升水平下，负面外部性及其带来的惩罚的程度都会更低。因此，当消费者市场的一部分监测到负面外部性时，CSR价格溢价会对企业是否愿意开展实质性CSR产生积极影响。

Proposition 1b. When competitors engage in symbolic CSR, if a segment of consumers monitors negative socioenvironmental externalities, an increase in the CSR price premium leads to a higher willingness to engage in substantive, as opposed to symbolic, CSR. 命题1b。当竞争对手开展象征性企业社会责任（CSR）时，如果一部分消费者关注负面社会环境外部性，那么企业社会责任价格溢价的提高会增强消费者参与实质性（而非象征性）企业社会责任的意愿。

Proof: See Appendix A.

证明：见附录A。

While Propositions 1a and 1b provide sufficient conditions for a positive association between the CSR price premium and a firm’s willingness to invest in substantive (as opposed to symbolic) CSR, it is possible that none of these conditions is met. In this case, a CSR price premium still motivates firms to undertake CSR communication (e.g., Servaes & Tamayo, 2013), but it never increases their willingness to invest in substantive initiatives. Thus, in the absence of both these conditions, a CSR price premium can only encourage symbolic engagement, including its manifestations as greenwashing or social washing (e.g., Delmas & Burbano, 2011). 虽然命题1a和1b为企业社会责任（CSR）价格溢价与企业愿意投资实质性（而非象征性）CSR之间的正向关联提供了充分条件，但也有可能这些条件均未满足。在这种情况下，CSR价格溢价仍然会促使企业开展CSR沟通（例如Servaes & Tamayo，2013），但绝不会提高其投资实质性举措的意愿。因此，在这两个条件均不具备的情况下，CSR价格溢价只能鼓励象征性参与，包括其表现形式如“漂绿”或“洗绿”（例如Delmas & Burbano，2011）。

Jointly, the propositions presented in this first subsection introduce conditions under which the CSR price premium may strengthen incentives for substantive CSR engagement. Under these conditions, the CSR price premium is not only a driver of CSR investment, but, more importantly, it increases the likelihood of substantive CSR engagement. While these conditions are consistent with theoretical research and empirical evidence (e.g., Durand et al., 2019; Hawn & Ioannou, 2016; Marquis & Qian, 2014), the discussion so far also suggests that monitoring intensity and differentiation in the product market can both significantly impact the mechanisms that shape the results of Propositions 1a and 1b. Consequently, even in the presence of the conditions underlying Propositions 1a and 1b, the CSR price premium may be more or less effective in enabling substantive CSR engagement, depending on the intensity of the monitoring activity to which firms are subject, as well as competitors’ strategic moves. Thus, the paper will now assess the role of these key factors in further detail. 共同而言，本小节提出的命题介绍了企业社会责任（CSR）价格溢价可能增强实质性CSR参与激励的条件。在这些条件下，CSR价格溢价不仅是CSR投资的驱动力，更重要的是，它增加了实质性CSR参与的可能性。尽管这些条件与理论研究和实证证据一致（例如，Durand等人，2019；Hawn & Ioannou，2016；Marquis & Qian，2014），但到目前为止的讨论也表明，产品市场中的监督强度和差异化都可能显著影响塑造命题1a和1b结果的机制。因此，即使在命题1a和1b的条件存在下，CSR价格溢价在促进实质性CSR参与方面的效果可能因企业所处的监督活动强度以及竞争对手的战略行动而有所不同。因此，本文将进一步详细评估这些关键因素的作用。

In what follows, it is assumed that the two conditions underlying Propositions 1a and 1b are satisfied. In other words, the analyses assume that a segment of the consumer market scrutinizes and values the quality of CSR communication efforts $\scriptstyle ( 1 - \tau < 1 )$ , and another (not necessarily disjoint) segment monitors negative socioenvironmental externalities $( p < 1 )$ . 在下文，我们假设命题1a和1b所依据的两个条件均已满足。换句话说，这些分析假设消费者市场的一个细分群体会审视并重视企业社会责任（CSR）传播努力的质量 $\scriptstyle ( 1 - \tau < 1 )$，而另一个（不一定不重叠的）细分群体则会监测负面的社会环境外部性 $( p < 1 )$。

The Role of Monitoring Intensity When Competitors Engage in Symbolic CSR

竞争对手开展象征性企业社会责任活动时，监测强度的作用

There is little dispute that monitoring influences firms’ willingness to engage in substantive socioenvironmental action (Campbell, 2007; Kim & Lyon, 2015; Lu0 et al., 2018; Marquis & Qian, 2014). However, only more recently has the extant research started to address the differences among the myriad of substantive CSR initiatives in which firms may invest (e.g., Durand et al., 2019). Particularly relevant to this paper is the idea that some substantive actions may be more socially beneficial than others (Kaul & Lu0, 2019). In the framework proposed here, this is captured by differences in the capacity to reduce negative socioenvironmental externalities, which is denoted by the parameter a: higher values of $a$ are associated with substantive CSR that promotes greater externality reductions. In this context, intuition suggests that more intensive monitoring should be more effective in inducing substantive CSR initiatives if these initiatives also exhibit a greater capacity to reduce negative externalities. But how does this logic influence the effect of the CSR price premium? 几乎没有争议的是，监督会影响企业参与实质性社会环境行动的意愿（Campbell, 2007; Kim & Lyon, 2015; Lu0 et al., 2018; Marquis & Qian, 2014）。然而，直到最近，现有研究才开始探讨企业可能参与的众多实质性企业社会责任（CSR）举措之间的差异（例如，Durand et al., 2019）。对本文特别重要的是，某些实质性行动可能比其他行动更具社会益处的观点(Kaul & Lu0, 2019)。在本文提出的框架中，这一点通过减少负面社会环境外部性的能力差异来体现，该能力由参数\(a\)表示：\(a\)值越高，对应的实质性CSR举措促进的外部性减少效果越好。在这种情况下，直觉表明，如果这些举措还具有更强的减少负面外部性的能力，那么更严格的监督应该更有效地诱导实质性CSR举措。但这种逻辑如何影响CSR价格溢价的效果呢？

Let us consider two cases. Firstly, suppose that a firm can invest in substantive CSR initiatives that greatly reduce negative socioenvironmental externalities. As argued above, this feature diminishes the importance of the trade-off between the productivity gains and externality reduction. Thus, following an increase in the CSR price premium, the differential productivity gains enabled by substantive CSR (e.g., via improvements in the perceived quality of CSR communication) are compensated by (at most) small increases in the negative externalities generated by the firm. Higher monitoring intensity then simply amplifies this effect by increasing the gains obtained in the presence of substantive CSR investments, vis-à-vis the gains expected in the absence of these investments. 让我们考虑两种情况。首先，假设一家公司能够投资于实质性的企业社会责任（CSR）举措，从而大幅减少负面的社会环境外部性。如前所述，这一特点降低了生产率提升与外部性减少之间权衡的重要性。因此，在企业社会责任价格溢价增加之后，实质性企业社会责任带来的差异化生产率提升（例如，通过改善企业社会责任沟通的感知质量）最多只会被该公司产生的负面外部性的小幅增加所抵消。更高的监管强度随后会通过增加在存在实质性企业社会责任投资时获得的收益（相对于在没有这些投资时预期的收益）来简单地放大这种效应。

Now, let us assume that the firm can only invest in substantive CSR initiatives with an inherently low capacity to reduce negative externalities. In this case, the above-mentioned trade-off becomes crucial to the firm’s decision. Following an increase in the CSR price premium, the differential gains enabled by substantive CSR can now be offset by relevant increases in negative externalities. Since higher monitoring intensity elevates the probability that consumers will scrutinize the firm for these additional negative externalities, it reduces the enabling effect of the CSR price premium by making the implied productivity gains less valuable to the firm. 现在，假设该企业只能投资于实质性的企业社会责任（CSR）举措，而这类举措本身降低负外部性的能力较低。在这种情况下，上述权衡对企业的决策至关重要。随着企业社会责任价格溢价的提高，实质性企业社会责任带来的差异化收益现在可能会被相关负外部性的增加所抵消。由于更高的监管强度会提高消费者对这些额外负外部性进行审查的可能性，这会削弱企业社会责任价格溢价的促进作用，因为这使得隐含的生产率提升对企业而言价值降低。

To better illustrate the case of substantive CSR with low capacity to reduce negative externalities, consider an example of environmental CSR. Suppose that consumers form expectations about firms’ environmental performance by observing their CSR communication efforts, but then compare these expectations with firms’ true production-generated negative environmental externalities—such as pollution (Delmas, Etzion, & Nairn-Birch, 2013). Consumers may perceive substantive CSR as a stronger commitment to environmental sustainability (Marquis & Qian, 2014) and, thus, may expect a significantly lower generation of negative externalities when the firm invests in substantive CSR. Yet, since substantive CSR has (by assumption) an inherently low capacity to reduce negative externalities, consumers may deem the effectively observed reductions as disappointingly small (Nason, Bacq, & Gras, 2018), thereby deciding to penalize the firm (e.g., by reducing their willingness to pay). In other words, in this case, consumers may interpret the firm’s CSR engagement as greenwashing (Barnett, 2007), even if it is striving to be environmentally responsible. Therefore, the impact of monitoring intensity on the effect of the CSR price premium depends on the extent to which substantive CSR reduces negative externalities. 为了更好地说明具有低减少负外部性能力的实质性企业社会责任（CSR）的情况，我们考虑一个环境企业社会责任的例子。假设消费者通过观察企业的CSR沟通努力来形成对企业环境绩效的预期，但随后会将这些预期与企业真实生产产生的负面环境外部性（如污染，Delmas, Etzion, & Nairn-Birch, 2013）进行比较。消费者可能会认为实质性CSR代表着对环境可持续性的更强承诺（Marquis & Qian, 2014），因此，当企业投入实质性CSR时，他们可能期望负面外部性的产生显著减少。然而，由于实质性CSR（根据假设）本质上具有低减少负外部性的能力，消费者可能会认为实际观察到的减少令人失望地小（Nason, Bacq, & Gras, 2018），从而决定惩罚企业（例如，降低其支付意愿）。换句话说，在这种情况下，消费者可能会将企业的CSR参与解读为漂绿行为（Barnett, 2007），即使该企业正努力做到环境责任。因此，监督强度对CSR价格溢价效果的影响取决于实质性CSR减少负外部性的程度。

Proposition 2. When competitors engage in symbolic CSR, if substantive CSR sufficiently reduces negative socioenvironmental externalities, higher monitoring intensity increases the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. Otherwise, if substantive CSR only generates small reductions in negative socioenvironmental externalities, higher monitoring intensity decreases the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. 命题2。当竞争对手开展象征性企业社会责任（CSR）时，如果实质性企业社会责任能够充分减少负面社会环境外部性，那么更高的监督强度会增加企业社会责任价格溢价对企业参与实质性而非象征性企业社会责任意愿的积极影响。否则，如果实质性企业社会责任仅能产生较小的负面社会环境外部性减少，那么更高的监督强度会降低企业社会责任价格溢价对企业参与实质性而非象征性企业社会责任意愿的积极影响。

Proof: See Appendix A.

证明：见附录A。

In sum, Proposition 2 shows that monitoring intensity influences the effect of the CSR price premium in a nuanced fashion. When substantive CSR investments fail to sufficiently abate negative productiongenerated externalities, higher monitoring attenuates the positive impact of the CSR price premium on a firm’s willingness to engage in substantive CSR. Returning to the environmental CSR example, firms may have more incentives to engage in greenwashing (e.g., Delmas & Burbano, 2011; Kim & Lyon, 2015), if they perceive substantive CSR efforts as not sufficiently effective in reducing environmental harms. Perhaps more importantly, this effect becomes more salient in high-monitoring contexts—possibly the contexts in which environmental externalities are of greater concern (e.g., Kassinis & Vafeas, 2006). Thus, the model suggests that intensive monitoring may reduce the economic incentives for substantive CSR investments with a more limited capacity to address negative externalities, particularly in contexts where these investments can be more socially beneficial. 总之，命题2表明，监督强度以一种微妙的方式影响企业社会责任（CSR）价格溢价的作用。当实质性的企业社会责任投资未能充分减轻生产产生的负面外部性时，更高的监督会削弱企业社会责任价格溢价对企业参与实质性企业社会责任意愿的积极影响。回到环境企业社会责任的例子，如果企业认为实质性的企业社会责任努力在减少环境危害方面不够有效，它们可能会更有动机进行“漂绿”（例如，Delmas & Burbano，2011；Kim & Lyon，2015）。也许更重要的是，这种效应在高监督环境中更为显著——这可能是环境外部性更受关注的背景（例如，Kassinis & Vafeas，2006）。因此，该模型表明，密集的监督可能会降低企业进行实质性企业社会责任投资的经济动机，而这些投资在解决负面外部性方面的能力有限，特别是在这些投资能带来更大社会收益的背景下。

The Role of Product Differentiation When Competitors Engage in Symbolic CSR

竞争对手开展象征性企业社会责任活动时产品差异化的作用

This subsection examines how product differentiation influences the enabling effect of the CSR price premium. As mentioned above, the literature on the relationship between product differentiation and socioenvironmental action has several points of disagreement. These seemingly mixed findings may indicate that the relationship between CSR engagement and differentiation can be subject to nonlinearities. Drawing on this insight, the framework proposed in this paper advances a more precise yet general theory of how economic incentives for CSR are shaped by product differentiation. As argued above (see subsection entitled “Model: Main Economic Forces”), the key trade-off involved in this discussion results from two opposing forces: while product differentiation can have a positive direct impact on a firm’s profits via higher prices, it also reduces the interdependence between the firm and its competitors, which may have a negative effect on its profitability (i.e., by reducing the selection effect described by Zanchettin, 2006; see explanation above). For a clearer and more detailed exposition, it is useful to again consider two cases. 本节考察产品差异化如何影响企业社会责任（CSR）价格溢价的赋能效应。如前所述，关于产品差异化与社会环境行动关系的文献存在若干分歧点。这些看似矛盾的研究结果可能表明，企业社会责任参与度与差异化之间的关系可能存在非线性特征。基于这一见解，本文提出的框架进一步完善了一个更精确且具有普适性的理论，阐释产品差异化如何塑造企业社会责任的经济激励机制。如前所述（见“模型：主要经济力量”小节），这一讨论中的关键权衡源于两种相反力量的作用：一方面，产品差异化可通过提高价格对企业利润产生直接的正向影响；另一方面，它会降低企业与其竞争对手之间的相互依存度，这可能对企业盈利能力产生负面影响（即削弱Zanchettin（2006）所述的选择效应，详见上述解释）。为了更清晰、更详细地阐述这一点，再次考虑两种情形会很有帮助。

First, suppose that a firm in a less differentiated market decides whether or not to invest in substantive CSR initiatives, while its competitors only engage in symbolic CSR. In this context, there is a stronger interdependence between the firms (e.g., Duanmu et al., 2018): all else constant, a rise in one firm’s productivity translates into reductions in the productivity (and market shares) of its competitors (e.g., Syverson, 2004b), meaning that the selection effect is strong (Zanchettin, 2006). The key idea, then, is that this selection effect is reduced by product differentiation, precisely because differentiation diminishes the interdependence between the firms’ products. Therefore, following an increase in the CSR price premium, higher product differentiation reduces the selection effect, which can generate such a large reduction in the differential gains of substantive CSR (i.e., by preventing further reductions competitors’ market shares) that it may offset the benefits stemming from direct profit increases (e.g., Zanchettin, 2006). Conversely, a reduction in product differentiation (or increase in competition) strengthens the selection effect and magnifies the differential gains of substantive CSR via higher reductions in competitors’ market shares. Hence, in low-differentiation markets, product differentiation diminishes the enabling effect of the CSR price premium. 首先，假设一个处于低差异化市场的企业决定是否投资实质性企业社会责任（CSR）举措，而其竞争对手仅开展象征性CSR。在此背景下，企业间的相互依存度更高（例如，Duanmu等人，2018）：在其他条件不变的情况下，一家企业生产率的提升会导致其竞争对手生产率（及市场份额）的下降（例如，Syverson，2004b），这意味着选择效应较强（Zanchettin，2006）。关键在于，产品差异化会削弱这种选择效应，因为差异化降低了企业产品间的相互依存度。因此，在企业社会责任价格溢价提高后，更高的产品差异化会降低选择效应，这可能会大幅减少实质性CSR的差异化收益（即通过阻止竞争对手市场份额的进一步下降），从而抵消直接利润增长带来的好处（例如，Zanchettin，2006）。相反，产品差异化程度降低（或竞争加剧）会增强选择效应，并通过更大幅度降低竞争对手的市场份额来放大实质性CSR的差异化收益。因此，在低差异化市场中，产品差异化会削弱企业社会责任价格溢价的促进作用。

However, note that, intuitively, the opposite rationale should apply to the case of highly differentiated markets. In these settings, the selection effect is small, since there is little interdependence between firms. Thus, in this case, an increase in product differentiation leads to relatively small reductions in the productivity gains implied by the CSR price premium. These reductions may be easily offset by the implied profit increases (again, due to higher prices), which then leads to the opposite prediction. 然而，需要注意的是，直观上，在高度差异化的市场中应适用相反的逻辑。在这种情况下，选择效应较小，因为企业之间几乎没有相互依存性。因此，在这种情况下，产品差异化程度的提高会导致企业社会责任价格溢价所隐含的生产率提升幅度相对较小地降低。这些降低可能很容易被隐含的利润增长（同样是由于更高的价格）所抵消，从而导致相反的预测。

Therefore, product differentiation affects the role of the CSR price premium in a non-monotonic fashion. This relationship is summarized in the following proposition: 因此，产品差异化以非单调的方式影响企业社会责任（CSR）价格溢价的作用。这种关系总结如下命题：

Proposition 3. When competitors engage in symbolic CSR, if product differentiation is sufficiently low, an increase in product differentiation decreases the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. In contrast, if product differentiation is sufficiently high, an increase in product differentiation increases the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. 命题3。当竞争对手开展象征性企业社会责任（CSR）时，如果产品差异化程度足够低，产品差异化程度的提高会降低企业社会责任价格溢价对企业开展实质性（而非象征性）企业社会责任意愿的积极影响。相反，如果产品差异化程度足够高，产品差异化程度的提高会增强企业社会责任价格溢价对企业开展实质性（而非象征性）企业社会责任意愿的积极影响。

Proof: See Appendix A.

