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Strategic corporate social responsibility, imperfect competition, and market concentration

Abstract

We examine the strategic use of corporate social responsibility (CSR) in imperfectly competitive markets. Before firms decide upon supply, they choose a level of CSR which determines the weight they put on consumer surplus in their objective function. First, we consider Cournot competition and show that the endogenous level of CSR is positive for any given number of firms. However, positive CSR levels imply smaller equilibrium profits. Second, we find that an incumbent monopolist can use CSR as an entry deterrent. Both results indicate that CSR may increase market concentration. Finally, we show that CSR levels decrease as the degree of product heterogeneity increases in Cournot competition and are zero in Bertrand Competition.

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Notes

  1. A second important branch relies on the assumption that (some) consumers have a higher willingness to pay for socially responsibly (Baron 2009; García-Gallego and Georgantzís 2009; Manasakis et al. 2013, 2014; Liu et al. 2015; Pecorino 2016) or environmentally friendly (Arora and Gangopadhyay 1995; Cremer and Thisse 1999; Tian 2003; Bansal and Gangopadhyay 2003) produced goods and models CSR as a form of product differentiation.

  2. Lambertini and Tampieri (2012, 2015), Lambertini (2013), and Lambertini et al. (2016) include both consumer surplus and some environmental externality in the objective function of a socially responsible firm. Incorporating consumer surplus in the objective function of a firm is also a widely-used way of taking all kinds of non-profit motives into account (see, e.g., Goering 2007, 2008; Lien 2002; Saha 2014). Models of consumer cooperatives (Mikami 2003; Marini and Zevi 2011; Kopel and Marini 2014) put full weight on consumer surplus and no weight on profits.

  3. In an extension to their baseline model, Fanti and Buccella (2017a, Supplement) also allow for a continuous decision on CSR levels which, however, leads to a different game structure and the possibility of asymmetric equilibria. In Sect. 5.1, we discuss the similarities and differences in more detail.

  4. Section 5.1 extends the model to heterogeneous goods. Section 5.2 illustrates that, under rather mild conditions, the strategic incentives remain unchanged for a general inverse demand function p(q) with \(dp/dq<0\).

  5. In fact, constant marginal costs do not influence the equilibrium level of CSR as long as they are symmetric.

  6. This two-stage game may be understood as a model of strategic delegation (Vickers 1985; Fershtman and Judd 1987; Sklivas 1987) offering a commitment to CSR (Baron 2008; Kopel and Brand 2012; Manasakis et al. 2014; Kopel and Lamantia 2016). Alternatively, it may be interpreted as an indirect evolutionary game (Güth and Yaari 1992; Königstein and Müller 2001) in which the most profitable CSR levels prevail.

  7. The following table contains the respective values of total surplus net of aggregate fixed costs in a market without CSR:

    figure a

    .

  8. This leads to the testable hypothesis that large firms engage more in CSR than small ones.

  9. The assumption of Cournot competition in the second stage of entry games is standard in a major part of the literature (see, e.g., Dixit 1980; Maskin 1999; Fanti and Buccella 2017c) and modern textbooks (see, e.g., Belleflamme and Peitz 2015) and allows for a close link to the analysis of Sect. 3. Assuming Stackelberg competition instead will increase (decrease) the range of blockaded/deterred entry if the incumbent is the leader (follower) but does not change the results qualitatively (Dixit 1980).

  10. \(e^* \approx 0.0034\).

  11. This basic tradeoff will remain qualitatively unchanged if we assume Stackelberg competition instead of Cournot competition in the second stage of the entry game, whereas its exact solution obviously depends on the form of competition.

  12. The inverse demand functions result as the solution to the problem of a representative household maximizing quadratic utility \(U=q_1+q_2-\frac{1}{2}(q_1^2+2\gamma q_1q_2+q_2^2)\); see, e.g., Singh and Vives (1984) or Häckner (2000).

  13. Notice that an increase in the CSR-level always implies an upward-shift of the reaction function (16) because \(\frac{dq_i}{d\theta _i}= \frac{1+\gamma q_j}{(2-\theta _i)^2} >0\) for all \(0< |\gamma | < 1\) and \(i \not = j\).

