Volume 36, Issue 4
Corporate social responsibility and endogenous competition structure
Toshihiro Matsumura
Institute of Social Sciences, University of Tokyo

Akira Ogawa
College of Liberal Arts, International Christian
University

Abstract
We assume that firms care about corporate social responsibility (CSR) and revisit the endogenous choice between
price and quantity contracts. We find that a significant (insignificant) asymmetric weight of CSR in their objectives
yields Bertrand (Cournot) competition.

We thank seminar participants at Hosei University, Osaka University, Chonnam National University, National Taiwan University, Korean
University, National University of Kaohsiung, and The University of Tokyo for their helpful comments. Needless to say, we are responsible forany remaining errors. This work was supported by Murata Science Foundation and JSPS KAKENHI (15k03347).
Citation: Toshihiro Matsumura and Akira Ogawa, (2016) ''Corporate social responsibility and endogenous competition structure'',Economics Bulletin, Volume 36, Issue 4, pages 2117-2127
Contact: Toshihiro Matsumura - matsumur@iss.u-tokyo.ac.jp, Akira Ogawa - ogawaa@icu.ac.jp.
Submitted: July 15, 2016. Published: November 09, 2016.

1 Introduction
In the last several decades, corporate social responsibility (CSR) has generated a large amountof interest in broad social science literature. Especially, economic researchers have intensively
discussed this problem (Kitzmueller and Shimshack, 2012) because many listed firms announce
that they are highly concerned with CSR (KPMG, 2013). For example, many big Japanese firms
as well as Japanese economic associations such as Japan Association of Corporate Executives, theJapan Business Federation, the Japan Iron and Steel Federation, the Federation of Electric Power
Companies of Japan emphasize CSR in their annual reports and websites.
In the literature on CSR, most works assume that competition structure (Bertrand or Cournot)
are given exogenously. However, CSR can affect the competition structure and endogenizing
the competition structure is important because the implications of CSR crucially depend on thecompetition structure in the product market (Liu et al, 2015). Furthermore, as Ghosh and Mitra(2014) discussed, Bertrand competition often yields the higher welfare level than the Cournot evenwhen firms are not profit-maximizers. If CSR changes the competition structure from Cournot to
Bertrand, CSR results in further welfare improving through the change of competition structure.
Regarding the endogenous competition structure, as Singh and Vives (1984) convincingly
pointed out, firms often choose whether to adopt a price contract or quantity contract. According to these studies, the competition structure should not be given exogenously.1
In their pioneering work, Singh and Vives (1984) formulated a model in which firms choose aprice or quantity contract and endogenize the competition structure (Cournot or Bertrand). They
showed that if the goods are substitutes, Cournot competition appears in equilibrium. Tanaka(2001) and Tasnádi (2006) showed that this result is quite robust and holds in various contexts.
However, these studies assumed that firms are profit-maximizers. In contrast, in the context of
mixed oligopolies, Matsumura and Ogawa (2012) showed that competition structure is changed
if one firm is a welfare maximizer and the other firm is a profit maximizer. This suggests thepossibility that non-profit maximizing objectives may change the competition structure.2
We introduce CSR into the model of Singh and Vives (1984). Following Ghosh and Mitra
1

Friedman (1988) considered the Cournot (res. Bertrand) model more appropriate for a quantity (res. price) change
if it is less flexible or more costly than price (res. quantity) change. However, firms should be able to commit toincreasing the costs of price changes. For example, declaring that they will not change their prices frequently, keeping
this policy, and establishing this reputation may be profitable for firms because this would deter the consumers fromwaiting for future price declines. If we consider a model where each firm first chooses whether to make such acommitment and then the firms compete in either price (commitment case) or quantity (noncommitment case), thiswould correspond to Singh and Vives’s (1984) model. We believe that this could be another rationale for these studies’
model.
2
The papers on endogenous competition structure and Cournot-Bertrand comparison in mixed oligopolies becomerich and diverse. See Chirco and Scrimitore (2013), Chirco et al. (2014), Scrimitore(2013, 2014) and Haraguchi andMatsumura (2016).