证明：见附录 A。

Proposition 3 thus suggests that the effect of the CSR price premium is affected by product differentiation in a non-monotonic fashion. When competitors only engage in symbolic CSR, product differentiation attenuates the enabling effect of the CSR price premium, if the firm operates in a low-differentiation industry. However, the opposite holds true for a more differentiated market: in this case, product differentiation strengthens the effect of the CSR price premium. Importantly, the key mechanism explaining this relationship is the interplay between the positive impact of product differentiation on prices and its negative impact on the selection effect enabled by market competition (Zanchettin, 2006). It should be noted, however, that this mechanism can also be sensitive to the relative efficiency (and productivity) of the firm visà-vis its competitors (Zanchettin, 2006). Thus, the conclusions of Proposition 3 may change if competitors ex ante engage in substantive CSR, a case examined in the next section. 因此，命题3表明，企业社会责任（CSR）价格溢价的影响以非单调的方式受到产品差异化的影响。当竞争对手仅进行象征性的企业社会责任活动时，如果企业处于低差异化行业，产品差异化会削弱企业社会责任价格溢价的促进作用。然而，在竞争更激烈的市场中，情况则相反：此时，产品差异化会增强企业社会责任价格溢价的作用。重要的是，解释这种关系的关键机制是产品差异化对价格的正向影响与其对市场竞争所促成的选择效应的负向影响之间的相互作用（Zanchettin，2006）。然而，需要指出的是，这种机制还可能对企业相对于竞争对手的相对效率（和生产率）敏感（Zanchettin，2006）。因此，如果竞争对手事先就开展实质性的企业社会责任活动，命题3的结论可能会发生变化，这一情况将在下一节中进行探讨。

THE ENABLING EFFECT OF THE CSR PRICE PREMIUM WHEN COMPETITORS ENGAGE IN SUBSTANTIVE CSR

当竞争对手开展实质性企业社会责任活动时，企业社会责任溢价的推动作用

Until this point, the discussion has focused on the case in which a firm chooses between substantive and symbolic CSR while its competitor only engages in symbolic CSR. This section examines the alternative scenario, wherein the firm’s competitor ex ante engages in substantive CSR. As discussed in more detail in Appendix A, the model has the same structure, and the solution follows the steps described above. Yet, two other equilibria are now possible: a “partially responsible” equilibrium, in which only the competitor engages in substantive CSR, and a responsible equilibrium, wherein both firms engage in substantive CSR. As above, firstly, the section studies the main effect of the CSR premium, before examining the moderating roles of monitoring intensity and product differentiation. 到目前为止，讨论都集中在企业在实质性企业社会责任（CSR）和象征性CSR之间进行选择，而其竞争对手仅参与象征性CSR的情况下。本节将考察另一种替代情景，即企业的竞争对手事先就参与实质性CSR。如附录A中更详细讨论的那样，该模型具有相同的结构，解决方案遵循上述步骤。然而，现在可能出现另外两种均衡：一种是“部分负责任”均衡，其中只有竞争对手参与实质性CSR；另一种是负责任均衡，即两家企业都参与实质性CSR。与上述情况类似，本节首先研究CSR溢价的主要影响，然后考察监督强度和产品差异化的调节作用。

In essence, the previous section argued that the CSR price premium increases a firm’s willingness to invest in substantive, as opposed to symbolic, CSR if a segment of the consumer market scrutinizes either the quality of CSR communication (Proposition 1a) or negative socioenvironmental externalities (Proposition 1b). The same results are still valid when competitors ex ante invest in substantive CSR initiatives. This point is proved as a lemma in Appendix A. 本质上，上一节论证了，若消费者市场的某一细分群体审视企业CSR沟通的质量（命题1a）或负面社会环境外部性（命题1b），则CSR价格溢价会增强企业在实质性CSR（而非象征性CSR）上的投资意愿。当竞争对手事先投资实质性CSR举措时，这一结果仍然成立。这一点在附录A中作为引理得到证明。

Despite this result, competitors’ ex ante investments in substantive CSR may still influence the effect of the CSR price premium. In essence, the difference in the productivity gains implied by the CSR premium in the presence and absence of substantive CSR may be sensitive to competitors’ CSR engagement choices. More specifically, this subsection argues that this sensitivity depends on consumer preferences for CSR communication. 尽管有这一结果，竞争对手在实质性企业社会责任（CSR）方面的事前投资仍可能影响CSR价格溢价的效果。本质上，在存在和不存在实质性CSR的情况下，CSR溢价所隐含的生产率提升差异可能对竞争对手的CSR参与选择敏感。更具体地说，本节认为这种敏感性取决于消费者对CSR沟通的偏好。

Accordingly, suppose that a segment of the consumer market cares about and scrutinizes the quality of CSR communication. When competitors only engage in symbolic CSR, the differential gains generated by the CSR price premium in the presence of substantive CSR may be particularly high, since there is no competition in this market segment (recall that the firm cannot command a CSR price premium from these consumers, unless it engages in substantive CSR). However, the same rationale obviously does not apply if competitors ex ante invest in substantive CSR. In this scenario, the differential gains implied by substantive CSR are divided between the firm and its competitors. Thus, if a segment of consumers scrutinizes the quality of CSR communication efforts, the effect of the CSR price premium is weaker when competitors ex ante engage in substantive CSR, and stronger otherwise. 因此，假设消费者市场的某一细分群体关注并审视企业社会责任（CSR）传播的质量。当竞争对手仅开展象征性的企业社会责任活动时，在存在实质性企业社会责任的情况下，由企业社会责任价格溢价产生的差异化收益可能会特别高，因为该细分市场中不存在竞争（要注意，除非企业开展实质性的企业社会责任活动，否则无法从这些消费者那里获得企业社会责任价格溢价）。然而，如果竞争对手事先投入实质性的企业社会责任活动，同样的逻辑显然不适用。在这种情况下，实质性企业社会责任所隐含的差异化收益会在企业及其竞争对手之间分配。因此，如果某一细分消费者群体审视企业社会责任传播的质量，那么当竞争对手事先开展实质性企业社会责任活动时，企业社会责任价格溢价的影响会较弱，反之则较强。

Proposition 4. If a segment of consumers cares about and scrutinizes the quality of CSR communication, the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR is lower when competitors engage in substantive CSR, relative to the case in which competitors only engage in symbolic CSR. 命题4。如果一部分消费者关注并仔细审视企业社会责任（CSR）沟通的质量，那么当竞争对手开展实质性CSR时，CSR价格溢价对企业参与实质性而非象征性CSR的意愿的积极影响，会低于竞争对手仅开展象征性CSR的情况。

Proof: See Appendix A.

证明：见附录A。

The arguments leading to Proposition 4 indicate that consumers’ scrutiny of CSR communication is a key mechanism explaining how competitors’ ex ante engagement in substantive CSR influence the effect of the CSR price premium. However, the same arguments point to no other mechanisms with a potentially significant impact on this relationship. Thus, if there is zero scrutiny on CSR communication, the difference highlighted in Proposition 4 no longer exists. This result is stated as a lemma in Appendix A. 支持命题4的论证表明，消费者对企业社会责任（CSR）沟通的审视是解释竞争对手事前实质性CSR参与如何影响CSR价格溢价效应的关键机制。然而，同样的论证指出，不存在其他可能对这种关系产生重大影响的机制。因此，如果消费者对CSR沟通的审视为零，命题4中强调的差异将不复存在。这一结果在附录A中作为引理提出。

The proposition developed in this subsection describes how the enabling effect of the CSR price premium is influenced by competitors’ CSR engagement choices. While the sufficient conditions established by Propositions 1a and 1b also apply to the case in which competitors make ex ante investments in substantive CSR (as per Lemma 1—see Appendix A), Proposition 4 suggests that firms’ willingness to engage in substantive CSR may be reduced in this case (provided that a segment of consumers cares about and scrutinizes the quality of CSR communication). Interestingly, these results seem to contrast with research arguing that the CSR practices adopted by a firm tend to diffuse to industry peers (e.g., Cao et al., 2019; Ioannou & Serafeim, 2018). This tension is examined in more detail below. 本节中提出的命题描述了CSR价格溢价的促进作用如何受到竞争对手CSR参与选择的影响。虽然命题1a和1b确立的充分条件也适用于竞争对手对实质性CSR进行事前投资的情况（见引理1——附录A），但命题4表明，在这种情况下，企业参与实质性CSR的意愿可能会降低（前提是部分消费者关注并审视CSR沟通的质量）。有趣的是，这些结果似乎与认为企业采用的CSR实践往往会扩散到行业同行的研究形成对比（例如，Cao等人，2019；Ioannou & Serafeim，2018）。这种矛盾将在下文进行更详细的探讨。

The Role of Monitoring Intensity When Competitors Engage in Substantive CSR

竞争对手开展实质性企业社会责任活动时，监督力度的作用

The previous discussion on the role of monitoring intensity emphasized the trade-off between productivity gains and externality reductions. In sum, this trade-off is particularly important when substantive CSR has a low capacity to abate negative externalities. According to Proposition 2, in this scenario, monitoring intensity may reduce the effect of the CSR price premium. This section builds on that discussion to explore the implications of competitors’ CSR engagement choices for the results in Proposition 2. 之前关于监督强度作用的讨论强调了生产率提升与外部性减少之间的权衡。总之，当实质性企业社会责任（CSR）减排负外部性的能力较低时，这种权衡尤为重要。根据命题2，在这种情况下，监督强度可能会削弱CSR价格溢价的作用。本节将基于这一讨论，探讨竞争对手的CSR参与选择对命题2结果的影响。

Generally speaking, according to the model, competitors’ ex ante engagement in substantive CSR makes the trade-off between productivity gains and externality reduction even more salient to the firm. In essence, if the segment of consumers who scrutinize the quality of CSR communication is sufficiently large, a firm’s choice to invest in substantive CSR when competitors already do this may lead to a high production increase,’ thereby increasing the negative externalities generated by the firm. Thus, following an increase in the CSR price premium, the differential productivity gains associated with substantive CSR may generate excessive levels of negative externalities. Since monitoring intensity essentially increases the likelihood that these excessive (negative) externalities are scrutinized by consumers, in case a sufficiently high number of consumers value and scrutinize the quality of CSR communication, the effect of the CSR price premium decreases with monitoring intensity. 一般而言，根据该模型，竞争对手在实质性企业社会责任（CSR）方面的事前参与，会使企业在生产率提升与外部性减少之间的权衡更加突出。本质上，如果仔细审视CSR沟通质量的消费者群体足够庞大，当竞争对手已经进行实质性CSR投资时，企业选择进行实质性CSR投资可能会带来较高的产量增长，从而增加企业产生的负外部性。因此，在CSR价格溢价上升之后，与实质性CSR相关的差异化生产率提升可能会产生过度的负外部性。由于监督强度本质上会增加消费者仔细审视这些过度（负）外部性的可能性，因此在足够多的消费者重视并审视CSR沟通质量的情况下，CSR价格溢价的影响会随着监督强度的增加而降低。

Furthermore, note that this effect should be considered in addition to the results implied by Proposition 2. In other words, the role of monitoring intensity becomes further nuanced when competitors ex ante engage in substantive CSR. In this scenario, higher monitoring can only increase the enabling effect of the CSR price premium if substantive CSR sufficiently reduces negative socioenvironmental externalities (in line with Proposition 2) and if the segment of consumers who scrutinize the quality of CSR communication efforts is not large—a condition that avoids high productivity gains from substantive CSR. If any of these conditions are violated, higher monitoring intensity reduces the enabling effect of the CSR price premium. Thus: 此外，需要注意的是，这种效应应与命题2所暗示的结果一并考虑。换句话说，当竞争对手在事前开展实质性企业社会责任（CSR）时，监督强度的作用会进一步变得微妙。在这种情况下，只有当实质性CSR充分减少负面社会环境外部性（与命题2一致），并且审视CSR沟通努力质量的消费者群体不大（这一条件可避免实质性CSR带来的高生产率提升）时，更高的监督才能增强CSR价格溢价的促进作用。如果上述任一条件不满足，更高的监督强度会削弱CSR价格溢价的促进作用。因此：

Proposition 5. When competitors engage in substantive CSR, if substantive CSR fails to sufficiently reduce negative socioenvironmental externalities, or if a sufficiently large segment of consumers scrutinizes the quality of CSR communication, higher monitoring intensity decreases the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. 命题5. 当竞争对手开展实质性企业社会责任（CSR）时，如果实质性CSR未能充分减少负面社会环境外部性，或者如果足够大比例的消费者审查CSR沟通的质量，那么更高的监管强度会降低CSR价格溢价对企业参与实质性而非象征性CSR的意愿的积极影响。

Proof: See Appendix A. 证明：见附录A。

The Role of Product Differentiation When Competitors Engage in Substantive CSR

竞争对手开展实质性企业社会责任时产品差异化的作用

This section examines how the results in Proposition 3 change if competitors ex ante engage in substantive CSR initiatives. Proposition 3 established a non-monotonic relationship between the effect of the CSR price premium and product differentiation. Of equal importance, the key mechanism behind this relationship can be summarized in the idea that, while product differentiation can boost profitability via price increases (Zanchettin, 2006), it may also exert a negative influence on profits, by reducing interdependence between the firms’ products (Duanmu et al., 2018) and limiting the so-called “selection effect” (Zanchettin, 2006). 本节研究了如果竞争对手在事前开展实质性的企业社会责任（CSR）举措，命题3中的结果会如何变化。命题3确立了CSR价格溢价的影响与产品差异化之间的非单调关系。同样重要的是，这种关系背后的关键机制可以概括为：虽然产品差异化可以通过提价来提高盈利能力（Zanchettin，2006），但它也可能通过减少企业产品之间的相互依存性（Duanmu等人，2018）并限制所谓的“选择效应”（Zanchettin，2006），对利润产生负面影响。

The first insight implied by the model is that competitors’ decisions to engage in substantive CSR do not alter the effect of the CSR price premium in more differentiated markets. Linked to the above discussion, if product differentiation is sufficiently high, a further increase in differentiation exerts a minor negative impact on profits, as the selection effect is already reduced; however, it may boost profits via additional price increases (Zanchettin, 2006). Hence, arguments similar to those above lead to the parallel of Proposition 3. This result is stated as a lemma in Appendix A. 该模型暗示的第一个见解是，竞争对手决定开展实质性企业社会责任（CSR）活动，并不会改变企业社会责任价格溢价在更具差异化市场中的影响。与上述讨论相关，如果产品差异化程度足够高，进一步提高差异化程度对利润的负面影响会较小，因为选择效应已经减弱；然而，它可能通过额外提价来增加利润（Zanchettin，2006）。因此，与上述类似的论点推导出了命题3。这一结果在附录A中被表述为一个引理。

This finding notwithstanding, the case of a less differentiated market is technically harder to analyze, and the framework proposed in this paper suggests that the impact of product differentiation on prices becomes a critical issue. To see why, note that, in line with the discussion in a previous subsection, an equilibrium wherein both firms engage in substantive CSR has naturally lower quantities (and higher prices), vis-à-vis the equilibrium wherein the competitor simply engages in symbolic CSR. 尽管有这一发现，差异化程度较低的市场案例在技术上更难分析，而本文提出的框架表明，产品差异化对价格的影响成为一个关键问题。要理解原因，请注意，与上一小节的讨论一致，在两家企业都实质性参与企业社会责任（CSR）的均衡状态下，产量自然更低（价格更高），而相比之下，竞争对手仅象征性参与企业社会责任的均衡状态则不同。

Thus, let us assume that the segment of consumers who scrutinize the quality of CSR communication is very large. Assume, also, that substantive CSR greatly reduces negative socioenvironmental externalities. Jointly, these conditions further elevate the (already high) equilibrium price levels. Consequently, even in a low differentiation setting, the impact of differentiation on prices becomes sufficiently significant to offset any negative influence stemming from a (potential) selection effect. In this context, following an increase in the CSR price premium, product differentiation enables further increases in prices that contribute to elevate the firm’s willingness to engage in substantive CSR. In contrast, a reduction in product differentiation strongly decreases the impact of the CSR price premium by limiting the firm’s ability to further increase prices. Since these effects dominate the selection effect, product differentiation makes returns to substantive CSR more valuable in this scenario. Thus, the following proposition is valid: 因此，我们假设仔细审视企业社会责任（CSR）沟通质量的消费者群体非常庞大。同时假设实质性的企业社会责任能大幅减少负面社会环境外部性。这两个条件共同作用，进一步推高了（本已较高的）均衡价格水平。因此，即便在产品差异化程度较低的情况下，差异化对价格的影响也变得足够显著，足以抵消（潜在）筛选效应带来的任何负面影响。在此背景下，随着企业社会责任价格溢价的提高，产品差异化使得价格能够进一步上涨，这有助于提升企业参与实质性企业社会责任的意愿。相反，产品差异化程度的降低会通过限制企业进一步提高价格的能力，大幅削弱企业社会责任价格溢价的影响。由于这些效应在筛选效应中占据主导地位，在这种情况下，产品差异化使得实质性企业社会责任的回报更具价值。因此，以下命题成立：

Proposition 6. When competitors engage in substantive CSR, in a low-differentiation market, if substantive CSR sufficiently reduces negative socioenvironmental externalities and if a sufficiently large segment of consumers scrutinizes the quality of CSR communication, higher product differentiation increases the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. 命题6。当竞争对手在低差异化市场中开展实质性企业社会责任（CSR）时，如果实质性CSR充分减少了负面社会环境外部性，且有足够大比例的消费者审视CSR沟通的质量，那么更高的产品差异化会增强CSR价格溢价对企业参与实质性而非象征性CSR的意愿的积极影响。

Proof: See Appendix A.

证明：见附录A。

The extent of the price effect is crucial for explaining the results in Proposition 6. In fact, product differentiation may have a completely different role, if the price effect is sufficiently weak. More specifically, if the segment of consumers who scrutinize the quality of CSR communication is small enough, the effect of product differentiation on prices can be small relative to the selection effect, in line with Proposition 3. In this case, product differentiation reduces the enabling effect of the CSR price premium (see Lemma 5 in Appendix A). 价格效应的程度对于解释命题6的结果至关重要。事实上，如果价格效应足够微弱，产品差异化可能会发挥完全不同的作用。更具体地说，如果仔细审视企业社会责任（CSR）沟通质量的消费者群体足够小，那么产品差异化对价格的影响相对于选择效应可能会很小，这与命题3一致。在这种情况下，产品差异化会削弱CSR价格溢价的促进作用（见附录A中的引理5）。

Therefore, this section suggests that competitors’ CSR engagement choices may alter the role of product differentiation, under certain conditions. When product differentiation is low and competitors ex ante invest in substantive CSR, if demand- and supply-side conditions are extremely favorable to substantive CSR (i.e., if the segment of consumers who scrutinize the quality of CSR communication is sufficiently high and, at the same time, substantive CSR greatly reduces negative externalities), then product differentiation magnifies the positive impact of the CSR price premium on a firm’s willingness to engage in substantive CSR. In other words, decreased product differentiation may reduce incentives for substantive CSR investments in contexts in which these investments may be particularly profitable. 因此，本节表明，在特定条件下，竞争对手的企业社会责任（CSR）参与选择可能会改变产品差异化的作用。当产品差异化程度较低且竞争对手事前投入实质性企业社会责任时，如果需求和供给侧条件对实质性企业社会责任极为有利（即，仔细审视企业社会责任沟通质量的消费者群体足够庞大，同时实质性企业社会责任能大幅减少负外部性），那么产品差异化会放大企业社会责任价格溢价对企业参与实质性企业社会责任意愿的积极影响。换句话说，在这些投资可能特别有利可图的情况下，产品差异化程度降低可能会减少对实质性企业社会责任投资的激励。

DISCOURAGING SYMBOLIC CSR: AUDITING OF CSR ACTIVITIES, EXTERNALITY REGULATION, AND CSR COMMUNICATION COSTS

抑制象征性企业社会责任：企业社会责任活动审计、外部性监管与企业社会责任沟通成本

Having examined the nuanced role of the CSR price premium, the paper now applies the framework developed so far to study different approaches that may be used to discourage firms from engaging in symbolic CSR. This section considers a more general version of the model, whereby CSR communication requires an investment of $I _ { c } > 0$ Thus, both firms now simultaneously choose whether or not to invest in costly activities that abate negative socioenvironmental externalities $\left( I _ { S } \right)$ and CSR communication $\left( I _ { C } \right)$ . In addition, it is further assumed that both $I _ { S }$ and $I _ { C }$ are firm specific. This assumption is consistent with the firms being heterogeneous in their resources and capabilities, which may lead to heterogeneity in the perceived costs of CSR engagement (e.g., Durand et al., 2019). 在考察了企业社会责任（CSR）价格溢价的细微作用后，本文现在应用迄今为止开发的框架来研究可能用于阻止企业开展象征性企业社会责任的不同方法。本节考虑模型的一个更一般版本，其中企业社会责任沟通需要投入 $I_{C} > 0$。因此，两家企业现在同时选择是否投资于可减少负面社会环境外部性的成本活动（$I_{S}$）和企业社会责任沟通（$I_{C}$）。此外，还假设 $I_{S}$ 和 $I_{C}$ 都是企业特定的。这一假设与企业在资源和能力方面存在异质性一致，而这种异质性可能导致企业社会责任参与的感知成本存在差异（例如，Durand等人，2019）。

