Strategic CSR in Asymmetric Cournot Duopoly

Planer-Friedrich, Lisa; Sahm, Marco Article — Published Version Strategic CSR in Asymmetric Cournot Duopoly Journal of Industry, Competition and Trade Provided in Cooperation with: Springer Nature Suggested Citation: Planer-Friedrich, Lisa; Sahm, Marco (2020) : Strategic CSR in Asymmetric Cournot Duopoly, Journal of Industry, Competition and Trade, ISSN 1573-7012, Springer US, New York, NY, Vol. 21, Iss. 1, pp. 33-42, https://doi.org/10.1007/s10842-020-00335-3 This Version is available at: https://hdl.handle.net/10419/288328 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Industry, Competition & Trade (2021) 21:33– 24 https://doi.org/10.1007/s10842-020-00335-3 Strategic CSR in Asymmetric Cournot Duopoly Lisa Planer-Friedrich1·Marco Sahm1,2 Received: 26 November 2019 / Revised: 19 February 2020 / Accepted: 24 February 2020 / ©The Author(s) 2020 Abstract We examine the strategic use of corporate social responsibility (CSR) in Cournot competition between two firms that differ in their marginal costs of production. The level of CSR determines the weight a firm puts on consumer surplus in its objective function before it decides upon supply. We show that the more efficient firm chooses a higher CSR level, reinforcing its dominant position. If there are sufficiently large fixed costs of CSR, only the more efficient firm will engage in CSR. Keywords Corporate social responsibility ·Cournot duopoly ·Asymmetric costs · Heterogenous firms JEL Classification D43 ·L13 ·L21 ·L22 1 Introduction Corporate social responsibility (CSR) refers to all social and environmentally friendly activities of a firm beyond its legal requirements (Kitzmueller and Shimshack 2012). In the past decades, CSR has increasingly become a concern for many firms, particularly large- and mid-cap companies (Benn and Bolton 2011;KPMG2017). Among the various motives for CSR, its strategic use in markets with imperfect competition plays an important role (Garriga and Mel´ e2004;B ´ enabou and Tirole 2010). The basic idea is that even pure profitmaximizing firms engage in CSR because it may serve as a commitment device for their strategy choices. Although overall empirical evidence on the relation between firms’ CSR activities and their financial performance is mixed, meta-analyses such as Aguinis and Glavas (2012) Lisa Planer-Friedrich [email protected] Marco Sahm [email protected] 1Department of Economics, Otto-Friedrich-Universit¨ at Bamberg, Feldkirchenstraße 21, 96052, Bamberg, Germany 2CESifo, Poschingerstraße 5, 81679 Munich, Germany Published online: 11 pril 2020 A Journal of Industry, Competition & Trade (2021) 21:33– 24 confirm a small positive relation. Indeed, many recent studies find a positive correlation (Jo and Harjoto 2011; Eccles et al. 2014; Flammer 2015). This raises the question about causality: does CSR boost profits or can more profitable firms afford more CSR? We address this question within a simple model of Cournot competition between two firms that differ in their marginal costs of production. The level of CSR determines the weight a firm puts on consumer surplus in its objective function before it decides upon supply. We find a mutual causality: the more efficient firm chooses a higher CSR level, reinforcing its dominant position. If there are sufficiently large fixed costs of CSR, an equilibrium will arise in which only the more efficient firm chooses a positive level of CSR. 2TheModel We consider Cournot competition between two profit-maximizing firms on the market for some homogeneous good with (normalized) linear inverse demand1p=1−(q1+q2), where pdenotes the price of the good and qidenotes the output of firm i∈{1,2}. Marginal costs of production are assumed to be constant with c1=0 (normalization) and c2=c, where 0 ≤c≤1, i.e., firm 1 is (possibly) more efficient than firm 2. Competition between firms is modeled as a two-stage game. In the first stage of the game, the firms simultaneously choose their level of CSR. The CSR level of firm i∈{1,2} is understood as the weight θi≥0 on consumer surplus CS in addition to profits πiin its objective function:2 Vi=πi+θi·CS =(1−qi−qj−ci)qi−Ki+1 2θi(qi+qj)2, where Kirepresents a quasi-fixed cost of