(2014), we assume that firms are assumed to maximize the weighted sum of total social surplus
and profits.3 As noted above, many private firms care about social responsibility as well as theirown profits, and it is quite natural to assume that firms are not always profit maximizers.4 We
derive a result containing those of Singh and Vives (1984) and Matsumura and Ogawa (2012) asa special case and fill the gap of the discussions on private and mixed oligopolies. We find that
Bertrand (Cournot) competition appears in equilibrium with significant (insignificant) asymmetryof the weight of CSR between the firms. This result implies that the asymmetry in objectives
rather than non-profit maximizing objective itself plays a crucial role in determining competition
structure.

2 ModelWe adopt a standard differentiated duopoly with linear demand (Dixit, 1979). The utility function of the representative consumer is U(q1 , q2 ) = α(q1 + q2 ) − β(q21 + 2δq1 q2 + q22 )/2 + y, where yis the consumption of an outside good that is provided competitively with a unit price. Parameters
α and β are positive constants, and δ ∈ (0, 1) represents the degree of product differentiation: asmaller δ indicates a larger degree of product differentiation.
Firms 1 and 2 produce differentiated commodities for which the inverse demand function is
given by pi = α − βqi − βδq j (i = 1, 2, i , j), where pi and qi are firm i’s price and quantity,
respectively. The marginal production costs are constant. Let m denote each firm’s marginal cost.
We assume that α > m, otherwise no firm produces.
Firm i’s payoff is Vi = θi S W + (1 − θi )πi , where θi ∈ [0, 1), SW is the total social surplus (i.e.,the sum of the firms’ profits and consumer surplus), and πi is firm i’s profit. θi (i = 1, 2) indicates
the weight of social responsibility in the payoff of each firm. πi (i = 1, 2) and S W are given by
πi = (pi − m)qi = (α − βqi − βδq j − m)qi ,[]β(q21 + 2δq1 q2 + q22 )S W = π1 + π2 + α(q1 + q2 ) −− p1 q1 − p2 q22
β= π1 + π2 + (q21 + 2δq1 q2 + q22 ).
2
The game runs as follows. In the first stage, each firm chooses whether it adopts a price contract
or a quantity one. In the second stage, after observing the rival’s choice in the first stage, each firm
simultaneously chooses p or q, according to the decision in the first stage.
3

This approach is widely adopted in the literature on mixed oligopolies where a partially privatized firm cares aboutboth its own profits and social welfare (see Matsumura,1998, Lee, 1999). They generalized this partial privatization
approach and considered the situation where all firms care about both social welfare and their own profits. See also
Matsumura and Ogawa (2014).
4
We obtain the same qualitative results if firms maximize the weighted sum of consumer surplus and profits.

3 Second-stage games
First, we discuss four possible subgames: both choose quantities (q − q game), both choose
prices (p − p game), only firm 1 chooses quantity (q − p game), and only firm 1 chooses price(p − q game). Let a := α − m.
3.1

q − q game

Consider the situation where both firms choose quantities. The first-order condition for firmi(= 1, 2) is given by∂Vi= a − 2qi β − q j βδ + qi βθi = 0 (i , j).
∂qi
The second-order condition is satisfied. From the first-order condition, we obtain the following
reaction function of firm i.

a − βδq j= 0 (i , j).
β(2 − θi )These lead to the following equilibrium quantities, and the resulting value of objective functions.
Rqq
i (q j ) =(2 − θ2 − δ)a,β(θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4)
(2 − θ1 − δ)a
qqq
,
2 =
β(θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4)
a2 B1
V1qq =,2β(θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4)2
a2 B2
qq
,
V2 =
2β(θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4)2qqq
1 =where the constant B1 , B2 , and other constants are reported in the Appendix.
3.2

p − p game

Consider the situation where both firms choose prices. The demand function is given byqi =α − αδ − pi + δp j
(i , j).
β(1 + δ)(1 − δ)The first-order condition for firms i is given by,∂Vi m − 2pi + α + p j δ − δα + pi θi − αθi − mδθi + δαθi=
= 0 (i , j).
∂pi
β(1 − δ)(1 + δ)
The second-order condition is satisfied. From the first-order condition, we obtain the following
reaction function of firm i.
Ripp (p j ) =m + α + p j δ − δα − αθi + δθi a.
2 − θi