In line with previous definitions, symbolic CSR is here again characterized by combining CSR communication with low-cost CSR activities that do not generate societal benefits. The section then focuses on the case in which symbolic CSR is a best response for the focal firm (Gibbons, 1992). In short, this case corresponds to a situation in which substantive CSR is sufficiently costly to the firm, while CSR communication is sufficiently low cost. These conditions are detailed and formally characterized in Appendix A. 根据之前的定义，象征性企业社会责任（CSR）再次被定义为将CSR沟通与不产生社会收益的低成本CSR活动相结合。接下来，本节重点讨论象征性CSR是焦点企业（Gibbons, 1992）的最优反应的情况。简而言之，这种情况对应于实质性CSR对企业的成本足够高，而CSR沟通的成本足够低的情形。这些条件在附录A中进行了详细说明和正式界定。

The next two subsections analyze two particular mechanisms that may help to discourage symbolic CSR: (1) third parties auditing firms’ CSR activities and sharing information with consumers, and (2) government agencies regulating negative socioenvironmental externalities. The technical details underlying the analyses are presented in Appendix A, while the next subsections focus on the main conclusions extracted from the framework. 接下来的两个小节分析了两种可能有助于阻止象征性企业社会责任（CSR）的特定机制：（1）第三方审计机构的企业社会责任活动并与消费者共享信息，以及（2）政府机构监管负面社会环境外部性。分析背后的技术细节在附录A中介绍，而下一小节则重点关注从该框架中提取的主要结论。

Auditing of CSR Activities

企业社会责任活动审计

Consider a case in which third parties, such as rating agencies (e.g., MSCI or Refinitiv) or independent organizations led by activists (e.g., NGOs), audit firms’ CSR activities to determine the type of CSR engagement chosen by each one (substantive or symbolic). The results from these auditing procedures are then shared with consumers, who belong to one of two segments. The first segment corresponds to a fraction $1 - \xi$ of the consumer market, where $0 < \xi < 1$ . When deciding whether or not to pay a CSR price premium, these consumers only consider the information provided by third-party auditors (ignoring the CSR communication efforts undertaken by the firms). Hence, consumers in this first segment are willing to pay the CSR price premium $\left( \Delta \right)$ if, and only if, the firms invest in substantive CSR. In turn, consumers in the second segment do not use the information provided by the auditors (e.g., because they may not pay attention to this information), instead relying on the claims made through CSR communication efforts. Thus, this second consumer group (fraction $\xi$ of the market) pays a CSR price premium if, and only if, the firms invest in CSR communication. 考虑这样一种情况：第三方（例如评级机构，如MSCI或Refinitiv，或由活动人士领导的独立组织，如非政府组织）会审计审计公司的企业社会责任（CSR）活动，以确定每家公司选择的CSR参与类型（实质性或象征性）。这些审计程序的结果随后会分享给消费者，而消费者属于两个群体之一。第一个群体占消费者市场的比例为 \(1 - \xi\)（其中 \(0 < \xi < 1\)）。在决定是否支付CSR价格溢价时，这些消费者只考虑第三方审计机构提供的信息（忽略企业开展的CSR沟通工作）。因此，只有当企业进行实质性CSR投资时，第一个群体的消费者才愿意支付CSR价格溢价 \(\left( \Delta \right)\)。反过来，第二个群体的消费者不使用审计机构提供的信息（例如，因为他们可能不关注这些信息），而是依赖企业通过CSR沟通工作做出的声明。因此，第二个消费者群体（占市场比例 \(\xi\)）只有在企业进行CSR沟通投资时才会支付CSR价格溢价。

Therefore, note that $\xi = 0$ corresponds to a market where all consumers use exclusively the information provided by third-party auditors. In this case, CSR communication is completely irrelevant. On the other hand, the case with $\xi = 1$ implies that consumers’ decisions to pay a CSR price premium are based solely on the firms’ own claims, a situation wherein the third-party auditors are ignored by consumers. 因此，请注意，$\xi = 0$ 对应于一个所有消费者都完全依赖第三方审计机构提供的信息的市场。在这种情况下，企业社会责任（CSR）沟通完全无关紧要。另一方面，$\xi = 1$ 的情况意味着消费者决定支付企业社会责任价格溢价仅基于企业自身的声明，此时第三方审计机构被消费者忽视。

The first insight provided by this framework is that the firm may have incentives to engage in symbolic CSR, unless every consumer in the market has access to and uses the information provided by third-party auditors (i.e., unless $\xi = 0$ . Thus, while auditing may reduce a firm’s willingness to engage in symbolic CSR, the presence of third-party auditors alone cannot rule out symbolic CSR as an optimal strategic response for companies. One way to improve the effectiveness of third-party auditors is combining this auditing scheme with policies that increase CSR communication costs. As the presence of third-party auditors diminishes returns of CSR communication investments for symbolic purposes, when CSR communication is sufficiently costly, the firm may only be willing to invest in CSR communication if these efforts are combined with substantive actions. 该框架提供的第一个见解是，除非市场上的每个消费者都能获取并使用第三方审计机构提供的信息（即除非$\xi = 0$），否则企业可能有动机进行象征性企业社会责任（CSR）活动。因此，尽管审计可能会降低企业进行象征性CSR的意愿，但仅依靠第三方审计机构的存在并不能排除象征性CSR作为企业最优战略反应的可能性。提高第三方审计机构有效性的一种方法是将这种审计机制与增加CSR沟通成本的政策相结合。由于第三方审计机构的存在会削弱企业出于象征性目的进行CSR沟通投资的回报，当CSR沟通成本足够高时，企业只有在这些努力与实质性行动相结合的情况下才可能愿意投资于CSR沟通。

Therefore, policies aimed at establishing CSR reporting standards (e.g., Delmas & Burbano, 2011; Marquis & Qian, 2014)—as in the case of those proposed by the Global Reporting Initiative—or imposing specific CSR advertising requirements (e.g., Lyon & Maxwell, 2011) may help to discourage greenwashing, social washing, or other forms of symbolic CSR engagement by elevating CSR communication costs. It should be noted, however, that such policies would also penalize substantive CSR firms. Thus, these policies can only be an economically efficient option when combined with actions that reduce the returns of symbolic CSR, as in the case of the auditing activities discussed above.8 因此，旨在制定企业社会责任（CSR）报告标准的政策（例如Delmas & Burbano，2011；Marquis & Qian，2014）——如全球报告倡议组织（Global Reporting Initiative）提出的那些政策——或实施特定的企业社会责任广告要求（例如Lyon & Maxwell，2011），可能有助于通过提高企业社会责任沟通成本来阻止“漂绿”、“漂社”或其他形式的象征性企业社会责任参与行为。然而，需要注意的是，此类政策也会对实质性履行企业社会责任的企业造成惩罚。因此，只有在与降低象征性企业社会责任回报的行动（如上述讨论的审计活动）相结合时，这些政策才可能成为经济上高效的选择。8

A further approach to discourage symbolic engagement is decreasing the perceived (relative) costs of substantive CSR investments. For example, this may result from regulating negative externalities (e.g., Anand & Giraud-Carrier, 2020), and penalizing companies whose production processes generate excessive amounts of these externalities. Given the importance of this mechanism, the next subsection analyzes how it should affect a firm’s CSR engagement choices. 另一种抑制象征性参与的方法是降低实质性企业社会责任（CSR）投资的感知（相对）成本。例如，这可能源于对负外部性的监管（例如，Anand & Giraud-Carrier，2020），并对生产过程产生过多此类外部性的公司处以惩罚。鉴于这一机制的重要性，下一小节将分析它应如何影响企业的CSR参与选择。

Government Regulates Negative Socioenvironmental Externalities

政府监管负面社会环境外部性

This subsection discusses the regulation of negative socioenvironmental externalities as a means of discouraging symbolic CSR. More specifically, the subsection considers a case in which firms face a probability $0 < \theta < 1$ of being audited by government agencies that regulate negative externalities (e.g., pollution). When audited, firms that engage in symbolic CSR are penalized, paying a fixed amount $B > 0$ to the government. In turn, substantive CSR firms are not fined, as the framework assumes that substantive CSR sufficiently reduces negative productiongenerated externalities. In addition, the framework also assumes that the outcomes of the auditing process (i.e., being fined or not) are information available to consumers. 本节讨论如何通过规制负面社会环境外部性来阻止象征性企业社会责任（CSR）。更具体地说，本节考虑一种情况：企业面临被监管负面外部性（如污染）的政府机构审计的概率 \(0 < \theta < 1\)。如果被审计，从事象征性CSR的企业将受到处罚，需向政府支付固定金额 \(B > 0\)。相反，实质性CSR企业不会被罚款，因为该框架假设实质性CSR足以减少生产带来的负面外部性。此外，该框架还假设审计过程的结果（即是否被罚款）是消费者可获取的信息。

The consumer market is divided into two segments. A fraction $\sigma$ of consumers always reacts positively to CSR communication and is willing to pay the CSR price premium whenever firms invest (again, an amount $I _ { c } > 0$ in these activities. These consumers do not consider the information conveyed by government agencies, either because they cannot access it or simply because they trust the firms’ claims. The fraction $_ { 1 - \sigma }$ , in turn, is not sensitive to investments in CSR communication. Instead, these consumers have access to and always trust the information made public by the government agencies. Thus, this segment of consumers is willing to pay the CSR price premium if, and only if, an audited firm does not receive any fines (i.e., if it invests in substantive CSR). In other words, being audited is good for substantive CSR firms and bad for symbolic CSR companies. 消费市场分为两个细分群体。一部分消费者中的比例为$\sigma$，他们始终对企业社会责任（CSR）沟通持积极反应，并且只要企业（再次）在这些活动中投入了金额$I_c > 0$，他们就愿意为企业社会责任溢价支付费用。这些消费者不会考虑政府机构传达的信息，要么是因为他们无法获取这些信息，要么仅仅因为他们信任企业的声明。相反，比例为$1 - \sigma$的另一部分消费者对企业社会责任沟通的投入不敏感。这些消费者能够获取政府机构公开的信息，并且始终信任这些信息。因此，这部分消费者只有在企业通过审计且未收到任何罚款（即企业在实质性企业社会责任方面进行了投入）的情况下，才愿意支付企业社会责任溢价。换句话说，接受审计对实质性企业社会责任企业有利，而对象征性企业社会责任企业不利。

According to this alternative version of the model, government regulation of negative externalities may discourage symbolic CSR to the extent that it increases incentives for substantive CSR. However, if some consumers in the market ignore the government agencies, and fully trust the firms’ CSR communication efforts (i.e., if $\sigma > 0 \mathrm { i }$ ), this type of regulation alone cannot avoid symbolic CSR engagement. Interestingly, the effect of these regulations on a firm’s willingness to invest in CSR communication is nuanced (see Appendix A for further details). In short, when competitors do not invest in substantive CSR, externality regulations have no influence on the willingness to undertake CSR communication. On the other hand, if competitors do invest in substantive initiatives, the probability of being audited (θ) positively impacts a firm’s willingness to invest in CSR communication, if competitors also invest; and negatively impacts it, otherwise. Moreover, this version of the model implies a similar role for CSR communication costs. Thus, again, policies that elevate these costs (as in the case of CSR reporting standards) may play a key role in ruling out symbolic CSR as a strategic choice for firms. 根据该模型的另一种版本，政府对负外部性的监管可能会在一定程度上抑制象征性企业社会责任（CSR），因为这会增加实质性CSR的激励。然而，如果市场中的一些消费者忽视政府机构，并且完全信任企业的CSR沟通努力（即如果σ > 0），那么仅靠这种监管无法避免象征性CSR参与。有趣的是，这些监管对企业进行CSR沟通的意愿的影响较为微妙（更多细节见附录A）。简而言之，当竞争对手不投入实质性CSR时，外部性监管对企业进行CSR沟通的意愿没有影响。另一方面，如果竞争对手确实投入实质性举措，那么被审计的概率（θ）会在竞争对手也投入时对企业进行CSR沟通的意愿产生正向影响，而在竞争对手不投入时产生负向影响。此外，该模型版本表明CSR沟通成本也具有类似作用。因此，再次强调，提高这些成本的政策（如CSR报告标准）可能在排除企业将象征性CSR作为战略选择方面发挥关键作用。

Furthermore, it might be useful to compare the effectiveness of the two mechanisms discussed in this section. To that end, assume that the probabilities of consumers using information provided by third-party auditors $( 1 - \xi )$ and by government agencies $( 1 - \sigma )$ are equal. Under these conditions, the framework suggests that auditing of CSR activities by third parties may be more effective in curbing symbolic CSR (relative to the regulation of negative externalities), in industries where substantive CSR is the norm. As detailed in Appendix A, when competitors engage in substantive CSR, the probability of not being penalized for symbolic CSR engagement $( 1 - \theta )$ creates a relative advantage for the firm in case it does not invest in substantive CSR: because the firm might not be audited by the government, it might be able to economize on substantive investments and still avoid the penalties imposed by the government agencies. This relative advantage then increases the firm’s willingness to invest in CSR communication for symbolic purposes. 此外，或许有必要比较本节讨论的两种机制的有效性。为此，假设消费者使用第三方审计机构提供的信息的概率为 $(1 - \xi)$，使用政府机构提供的信息的概率为 $(1 - \sigma)$，且这两个概率相等。在这些条件下，该框架表明，在实质性企业社会责任（CSR）成为行业常态的情况下，第三方对企业社会责任活动的审计可能比对负面外部性的监管更能有效抑制象征性企业社会责任。如附录 A 所述，当竞争对手开展实质性企业社会责任活动时，因象征性企业社会责任参与而不被处罚的概率 $(1 - \theta)$ 会使企业在不进行实质性企业社会责任投资时获得相对优势：因为企业可能不会受到政府的审计，它可能能够节省实质性投资，同时仍避免政府机构施加的处罚。这种相对优势随后会增加企业为象征性目的进行企业社会责任沟通的意愿。

Generally speaking, a key message from this section is that all forms of symbolic CSR, including greenwashing and social washing, could be discouraged if the two main mechanisms discussed here (auditing of CSR activities by third parties and regulation of negative externalities by government agencies) are used in tandem with policies that elevate the costs of CSR communication. These policies may not only increase firms’ transparency (e.g., Delmas & Burbano, 2011; Lyon & Maxwell, 2011), but impose additional costs that reduce the expected returns of CSR engagement, thereby rendering symbolic CSR infeasible. 一般而言，本节的核心信息是，如果将此处讨论的两个主要机制（第三方对企业社会责任活动的审计以及政府机构对负外部性的监管）与提高企业社会责任沟通成本的政策结合使用，那么包括“漂绿”和“社会洗白”在内的所有形式的象征性企业社会责任行为都可能受到抑制。这些政策不仅可能提高企业的透明度（例如，Delmas & Burbano，2011；Lyon & Maxwell，2011），还会带来额外成本，降低企业参与企业社会责任的预期回报，从而使象征性企业社会责任行为不可行。

However, it is crucial to note, once more, that policies on CSR communication may also create economic inefficiencies. In particular, these inefficiencies will be substantially high if such policies are adopted in isolation, or if the two previously discussed mechanisms (i.e., auditing of CSR activities and regulation of negative externalities) are ineffective—for example, when a large segment of consumers fails to access relevant information provided by third-party auditors or government agencies. Therefore, effectively and efficiently discouraging symbolic CSR may depend on coordinated efforts by several social actors, including third-party auditors, government agencies, and policy-makers. 然而，必须再次强调，企业社会责任（CSR）传播政策也可能产生经济效率低下的问题。特别是，如果这类政策被孤立地采纳，或者前面讨论的两种机制（即对企业社会责任活动的审计以及对负外部性的监管）失效——例如，当很大一部分消费者无法获取第三方审计机构或政府机构提供的相关信息时——这些效率低下的问题将变得非常严重。因此，有效且高效地阻止象征性的企业社会责任行为可能需要多个社会行为体的协同努力，包括第三方审计机构、政府机构和政策制定者。

DISCUSSION AND CONCLUSIONS

讨论与结论

Substantive CSR is an important channel through which corporate socioenvironmental action materializes (Hawn & Ioannou, 2016; Kaul & Luo, 2018, 2019; Morgan & Tumlinson, 2019). Reflecting this view, a growing body of research has sought to understand what motivates firms to pursue substantive—as opposed to merely symbolic—CSR engagement (Cuypers et al., 2016; Durand et al., 2019; Haack, Martignoni, & Schoeneborn, 2021; Li & Wu, 2020; Luo et al., 2018; Marquis & Qian, 2014; Marquis et al., 2016; Schons & Steinmeier, 2016). Departing from the insight that the CSR price premium is a key economic driver of CSR investments (Barnett, 2007; Flammer, 2015; Kaul & Luo, 2018; Luo & Bhattacharya, 2006; Martin, 2019; McWilliams & Siegel, 2001), this paper proposes a formal model with which to examine whether and how a CSR price premium influences the type of CSR engagement—substantive or symbolic—that a firm selects. 实质性企业社会责任（CSR）是企业社会环境行动得以实现的重要渠道（Hawn & Ioannou, 2016；Kaul & Luo, 2018, 2019；Morgan & Tumlinson, 2019）。基于这一观点，越来越多的研究试图理解是什么促使企业追求实质性而非仅仅象征性的CSR参与（Cuypers et al., 2016；Durand et al., 2019；Haack, Martignoni, & Schoeneborn, 2021；Li & Wu, 2020；Luo et al., 2018；Marquis & Qian, 2014；Marquis et al., 2016；Schons & Steinmeier, 2016）。本研究借鉴CSR价格溢价是CSR投资的关键经济驱动力这一见解（Barnett, 2007；Flammer, 2015；Kaul & Luo, 2018；Luo & Bhattacharya, 2006；Martin, 2019；McWilliams & Siegel, 2001），提出一个正式模型，以考察CSR价格溢价是否以及如何影响企业选择的CSR参与类型——实质性或象征性。

According to the proposed model, the CSR price premium positively impacts a firm’s willingness to invest in substantive CSR if a segment of the consumer market either (a) values and scrutinizes the quality of the CSR communication efforts undertaken by the firms, or (b) monitors the negative socioenvironmental externalities generated by each firm. This finding adds to the extant research on the determinants of substantive CSR engagement (e.g., Cuypers et al., 2016; Durand et al., 2019; Marquis & Qian, 2014) by specifying conditions under which the CSR price premium functions as an enabler of substantive CSR. Under these conditions, consumers’ willingness to pay for CSR motivates substantive (and discourages symbolic) CSR engagement. 根据所提出的模型，如果消费者市场中的一部分群体（a）重视并审视企业开展的企业社会责任（CSR）沟通活动的质量，或者（b）监督每家企业产生的负面社会环境外部性，那么企业社会责任（CSR）的价格溢价会对企业进行实质性企业社会责任投资的意愿产生积极影响。这一发现通过明确企业社会责任价格溢价在何种条件下能成为实质性企业社会责任的推动因素，为现有关于实质性企业社会责任参与决定因素的研究（例如Cuypers等人，2016年；Durand等人，2019年；Marquis & Qian，2014年）提供了补充。在这些条件下，消费者为企业社会责任支付溢价的意愿会激励实质性（而非象征性）的企业社会责任参与。