CSR, i.e., Ki=0ifθi=0andKi=Z≥0 if θi>0.3Such a commitment to an objective function can be thought of as signing an appropriate corporate charter or hiring a manager known to have appropriate preferences. Our framework may thus also be interpreted as a model of strategic delegation (Vickers 1985; Fershtman and Judd 1987;Sklivas1987). In the second stage of the game, firms decide simultaneously on their output levels qi≥0 in order to maximize their objective functions Vi. 3Analysis In this section, we abstract from costs of CSR (Z=0) and solve the game by backward induction for its subgame perfect equilibria (SPE). We focus on potential SPE in which θi∈[0,1]for i∈{1,2}, i.e., no firm puts more weight on consumer surplus than on profits. 1In the present framework, a large class of more general demand functions yields the same strategic incentives (Planer-Friedrich and Sahm 2020). 2Incorporating consumer surplus into the firm’s objective function is a standard way of modeling CSR (e.g., Goering 2008; Kopel et al. 2014;Wang2016; Fanti and Buccella 2017;Zennyo2017; Nakamura 2018; Planner-Friedrich and Sahm 2020; Leal et al. 2019). An alternative approach considers CSR as a means of vertical product differentiation (e.g., Arora and Gangopadhyay 1995; Cremer and Thisse 1999;Garc ´ ıa- Gallego and Georgantz´ ıs 2009; Manasakis et al. 2013; Manasakis et al. 2014; Liu et al. 2015). 3In this model, firms choose their CSR level strategically to commit to a higher output. For this, firms need to believably signal their commitment. Thus, fixed costs of CSR may arise, e.g., due to efforts to obtain a CSR label or the preparation of a CSR report (Sharma 2018). 34 Journal of Industry, Competition & Trade (2021) 21:33– 24 At the second stage of the game, the first-order conditions ∂Vi/∂qi=0 imply the reaction functions q1(q2)=1−(1−θ1)q2 2−θ1 , q2(q1)=1−c−(1−θ2)q1 2−θ2 , and thus, the second stage quantity choices as functions of the CSR levels: q1=1−θ2+θ1+c(1−θ1) 3−θ1−θ2 ,(1) q2=1−θ1+θ2−c(2−θ1) 3−θ1−θ2 .(2) At the first stage, the firms anticipate these choices and maximize their respective profits π1=(1−θ2+c−θ1)(1−θ2+c+(1−c)θ1) (3−θ1−θ2)2,(3) π2=(1−2c−(1−c)θ1−(1−c)θ2)(1−2c−(1−c)θ1+θ2) (3−θ1−θ2)2,(4) by the choice of their CSR levels. The first-order conditions ∂πi/∂θi=0imply θ1(θ2)=(1−θ2)2+(1−θ2)c 3−θ2−c,(5) θ2(θ1)=(1−θ1)2−(1−θ1)(2−θ1)c 3−θ1−(2−θ1)c .(6) It is straightforward to show that 0 ≤θ1(θ2)<1forall0<c<1andallθ2∈[0,1]as well as θ2(θ1)<1forall0<c<1andallθ1∈[0,1]. Moreover, 0 <θ 2(θ1)for 0 <c<1 and θ1∈[0,1]if and only if θ1<1−2c 1−c.(7) Consequently, for all 0 <c<1andθ1,θ 2∈[0,1], the first stage best responses of the firms are given by the reaction functions r1(θ2):= θ1(θ2)and r2(θ1):= max{θ2(θ1), 0}, where θ1(θ2)and θ2(θ1)are defined by Eqs. 5and 6, respectively. Figure 1illustrates the equilibrium CSR levels depicting the reaction functions r1and r2for the cost differentials c=0, c=1/4, and c=1/3, respectively. Lemma 1 in the Appendix provides the comparative statics properties of the reaction functions. In particular, it shows that an increase in cincreases r1and decreases r2wherever positive. For c=1/3, we have r1(0)=θ1(0)=1/2andr2(1/2)=θ2(1/2)=0 according to Eqs. 5and 6,and thus, r1and r2intersect at (θ1,θ 2)=(1/2,0). Lemma 1 then implies that, for any c≥1/3, we always have θ2=0wherer1and r2intersect. If θ2=0, however, Eq. 5implies the best response θ1=(1+c)/(3−c), and thus, q2<0forallc>1/3byEq.2, i.e., the non-negativity constraint on the quantity of firm 2 will be violated. This proves 35 Journal of Industry, Competition & Trade (2021) 21:33– 24 Fig. 1 CSR levels in the SPE with asymmetric marginal costs Proposition 1 If c≥1/3, the less efficient firm will leave the market. Notice that, without the strategic use of CSR (θ1=θ2=0), the threshold marginal cost above which the less efficient firm leaves the market is larger (c=1/2). Strategic CSR may thus increase the market power of more efficient firms and foster market consolidation as well as the adaption of new technologies. For smaller marginal costs, the intersection of the reaction functions r1and r2constitutes a SPE. We asterisk the corresponding equilibrium values. Proposition 2 For all c∈(0,1/3), the two-stage game with strategic CSR and Cournot