These lead to the following equilibrium prices and resulting values of objective functions.
[α(1 − θ1 ) + m + δθ1 a](2 − θ2 ) − δa − δ2 α + δ2 θ2 a,
θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4[α(1 − θ2 ) + m + δθ2 a](2 − θ1 ) − δa − δ2 α + δ2 θ1 a.
=
θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4
a2 B3
,
=
β(δ + 1)(1 − δ)(θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4)2
a2 B4
=
.
β(δ + 1)(1 − δ)(θ1 θ2 − 2θ2 − 2θ1 − δ2 + 4)2

p1pp =
p2pp
V1pp
V2pp

3.3

p − q game

Consider the situation where firm 1 chooses price and firm 2 chooses quantity. The first-orderconditions for firms 1 and 2 are respectively,m − 2p1 + α + p1 θ1 − αθ1 − q2 βδ + q2 βδθ1
∂V1
=
= 0,
∂p1
β
∂V2
= α − m + p1 δ − 2q2 β − δα + mδθ2 − p1 δθ2 + q2 βθ2 + 2q2 βδ2 − q2 βδ2 θ2 = 0.
∂q2
The second-order conditions are satisfied. From the first-order conditions, we obtain the following
reaction functions of firms 1 and 2.
α(1 − θ1 ) + m − βδ(1 − θ1 )q2,
2 − θ1α(1 − δ) − m + δp1 + mδθ2 + δθ2 p1
R2pq (p1 ) =.
β(1 − δ)(1 + δ)(2 − θ2 )R1pq (q2 ) =These lead to the following equilibrium choice of each firm and resulting values of objective functions.
(α + m)(2 − θ2 ) − δa − 2αθ1 + δθ1 a + αθ1 θ2 − 2mδ2 − δ2 α(1 − θ1 − θ2 ) − δ2 θ1 θ2 a,
θ1 θ2 − 2θ2 − 2θ1 − 3δ2 + δ2 θ1 + δ2 θ2 + 4a(−δ − θ1 − δθ2 + δθ1 θ2 + 2)=,β(θ1 θ2 − 2θ2 − 2θ1 − 3δ2 + δ2 θ1 + δ2 θ2 + 4)
a2 B5
,
=
2β(−2θ1 − 2θ2 + θ1 θ2 − 3δ2 + δ2 θ1 + δ2 θ2 + 4)2
a2 B6
=
.
2β(−2θ1 − 2θ2 + θ1 θ2 − 3δ2 + δ2 θ1 + δ2 θ2 + 4)2

p1pq =
q2pq
V1pq
V2pq

3.4

q − p game

Consider the situation where firm 1 chooses quantity and firm 2 chooses price. The first-orderconditions for firms 1 and 2 are respectively,∂V1= α − m + p2 δ − 2q1 β − δα + mδθ1 − p2 δθ1 + q1 βθ1 + 2q1 βδ2 − q1 βδ2 θ1 = 0,∂q1
m − 2p2 + α + p2 θ2 − αθ2 − q1 βδ + q1 βδθ2
∂V2
=
= 0.
∂p2
β
The second-order conditions are satisfied. From the first-order conditions, we obtain the following
reaction functions of firms 1 and 2.
α(1 − δ) − m + δp2 + mδθ1 + δθ1 p2.
β(1 − δ)(1 + δ)(2 − θ1 )α(1 − θ2 ) + m − βδ(1 − θ2 )q1
Rqp,
2 (q1 ) =2 − θ2Rqp
1 (p2 ) =These lead to the following equilibrium choice of each firm and resulting value of objective functions.
a(−δ − θ2 − δθ1 + δθ2 θ1 + 2),β(θ2 θ1 − 2θ1 − 2θ2 − 3δ2 + δ2 θ2 + δ2 θ1 + 4)
(α + m)(2 − θ1 ) − δa − 2αθ2 + δθ2 a + αθ2 θ1 − 2mδ2 − δ2 α(1 − θ2 − θ1 ) − δ2 θ2 θ1 a=,
θ2 θ1 − 2θ1 − 2θ2 − 3δ2 + δ2 θ2 + δ2 θ1 + 4
a2 B7
,
=
2β(−2θ1 − 2θ2 + θ1 θ2 − 3δ2 + δ2 θ1 + δ2 θ2 + 4)2
a2 B8
=
.
2β(−2θ1 − 2θ2 + θ1 θ2 − 3δ2 + δ2 θ1 + δ2 θ2 + 4)2