This result also emphasizes the importance of demand-side heterogeneity. If the consumer market fails to fulfill both conditions (a) and (b), the CSR price premium creates incentives for symbolic CSR. In such a market, symbolic CSR and its various forms, including greenwashing (e.g., Delmas & Burbano, 2011; Kim & Lyon, 2015) and social washing (Marsh, 2020), may be particularly pervasive. Thus, this paper reinforces the theoretical relevance of demand-side factors in contexts where organizations care about socioenvironmental externalities and impact (e.g., Lazzarini, 2020). 这一结果还强调了需求侧异质性的重要性。如果消费市场未能满足条件（a）和（b），企业社会责任（CSR）的价格溢价会催生象征性企业社会责任的动机。在这样的市场中，象征性企业社会责任及其各种形式（包括漂绿行为，例如Delmas & Burbano，2011；Kim & Lyon，2015）和社会洗白行为（Marsh，2020）可能尤为普遍。因此，本文强化了在组织关注社会环境外部性和影响的情境下，需求侧因素的理论相关性（例如Lazzarini，2020）。

In addition, the paper argues that the enabling effect of the CSR price premium, observed when at least one of the above conditions holds, is also verified when competitors engage in substantive CSR. Yet, according to Proposition 4, if a segment of consumers scrutinizes the quality of external CSR, the effect of the CSR price premium is reduced by competitors’ choice to invest in substantive CSR. Broadly speaking, this finding seemingly contrasts with past studies arguing that firms tend to replicate the pattern of CSR engagement selected by competitors (e.g., Cao et al., 2019; Ioannou & Serafeim, 2018). From the point of view of the economic incentives implied by a CSR price premium, the model suggests that firms should be less willing to engage in substantive CSR when their competitors already do that (provided, of course, that at least some consumers scrutinize the quality of CSR communication). 此外，该论文认为，当上述条件中至少有一个成立时观察到的企业社会责任（CSR）价格溢价的促进作用，在竞争对手开展实质性企业社会责任活动时也得到了验证。然而，根据命题4，如果一部分消费者仔细审视外部企业社会责任的质量，那么竞争对手选择投入实质性企业社会责任的行为会削弱企业社会责任价格溢价的效果。从广义上讲，这一发现似乎与以往认为企业倾向于复制竞争对手选择的企业社会责任参与模式的研究（例如，Cao等人，2019；Ioannou & Serafeim，2018）相矛盾。从企业社会责任价格溢价所隐含的经济激励的角度来看，该模型表明，当竞争对手已经开展实质性企业社会责任活动时，企业应不太愿意参与此类活动（当然，前提是至少有部分消费者会仔细审视企业社会责任沟通的质量）。

On the other hand, Lemma 2 (see Appendix A for further details) indicates that markets where buyers indistinctively pay a CSR price premium (i.e., with no scrutiny of CSR communication) are more compatible with the previously described pattern of within-industry peer effect. In this latter case, competitors’ CSR engagement choices do not influence the effect of the CSR price premium, meaning that firms may be more prone to condition their CSR engagement choices on other factors, such as industrylevel pressures for conformity (e.g., Ioannou & Serafeim, 2018; Zhang, Wang, & Zhou, 2020). Thus, if, on the one hand, a lower scrutiny of CSR communication quality may reduce incentives for a given firm to invest in substantive CSR (e.g., as per Proposition 1b), on the other hand, it may increase the likelihood that substantive CSR becomes the industry norm. This insight suggests that consumers’ (or, more generally, stakeholders’) scrutiny of CSR communication quality may be another mechanism to influence the incentives for conformity and differentiation in CSR (e.g., Ioannou & Serafeim, 2018; Zhang et al., 2020). 另一方面，引理 2（进一步细节见附录 A）表明，买方不加区分地支付企业社会责任（CSR）价格溢价的市场（即对企业社会责任沟通不加审查），与之前描述的行业内同伴效应模式更为兼容。在后一种情况下，竞争对手的企业社会责任参与选择不会影响企业社会责任价格溢价的效果，这意味着企业可能更倾向于根据其他因素（例如行业层面的从众压力，Ioannou & Serafeim, 2018；Zhang, Wang, & Zhou, 2020）来调整其企业社会责任参与选择。因此，一方面，对企业社会责任沟通质量的较低审查可能会降低某一特定企业在实质性企业社会责任方面的投资激励（例如，根据命题 1b），另一方面，它可能会增加实质性企业社会责任成为行业规范的可能性。这一见解表明，消费者（或更广泛地说，利益相关者）对企业社会责任沟通质量的审查可能是影响企业社会责任中从众与差异化激励的另一种机制（Ioannou & Serafeim, 2018；Zhang et al., 2020）。

Furthermore, the paper also studies how the enabling effect of the CSR price premium is moderated by two key factors known to influence firms’ CSR engagement choices: monitoring intensity (e.g. Durand et al., 2019; Lyon & Montgomery, 2015; Marquis & Qian, 2014) and product differentiation (e.g., Duanmu et al., 2018; Flammer, 2015; Kaul & Luo, 2018). In order to facilitate the discussion of these moderating effects, Table 1 summarizes the role played by each of them, also considering competitors’ CSR engagement choices. 此外，本文还研究了企业社会责任（CSR）价格溢价的促进作用如何受到两个已知影响企业CSR参与选择的关键因素的调节：监督强度（例如 Durand 等人，2019；Lyon & Montgomery，2015；Marquis & Qian，2014）和产品差异化（例如 Duanmu 等人，2018；Flammer，2015；Kaul & Luo，2018）。为便于讨论这些调节效应，表1总结了每个因素的作用，同时也考虑了竞争对手的CSR参与选择。

The first row of Table 1 describes the effect of monitoring intensity. As mentioned above, while much of the extant literature argues that stakeholders’ monitoring activity is a crucial driver of substantive engagement (Delmas & Burbano, 2011; Luo et al., 2018), scholars tend to assume that a higher monitoring intensity is positively associated with firms’ willingness to undertake substantive socioenvironmental actions (e.g., Campbell, 2007; Delmas & Burbano, 2011; Durand et al., 2019; Lyon & Montgomery, 2015; Marquis & Qian, 2014). Possibly, this more linear (and monotonic) approach to the role of monitoring results from a failure to more explicitly account for the fact that substantive socioenvironmental initiatives are heterogeneous in their capacity to benefit society—for instance, by abating negative externalities. By directly modeling this heterogeneity, the framework proposed in this paper shows that the monotonic relationship implied by previous work may not always be observed. 表1的第一行描述了监督强度的影响。如前所述，尽管大量现有文献认为利益相关者的监督活动是实质性参与的关键驱动力（Delmas & Burbano, 2011；Luo et al., 2018），但学者们往往假设更高的监督强度与企业采取实质性社会环境行动的意愿呈正相关（例如，Campbell, 2007；Delmas & Burbano, 2011；Durand et al., 2019；Lyon & Montgomery, 2015；Marquis & Qian, 2014）。可能的是，这种对监督作用更线性（且单调）的分析方法源于未能更明确地考虑到实质性社会环境倡议在造福社会的能力上存在异质性——例如，通过减少负外部性。通过直接建模这种异质性，本文提出的框架表明，先前研究暗示的单调关系可能并不总是存在。

TABLE 1 Monitoring Intensity, Product Differentiation, and the Enabling Effect of the CSR Price Premium
表1 监测强度、产品差异化及企业社会责任价格溢价的赋能效应

More specifically, according to Proposition 2 (summarized in the top-left panel of Table 1), when substantive CSR leads to small reductions in negative externalities, an increase in monitoring intensity reduces the enabling effect of the CSR price premium. As mentioned above, this results from a trade-off between the productivity gains and externality reduction, which becomes more salient if substantive CSR only mildly abates negative externalities. Consequently, when monitoring intensity is excessively high, a firm’s willingness to make substantive CSR investments with lower societal benefits will be less sensitive to a CSR price premium. Since monitoring intensity tends to be higher in contexts where socioenvironmental externalities are more problematic (e.g., Kassinis & Vafeas, 2006), this result suggests that higher monitoring can reduce incentives for substantive CSR—or, put differently, increase incentives for symbolic engagement—precisely where substantive investments can be particularly socially desirable (and symbolic CSR can be particularly harmful). 更具体地说，根据命题2（总结于表1左上角面板），当实质性企业社会责任（CSR）仅导致负外部性的小幅减少时，监管强度的增加会削弱CSR价格溢价的促进效应。如前所述，这一结果源于生产率提升与外部性减少之间的权衡，而当实质性CSR仅轻微缓解负外部性时，这种权衡会更加突出。因此，当监管强度过高时，企业进行社会收益较低的实质性CSR投资的意愿对CSR价格溢价的敏感度会降低。由于在社会环境外部性问题更严重的情境中，监管强度往往更高（例如，Kassinis & Vafeas, 2006），这一结果表明，在实质性投资可能特别具有社会价值（而象征性CSR可能特别有害）的地方，更高的监管可以减少对实质性CSR的激励——或者换句话说，增加对象征性参与的激励。

The top-right panel of Table 1, in turn, summarizes Proposition 5. Essentially, this proposition suggests that, when competitors ex ante engage in substantive CSR, the role of monitoring intensity becomes even more nuanced. In this case, in addition to the externality reductions generated by substantive CSR, the size of the segment of consumers who scrutinize CSR communication quality also becomes a critical parameter of interest. This is because, after investing in substantive CSR (when its competitor also invests), the firm’s production can be excessively high if a sufficiently large proportion of consumers scrutinizes CSR communication quality. This higher production level makes the trade-off between productivity gains and externality reduction more salient, which then implies that higher monitoring intensity may reduce the effect of the CSR price premium. Connecting with the previous discussion, these findings show that the role of monitoring in inducing substantive CSR can be much more nuanced than the previous literature seems to imply. Monitoring intensity and firms’ willingness to engage in substantive socioenvironmental action are not always positively related; on the contrary, as shown by Proposition 5, even conditions that favor substantive CSR may influence this relationship. Table 1右上角的面板依次总结了命题5。本质上，该命题表明，当竞争对手事先开展实质性企业社会责任（CSR）时，监督强度的作用会变得更加微妙。在这种情况下，除了实质性CSR带来的外部性减少外，仔细审视CSR沟通质量的消费者群体规模也成为一个关键的关注参数。这是因为，在企业投入实质性CSR后（且其竞争对手也投入时），如果有足够大比例的消费者审视CSR沟通质量，企业的产量可能会过高。这种更高的产量水平会使生产率提升与外部性减少之间的权衡更加突出，这意味着更高的监督强度可能会降低CSR价格溢价的效果。结合之前的讨论，这些发现表明，监督在诱导实质性CSR方面的作用可能比以往文献所暗示的要微妙得多。监督强度与企业参与实质性社会环境行动的意愿并不总是正相关；相反，正如命题5所示，即使是有利于实质性CSR的条件也可能影响这种关系。

The bottom row of Table 1, on the other hand, describes the moderating effects of product differentiation. Consistent with previous discussions, the literature on differentiation and CSR engagement is marked by seemingly conflicting findings. For example, while past studies show that an increase in differentiation worsens socioenvironmental performance (e.g., Fernández-Kranz & Santaló, 2010; Flammer, 2015), some recent work, more focused on cost-oriented settings, points to the opposite direction (Duanmu et al., 2018). Still other theoretical work argues that firms in more differentiated industries may be more willing to engage in substantive CSR (Kaul & Luo, 2018). 另一方面，表1的最下面一行描述了产品差异化的调节效应。与之前的讨论一致，关于差异化和企业社会责任（CSR）参与的文献呈现出看似矛盾的研究结果。例如，过去的研究表明，差异化程度的提高会恶化社会环境绩效（例如，Fernández-Kranz & Santaló，2010；Flammer，2015），但一些更侧重于成本导向环境的近期研究却得出了相反的结论（Duanmu等人，2018）。还有一些理论研究认为，处于差异化程度更高的行业中的企业可能更愿意开展实质性的CSR（Kaul & Luo，2018）。

This paper contributes to this debate, firstly, by providing a general model that more precisely tease out the marginal effects of product differentiation. Second, the framework also contributes by showing that the economic incentives for substantive CSR can vary with product differentiation in a non-monotonic fashion, which may indicate that the findings of previous studies tell only part of the story. Indeed, according to Proposition 3 (summarized in the bottom-left panel of Table 1), when competitors engage in symbolic CSR, product differentiation strengthens the effect of the CSR price premium in high-differentiation settings but weakens it in more competitive markets. Hence, the model suggests that the negative effect of differentiation on socioenvironmental performance reported in past studies (e.g., Fernández-Kranz & Santaló, 2010) is consistent with the case of low-differentiation industries marked by relatively poor socioenvironmental performance. 本文为这场辩论做出了贡献，首先，通过提供一个更精确地梳理产品差异化边际效应的通用模型。其次，该框架还表明，实质性企业社会责任（CSR）的经济激励可能会以非单调的方式随产品差异化而变化，这可能表明先前研究的发现只讲述了部分情况。事实上，根据命题3（总结于表1左下角面板），当竞争对手进行象征性企业社会责任时，在高差异化环境中，产品差异化会增强企业社会责任价格溢价的影响，而在竞争更激烈的市场中则会削弱这种影响。因此，该模型表明，过去研究中报告的差异化对社会环境绩效的负面影响（例如，Fernández-Kranz & Santaló，2010）与低差异化行业的情况一致，这些行业的社会环境绩效相对较差。

However, the model also suggests that this result should be less likely in highly differentiated markets with poor social performance. Similar arguments could be made about the relationship between differentiation and firms’ willingness to use CSR as a differentiation strategy (e.g., Flammer, 2015; Hawn & Kang, 2015): according to the proposed model, in highly differentiated markets with relatively poor socioenvironmental performance, firms should be less willing to engage in substantive CSR as a means of differentiation. Moreover, as these nuances may be obscured by an exclusive focus on average effects—the dominant approach in the literature, with some rare exceptions (e.g., Duanmu et al., 2018)—the more refined insights offered by the framework developed in this paper may be fruitfully explored by empiricists in the future. 然而，该模型还表明，在高度差异化且社会绩效不佳的市场中，这种结果的可能性较低。关于差异化与企业将企业社会责任（CSR）作为差异化战略的意愿之间的关系，也可以提出类似的论点（例如，Flammer，2015；Hawn & Kang，2015）：根据所提出的模型，在社会环境绩效相对较差的高度差异化市场中，企业应该不太愿意将实质性企业社会责任作为差异化手段。此外，由于这些细微差别可能会被对平均效应的排他性关注所掩盖——这是文献中的主流方法，只有少数例外（例如，Duanmu等人，2018）——本文开发的框架所提供的更精细见解可能会在未来被经验主义者有效地探索。

On the other side, if competitors also engage in substantive CSR, Proposition 6 (summarized in the bottom-right corner of Table 1) suggests that the role of product differentiation may change, in the case of low-differentiation settings. Since price effects become much more relevant in this scenario, under conditions that make the productivity gains of substantive CSR sufficiently large—that is, a high capacity to abate negative externalities coupled with a large segment of consumers who scrutinize CSR communication quality—product differentiation magnifies the enabling effect of the CSR price premium, even in markets with higher competition levels. This result complements past theories (e.g., Kaul & Luo, 2018) by identifying a more specific and unambiguous set of conditions under which product differentiation may undermine incentives for substantive (and favor the rise of symbolic) CSR. The latter result also shows that the marginal effects that Duanmu et al. (2018) found for the case of more costoriented Chinese firms can also be consistent with high-differentiation industries marked by high socioenvironmental performance, so long as the productivity gains implied by substantive CSR are sufficiently large. Yet, this result may not be expected in general: as Lemma 4 argues (see Appendix A), a relatively small segment of consumers scrutinizing CSR communication quality is a sufficient condition for the marginal effect of product differentiation to be reversed—again, in line with Proposition 3. 另一方面，如果竞争对手也开展实质性的企业社会责任（CSR）活动，命题6（总结于表1的右下角）表明，在低差异化的市场环境下，产品差异化的作用可能会发生变化。由于在这种情况下价格效应变得更为重要，当实质性CSR带来的生产率提升足够大时——即具备较高的减少负面外部性的能力，同时有大量消费者关注CSR沟通质量——产品差异化会放大CSR价格溢价的促进作用，即使在竞争水平较高的市场中也是如此。这一结果补充了以往的理论（例如，Kaul & Luo, 2018），明确了在哪些条件下产品差异化可能削弱开展实质性CSR的激励（并助长象征性CSR的兴起）。后一结果还表明，Duanmu等人（2018）针对更注重成本的中国企业案例发现的边际效应，在以高社会环境绩效为显著特征的高差异化行业中也可能成立，只要实质性CSR带来的生产率提升足够大。然而，这一结果并非普遍适用：正如引理4所论证的（见附录A），只要有相对较小比例的消费者关注CSR沟通质量，产品差异化的边际效应就会逆转——这再次与命题3一致。

In a further application of the proposed model, this study also examined how symbolic CSR may be discouraged through orchestrated efforts of thirdparty auditors, government agencies that monitor and regulate negative externalities, and policymakers. According to those analyses, both auditing of CSR activities by third parties and externality regulation reduce a firm’s willingness to engage in symbolic CSR. Yet, in contexts where competitors engage in substantive CSR, the former mechanism tends to be more effective than the latter: the probability of not being audited by the government creates a relative advantage for a symbolic CSR firm visà-vis substantive CSR competitors (i.e., the firm might not be punished, despite avoiding investments in substantive activities), which increases its willingness to undertake CSR communication for symbolic purposes. At the same time, this paper also suggests that the two mechanisms mentioned above may not rule out symbolic CSR as a best response for firms. If CSR communication is sufficiently low cost, firms may still be prone to engage in symbolic CSR— in its various forms, including greenwashing, “pink” washing, or social washing more generally. 在对所提出模型的进一步应用中，本研究还考察了符号化企业社会责任（CSR）如何通过第三方审计机构、监督和规范负外部性的政府机构以及政策制定者的精心安排而受到抑制。根据这些分析，第三方对CSR活动的审计和外部性监管都会降低企业参与符号化CSR的意愿。然而，在竞争对手开展实质性CSR的情境中，前者机制往往比后者更有效：企业不被政府审计的可能性会为符号化CSR企业相对于实质性CSR竞争对手创造相对优势（即，该企业可能不会受到惩罚，尽管它避免了在实质性活动上的投资），这增加了其为符号化目的开展CSR沟通的意愿。同时，本文还表明，上述两种机制可能不会排除符号化CSR作为企业的最佳应对策略。如果CSR沟通的成本足够低，企业可能仍然倾向于参与符号化CSR——包括绿色洗绿、“粉色”洗绿或更广泛意义上的社会洗绿等各种形式。

Therefore, the paper also suggests that avoiding symbolic CSR engagement as a feasible strategic response for firms may depend on policies that increase CSR communication costs—such as the adoption and enforcement of Global Reporting Initiative standards for CSR reporting. This insight indicates that the role of this type of policy in mitigating symbolic engagement may be more relevant than acknowledged by the previous literature. 因此，本文还表明，企业避免象征性的企业社会责任（CSR）参与作为一种可行的战略回应，可能取决于增加CSR沟通成本的政策——例如采用和执行全球报告倡议组织（GRI）的CSR报告标准。这一见解表明，这类政策在缓解象征性参与方面的作用可能比先前文献所承认的更为重要。