competition between two asymmetric firms has a SPE in which (a) The firm with the lower marginal costs chooses a higher CSR level, produces more output, and earns higher profits, i.e., θ∗ 1>θ ∗ 2>0,q∗ 1>q ∗ 2>0, and π∗ 1>π ∗ 2>0 for all 0<c<1/3. (b) An increase in the cost differential increases the CSR level of the advantaged firm and decreases the CSR level of the disadvantaged firm, i.e., dθ∗ 1/dc > 0and dθ∗ 2/dc < 0 for all c∈(0,1/3). The proof can be found in the Appendix. For the intuition behind these results, note that in this model a higher CSR level (i.e., more weight on consumer surplus) represents a strategic commitment to a higher output. Since the more efficient firm faces lower costs of production, increasing its output is less costly for this firm. Therefore, it has stronger 36 Journal of Industry, Competition & Trade (2021) 21:33– 24 incentives to use this commitment device.4The model thus applies particularly well to environments in which CSR measures aim at a high market coverage, e.g., in the provision of pharmaceuticals in developing countries. Proposition 2 is in line with several findings in the recent literature on strategic delegation. Straume (2006) and Fanti and Meccheri (2017) also find that the more efficient firm chooses a higher weight on the additional objective if managers maximize a weighted combination of profits and sales. For revenues as additional objective, Delbono et al. (2016) show that the more efficient firm earns higher equilibrium profits.5Moreover, Colombo (2019) finds that for sufficiently high cost differences the more efficient firm may even earn higher profits in the delegation equilibrium than if both firms abstained from delegation. 4 Inclusion of Fixed Costs for CSR Fixed costs for CSR may induce firms to shy away from its strategic use. Based on numerical computations, we demonstrate that, depending on the level of fixed costs Z, different types of equilibria may exist: as Fig. 2illustrates (for c=0.02), we may find not only interior solutions, I, in which both firms choose positive CSR levels, but also right (left) corner solutions, R(L), in which only the more (less) efficient firm chooses a positive CSR level, or an equilibrium, O, in which neither firm engages in CSR. Figure 3depicts which equilibria may occur for different combinations of asymmetric marginal costs of production, c, and symmetric quasi-fixed costs of CSR, Z. Using Eqs. 3 through 6, we compute the threshold values for Zfor each given cin the following way: Z0=π2(θ1(0), θ2(θ1(0))) −π2(θ1(0), 0), Z1=π2(θ∗ 1,θ∗ 2)−π2(θ∗ 1,0), Z2=π1(θ1(θ2(0)), θ2(0)) −π1(0,θ 2(0)), Z3=π2(0,θ 2(0)) −π2(0,0), Z4=π1(θ1(0), 0)−π1(0,0). Intuitively, if the costs of CSR are sufficiently small (below Z1), it may pay off for both firms to choose positive CSR levels resulting in an interior solution (I). By contrast, if the costs of CSR are prohibitively large (above Z4), both firms will abandon CSR in equilibrium (O). In the range of intermediate costs of CSR (above Z0and below Z4), corner solutions may arise: investing these costs and choosing a sufficiently high level of CSR, one firm can “take the lead” and commit to a quantity that makes such a costly commitment unprofitable for the other firm. Since a commitment to a larger quantity is less attractive for the less efficient firm (and the less so the higher its production costs c), the range of parameters for 4Intuitively, the same reasoning also applies to Cournot competition with differentiated products. On markets with price (Bertrand) competition, however, the strategic use of CSR as a commitment to increase output is of no avail: it would be understood as a commitment to lower prices where instead some commitment to higher prices would be needed (Fershtman and Judd 1987). Planer-Friedrich and Sahm (2020) offer a formal treatment of these issues in a framework with symmetric firms. 5This result also holds for sufficiently high cost differences in the analysis of Fanti and Meccheri (2017). 