  14. Notice, however, that this negative result hinges on our assumption that a firm’s demand does not depend directly on its level of CSR. Instead, if consumers have a preference for socially responsibly produced goods CSR may be used strategically as a means of product differentiation and possibly reduce competition this way (Conrad 2005; Liu et al. 2015).

  15. The reason is that a CSR level of zero will never be a best response if it can be freely adjusted but might be a better response (to 0 or k) than k.

  16. See Planer-Friedrich and Sahm (2018) for an explicit formulation of such a game structure in the context of CSR.

  17. Hahn’s condition is known to be a sufficient condition for the strategic success of various kinds of manipulations of a firm’s objective function, while often it imposes a stricter condition than necessary (Cornes and Itaya 2016).

  18. Although the formal analysis (of the first stage of the game) is not tractable for an arbitrary number of firms (\(n>2\)), the corresponding reaction function (in the second stage of the game) is then given by \(q_i = \frac{1-\gamma (1-\theta _i)\sum _{j \not = i}q_j}{2-\theta _i}\) and illustrates that the subgames of the second stage are aggregative in the sense that a firm’s output decision depends only on the sum of all other firms’ outputs. Therefore, firm i’s strategic incentives to commit to a certain reaction function by the choice of an appropriate CSR-level \(\theta _i\) in stage 1 of the game are, qualitatively, the same as in the case with only one opponent (n = 2).

  19. The system of equations (19) has three symmetric and two asymmetric real valued solutions, but only the symmetric solution in (20) is feasible in the sense that \(0 \le \theta _i \le 1\) for all \(0< |\gamma | < 1\).

  20. Although the formal analysis (of the first stage of the game) is not tractable for an arbitrary number of firms (\(n>2\)), the corresponding reaction function (in the second stage of the game) is then given by \(p_i = \frac{(1-\theta _i)(1-\gamma +\gamma \sum _{j \not = i}p_j)}{(2-\theta _i)[1+(n-2)\gamma ]}\) and illustrates that the subgames of the second stage are aggregative in the sense that a firm’s price decision depends only on the sum of all other firms’ prices. Therefore, firm i’s strategic incentives to commit to a certain reaction function by the choice of an appropriate CSR-level \(\theta _i\) in stage 1 of the game are, qualitatively, the same as in the case with only one opponent (n = 2).

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Acknowledgements

We thank two anonymous referees and the participants of the following conferences, workshops, and seminars for their helpful comments and suggestions: Oligo Workshop 2015 (Madrid), 6th Bavarian Micro Day 2015 (Bamberg), Public Economics Research Seminar 2015 (Munich), Annual Meeting of the European Economic Association 2015 (Mannheim), Economic Research Seminar at TUM 2015 (Munich), CESifo Area Conference on Applied Microeconomics 2016 (Munich), Joint Annual Meeting of the Slovak Economic Association and the Austrian Economic Association (NOeG-SEA) 2016 (Bratislava), 22nd BGPE Research Workshop 2016 (Munich), 5th World Congress of the Game Theory Society (GAMES) 2016 (Maastricht), 43rd Annual Conference of the European Association for Research in Industrial Economics (EARIE) 2016 (Lisbon), Economics Research Seminar at UJI 2018 (Castellón de la Plana).

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Appendices

Appendix

A Proof of Proposition 3 and Corollary 5

Given the inverse demands (14), consumer surplus can be written as follows:

$$\begin{aligned} CS = \frac{1}{2} \cdot \left[ \gamma (q_1+q_2)^2 + (1-\gamma ) (q_1^2+q_2^2)\right] = q_1^2 + q_2^2 + 2 \gamma q_1q_2. \end{aligned}$$
(15)