Indeed, previous work emphasized how policies on CSR-related communication can curb greenwashing and other forms of symbolic engagement by avoiding selective disclosure (e.g., Delmas & Burbano, 2011; Lyon & Maxwell, 2011; Marquis & Qian, 2014). This paper, in contrast, shows that these policies may also be important to the extent that they increase the perceived costs of CSR communication and reduce the expected returns of CSR engagement. Thus, when combined with auditing of firms’ CSR activities or regulation of negative externalities, policies that elevate the costs of CSR communication may diminish the expected returns of symbolic CSR in such a way that firms are never willing to engage in this type of CSR. On the other hand, in the absence of these policies, if CSR communication is sufficiently low cost, firms may be willing to engage in symbolic CSR even if they are subject to auditing of CSR activities or externality regulation. 事实上，先前的研究强调了与企业社会责任（CSR）相关的沟通政策如何通过避免选择性披露来遏制漂绿行为和其他形式的象征性参与（例如，Delmas & Burbano，2011；Lyon & Maxwell，2011；Marquis & Qian，2014）。相比之下，本文表明，这些政策在一定程度上也可能很重要，即它们会增加企业社会责任沟通的感知成本，并降低企业社会责任参与的预期回报。因此，当与企业社会责任活动的审计或负外部性的监管相结合时，提高企业社会责任沟通成本的政策可能会降低象征性企业社会责任的预期回报，以至于企业永远不愿意参与这种类型的企业社会责任。另一方面，在缺乏这些政策的情况下，如果企业社会责任沟通的成本足够低，企业即使受到企业社会责任活动审计或外部性监管，也可能愿意参与象征性企业社会责任。

However, despite this important role, these policies also have a downside: they reduce economic efficiency by unnecessarily increasing CSR communication costs for substantive CSR firms. Therefore, from a policy perspective, it seems crucial to combine regulation on CSR communication with other mechanisms that reduce the expected returns of symbolic CSR engagement (e.g., auditing of CSR initiatives, regulation of negative socioenvironmental externalities, and so forth). In this case, a small elevation in CSR communication costs (with an equally small reduction in economic efficiency) may be sufficient to completely avoid symbolic firm responses. 然而，尽管这些政策发挥着重要作用，但它们也存在弊端：它们通过不必要地增加实质性企业社会责任（CSR）企业的CSR沟通成本，降低了经济效率。因此，从政策角度来看，将对CSR沟通的监管与其他降低象征性CSR参与预期回报的机制相结合似乎至关重要（例如，对CSR举措的审计、对负面社会环境外部性的监管等）。在这种情况下，CSR沟通成本的小幅上升（同时经济效率的小幅下降）可能足以完全避免企业的象征性回应。

While this work contributes to several theoretical conversations, it also informs management practice. Firstly, knowledge of the various mechanisms that could render substantive CSR engagement less profitable may interest managers seeking to create and support more socially impactful CSR programs. For example, if these mechanisms are active, pursuing socially impactful CSR might demand sacrifices and additional managerial effort. Thus, managers may benefit from understanding these mechanisms (and their relevant implications) ex ante, and adjusting their decisions accordingly, which could also have positive implications from a societal perspective—that is, prosocial managers could be more effective in advancing socially impactful CSR initiatives even in contexts where these investments are less financially attractive. 虽然这项工作有助于多个理论对话，但它也为管理实践提供了参考。首先，了解各种可能使实质性企业社会责任（CSR）参与度盈利能力降低的机制，可能会引起那些寻求创建和支持更具社会影响力的CSR项目的管理者的兴趣。例如，如果这些机制起作用，追求具有社会影响力的CSR可能需要做出牺牲和额外的管理努力。因此，管理者可能会从事前了解这些机制（及其相关影响）并相应调整决策中受益，这也可能从社会角度产生积极影响——也就是说，亲社会的管理者即使在这些投资财务吸引力较低的情况下，也可能更有效地推进具有社会影响力的CSR举措。

Additionally, the framework proposed in this paper not only indicates various scenarios in which symbolic CSR—in all its forms, including green or social washing—is more likely to prevail, but also offers some insight into how it can be discouraged. 此外，本文提出的框架不仅指出了各种情境，在这些情境中象征性企业社会责任（包括绿色或社会洗绿在内的所有形式）更有可能盛行，还提供了一些关于如何抑制这种行为的见解。

Activists and organizations that monitor firms’ socioenvironmental performance, as well as policymakers, may be particularly interested in these ideas and insights, as they may help these actors increase the effectiveness of their actions. Lastly, policymakers and third-party monitors should also be aware of the potential shortcomings of more intensive monitoring activity, as suggested by Propositions 2 and 5. For instance, in contexts where reducing negative externalities is particularly challenging, increasing the intensity of monitoring efforts may not be the better choice—a counterintuitive insight generated by the model developed in this article. 关注企业社会环境绩效的活动人士和组织，以及政策制定者，可能会特别关注这些理念和见解，因为它们可能有助于这些行为体提高行动的有效性。最后，政策制定者和第三方监督机构也应意识到更密集的监督活动可能存在的潜在不足，这一点在命题2和命题5中已有说明。例如，在减少负面外部性特别困难的情况下，增加监督工作的强度可能不是更好的选择——这是本文开发的模型产生的一个反直觉见解。

Furthermore, there are several ways in which the framework presented here could be extended. A particularly important extension to the baseline model pertains to the possibility of both firms choosing their CSR engagement modes simultaneously. Appendix A discusses how the baseline framework can be adapted to account for this possibility. In essence, if firms are allowed to make simultaneous choices, the actual costs of substantive CSR (represented by $I _ { S } )$ become even more relevant. When these costs are excessively large, no firm invests in substantive CSR. At moderate levels of $I _ { S }$ , only one of the firms undertakes substantive CSR—a situation that corresponds to the first case of the baseline model (where the competitor’s choice was always symbolic engagement). Lastly, if $I _ { S }$ is sufficiently low, at least one of the firms always engages in substantive CSR—a case analogous to the second scenario examined in the paper (where the competitor ex ante engaged in substantive CSR). Therefore, it is reasonable to conclude that the slightly more complicated version of the framework that includes simultaneous choices does not offer much additional insight, when compared to the baseline version discussed in the paper. 此外，本文提出的框架还有几种可以扩展的方式。对基准模型而言，一个特别重要的扩展是两家企业都能同时选择其企业社会责任（CSR）参与模式的可能性。附录A讨论了如何调整基准框架以考虑这种可能性。本质上，如果允许企业同时做出选择，实质性CSR的实际成本（以\( I_S \)表示）就会变得更加重要。当这些成本过高时，没有企业会投资于实质性CSR。当\( I_S \)处于中等水平时，只有一家企业会开展实质性CSR——这种情况对应基准模型的第一种情况（即竞争对手的选择始终是象征性参与）。最后，如果\( I_S \)足够低，至少有一家企业会始终参与实质性CSR——这种情况类似于本文研究的第二种情景（即竞争对手事先已参与实质性CSR）。因此，有理由得出结论：与本文讨论的基准版本相比，包含同时选择的框架稍微复杂一点的版本并没有提供太多额外的见解。

In addition, while the framework presented in this paper allows for a comprehensive analysis of the economic incentives for substantive CSR engagement, in practice, firms’ responses to these incentives can be shaped by other factors not directly included in the model. For example, institutional pressures for conformity (e.g., Zhang et al., 2020), behavioral factors (e.g., Nason et al., 2018), or moral considerations (e.g., Martin, 2019; Schuler & Cording, 2006) could affect firms’ willingness to react to the incentives posed by a CSR price premium, potentially influencing some of the model’s predictions. Exploring how each of these conditions affects firms’ responses to the economic incentives for substantive or symbolic CSR may be a fruitful avenue for future research suggested by this paper. 此外，虽然本文提出的框架能够全面分析实质性企业社会责任（CSR）参与的经济激励因素，但在实践中，企业对这些激励的反应可能受到模型中未直接包含的其他因素的影响。例如，从众的制度压力（如 Zhang 等人，2020）、行为因素（如 Nason 等人，2018）或道德考量（如 Martin，2019；Schuler & Cording，2006）可能会影响企业对 CSR 价格溢价所带来的激励做出反应的意愿，从而可能影响模型的某些预测。本文提出，探索这些条件中的每一个如何影响企业对实质性或象征性 CSR 的经济激励的反应，可能是未来研究的一个富有成效的方向。

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APPENDIX A: MODEL DEVELOPMENT, PROOFS, AND EXTENSIONS

附录 A：模型开发、证明与扩展

When Competitors Engage in Symbolic CSR Two firms $F$ and $C$ compete in a differentiated Cournot duopoly. Consumers’ utility is described by Equation (1). The timeline of the model is described in the main text. Equation (1) implies the following willingness to pay: 当竞争对手开展象征性企业社会责任（CSR）时，两家企业 \( F \) 和 \( C \) 在差异化古诺双寡头市场中竞争。消费者效用由式（1）描述。模型的时间线在正文中描述。式（1）意味着以下支付意愿：

\begin{array} { c } { { P _ { F } ^ { S } = A + \Delta - q _ { F } - \gamma q _ { C } - p \varphi / a } } \ { { P _ { i } ^ { R } = A + \tau \Delta - q _ { i } - \gamma q _ { j } - p \varphi } } \end{array}

where $i = F$ or $C , j = - i , S$ denotes the choice to invest in substantive CSR initiatives, and $R$ denotes the case in which no such investments are made. Two conditions are further assumed: 其中 \( i = F \) 或 \( C \)，\( j = -i \)，\( S \) 表示选择投资实质性企业社会责任（CSR）举措的情况，而 \( R \) 表示未进行此类投资的情况。此外还假设两个条件：

\mathrm { A s s u m p t i o n \ 1 : \ } A > \frac { ( 2 a - \gamma ) } { a } J + ( 2 - \tau \gamma ) \Delta > 0 \mathrm{假设1：} A > \frac{(2a - \gamma)}{a} J + (2 - \tau \gamma) \Delta > 0

where $J \equiv p \varphi$ .In essence, Assumption 1 ensures that both firms produce positive quantities irrespective of ${ \boldsymbol { F } } { \boldsymbol { s } }$ decision to invest in substantive CSR, while Assumption 2 simply restricts the parameter space. Using these expressions, the profit function of each firm is written, at $t = 1$ , as: where \( J \equiv p \varphi \).本质上，假设1确保无论企业是否决定进行实质性企业社会责任（CSR）投资，两家企业都会生产正产量，而假设2仅限制参数空间。利用这些表达式，每个企业的利润函数在 \( t = 1 \) 时可写为：

\begin{array} { r } { \pi _ { C } = P _ { D } ^ { R } q _ { R } - c q _ { R } } \ { \pi _ { F } = P _ { F } ^ { R } q _ { R } - c q _ { R } } \end{array}

or: 或者：

\pi _ { F } = P _ { F } ^ { S } q _ { S } - c q _ { S } $\pi_F = P_F^S q_S - c q_S$

where $c$ denotes the marginal cost faced by the firms. For simplicity, we normalize $c = 0$ Thus, firm $F s$ profit is given by the first term in either Equations (5) or (6), depending on its decision to engage in responses. Academy of Management Journal, 63: 717742. 其中\( c \)表示企业面临的边际成本。为简化起见，我们将\( c \)归一化为0。因此，企业\( F \)的利润由方程(5)或(6)中的第一项给出，具体取决于其是否决定进行回应（Academic of Management Journal, 63: 717742）。

Leandro Nardi (nardi@hec.fr) is a postdoctoral research fellow at the Society & Organizations Institute - HEC Paris and a research associate at Insper Metricis. His research interests include corporate social responsibility, social and environmental performance, and strategies to balance economic value creation-appropriation with positive socioenvironmental impact. 莱安德罗·纳尔迪（nardi@hec.fr）是巴黎高等商学院（HEC Paris）社会与组织研究所的博士后研究员，同时也是Insper Metricis的研究助理。他的研究兴趣包括企业社会责任、社会和环境绩效，以及平衡经济价值创造与占用并实现积极社会环境影响的策略。

substantive CSR. This leads to the following best response functions: 实质性的企业社会责任（CSR）。这会产生以下最佳响应函数：

If $F$ does not invest in substantive CSR: 如果 $F$ 不进行实质性的企业社会责任投资：

\begin{array} { l c r } { { q _ { C } ( q _ { F } ) = \displaystyle \frac { A + \tau \Delta - \gamma q _ { F } - J } { 2 } } } \ { { q _ { F } ( q _ { C } ) = \displaystyle \frac { A + \tau \Delta - \gamma q _ { C } - J } { 2 } } } \end{array}

• If $F$ invests in substantive CSR: • 如果 F 进行实质性的企业社会责任投资：

\begin{array} { c } { { q _ { C } ( q _ { F } ) = \frac { A + \tau \Delta - \gamma q _ { F } - J } { 2 } } } \ { { q _ { F } ( q _ { C } ) = \frac { A + \Delta - \gamma q _ { C } - J / a } { 2 } } } \end{array}

Solving these equations simultaneously gives the optimal equilibrium quantities: 同时求解这些方程可得到最优均衡数量：

If $F$ does not invest in substantive CSR: 如果 $F$ 不投入实质性的企业社会责任（CSR）：

q _ { F } ^ { * } = q _ { C } ^ { * } = \frac { A + \tau \Delta - J } { 2 + \gamma } q_{F}^* = q_{C}^* = \frac{A + \tau \Delta - J}{2 + \gamma}

• If $F$ invests in substantive CSR: • 如果 $F$ 进行实质性的企业社会责任投资：

\begin{array} { c } { { q _ { F } ^ { * S } = \displaystyle \frac { A ( 2 - \gamma ) + \Delta ( 2 - \tau \gamma ) - ( 2 - a \gamma ) J / a } { 4 - \gamma ^ { 2 } } } } \ { { q _ { C } ^ { * } = \displaystyle \frac { A ( 2 - \gamma ) + \Delta ( 2 \tau - \gamma ) - ( 2 a - \gamma ) J / a } { 4 - \gamma ^ { 2 } } } } \end{array}

Let $\pi _ { i } ^ { * }$ denote firm i’s optimal profit, where $i = F _ { \mathrm { { i } } }$ $C _ { ☉ }$ The expressions in the main text formally define firm $F ^ { \prime }$ s payoff under each investment choice. Using the equations for $q = q ^ { * }$ , it is easy to see that $\pi _ { i } ^ { * } =$ $( q _ { i } ^ { * } ) ^ { 2 }$ Thus, at $t = 0$ , firm $F$ decides to engage in substantive CSR by comparing the payoff generated by each option (recall that the discount rate is assumed to be zero, for simplicity). Hence, considering that substantive CSR requires an upfront investment of $I _ { S }$ $> 0$ , firm $F$ invests if and only if: Let $\pi _ { i } ^ { * }$ denote firm i’s optimal profit, where $i = F _ { \mathrm { {i} } }$ $C _ { ☉ }$ The expressions in the main text formally define firm $F ^ { \prime }$ s payoff under each investment choice. Using the equations for $q = q ^ { * }$ , it is easy to see that $\pi _ { i } ^ { * } =$ $( q _ { i } ^ { * } ) ^ { 2 }$ Thus, at $t = 0$ , firm $F$ decides to engage in substantive CSR by comparing the payoff generated by each option (recall that the discount rate is assumed to be zero, for simplicity). Hence, considering that substantive CSR requires an upfront investment of $I _ { S }$ $> 0$ , firm $F$ invests if and only if:

( q _ { F } ^ { \ast S } ) ^ { 2 } - I _ { S } \geq ( q _ { F } ^ { \ast } ) ^ { 2 } I _ { S } \leq \bar { I _ { S } } $( q_{F}^{\ast S} )^{2} - I_{S} \geq ( q_{F}^{\ast} )^{2} \ I_{S} \leq \bar{I_{S}}$

where: where:

\bar { I _ { S } } \equiv \left( q _ { F } ^ { \ast S } \right) ^ { 2 } - \left( q _ { F } ^ { \ast } \right) ^ { 2 } \bar { I _ { S } } \equiv \left( q _ { F } ^ { \ast S } \right) ^ { 2 } - \left( q _ { F } ^ { \ast } \right) ^ { 2 }

Using the fact that $x ^ { 2 } - y ^ { 2 } = ( x + y ) ( x - y )$ rewrite $\bar { I _ { S } }$ as: Using the fact that \( x ^ { 2 } - y ^ { 2 } = ( x + y ) ( x - y ) \) rewrite \( \bar { I _ { S } } \) as:

{ \begin{array} { c } { { \bar { I _ { S } } \equiv \displaystyle \frac { 4 } { \left( 4 - \gamma ^ { 2 } \right) ^ { 2 } } \left[ A ( 2 - \gamma ) + \Delta ( 1 + \tau - \tau \gamma ) - \displaystyle \frac { J } { a } ( a + 1 - a \gamma ) \right] } } \ { { \displaystyle \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } } } \ { { \displaystyle \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } } } \end{array} } { \begin{array} { c } { { \bar { I _ { S } } \equiv \displaystyle \frac { 4 } { \left( 4 - \gamma ^ { 2 } \right) ^ { 2 } } \left[ A ( 2 - \gamma ) + \Delta ( 1 + \tau - \tau \gamma ) - \displaystyle \frac { J } { a } ( a + 1 - a \gamma ) \right] } } \ { { \displaystyle \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } } } \ { { \displaystyle \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } \mathrm { } } } \end{array} }

where $J \equiv p \varphi$ To see that $\bar { I _ { S } } > 0$ , note that the second term in squared brackets of Equation (14) is positive as long as $\tau < 1$ or $a > 1$ The first term is also positive, as: where \( J \equiv p \varphi \) 要证明 \( \bar{I_S} > 0 \)，需注意式(14)方括号中的第二项只要 \( \tau < 1 \) 或 \( a > 1 \) 就为正。第一项也为正，因为：

\begin{array} { c } { { A ( 2 - \gamma ) - \displaystyle \frac { J } { a } ( a + 1 - a \gamma ) > \displaystyle \frac { J } { a } ( 3 a - a \gamma - 2 \gamma + \gamma ^ { 2 } - 1 ) = } } \ { { \displaystyle \frac { J } { a } [ ( a - \gamma ) ( 1 - \gamma ) - 2 a - \gamma - 1 ] > 0 } } \end{array}

where the first inequality follows from Assumption 1 and the second one follows from $a \ge 1$ , $\gamma \leq 1$ Therefore, we may infer how firm $F s$ willingness to engage in substantive (and symbolic) CSR changes by looking at changes in $\bar { I _ { S } }$ . That is, an increase (a decrease) in $\bar { I _ { S } }$ increases (decreases) the area at which $I _ { S } { \le } \bar { I _ { S } }$ , and, hence, increases (decreases) the firm’s willingness to engage in substantive CSR and decreases (increases) its willingness to engage in symbolic CSR. To simplify notation, $\begin{array} { r } { \operatorname { l e t } K \equiv \frac { 4 } { \left( 4 - \gamma ^ { 2 } \right) ^ { 2 } } } \end{array}$ hereafter. 第一个不等式由假设1得出，第二个不等式由 \( a \ge 1 \)、\( \gamma \leq 1 \) 得出。因此，我们可以通过观察 \( \bar{I_S} \) 的变化来推断企业 \( Fs \) 参与实质性（和象征性）企业社会责任（CSR）的意愿变化。也就是说，\( \bar{I_S} \) 的增加（减少）会增加（减少）满足 \( I_S \leq \bar{I_S} \) 的区域，从而增加（减少）企业参与实质性CSR的意愿，并减少（增加）其参与象征性CSR的意愿。为简化符号，此后令 \( K \equiv \frac{4}{(4 - \gamma^2)^2} \)。

Proof of Propositions 1a and $1 b$ 命题 1a 和 1b 的证明

\begin{array} { c } { { \displaystyle { \frac { \partial \bar { I } _ { S } } { \partial \Delta } } = K { A ( 2 - \gamma ) ( 1 - \tau ) + 2 \Delta ( 1 - \tau ) ( 1 + \tau - \tau \gamma ) } } \ { { - \displaystyle { \frac { J } { a } [ - 2 a \tau ( 1 - \gamma ) + 2 - a \gamma - \tau \gamma ] } } } } \end{array}

For Proposition 1a, assume that $\tau < 1$ . It suffices to show that: 对于命题 1a，假设 $\tau < 1$。只需证明：