37 Journal of Industry, Competition & Trade (2021) 21:33– 24 Fig. 2 Best responses and equilibria at different levels of Z(c=0.02) 38 Journal of Industry, Competition & Trade (2021) 21:33– 24 Z1 Z2 Z3 Z4 Z0 I I+R I+R+L R+L R R R O 0.05 0.10 0.15 0.20 0.25 0.30 c 0.005 0.010 0.015 0.020 0.025 Z Fig. 3 Occurrence of equilibria depending on cand Z a left corner solution (L), where only the less efficient firm engages in CSR, is restricted to the area above Z2and below Z3. By contrast, in the whole area between Z0and Z4,there always exists a right corner solution (R), where only the more efficient firm engages in CSR. Including fixed costs for CSR, our model thus provides an explanation why firms with and without CSR engagement may coexist. 5 Conclusion We have examined the strategic use of corporate social responsibility (CSR) in Cournot competition between two firms that differ in their marginal costs of production. The level of CSR determines the weight a firm puts on consumer surplus in its objective function before it decides upon supply. The results demonstrate that the strategic use of CSR complements cost advantages and reinforces differences in market power. Moreover, (symmetric) fixed costs of CSR provide an explanation for the coexistence of (highly profitable) firms that engage in CSR and (less profitable) firms that abstain from CSR. In the long-run, strategic CSR may thus foster market consolidation and accelerate the adoption of superior technologies. The lessons for policymakers are twofold: First, the observation of differing CSR levels may convey information on differing costs of production. On markets with imperfect competition, a firm’s CSR level may also be an indicator of market power. Thus, such information may be useful for regulatory purposes. Second, if politics can control the fixed costs of CSR, e.g., by establishing an official CSR label, it may be able to influence the (type of) market equilibrium and outcome. We find both cases in which the government can increase consumer surplus by reducing the fixed costs of CSR and cases in which it can do so by 39 Journal of Industry, Competition & Trade (2021) 21:33– 24 raising them.6A comprehensive welfare analysis is, however, beyond the scope of this short paper. Acknowledgments We thank the editor and an anonymous referee. Open Access funding provided by Projekt DEAL. 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Appendix: Proof of Proposition 2 In order to prove part (a) of Proposition 2, first notice that for c=0, a (unique) SPE exists (Planer-Friedrich and Sahm 2020) and is symmetric with θ∗ 1=θ∗ 2=(5−√17)/4 according to Eqs. 5and 6. Now, suppose that an SPE with θ∗ i∈[0,1]for i∈{1,2}exists for all 0<c<1 and has the properties stated in part (b) of Proposition 2. Then these properties imply θ∗ 1>θ ∗ 2for all 0 <c<1, which, in turn, implies q∗ 1>q ∗ 2according to Eqs. 1and 2, and, consequently, π∗ 1>π ∗ 2. It remains to show that an SPE with θ∗ i∈[0,1]for i∈{1,2}exists for all 0 <c<1 and has the properties stated in part (b). Notice that r1(1)=r2(1)=0andr1(0)>0for all 0 <c<1. For c=1/3, we have r1(0)=θ1(0)=1/2andr2(1/2)=θ2(1/2)=0 according to Eqs. 5and 6, and thus, θ∗ 1=1/2andθ∗ 2=0 constitute an SPE. The existence of an SPE for all 0 <c<1inwhichθ∗ i∈[0,1]for i∈{1,2}and the respective comparative statics dθ∗ 1/dc > 0forallc∈(0,1)and dθ∗ 2/dc < 0forallc∈(0,1/3)as well as θ∗ 2=0forallc∈[1/3,1)now result from the following: Lemma 1 For all 0<c<1and θ1,θ 2∈[0,1], the reaction function (a) r1strictly decreases in θ2, i.e., ∂r1/∂θ2<0, (b) r2strictly decreases in θ1, i.e., ∂r2/∂θ1<0, wherever positive. (c) r1shifts strictly upward in c, i.e., ∂r1/∂c > 0, for all θ2∈[0,1) (d) r2shifts strictly downward in c, i.e., ∂r2/∂c < 0, for all θ1∈[0,1)wherever positive. 6For the example from above with c=0.02, the table below displays the consumer surplus and the firms’ profits in the different equilibria (rounded to four decimals). Starting from a corner solution or an equilibrium without CSR, the government may enforce an interior solution and increase consumer surplus by reducing the fixed costs of CSR (below Z0;seeFig.3). If such a reduction is not feasible, the government may still be able to reach an improvement: starting from a left corner solution, raising the fixed costs (above Z3;seeFig.3) leads to a right corner solution and increases consumer surplus. CS π1π2 I0.2988 0.0925 −Z0.0757 −Z R0.2775 0.1301 −Z0.0552 L0.2738 0.0676 0.1152 −Z O0.2178 0.1156 0.1024 40