In the second stage of the game, firm \(i \in \{1,2\}\) chooses \(q_i\) in order to maximize \(V_i=\pi _i + \theta _i CS\). For \(i,j \in \{1,2\}\), \(i \not = j\), the first-order conditions \(\frac{\partial V_i}{\partial q_i} = 0\) imply the reaction functionsFootnote 18

$$\begin{aligned} q_i = \frac{1-\gamma (1-\theta _i)q_j}{2-\theta _i}. \end{aligned}$$
(16)

Solving the system of equations (16) yields

$$\begin{aligned} q_i = \frac{(1-\gamma )+(1-\theta _j)+\gamma \theta _i}{2+(2-\gamma ^2)(1-\theta _j) -[1+(1-\gamma ^2)(1-\theta _j)]\theta _i} \end{aligned}$$
(17)

for \(i,j \in \{1,2\}\), \(i \not = j\). We now use (14) and (17) to compute the corresponding prices

$$\begin{aligned} p_i = \frac{(1-\gamma )+(1-\theta _j)-[1+(1-\gamma ^2)(1-\theta _j)]\theta _i}{2+(2-\gamma ^2)(1-\theta _j)-[1+(1-\gamma ^2)(1-\theta _j)]\theta _i}. \end{aligned}$$
(18)

In the first stage of the game, firm \(i \in \{1,2\}\) chooses \(\theta _i\) in order to maximize \(\pi _i=p_iq_i\). Using (17) and (18), the first-order conditions \(\frac{\partial \pi _i}{\partial \theta _i} = 0\) imply the reaction functions

$$\begin{aligned} \theta _i = \frac{\gamma ^2(1-\theta _j)(2-\theta _j-\gamma )}{[2-\theta _j-(1-\theta _j) \gamma ^2](2-\theta _j+\gamma )} \end{aligned}$$
(19)

for \(i,j \in \{1,2\}\), \(i \not = j\). Solving the system of equations (19) for \(i,j \in \{1,2\}\), \(i \not = j\) yields a unique feasible solution:Footnote 19

$$\begin{aligned} \theta _i = \frac{2(1+\gamma )+\gamma ^2-\sqrt{[2(1+\gamma )]^2+\gamma ^4}}{2(1+\gamma )} =: \theta _C^*(\gamma ) > 0. \end{aligned}$$
(20)

Using (20), it is straightforward to show that \(\frac{d\theta _C^*(\gamma )}{d\gamma } > 0\) for \(\gamma >0\), and \(\frac{d\theta _C^*(\gamma )}{d\gamma } < 0\) for \(\gamma <0\). This proves Proposition 3.

Finally, to prove Corollary 5, we use (20) and compute firm i’s equilibrium profit

$$\begin{aligned} \pi _i^* = \frac{2\left( \sqrt{[2(1+\gamma )]^2+\gamma ^4}-\gamma ^2-2\gamma )\right) }{\left( \sqrt{[2(1+\gamma )]^2+\gamma ^4}-\gamma ^2+2\right) ^2} \end{aligned}$$

whereas the regular Cournot profit without strategic CSR (\(\theta _1=\theta _2=0\)) equals \(\pi _i^C=\frac{1}{(2+\gamma )^2}\). A comparison shows that, in the relevant range, \(\pi _i^* > \pi _i^C\) if and only if \(-1< \gamma <0\).

B Proof of Proposition 4

The inverse demand functions (14) imply the following direct demands

$$\begin{aligned} q_i = \frac{1-\gamma - p_i + \gamma p_j}{1-\gamma ^2} \end{aligned}$$
(21)

for \(i,j \in \{1,2\}\), \(i\ne j\). Using (15) and (21), consumer surplus can be expressed in terms of prices:

$$\begin{aligned} CS = \frac{2(1-\gamma )(1-p_1-p_2) - 2\gamma p_1p_2 + p_1^2 +p_2^2}{2(1-\gamma ^2)}. \end{aligned}$$

In the second stage of the game, firm \(i \in \{1,2\}\) chooses \(p_i\) in order to maximize \(V_i=\pi _i + \theta _i CS\). For \(i,j \in \{1,2\}\), \(i \not = j\), the first-order conditions \(\frac{\partial V_i}{\partial p_i} = 0\) imply the reaction functionsFootnote 20

$$\begin{aligned} p_i = \frac{(1-\theta _i)(1 - \gamma + \gamma p_j)}{2-\theta _i}. \end{aligned}$$
(22)