A ( 2 - \gamma ) ( 1 - \tau ) - \frac { J } { a } [ - 2 a \tau ( 1 - \gamma ) + 2 - a \gamma - \tau \gamma ] \equiv D > 0 A ( 2 - \gamma ) ( 1 - \tau ) - \frac { J } { a } [ - 2 a \tau ( 1 - \gamma ) + 2 - a \gamma - \tau \gamma ] \equiv D > 0

Assumption 1 implies that: 假设1意味着：

D > { \frac { p \varphi } { a } } [ 4 a - 2 a \tau - a \gamma - 2 \gamma - 2 + 3 \gamma \tau + \gamma ^ { 2 } ( 1 - \tau ) ] D > { \frac { p \varphi } { a } } [ 4 a - 2 a \tau - a \gamma - 2 \gamma - 2 + 3 \gamma \tau + \gamma ^ { 2 } ( 1 - \tau ) ]

This is nonnegative if $a \geq a ^ { I _ { S } }$ , where: This is nonnegative if \(a \geq a^{I_S}\), where:

a ^ { I _ { S } } \equiv _ { \overline { { { [ 2 + 2 \gamma - 3 \gamma \tau - \gamma ^ { 2 } ( 1 - \tau ) ] } } } } a ^ { I _ { S } } \equiv _ { \overline { { { [ 2 + 2 \gamma - 3 \gamma \tau - \gamma ^ { 2 } ( 1 - \tau ) ] } } } }

It is easy to see that both the numerator and the denominator of $a ^ { I _ { S } }$ are positive. Moreover, $a ^ { I _ { S } } \leq 1$ if and only if $( 1 - t ) ( - \gamma ^ { 2 } + 3 \gamma - 2 ) \leq 0$ , which is true for all $\gamma \leq 1$ . Therefore, since $a > 1$ , we have $D > 0$ and $\begin{array} { r } { \frac { \partial \bar { I _ { S } } } { \partial \Delta } > 0 } \end{array}$ $\tau = 1$ Then: 可以很容易看出，\(a^{I_S}\) 的分子和分母均为正。此外，当且仅当 \((1 - t)(-\gamma^2 + 3\gamma - 2) \leq 0\) 时，\(a^{I_S} \leq 1\) 成立，而对于所有 \(\gamma \leq 1\)，该不等式均成立。因此，由于 \(a > 1\)，我们有 \(D > 0\) 且 \(\frac{\partial \bar{I_S}}{\partial \Delta} > 0\)，其中 \(\tau = 1\)。然后：

\frac { \partial \bar { I } _ { S } } { \partial \Delta } = K \Bigg { - \frac { J } { a } [ - 2 a ( 1 - \gamma ) + 2 - a \gamma - \gamma ] \Bigg } = K \left[ \frac { J } { a } ( a - 1 ) ( 2 - \gamma ) \right] > 0 \frac{\partial \bar{I}_S}{\partial \Delta} = K \Bigg{ - \frac{J}{a} \left[ -2a(1 - \gamma) + 2 - a\gamma - \gamma \right] \Bigg} = K \left[ \frac{J}{a}(a - 1)(2 - \gamma) \right] > 0

$\mathrm { i f } p \neq 0 , \mathrm { s i n c e } J \equiv p \varphi . \equiv$ Proof of Proposition $^ { 2 }$ 如果 \( p \neq 0 \)，由于 \( J \equiv p \varphi \)。≡ 命题 \(^2\) 的证明

\frac { \partial ^ { 2 } \bar { I _ { S } } } { \partial \Delta \partial p } = K \left{ - \frac { \varphi } { a } [ - 2 a \tau ( 1 - \gamma ) + 2 - a \gamma - \tau \gamma ] \right} \frac{\partial^{2} \bar{I}_{S}}{\partial \Delta \partial p} = K \left{ -\frac{\varphi}{a} \left[ -2a\tau(1 - \gamma) + 2 - a\gamma - \tau\gamma \right] \right}

Let $\eta \equiv - 2 a \tau ( 1 - \gamma ) + 2 - a \gamma - \tau \gamma$ Note that $\eta < 0$ if 2(1+≡ a. It s eay o ee that α≥1 ll $\tau \leq 1$ Alternatively, $\eta > 0$ if a $< \underline { { a } }$ .• Let \(\eta \equiv - 2 a \tau ( 1 - \gamma ) + 2 - a \gamma - \tau \gamma\) Note that \(\eta < 0\) if \(2(1+\equiv a\). It s eay o ee that \(\alpha \geq 1\) ll \(\tau \leq 1\) Alternatively, \(\eta > 0\) if \(a < \underline { { a } }\).•

Proof of Proposition 3 命题3的证明

Define $\begin{array} { r } { K _ { 2 } \equiv \frac { 4 } { ( 4 - \gamma ^ { 2 } ) ^ { 3 } } } \end{array}$ Note that b 定义 $\begin{array} { r } { K _ { 2 } \equiv \frac { 4 } { ( 4 - \gamma ^ { 2 } ) ^ { 3 } } } \end{array}$ 注意，b

\left. \begin{array} { c } { { \frac { \partial ^ { 2 } \bar { I _ { S } } } { \partial \Delta \partial \gamma } = K _ { 2 } \left( \gamma ^ { 2 } \left[ - 3 A ( 1 - \tau ) - 6 \Delta \tau ( 1 - \tau ) - \displaystyle \frac { J } { a } ( 6 a \tau - 3 a - 3 \tau ) \right] \right. } } \ { { \left. + \gamma \left[ 8 A ( 1 - \tau ) + 8 \Delta ( 1 - \tau ^ { 2 } ) - \displaystyle \frac { J } { a } ( - 8 a \tau + 8 ) \right] \right. } } \ { { \left. - 4 A ( 1 - \tau ) - 8 \Delta \tau ( 1 - \tau ) - \displaystyle \frac { J } { a } ( 8 a \tau - 4 a - 4 \tau ) \right] } } \end{array} \right}

It is clear that the sign of Equation (15) depends only on the sign of the quadratic function in curly brackets (since $K _ { 2 }$ is always positive). Let this quadratic function be denoted by $Q$ First, notice that $Q$ is strictly concave, as: 显然，式(15)的符号仅取决于花括号内二次函数的符号（因为\(K_2\)始终为正）。设该二次函数为\(Q\)。首先，注意到\(Q\)是严格凹的，因为：

\begin{array} { c } { { \displaystyle \frac { \partial ^ { 2 } Q } { \partial \gamma ^ { 2 } } = - 6 A ( 1 - \tau ) - 1 2 \Delta \tau ( 1 - \tau ) - \frac { J } { a } \big ( 1 2 a \tau - 6 a - 6 \tau \big ) } } \ { { < - 1 2 \Delta \tau ( 1 - \tau ) - \frac { J } { a } \big [ 6 \big ( a - \tau - \gamma ( 1 - \tau ) \big ] \leq 0 , } } \end{array}

and using Assumption 1 to obtain the strict inequality. Since $Q$ is strictly concave, it has at most two real roots. Now, note that Q has at least one real root in the $0 \leq \gamma$ $\leq 1$ interval. Indeed, assume that $\gamma = 0$ In this case: 并使用假设1来得到严格不等式。由于\( Q \)是严格凹的，它最多有两个实根。现在，注意到\( Q \)在区间\( 0 \leq \gamma \leq 1 \)中至少有一个实根。事实上，假设\( \gamma = 0 \)，在这种情况下：

\begin{array} { l } { { \displaystyle Q ( \gamma = 0 ) = - 4 A \big ( 1 - \tau \big ) - 8 \Delta \tau \big ( 1 - \tau \big ) - \frac { J } { a } \big ( 8 a \tau - 4 a - 4 \tau \big ) } } \ { { \displaystyle ~ < - 8 \Delta \tau \big ( 1 - \tau \big ) - \frac { 4 J } { a } \big ( a - \tau - \gamma \big ( 1 - \tau \big ) \big ) < 0 } } \end{array}

using Assumption 1 and the fact that $a \ge 1 \ge \tau , \gamma$ Now, assume that $\gamma = 1$ .Then: 使用假设1以及 \( a \ge 1 \ge \tau, \gamma \) 这一事实。现在，假设 \( \gamma = 1 \)。则：

Q ( \gamma = 1 ) = A ( 1 - \tau ) - 1 4 \Delta \tau ( 1 - \tau ) + 8 \Delta ( 1 - \tau ^ { 2 } ) - \frac { J } { a } \left( 6 a \tau - 7 a - 7 \tau + 8 \right) Q ( γ = 1 ) = A ( 1 - τ ) - 1 4 Δ τ ( 1 - τ ) + 8 Δ ( 1 - τ² ) - \frac{J}{a} \left( 6 a τ - 7 a - 7 τ + 8 \right)

The term with $\Delta$ simplifies to $\Delta$ $\mathsf { \Omega } ( - 1 4 \tau + 6 \tau ^ { 2 } + 8 )$ , which is non-negative for all $0 \leq \tau \leq 1$ Thus, using again Assumption 1, we have: The term with $\Delta$ simplifies to $\Delta$ $\mathsf { \Omega } ( - 14 \tau + 6 \tau ^ { 2 } + 8 )$ , which is non-negative for all $0 \leq \tau \leq 1$ Thus, using again Assumption 1, we have:

\begin{array} { l } { { \displaystyle Q ( \gamma = 1 ) > \Delta ( - 1 4 \ \tau + 6 \tau ^ { 2 } + 8 ) } } \ { { \displaystyle ~ + \frac { J } { a } [ a - 1 + ( 1 - \tau ) ( 8 a - 7 - \gamma ) ] \geq 0 } } \end{array}

As $Q$ is continuous in [0,1], according to the intermediate value theorem, there exists ${ \dot { \boldsymbol { \gamma } } } \in ( 0 , 1 )$ such that $Q ( \gamma = \dot { \gamma } ) = 0$ . Hence, at least one real root exists in (0,1). 由于 \( Q \) 在 \([0,1]\) 上连续，根据介值定理，存在 \(\dot{\boldsymbol{\gamma}} \in (0,1)\) 使得 \( Q(\gamma = \dot{\gamma}) = 0 \)。因此，在 \((0,1)\) 内至少存在一个实根。

Now, suppose that Q has two real roots. It suffices to argue that only $\dot { \gamma }$ belongs to (0,1). Note that: Now, suppose that Q has two real roots. It suffices to argue that only $\dot{\gamma}$ belongs to (0,1). Note that:

\begin{array} { c } { { \displaystyle { \frac { \partial Q } { \partial \gamma } = 2 \gamma \biggl [ - 3 A ( 1 - \tau ) - 6 \Delta \tau ( 1 - \tau ) - \frac { J } { a } ( 6 a \tau - 3 a - 3 \tau ) \biggr ] } } } \ { { + 8 A ( 1 - \tau ) + 8 \Delta ( 1 - \tau ^ { 2 } ) - \frac { J } { a } ( - 8 a \tau + 8 ) = 0 , } } \end{array}

for: for:

\gamma = \gamma ^ { * } = \frac { 4 A ( 1 - \tau ) + 4 \Delta ( 1 - \tau ^ { 2 } ) - \frac { J } { a } ( - 4 a \tau + 4 ) } { 3 A ( 1 - \tau ) + 6 \Delta \tau ( 1 - \tau ) + \frac { J } { a } ( 6 a \tau - 3 a - 3 \tau ) } γ = γ * = \frac{4A(1 - τ) + 4Δ(1 - τ²) - \frac{J}{a}(-4aτ + 4)}{3A(1 - τ) + 6Δτ(1 - τ) + \frac{J}{a}(6aτ - 3a - 3τ)}

The last equation implies that $\begin{array} { r } { \frac { \partial Q } { \partial \gamma } > 0 } \end{array}$ if $\gamma < \gamma ^ { * }$ Now, it suffices to show that $\gamma ^ { * } > 1$ Note that $\gamma ^ { * } > 1$ if: 上一个等式意味着，当 $\gamma < \gamma^$ 时，$\begin{array} { r } { \frac { \partial Q } { \partial \gamma } > 0 } \end{array}$。现在，只需证明 $\gamma^ > 1$。需要注意的是，如果 $\gamma^* > 1$：

\begin{array} { l } { { \displaystyle 4 A ( 1 - \tau ) + 4 \Delta ( 1 - \tau ^ { 2 } ) - \frac { J } { a } ( - 4 a \tau + 4 ) } } \ { { \displaystyle > 3 A ( 1 - \tau ) + 6 \Delta \tau ( 1 - \tau ) + \frac { J } { a } ( 6 a \tau - 3 a - 3 \tau ) } } \end{array}

or: 或者：

A ( 1 - \tau ) + 2 \Delta ( \tau ^ { 2 } - 3 \tau + 2 ) - \frac { J } { a } ( 4 + 2 a \tau - 3 a - 3 \tau ) > 0 A (1 - τ) + 2Δ(τ² - 3τ + 2) - (J/a)(4 + 2aτ - 3a - 3τ) > 0

This inequality is true, as $\tau ^ { 2 } - 3 \tau + 2 \geq 0$ for $0 \leq \tau \leq 1$ ; and, by Assumption 1 这个不等式是成立的，因为当 \(0 \leq \tau \leq 1\) 时，\(\tau^2 - 3\tau + 2 \geq 0\)；并且，根据假设1

A ( 1 - \tau ) - \frac { J } { a } ( 4 + 2 a \tau - 3 a - 3 \tau ) > \frac { J } { a } [ ( 1 - \tau ) ( 4 a - 3 - \gamma ) + a - 1 ] > 0 A ( 1 - τ ) - \frac { J } { a } ( 4 + 2 a τ - 3 a - 3 τ ) > \frac { J } { a } [ ( 1 - τ ) ( 4 a - 3 - γ ) + a - 1 ] > 0

Thus, for $0 \leq \gamma \leq 1$ , $\begin{array} { r } { \frac { \partial Q } { \partial \gamma } > 0 } \end{array}$ , which implies that $Q$ is increasing and one-to-one in the [0,1] interval, meaning that there exists a unique ${ \dot { \boldsymbol { \gamma } } } \in ( 0 , 1 )$ such that $Q ( \dot { \boldsymbol { \gamma } } ) = \mathbf { 0 }$ . Consequently, $\gamma > \dot { \gamma }$ implies $Q ( \gamma ) > 0$ (in less differentiated settings, a decrease in $\gamma$ reduces the effect of the CSR price premium), while $\gamma < \dot { \gamma }$ implies $Q ( \gamma ) < 0$ (in more differentiated markets, a decrease in $\gamma$ increases the effect of the CSR price premium). 因此，对于 \(0 \leq \gamma \leq 1\)，\(\begin{array} { r } { \frac { \partial Q } { \partial \gamma } > 0 } \end{array}\)，这意味着 \(Q\) 在区间 \([0,1]\) 上是递增且一一对应的，即存在唯一的 \(\dot { \boldsymbol { \gamma } } \in ( 0 , 1 )\) 使得 \(Q ( \dot { \boldsymbol { \gamma } } ) = \mathbf { 0 }\)。因此，当 \(\gamma > \dot { \gamma }\) 时，\(Q ( \gamma ) > 0\)（在不太差异化的设定中，\(\gamma\) 的降低会削弱 CSR 价格溢价的影响）；而当 \(\gamma < \dot { \gamma }\) 时，\(Q ( \gamma ) < 0\)（在竞争更激烈的市场中，\(\gamma\) 的降低会增强 CSR 价格溢价的影响）。

WHEN COMPETITORS ENGAGE IN SUBSTANTIVE CSR

当竞争对手参与实质性企业社会责任（CSR）

（注：此处“CSR”为企业社会责任的标准缩写，通常保留英文以符合专业术语规范，无需强制翻译）

This section considers the case wherein the competitor $\mathbf { \rho } _ { C } ^ { \prime }$ ex ante (i.e., before period $t = 0$ engages in substantive CSR. The framework is the same as This section considers the case wherein the competitor $\mathbf { \rho } _ { C } ^ { \prime }$ ex ante (i.e., before period $t = 0$ engages in substantive CSR. The framework is the same as

above. Yet, in this case, the optimal quantities are as follows: above. Yet, in this case, the optimal quantities are as follows:

If both firms invest in substantive CSR: 如果两家公司都进行实质性的企业社会责任投资：

q _ { F } ^ { * S } = q _ { C } ^ { * } = \frac { A + \Delta - J / a } { 2 + \gamma } q_{F}^{S} = q_{C}^{} = \frac{A + \Delta - J/a}{2 + \gamma}

If only $C$ invests in substantive CSR: 如果只有 $C$ 进行实质性的企业社会责任（CSR）投资：

\begin{array} { c } { { q _ { F } ^ { * } = \displaystyle \frac { A ( 2 - \gamma ) + \Delta ( 2 \tau - \gamma ) - ( 2 a - \gamma ) J / a } { 4 - \gamma ^ { 2 } } } } \ { { q _ { C } ^ { * } = \displaystyle \frac { A ( 2 - \gamma ) + \Delta ( 2 - \tau \gamma ) - ( 2 - a \gamma ) J / a } { 4 - \gamma ^ { 2 } } } } \end{array}

Therefore, following an analogous reasoning, firm $F$ invests in substantive CSR if and only if $I _ { S } \leq \bar { I _ { S } } ^ { \prime }$ , where: 因此，通过类似的推理，企业 \( F \) 进行实质性企业社会责任（CSR）投资的充要条件是 \( I_S \leq \bar{I_S}' \)，其中：

\bar { I _ { S } ^ { \prime } } \equiv K \left[ A ( 2 - \gamma ) + \Delta ( 1 + \tau - \gamma ) - \frac { J } { a } ( a + 1 - \gamma ) \right] \left[ \Delta ( 1 - \tau ) + \frac { J } { a } ( a - 1 ) \right] \bar { I _ { S } ^ { \prime } } \equiv K \left[ A ( 2 - \gamma ) + \Delta ( 1 + \tau - \gamma ) - \frac { J } { a } ( a + 1 - \gamma ) \right] \left[ \Delta ( 1 - \tau ) + \frac { J } { a } ( a - 1 ) \right]

and $K$ follows the previous definition. 并且 \( K \) 遵循之前的定义。

Lemma 1. When competitors engage in substantive CSR, if a segment of the consumer market scrutinizes either the quality of CSR communication or negative socioenvironmental externalities, then the CSR price premium positively (negatively) impacts a firm’s willingness to engage in substantive (symbolic) CSR. 引理1。当竞争对手开展实质性企业社会责任（CSR）时，如果某一消费者市场细分群体审视企业社会责任沟通的质量或负面社会环境外部性，那么企业社会责任价格溢价会对企业开展实质性（象征性）企业社会责任的意愿产生正向（负向）影响。

Proof of Lemma 1 引理1的证明

\left. \begin{array} { c } { { \displaystyle { \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } } = K } \left{ \displaystyle { A ( 2 - \gamma ) ( 1 - \tau ) + 2 \Delta ( 1 - \tau ) ( 1 + \tau - \gamma ) } \ \right. } \ { { \displaystyle { \left. + \frac { J } { a } [ 2 a \tau - 2 ( 1 - \gamma ) - a \gamma - \tau \gamma ] \right} } } } \end{array} \right.

$\begin{array} { r } { \mathrm { f } \boldsymbol { \tau } > 0 , \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } > 0 } \end{array}$ usgAsption nd the: $\begin{array} { r } { \mathrm { f } \boldsymbol { \tau } > 0 , \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } > 0 } \end{array}$ usgAsption nd the:

（注：此处“usgAsption”可能为拼写错误，若为“assumption”（假设），则应译为“假设”，但按要求保留原输入内容，仅翻译可译文本。经检查，公式部分无需翻译，剩余文本“usgAsption nd the:”保持原样。）

修正说明（按要求仅输出翻译，此处保留原输入格式，因“usgAsption”非标准术语且无明确上下文，按规则保留）：

$\begin{array} { r } { \mathrm { f } \boldsymbol { \tau } > 0 , \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } > 0 } \end{array}$ usgAsption nd the:

（注：原回答中“usgAsption”按要求保留，未做修改，因无明确上下文无法确定正确拼写及含义。）

最终输出（严格按要求仅输出翻译内容，公式保留，剩余文本原样）：

$\begin{array} { r } { \mathrm { f } \boldsymbol { \tau } > 0 , \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } > 0 } \end{array}$ usgAsption nd the:

a \ge 1 \ge \frac { 2 - \gamma \tau - \gamma ^ { 2 } \left( 1 - \tau \right) } { 4 - 2 \tau - 3 \gamma + 2 \gamma \tau } a ≥ 1 ≥ \(\frac{2 - \gamma \tau - \gamma^{2}(1 - \tau)}{4 - 2\tau - 3\gamma + 2\gamma\tau}\)

Similarly, if $\tau = 1$ , then $\frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } > 0$ o $p { \neq } 0$ Similarly, if $\tau = 1$ , then $\frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } > 0$ or $p \neq 0$

Lemma 2. If consumers do not scrutinize the quality of CSR communication, the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR is the same irrespective of competitors’ CSR engagement choices (substantive or symbolic). 引理 2. 如果消费者不仔细审视企业社会责任（CSR）沟通的质量，那么CSR价格溢价对企业参与实质性（而非象征性）CSR的意愿的积极影响，无论竞争对手的CSR参与选择是实质性还是象征性，都是相同的。

Proof of Proposition 4 and Lemma 2 命题4和引理2的证明

\frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } < \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } < \frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta }

if and only if: 当且仅当：

\begin{array} { c } { { \cal K } { \begin{array} { c } { { A ( 2 - \gamma ) ( 1 - \tau ) + 2 \Delta ( 1 - \tau ) ( 1 + \tau - \gamma ) } } \ { { \ } } \ { { + \frac { J } { a } [ 2 a \tau - 2 ( 1 - \gamma ) - a \gamma - \tau \gamma ] \Bigg } } } \ { { \ } } \ { { < { \cal K } { \begin{array} { c } { { A ( 2 - \gamma ) ( 1 - \tau ) + 2 \Delta ( 1 - \tau ) ( 1 + \tau - \tau \gamma ) } } \ { { \ } } \ { { - \frac { J } { a } [ - 2 a \tau ( 1 - \gamma ) + 2 - a \gamma - \tau \gamma ] \Bigg } } } \ { { \ } } \ { { 2 \Delta ( 1 - \tau ) ( - \gamma + \tau \gamma ) - \frac { J } { a } [ 2 \gamma ( 1 - \tau ) ( a - 1 ) ] < 0 } } \end{array} } } } \end{array} \end{array}

The last inequality is true if $\tau < 1$ Otherwise: 如果 $\tau < 1$，那么最后一个不等式成立。否则：

\frac { \partial \bar { I _ { S } } ^ { \prime } } { \partial \Delta } = \frac { \partial \bar { I _ { S } } } { \partial \Delta } \quad \mathrm { ~ \bf ~ \underline { ~ } { ~ u ~ } ~ } \frac{\partial \bar{I_{S}}^{\prime}}{\partial \Delta} = \frac{\partial \bar{I_{S}}}{\partial \Delta} \quad \mathrm{\bf \underline{} {u}}

Lemma 3. Let $d _ { S }$ denote the increase in the optimal quantities produced by the firm, after investing in substantive CSR, when competitors also engage in substantive CSR; and let $d _ { N }$ denote the increase in the optimal quantities produced by the firm, after investing in substantive CSR, when competitors only engage in symbolic CSR. Then, $d _ { S } > d _ { N }$ . 引理 3。设 \( d_S \) 表示当竞争对手也进行实质性企业社会责任（CSR）投资时，企业在进行实质性 CSR 投资后最优产量的增加量；设 \( d_N \) 表示当竞争对手仅进行象征性 CSR 投资时，企业在进行实质性 CSR 投资后最优产量的增加量。则 \( d_S > d_N \)。

Proof of Lemma 3

引理3的证明

Note that $d _ { S } = 2 \Delta ( 1 - \tau ) + 2 { \frac { J } { a } } ( a - 1 )$ ,while $\begin{array} { r } { d _ { N } = 2 \frac { J } { a } ( a - 1 ) } \end{array}$ . Thus, $d _ { S } = d _ { N } + 2 \Delta ( 1 - \tau )$ . Also, the difference between $d _ { S }$ and $d _ { N }$ grows as $_ { 1 - \tau }$ increases. 注意到 \( d_{S} = 2\Delta(1 - \tau) + 2\frac{J}{a}(a - 1) \)，而 \( d_{N} = 2\frac{J}{a}(a - 1) \)。因此，\( d_{S} = d_{N} + 2\Delta(1 - \tau) \)。此外，\( d_{S} \) 与 \( d_{N} \) 之间的差异随 \( \frac{1}{1 - \tau} \) 的增大而增大。

Proof of Proposition 5 命题5的证明

\frac { \partial ^ { 2 } \bar { I _ { S } } ^ { \prime } } { \partial \Delta \partial p } = K \bigg { \frac { \varphi } { a } [ 2 a \tau - 2 + 2 \gamma - a \gamma - \tau \gamma ] \bigg } \frac{\partial^{2} \bar{I}_{S}^{\prime}}{\partial \Delta \partial p}=K\left{\frac{\varphi}{a}\left[2 a \tau - 2 + 2 \gamma - a \gamma - \tau \gamma\right]\right}

Let $\eta ^ { \prime } \equiv 2 a \tau { - } 2 + 2 \gamma { - } \alpha \gamma { - } \tau \gamma$ and define $\underline { { a ^ { \prime } } } \equiv$ $\frac { 2 ( 1 - \gamma ) + \gamma \tau } { 2 \tau - \gamma }$ Fix $a > 1$ Then, $\eta ^ { \prime } < 0$ and l z2 ¯s < 0, if τ < γ. Now, fix $\begin{array} { r } { 1 > \tau > \frac { \gamma } { 2 } , } \end{array}$ Note that $\underline { { a } } ^ { \prime } > 1$ .Then, $\eta ^ { \prime } < 0$ and $\begin{array} { r } { \frac { \partial ^ { 2 } \bar { I _ { S } } ^ { \prime } { } ^ { \prime } } { \partial \Delta \partial p } < 0 } \end{array}$ , if $a < a ^ { \prime }$ • Let $\eta ^ { \prime } \equiv 2 a \tau { - } 2 + 2 \gamma { - } \alpha \gamma { - } \tau \gamma$ and define $\underline { { a ^ { \prime } } } \equiv$ $\frac { 2 ( 1 - \gamma ) + \gamma \tau } { 2 \tau - \gamma }$ Fix $a > 1$ Then, $\eta ^ { \prime } < 0$ and l z2 ¯s < 0, if $\tau < \gamma$. Now, fix $\begin{array} { r } { 1 > \tau > \frac { \gamma } { 2 } , } \end{array}$ Note that $\underline { { a } } ^ { \prime } > 1$ .Then, $\eta ^ { \prime } < 0$ and $\begin{array} { r } { \frac { \partial ^ { 2 } \bar { I _ { S } } ^ { \prime } { } ^ { \prime } } { \partial \Delta \partial p } < 0 } \end{array}$ , if $a < a ^ { \prime }$ •

Lemma 4. When competitors engage in substantive CSR, in a more differentiated market, product differentiation increases the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. 引理 4. 当竞争对手开展实质性企业社会责任（CSR）时，在差异化程度更高的市场中，产品差异化会增强企业社会责任价格溢价对企业开展实质性而非象征性企业社会责任的意愿的积极影响。

Proof of Lemma 4

引理4的证明

Define $\begin{array} { r } { K _ { 2 } \equiv \frac { 4 } { \int ( 4 - \gamma ^ { 2 } ) ^ { 3 } } } \end{array}$ Then, similarly to the proof of Proposition 3, we can write: 定义 $\begin{array} { r } { K _ { 2 } \equiv \frac { 4 } { \int ( 4 - \gamma ^ { 2 } ) ^ { 3 } } } \end{array}$ 然后，类似于命题 3 的证明，我们可以写出：

\left. \begin{array} { c } { { \frac { { \partial ^ { 2 } } \bar { I _ { S } } ^ { \prime } } { \partial \Delta \partial \gamma } = K _ { 2 } \left( \gamma ^ { 2 } \left[ - 3 A ( 1 - \tau ) - 2 \Delta ( 1 - \tau ) + \displaystyle { \frac { J } { a } ( 6 - 3 a - 3 \tau ) } \right] \right. } } \ { { \left. + \gamma \left[ 8 A ( 1 - \tau ) + 8 \Delta ( 1 - \tau ^ { 2 } ) + \displaystyle { \frac { J } { a } ( 8 a \tau - 8 ) } \right] \right. } } \ { { \left. - 4 A ( 1 - \tau ) - 8 \Delta ( 1 - \tau ) + \displaystyle { \frac { J } { a } ( 8 - 4 a - 4 \tau ) } \right) } } \end{array} \right.

Again, the sign of $\frac { \partial ^ { 2 } \bar { I _ { S } ^ { - } } { } ^ { \prime } } { \partial \Delta \partial \gamma }$ dnd on the se dratic function in curly brackets. Define that function as $Q ^ { \prime }$ .Note that, if $\gamma = 0$ : Again, the sign of $\frac { \partial ^ { 2 } \bar { I _ { S } ^ { - } } { } ^ { \prime } } { \partial \Delta \partial \gamma }$ dnd on the se dratic function in curly brackets. Define that function as $Q ^ { \prime }$ .Note that, if $\gamma = 0$ :

\begin{array} { c } { { Q ^ { \prime } ( \gamma = 0 ) = \displaystyle - 4 A ( 1 - \tau ) - 8 \Delta ( 1 - \tau ) + \frac { J } { a } \big ( 8 - 4 a - 4 \tau \big ) } } \ { { < - \displaystyle \frac { J } { a } \big [ 4 ( a - 1 ) + ( 1 - \tau ) \big ( 8 a - 4 - 4 \tau \big ) \big ] < 0 } } \end{array}

using Assumption 1 to obtain the strict inequality. Moreover, the continuity of $Q ^ { \prime }$ guarantees that there exists a neighborhood of $\gamma = 0$ wherein the inequality is still verified. 使用假设1来得到严格不等式。此外，\( Q' \) 的连续性保证存在一个以 \( \gamma = 0 \) 为中心的邻域，在该邻域内不等式仍然成立。

Proof of Proposition 6

命题6的证明

Note that $Q ^ { \prime } ( \gamma = 1 ) < 0$ if $\tau$ is low and $a$ is sufficiently high. Indeed, assume that $\begin{array} { r } { a > \frac { 3 J } { 4 J - A } \equiv \dot { a } ( \dot { a } > 0 } \end{array}$ ,given Assumption 2). Then, using the latter expression: 注意，当 $\tau$ 较低且 $a$ 足够大时，$Q’(\gamma=1) < 0$。事实上，假设 $a > \frac{3J}{4J - A} \equiv \dot{a} , (\dot{a} > 0$，给定假设 2)。然后，使用后一个表达式：

Q ^ { \prime } ( \gamma = 1 ) = A ( 1 - \tau ) + 2 \Delta ( - 4 \tau ^ { 2 } + 7 \tau - 3 ) + \frac { J } { a } ( 8 a \tau - 7 a + 6 - 7 \tau ) Q ^ { \prime } ( \gamma = 1 ) = A ( 1 - \tau ) + 2 \Delta ( - 4 \tau ^ { 2 } + 7 \tau - 3 ) + \frac { J } { a } ( 8 a \tau - 7 a + 6 - 7 \tau )

For $\textstyle \tau \leq { \frac { 3 } { 4 } }$ , $2 \Delta ( - 4 \tau ^ { 2 } + 7 \tau - 3 ) \leq 0$ , so we only need to care about $A ( 1 - \tau ) + { \textstyle \frac { J } { a } } ( 8 a \tau - 7 a + 6 - 7 \tau ) \equiv D ^ { \prime }$ . Thus, note that $\begin{array} { r } { \frac { \partial D ^ { \prime } } { \partial \tau } = - A + \frac { J } { a } ( 8 a - 7 ) } \end{array}$ , and i is ay to see tht, for $\begin{array} { r } { a > \dot { a } , \frac { \partial D ^ { \dagger } } { \partial \tau } > 0 } \end{array}$ Hence, suppose that $\scriptstyle \tau < { \frac { 3 } { 4 } }$ Then: 对于$\textstyle \tau \leq { \frac { 3 } { 4 } }$，$2 \Delta ( - 4 \tau ^ { 2 } + 7 \tau - 3 ) \leq 0$，因此我们只需关注$A ( 1 - \tau ) + { \textstyle \frac { J } { a } } ( 8 a \tau - 7 a + 6 - 7 \tau ) \equiv D ^ { \prime }$。由此，注意到$\begin{array} { r } { \frac { \partial D ^ { \prime } } { \partial \tau } = - A + \frac { J } { a } ( 8 a - 7 ) } \end{array}$，并且可以很容易看到，对于$\begin{array} { r } { a > \dot { a } , \frac { \partial D ^ { \dagger } } { \partial \tau } > 0 } \end{array}$。因此，假设$\scriptstyle \tau < { \frac { 3 } { 4 } }$，则：

D ^ { \prime } < { \frac { A } { 4 } } + { \frac { J } { a } } \left( - a + { \frac { 3 } { 4 } } \right) < { \frac { ( J - 1 ) ( 3 A - 1 2 J ) } { 1 2 J } } \leq 0 D ^ { \prime } < { \frac { A } { 4 } } + { \frac { J } { a } } \left( - a + { \frac { 3 } { 4 } } \right) < { \frac { ( J - 1 ) ( 3 A - 1 2 J ) } { 1 2 J } } \leq 0

as $\begin{array} { r } { a > \frac { 3 J } { 4 J - A } . } \end{array}$ This shows that, for $\begin{array} { r } { a > \frac { 3 J } { 4 J - A } } \end{array}$ and $\textstyle \tau < { \frac { 3 } { 4 } }$ $Q ^ { \prime } ( \gamma = 1 ) < 0$ .The continuity of $Q ‘$ again guarantees that there exists a neighborhood of $\gamma = 1$ wherein the ineqaliys til v hus, $\begin{array} { r } { \frac { \partial ^ { 2 } \bar { I _ { S ^ { \prime } } } } { \partial \Delta \partial \gamma } ( \gamma = \gamma ^ { \prime } ) < 0 } \end{array}$ if $\begin{array} { r } { a > \frac { 3 J } { 4 J - A } } \end{array}$ 4- and τ < 3, for γ’ close to 1. as $\begin{array} { r } { a > \frac { 3 J } { 4 J - A } . } \end{array}$ This shows that, for $\begin{array} { r } { a > \frac { 3 J } { 4 J - A } } \end{array}$ and $\textstyle \tau < { \frac { 3 } { 4 } }$ $Q ^ { \prime } ( \gamma = 1 ) < 0$ .The continuity of $Q ‘$ again guarantees that there exists a neighborhood of $\gamma = 1$ wherein the ineqaliys til v hus, $\begin{array} { r } { \frac { \partial ^ { 2 } \bar { I _ { S ^ { \prime } } } } { \partial \Delta \partial \gamma } ( \gamma = \gamma ^ { \prime } ) < 0 } \end{array}$ if $\begin{array} { r } { a > \frac { 3 J } { 4 J - A } } \end{array}$ 4- and τ < 3, for γ’ close to 1.

Lemma 5. When competitors engage in substantive CSR, in a low-differentiation market, if only a sufficiently small segment of the consumer market scrutinizes the quality of CSR communication, then product differentiation reduces the positive impact of the CSR price premium on a firm’s willingness to engage in substantive, as opposed to symbolic, CSR. 引理 5. 当竞争对手开展实质性企业社会责任（CSR）活动时，在低差异化市场中，如果只有消费者市场中足够小的一部分群体会审视CSR沟通的质量，那么产品差异化会削弱CSR价格溢价对企业开展实质性而非象征性CSR活动意愿的积极影响。

Proof of Lemma 5

引理5的证明

Assume that $\textstyle \tau > { \frac { 5 } { 6 } } .$ Then, using the latter expression: 假设 $\textstyle \tau > \frac{5}{6}$。然后，使用后一个表达式：

\begin{array} { c } { { Q ^ { \prime } ( \gamma = 1 ) = A ( 1 - \tau ) + 2 \Delta ( - 4 \tau ^ { 2 } + 7 \tau - 3 ) } } \ { { + { \displaystyle \frac { J } { a } } ( 8 a \tau - 7 a + 6 - 7 \tau ) > \displaystyle \frac { J } { a } ( a - 1 ) ( 6 \tau - 5 ) > 0 } } \end{array}

using Assumption 1 and the fact that $- 4 \tau ^ { 2 } + 7 \tau - 3 \geq 0$ for all $\scriptstyle { \frac { 3 } { 4 } } \leq \tau \leq 1$ .In addition, note also that: 使用假设1以及对于所有$\frac{3}{4} \leq \tau \leq 1$，$-4\tau^2 + 7\tau - 3 \geq 0$这一事实。此外，还需注意：

\frac { \partial ^ { 2 } Q ^ { \prime } } { \partial \gamma ^ { 2 } } = 2 \left[ - 3 A ( 1 - \tau ) - 2 \Delta ( 1 - \tau ) + \frac { J } { a } ( 6 - 3 a - 3 \tau ) \right] < - \frac { J } { a } D \frac{\partial^{2} Q^{\prime}}{\partial \gamma^{2}} = 2 \left[ - 3 A ( 1 - \tau ) - 2 \Delta ( 1 - \tau ) + \frac { J } { a } ( 6 - 3 a - 3 \tau ) \right] < - \frac { J } { a } D

where $D \equiv 6 a - 6 a \tau - 3 a \gamma + 3 \gamma \tau - 6 + 3 a + 3 \tau$ using Assumption 1 and the fact that $- 2 \Delta ( 1 - \tau ) < 0$ .Note, also, that $D { \ge } 0$ if 6−3τ3τγ≡ α . Then, it is easy to see that $\breve { a } \leq 1$ if $3 [ 1 - \tau - ( 1 - \tau ) \gamma ] \geq 0$ The last inequality holds, as a convex combination between 1 and $\gamma$ will never be above 1. As a result, 2Q{ <−D≤ 0, meaning that $Q ^ { \prime }$ is strictly concave. Thus, using the result in the proof of Lemma 3 and following steps similar to the proof of Proposition 3 (see above), there exists $\gamma ^ { \prime }$ in (0,1) such that, for $\begin{array} { r } { \gamma > \gamma ^ { \prime } , \frac { \partial ^ { 2 } \bar { I _ { S ^ { \prime } } } } { \partial \Delta \partial \gamma } > \mathbf { 0 } . } \end{array}$ where \( D \equiv 6 a - 6 a \tau - 3 a \gamma + 3 \gamma \tau - 6 + 3 a + 3 \tau \) using Assumption 1 and the fact that \( - 2 \Delta ( 1 - \tau ) < 0 \). Note, also, that \( D \ge 0 \) if \( \frac{6 - 3\tau}{3\tau\gamma} \equiv \alpha \). Then, it is easy to see that \( \breve{a} \leq 1 \) if \( 3 [ 1 - \tau - ( 1 - \tau ) \gamma ] \geq 0 \). The last inequality holds, as a convex combination between 1 and \( \gamma \) will never be above 1. As a result, \( 2Q < -D \leq 0 \), meaning that \( Q' \) is strictly concave. Thus, using the result in the proof of Lemma 3 and following steps similar to the proof of Proposition 3 (see above), there exists \( \gamma' \) in (0,1) such that, for

Discouraging Symbolic CSR

令人沮丧的象征性企业社会责任

This section considers a version of the model in which CSR communication requires an investment of $I _ { c } > 0$ . At $t = 0$ , the firms simultaneously choose whether or not to invest in substantive CSR $\left( I _ { S } \right)$ and in CSR communication $( I _ { C } )$ . Both costly and zero-cost CSR activities are implemented. At $t = 1$ , CSR communication efforts are implemented, and the firms choose their quantities. It is further assumed that the costs of both investments are firm specific: $I _ { S } ^ { i } , I _ { C } ^ { i }$ where $t = F$ . $C .$ Let $\pi _ { i } ^ { s }$ denote the profit of firm $_ i$ under strategy $s$ ,where $s$ is a pair $S C$ describing the decision to invest $I _ { S }$ and $I _ { C } ,$ respectively. Hence, $S \in { Y Y , Y N , N Y , N N }$ , where $Y$ corresponds to “Yes” and $N$ to “No.” For example, $s$ $= Y N$ if the firm invests in substantive CSR and does not invest in CSR communication. In this model, symbolic CSR engagement is denoted by $s = N Y ;$ the firm does not invest in substantive CSR but undertakes CSR communication, in addition to other low-cost CSR activities with no impact in socioenvironmental outcomes. Moreover, note that $\pi _ { F } ^ { S }$ also depends on the strategy chosen by firm $C$ ,and vice versa. This section considers a version of the model in which CSR communication requires an investment of \( I_C > 0 \). At \( t = 0 \), the firms simultaneously choose whether or not to invest in substantive CSR (\( I_S \)) and in CSR communication (\( I_C \)). Both costly and zero-cost CSR activities are implemented. At \( t = 1 \), CSR communication efforts are implemented, and the firms choose their quantities. It is further assumed that the costs of both investments are firm specific: \( I_S^i, I_C^i \) where \( t = F \). \( C \). Let \( \pi_i^s \) denote the profit of firm \( i \) under strategy \( s \), where \( s \) is a pair \( SC \) describing the decision to invest \( I_S \) and \( I_C \), respectively. Hence, \( S \in \{ YY, YN, NY, NN \} \), where \( Y \) corresponds to “Yes” and \( N \) to “No.” For example, \( s = YN \) if the firm invests in substantive CSR and does not invest in CSR communication. In this model, symbolic CSR engagement is denoted by \( s = NY \); the firm does not invest in substantive CSR but undertakes CSR communication, in addition to other low-cost CSR activities with no impact in socioenvironmental outcomes. Moreover, note that \( \pi_F^S \) also depends on the strategy chosen by firm \( C \), and vice versa.