Solving the system of equations (22) yields

$$\begin{aligned} p_i =\frac{(1-\gamma )(1-\theta _i)[2-\theta _j+\gamma (1-\theta _j)]}{(2-\theta _i)(2-\theta _j)-(1-\theta _i)(1-\theta _j)\gamma ^2} \end{aligned}$$
(23)

for \(i,j \in \{1,2\}\), \(i \not = j\). We now use (21) and (23) to compute the corresponding profits

$$\begin{aligned} \pi _i = p_iq_i = \frac{(1-\gamma )(1-\theta _i)[2-\theta _j+\gamma (1-\theta _j)]^2}{(1+\gamma ) [(2-\theta _i)(2-\theta _j)-(1-\theta _i)(1-\theta _j)\gamma ^2]^2}. \end{aligned}$$
(24)

In the first stage of the game, firm \(i \in \{1,2\}\) chooses \(\theta _i\) in order to maximize \(\pi \). Using (24), it is straightforward to show that for \(i,j \in \{1,2\}\), \(i \not = j\)

$$\begin{aligned} \frac{\partial \pi _i}{\partial \theta _i} = - \frac{(1-\gamma )[(2-\theta _j)\theta _i+(1-\theta _i)(1-\theta _j)\gamma ^2] [2-\theta _j+\gamma (1-\theta _j)]^2}{(1+\gamma )[(2-\theta _i)(2-\theta _j) -(1-\theta _i)(1-\theta _j)\gamma ^2]^3} < 0 \end{aligned}$$
(25)

for all \(0<|\gamma |<1\). Consequently, each firm \(i \in \{1,2\}\) will choose the lowest CSR level possible, i.e., \(\theta _i=0=:\theta ^*_B(\gamma )\).

C Proof of Proposition 5

At the second stage, the objective functions of the two firms are given by

$$\begin{aligned} V_1&=p(q_1+q_2)q_1+\theta _1CS(q_1+q_2),\\ V_2&=p(q_1+q_2)q_2+\theta _2CS(q_1+q_2). \end{aligned}$$

The maximizing quantities satisfy the first-order conditions

$$\begin{aligned} \dfrac{\partial V_1}{\partial q_1}&=p'(q_1+q_2)q_1+p(q_1+q_2)+\theta _1CS'(q_1+q_2)=0, \end{aligned}$$
(26)
$$\begin{aligned} \dfrac{\partial V_2}{\partial q_2}&=p'(q_1+q_2)q_2+p(q_1+q_2)+\theta _2CS'(q_1+q_2)=0, \end{aligned}$$
(27)

as well as the second order conditions \(\dfrac{\partial ^2 V_i}{\partial q_i^2} < 0\). Using \(CS(q_1+q_2)=\int _0^{q_1+q_2}[p(q)-p(q_1+q_2)]dq\) and thus \(CS'(q_1+q_2)=-(q_1+q_2)p'(q_1+q_2)\), we rewrite Eqs. (26) and (27):

$$\begin{aligned}{}[(1-\theta _1)q_1-\theta _1q_2]p'(q_1+q_2)+p(q_1+q_2)&=0, \end{aligned}$$
(28)
$$\begin{aligned} p'(q_1+q_2)+p(q_1+q_2)&=0. \end{aligned}$$
(29)

Denote the left-hand side of Eqs. (28) and (29) by \(F_1(\theta _1,\theta _2,q_1,q_2)\) and \(F_2(\theta _1,\theta _2, q_1,q_2)\), respectively.