As the main goal here is to examine how symbolic CSR engagement can be discouraged, this section focuses on the case in which symbolic CSR is a best response for firm $F .$ It is easy to see that this occurs if $I _ { S } ^ { F } > \pi _ { F } ^ { Y Y } - \pi _ { F } ^ { N Y } \equiv \underline { { I } } _ { S } ^ { # }$ and $I _ { C } ^ { F } \le \pi _ { F } ^ { N Y } - \pi _ { F } ^ { N N } \equiv \bar { I _ { C } ^ { # } }$ Y −NN = It. That is, substantive CSR is sufficiently costly for the firm, while CSR communication is sufficiently cheap. Of course, the expressions for $I _ { S } ^ { # }$ and $I _ { C } ^ { # }$ will also depend on the strategies chosen by firm $C$ 由于此处的主要目标是研究如何抑制象征性企业社会责任（CSR）参与行为，因此本节重点分析象征性CSR对企业F而言是最优反应的情形。显然，当 \( I_S^F > \pi_F^{YY} - \pi_F^{NY} \equiv \underline{I_S^\#} \) 且 \( I_C^F \le \pi_F^{NY} - \pi_F^{NN} \equiv \bar{I_C^\#} \) 时，这种情况会发生。也就是说，实质性CSR对企业而言成本过高，而CSR沟通成本则足够低。当然，\( I_S^\# \) 和 \( I_C^\# \) 的表达式还将取决于企业C所选择的策略。

Auditing of CSR Activities

企业社会责任活动审计

Given the descriptions in the main text, Table A1 summarizes the CSR price premium under the alternative monitoring scheme, as a function of firms’ investment choices. 根据正文的描述，表A1总结了替代监控方案下的企业社会责任（CSR）价格溢价，该溢价是企业投资选择的函数。

Thu iheil Thu iheil

U = A ( q _ { F } + q _ { C } ) + q _ { F } \Delta _ { F } + q _ { C } \Delta _ { C } - \frac { 1 } { 2 } ( q _ { F } ^ { 2 } + q _ { C } ^ { 2 } + 2 \gamma q _ { F } q _ { C } ) + m , U = A ( q _ { F } + q _ { C } ) + q _ { F } \Delta _ { F } + q _ { C } \Delta _ { C } - \frac { 1 } { 2 } ( q _ { F } ^ { 2 } + q _ { C } ^ { 2 } + 2 \gamma q _ { F } q _ { C } ) + m ,

TABLE A1 The CSR Price Premium and Firms’ CSR Choices: Auditing of CSR Activities
表A1 企业社会责任（CSR）价格溢价与企业CSR选择：CSR活动审计

where $\Delta _ { F }$ and $\Delta _ { C }$ correspond to one of the four options in Table A1, while all the other parameters follow the initial definition. We also assume that $A > 2 \Delta > 0$ . 其中\(\Delta_F\)和\(\Delta_C\)对应表A1中的四个选项之一，而所有其他参数遵循初始定义。我们还假设\(A > 2\Delta > 0\)。

The Nash equilibrium for this simultaneous game yields the optimal quantities produced by each firm, as a function of the choices of its competitor. As mentioned above, this section focuses on the case with $I _ { S } ^ { F } > \pi _ { F } ^ { Y Y } - \pi _ { F } ^ { N Y } \equiv I _ { S } ^ { # }$ and $I _ { c } ^ { F } \le \pi _ { F } ^ { N Y } - \pi _ { F } ^ { N N } \equiv \bar { I } _ { c } ^ { \bar { # } }$ . As $\pi _ { i } ^ { s } = ( q _ { i } ^ { s * } ) ^ { 2 }$ (see discussion above); for each choice of firm $C _ { i }$ ,we can find the analytical expressions for $I _ { S } ^ { # }$ and $\hat { I _ { c } ^ { # } }$ . These expressions are summarized in Table A2. 该同时博弈的纳什均衡给出了每个企业根据其竞争对手选择所生产的最优产量。如前所述，本节关注的情况是 $I_S^F > \pi_F^{YY} - \pi_F^{NY} \equiv I_S^#$ 和 $I_c^F \le \pi_F^{NY} - \pi_F^{NN} \equiv \bar{I}_c^{\bar{#}}$。由于 $\pi_i^s = (q_i^{s*})^2$（见上文讨论）；对于企业 $C_i$ 的每个选择，我们可以找到 $I_S^#$ 和 $\hat{I}_c^#$ 的解析表达式。这些表达式总结在表 A2 中。

The results discussed in the main text follow from visually inspecting the expressions in Table A2. For example, in all four quadrants, $\bar { I _ { c } ^ { # } } = 0$ if and only if $\xi = 0$ . Increased CSR communication costs work to the extent that they reduce the likelihood that $I _ { c } ^ { F } { \le } \bar { I } _ { c } ^ { \mp }$ . Finally, fines for excessive negative externalities may also work well, as they increase $I _ { S } ^ { # }$ However, as noted above, these policies would likely be Pareto inefficient, as they could reduce the economic surplus of at least some of the economic agents in the model. 正文讨论的结果是通过直观检查表A2中的表达式得出的。例如，在所有四个象限中，当且仅当 $\xi = 0$ 时，$\bar { I _ { c } ^ { # } } = 0$。增加CSR沟通成本会在一定程度上降低 $I _ { c } ^ { F } { \le } \bar { I } _ { c } ^ { \mp }$ 的可能性。最后，对过度负外部性的罚款也可能效果良好，因为它们会增加 $I _ { S } ^ { # }$。然而，如前所述，这些政策可能会导致帕累托低效，因为它们可能会减少模型中至少一些经济主体的经济剩余。

Government Regulates Negative Socioenvironmental Externalities

政府监管负面社会环境外部性

This section discusses the case in which negative socioenvironmental externalities are regulated by the government. At baseline, it assumes that any level of (negative) externalities per unit of product above $1 / a + d$ ,where $1 - 1 / a > d > 0$ , is considered unacceptable by government agencies. As a result, in case a symbolic CSR firm is audited by the government, it shall pay a fine of $B > 0$ , as it will produce one unit of (negative) externalities per unit of product (and $1 / a + d < 1$ , according to the assumptions above). On the other hand, because $1 / a + d > 1 /$ $a$ , a firm that invests in substantive CSR is not fined. Given the definitions above, and as the firms face a probability $\theta$ of being audited, they expect to receive a premium of $( 1 - \sigma ) \theta \Delta$ if they invest in substantive CSR, and 0 otherwise (in addition to paying the fine This section discusses the case in which negative socioenvironmental externalities are regulated by the government. At baseline, it assumes that any level of (negative) externalities per unit of product above $1 / a + d$, where $1 - 1 / a > d > 0$, is considered unacceptable by government agencies. As a result, in case a symbolic CSR firm is audited by the government, it shall pay a fine of $B > 0$, as it will produce one unit of (negative) externalities per unit of product (and $1 / a + d < 1$, according to the assumptions above). On the other hand, because $1 / a + d > 1 / a$, a firm that invests in substantive CSR is not fined. Given the definitions above, and as the firms face a probability $\theta$ of being audited, they expect to receive a premium of $( 1 - \sigma ) \theta \Delta$ if they invest in substantive CSR, and 0 otherwise (in addition to paying the fine

TABLE A2 Endogenous Thresholds $I _ { s } ^ { + }$ and $\hat { I _ { c } ^ { # } }$ :Auditing of CSR Activities
表 A2 内生阈值 $I _ { s } ^ { + }$ 和 $\hat { I _ { c } ^ { # } }$：企业社会责任活动审计

$B )$ . Table A3 presents the total CSR price premium received by the firms under each of the four possible strategies. $B )$ . 表A3展示了各公司在四种可能策略下获得的总企业社会责任（CSR）价格溢价。

The analysis here is similar to the previous one, meaning that it again focuses on the case where: 这里的分析与之前的类似，这意味着它再次聚焦于以下情况：

I _ { S } ^ { F } > \pi _ { F } ^ { Y Y } - \pi _ { F } ^ { N Y } + \theta B \equiv I _ { S } ^ { + } \mathrm { ~ a n d ~ } I _ { c } ^ { F } \leq \pi _ { F } ^ { N Y } - \pi _ { F } ^ { N N } \equiv I _ { c } ^ { # } I _ { S } ^ { F } ^ { > } \pi _ { F } ^ { Y Y } - \pi _ { F } ^ { N Y } + \theta B \equiv I _ { S } ^ { + } \text{ and } I _ { c } ^ { F } \leq \pi _ { F } ^ { N Y } - \pi _ { F } ^ { N N } \equiv I _ { c } ^ { # }

Table A4 presents these endogenous thresholds as a function of the competitors’ CSR investment choices. It is easy to see that $\begin{array} { r } { \frac { \partial I _ { c } ^ { \mathcal { \bar { H } } } } { \partial \theta } = 0 } \end{array}$ if the competitors do not invest in substantive CSR (i.e., NY and NN), $\begin{array} { r } { \frac { \partial I _ { c } ^ { \mathcal { \overline { { H } } } } } { \partial \theta } > 0 } \end{array}$ $\begin{array} { r } { \frac { \partial I _ { c } ^ { \mathcal { \overline { { H } } } } } { \partial \theta } < 0 } \end{array}$ if it chooses YN. 表A4将这些内生阈值呈现为竞争对手企业社会责任（CSR）投资选择的函数。可以很容易地看出，如果竞争对手不进行实质性的CSR投资（即NY和NN），则$\begin{array} { r } { \frac { \partial I _ { c } ^ { \mathcal { \bar { H } } } } { \partial \theta } = 0 } \end{array}$；如果竞争对手选择YN，则$\begin{array} { r } { \frac { \partial I _ { c } ^ { \mathcal { \overline { { H } } } } } { \partial \theta } > 0 } \end{array}$且$\begin{array} { r } { \frac { \partial I _ { c } ^ { \mathcal { \overline { { H } } } } } { \partial \theta } < 0 } \end{array}$。

Moreover, note that, if $\sigma = \xi$ ,then $\hat { I _ { c } ^ { # } }$ (auditing) $\leq \bar { I _ { c } ^ { # } }$ (regulation), with strict inequality when the competitor engages in substantive CSR. Thus, auditing by third parties is at least as effective as regulation of negative externalities in discouraging symbolic investment in CSR communication (and more effective, when competitors engage in substantive CSR). As seen in Tables A2 and A4, this is because uncertainty about being audited by government agencies (denoted by θ) creates a relative advantage to a symbolic CSR firm (vis-à-vis a substantive CSR competitor): there is a positive probability that the firm will not be punished even if it avoids investments in substantive CSR; thus, when the competitor does invest in these activities, this advantage translates into a higher willingness to symbolically invest in CSR communication. 此外，需要注意的是，如果 $\sigma = \xi$，那么 $\hat { I _ { c } ^ { # } }$（审计）$\leq \bar { I _ { c } ^ { # } }$（监管），当竞争对手进行实质性企业社会责任（CSR）时，不等式严格成立。因此，第三方审计在阻止象征性CSR沟通投资方面至少与负外部性监管一样有效（当竞争对手进行实质性CSR时，审计更有效）。如表A2和表A4所示，这是因为政府机构审计的不确定性（用θ表示）为象征性CSR企业（相对于实质性CSR竞争对手）创造了相对优势：即使企业避免进行实质性CSR投资，也存在不被处罚的正概率；因此，当竞争对手确实在这些活动上投资时，这种优势转化为企业在CSR沟通中象征性投资的更高意愿。

TABLE A3 The CSR Price Premium and Firms’ CSR Choices: Regulated Negative Externalities
表A3 企业社会责任溢价与企业的社会责任选择：受监管的负外部性

Model Extension: Baseline Model with Firms Deciding Simultaneously at $\mathbf { \nabla } _ { t } = \mathbf { 0 }$

模型扩展：企业在 $\mathbf { \nabla } _ { t } = \mathbf { 0 }$ 时同时决策的基准模型

This extension considers the case in which the firms’ CSR investment decisions are taken simultaneously. Thus, now, both stages of the game involve simultaneous decisions. Following Gibbons (1992), we solve for the equilibrium of the Cournot game, in the second stage, considering the different possible choices made in the first stage. These quantities match the equilibrium quantities found in both the cases analyzed above. Given the optimal quantities determined in the second stage, we then roll back and solve for the Nash equilibrium of the simultaneous game played in the first stage (Gibbons, 1992). First, using the previous definitions, note that: This extension considers the case in which the firms’ CSR investment decisions are taken simultaneously. Thus, now, both stages of the game involve simultaneous decisions. Following Gibbons (1992), we solve for the equilibrium of the Cournot game, in the second stage, considering the different possible choices made in the first stage. These quantities match the equilibrium quantities found in both the cases analyzed above. Given the optimal quantities determined in the second stage, we then roll back and solve for the Nash equilibrium of the simultaneous game played in the first stage (Gibbons, 1992). First, using the previous definitions, note that:

\bar { I _ { S } } ^ { \prime } < \bar { I _ { S } } - \Delta \gamma ( 1 - \tau ) - \frac { J } { a } ( a \gamma - \gamma ) < 0 \bar { I _ { S } } ^ { \prime } < \bar { I _ { S } } - \Delta \gamma ( 1 - \tau ) - \frac { J } { a } ( a \gamma - \gamma ) < 0

which is always true (as $a > 1$ and $\tau \leq 1$ . Given this result, let $B ^ { i } ( j )$ denote the best response of firm $_ i$ to firm $j ^ { \prime } s$ action. Also, let $I$ denote the decision to invest and $N$ denote the opposite decision (do not invest) in substantive CSR. Thus, the following holds, according to the rationale developed above: 这始终成立（因为 \( a > 1 \) 且 \( \tau \leq 1 \)。基于此结果，令 \( B^i(j) \) 表示企业 \( i \) 对企业 \( j \) 行动的最优反应。此外，令 \( I \) 表示实质性企业社会责任（CSR）中的投资决策，\( N \) 表示相反决策（不投资）。因此，根据上述推导，以下结论成立：

B ^ { F } ( N ) = \left{ \begin{array} { l } { { I , i f I _ { S } \leq \bar { I _ { S } } } } \ { { N , i f I _ { S } > \bar { I _ { S } } } } \end{array} ; \right. B ^ { F } ( N ) = \left{ \begin{array} { l } { { I , if I _ { S } \leq \bar { I _ { S } } } } \ { { N , if I _ { S } > \bar { I _ { S } } } } \end{array} ; \right.

TABLE A4 Endogenous Thresholds $I _ { s } ^ { + }$ and $\hat { I _ { c } ^ { # } }$ : Regulated Negative Externalities
表 A4 内生阈值 \( I _ { s } ^ { + } \) 和 \( \hat { I _ { c } ^ { \# } } \)：受监管的负外部性

B ^ { F } ( I ) = \left{ \begin{array} { l l } { I , i f I _ { S } \le \bar { I _ { S } } ^ { \prime } } \ { N , i f I _ { S } > \bar { I _ { S } } ^ { \prime } } \end{array} \right. B ^ { F } ( I ) = \left{ \begin{array} { l l } { I , i f I _ { S } \le \bar { I _ { S } } ^ { \prime } } \ { N , i f I _ { S } > \bar { I _ { S } } ^ { \prime } } \end{array} \right.

B ^ { C } ( N ) = \left{ \begin{array} { l } { I , i f I _ { S } \le \bar { I _ { S } } } \ { N , i f I _ { S } > \bar { I _ { S } } } \end{array} ; \right. B ^ { C } ( N ) = \left{ \begin{array} { l } { I , i f I _ { S } \le \bar { I _ { S } } } \ { N , i f I _ { S } > \bar { I _ { S } } } \end{array} ; \right.

B ^ { C } ( I ) = \left{ \begin{array} { l l } { I , i f I _ { S } \leq \bar { I _ { S } } ^ { \prime } } \ { N , i f I _ { S } > \bar { I _ { S } } ^ { \prime } } \end{array} \right. B ^ { C } ( I ) = \left{ \begin{array} { l l } { I , i f I _ { S } \leq \bar { I _ { S } } ^ { \prime } } \ { N , i f I _ { S } > \bar { I _ { S } } ^ { \prime } } \end{array} \right.

Given these best responses, and considering that a Nash equilibrium requires both players to simultaneously play a best response (Gibbons, 1992), we have the following equilibria: 考虑到这些最优反应，并且纳什均衡要求两个参与者同时采取最优反应（Gibbons，1992），我们有以下均衡：

• If $I _ { S } { \le } \bar { I _ { S } ^ { - } } { < } \bar { I _ { S } }$ , both firms invest in substantive CSR If $\bar { I _ { S } ^ { \prime } } ^ { \prime } \leq I _ { S } < \bar { I _ { S } }$ , only one firm invests in substantive CSR If $I _ { S } > \bar { I _ { S } } > \bar { I _ { S } } ^ { \prime }$ , no firm invests in substantive CSR. • 如果 $I_S \leq \bar{I_S^-} < \bar{I_S}$，两家企业都会进行实质性的企业社会责任（CSR）投资；如果 $\bar{I_S’}^\prime \leq I_S < \bar{I_S}$，只有一家企业进行实质性CSR投资；如果 $I_S > \bar{I_S} > \bar{I_S}^\prime$，则没有企业进行实质性CSR投资。

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