First, we compute the sign of \(dq_1/d\theta _1\). Treating \(\theta _2\) as fixed and applying the implicit function theorem yields

$$\begin{aligned} \dfrac{dq_1}{d\theta _1}= \dfrac{-\dfrac{\partial F_1}{\partial \theta _1}\dfrac{\partial F_2}{\partial q_2}}{\dfrac{\partial F_1}{\partial q_1}\dfrac{\partial F_2}{\partial q_2}-\dfrac{\partial F_1}{\partial q_2}\dfrac{\partial F_2}{\partial q_1}}. \end{aligned}$$
(30)

Notice that \(\partial F_1/\partial \theta _1=-(q_1+q_2)p'(q_1+q_2)>0\). Moreover, \(\partial F_i/\partial q_i=\partial ^2V_i/\partial q_i^2<0\) for \(i \in \{1,2\}\), as implied by the second order conditions on the solution of the maximization problem. Thus the numerator of (30) is positive. Taking the respective derivatives, using the symmetry \(\theta _1=\theta _2=\theta \) in equilibrium, writing \(q_1+q_2=Q\), and simplifying terms, we compute the denominator

$$\begin{aligned} \dfrac{\partial F_1}{\partial q_1}\dfrac{\partial F_2}{\partial q_2}-\dfrac{\partial F_1}{\partial q_2}\dfrac{\partial F_2}{\partial q_1}=p'(Q)[(3-2\theta )p'(Q)+(1-2\theta )Qp''(Q)]. \end{aligned}$$
(31)

Due to \(p'(Q)<0\), an increase in a firm’s CSR level will increase its output, i.e., \(dq_1/d\theta _1>0\), if and only if

$$\begin{aligned} (3-2\theta )p'(Q)+(1-2\theta )Qp''(Q)<0. \end{aligned}$$
(32)

Next, we compute the sign of \(d q_1/d \theta _2\). Treating \(\theta _1\) as fixed now and applying the implicit function theorem yields

$$\begin{aligned} \dfrac{dq_1}{d\theta _2}= \dfrac{\dfrac{\partial F_2}{\partial \theta _2}\dfrac{\partial F_1}{\partial q_2}}{\dfrac{\partial F_1}{\partial q_1}\dfrac{\partial F_2}{\partial q_2}-\dfrac{\partial F_1}{\partial q_2}\dfrac{\partial F_2}{\partial q_1}}. \end{aligned}$$
(33)

The denominator of (33) equals that of (30). Again due to the symmetry in equilibrium, the numerator simplifies to

$$\begin{aligned} \dfrac{\partial F_2}{\partial \theta _2}\dfrac{\partial F_1}{\partial q_2}=-Qp'(Q)[(1-\theta )p'(Q)+(1-2\theta )Qp''(Q)]. \end{aligned}$$
(34)

Due to \(-Qp'(Q)>0\), an increase in a firm’s CSR level will decrease its rival’s output, \(dq_1/d\theta _2<0\), if and only if

$$\begin{aligned} (3-2\theta )p'(Q)+(1-2\theta )Qp''(Q) \end{aligned}$$
(35)

and

$$\begin{aligned} (1-\theta )p'(Q)+(1-2\theta )Qp''(Q) \end{aligned}$$
(36)

are either both positive or both negative, such that either the numerator of (33) is positive and the denominator of (33) is negative or vice versa. Note that (35) < (36) and thus we obtain the condition that \(dq_1/d\theta _2<0\) if and only if either

$$\begin{aligned} (3-2\theta )p'(Q)+(1-2\theta )Qp''(Q)>0 \end{aligned}$$
(37)

or

$$\begin{aligned} (1-\theta )p'(Q)+(1-2\theta )Qp''(Q)<0. \end{aligned}$$
(38)

Finally, notice that (37) and (32) can never both be fulfilled at the same time and that (38) already implies (32).

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Planer-Friedrich, L., Sahm, M. Strategic corporate social responsibility, imperfect competition, and market concentration. J Econ 129, 79–101 (2020). https://doi.org/10.1007/s00712-019-00663-x

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  • DOI: https://doi.org/10.1007/s00712-019-00663-x

Keywords

  • Corporate social responsibility
  • Cournot competition
  • Market concentration
  • Entry deterrence
  • Strategic delegation
  • Bertrand competition

JEL Classification

  • D42
  • D43
  • L12
  • L13
  • L21
  • L22