qqp
=
1
pqp
2
V1qp
V2qp

4 Result
We discuss the choice at the first stage. Table 1 summarizes this game.
1\2
quantity
price
qq
qq
quantity (V1 , V2 ) (V1qp , V2qp )price(V1pq , V2pq ) (V1pp , V2pp )Table 1: First Stage GameIf both firms are welfare-maximizers, the first-best outcome is achieved regardless of the firststage choices, and thus they do not matter for welfare-maximizers. Henceforth, we restrict ourattention to the cases where (θ1 , θ2 ) , (1, 1).
Although we cannot solve the game explicitly in the case of general asymmetric objectivefunctions, we can show this tendency using the numerical results for four values of δ.Figure 1

shows the conditions for Bertrand and Cournot outcomes to appear in equilibrium, implying thatthe Bertrand outcome is more likely to be in equilibrium when the difference between θ1 and θ2 islarge.
We explain the intuition behind why a Bertrand outcome appears in equilibrium when the
payoff asymmetry is significant.
First, we explain why choosing a price contract is more profitable for firm 2 that is muchcloser to being a profit-maximizer than firm 1. As Singh and Vives (1984) suggested, the demand
elasticity of both firms increases when firm 2 chooses p than when it chooses q. Because firm 1
is highly concerned with welfare, firm 1 does not want to reduce the output of firm 2, and thus it
becomes less aggressive when firm 2 chooses p than when it chooses q. In order to make the rival
less aggressive, firm 2 chooses p.
Second, we explain why choosing a price contract is better for firm, which is much closer tobeing a welfare-maximizer than firm 1. The demand elasticity of both firms becomes larger whenfirm 1 chooses p than when it chooses q. Because firm 2 is closer to being a profit-maximizer,
firm 1 becomes more aggressive when firm 1 chooses p than when it chooses q. This aggressive
behavior improves firm 1’s payoff because it is more concerned with welfare. Thus, firm 1 alsochooses p.
Finally, we explain the intuition behind why a Cournot outcome appears in equilibrium when
the payoff asymmetry is insignificant.5
Suppose that both θ1 and θ2 are small (θ1 , θ2 < δ). Suppose that firm 2 chooses the quantity
contract. Each firm prefers a smaller output of the rival because it increases its demand and thus
its profit. When firm 1 chooses the price contract, an increase in the firm 2’s output reduces firm
1’s output. When firm 1 chooses the quantity contract, this effect disappears because the firm 1’s
output is determined before observing the firm 2’s output. Thus, firm 2 chooses a smaller output
when firm 1 also chooses the quantity contract. To make the rival less aggressive, firm 1 chooses
the quantity contract.
Suppose that both θ1 and θ2 are large (θ1 , θ2 > δ). Suppose that firm 2 chooses the quantity
contract. Each firm prefers a larger output of the rival because it enhances welfare. When firm 1chooses the price contract, an increase in the firm 2’s output reduces firm 1’s output. When firm
1 chooses the quantity contract, this effect disappears. Thus, firm 2 chooses a larger output whenfirm 1 also chooses the quantity contract. To make the rival more aggressive, firm 1 chooses thequantity contract.

5

Ghosh and Mitra (2014) showed that Cournot competition appears in equilibrium when θ1 = θ2 .

Appendix
B1 = 8θ1 − 8δ − 8θ2 + 4δθ2 − 4θ1 θ2 + 2δθ1 θ2 + 2δ2 − 12θ12 + 3θ13 + 2θ22 + 2δθ12−6δ2 θ1 + 2δ3 θ1 − θ1 θ22 + 8θ12 θ2 − 2θ13 θ2 − 2δθ12 θ2 + 2δ2 θ12 + 8,
B2 = 8θ2 − 8θ1 − 8δ + 4δθ1 − 4θ1 θ2 + 2δθ1 θ2 + 2δ2 + 2θ12 − 12θ22 + 3θ23 + 2δθ22−6δ2 θ2 + 2δ3 θ2 + 8θ1 θ22 − θ12 θ2 − 2θ1 θ23 − 2δθ1 θ22 + 2δ2 θ22 + 8.
B3 = 8θ1 − 8θ2 + 8δθ1 − 4δθ2 − 4θ1 θ2 − 6δθ1 θ2 − 6δ2 − 2δ3 − 12θ12 + 3θ13 + 2θ22
−10δθ12 − 2δ2 θ1 + 3δθ13 + 2δθ22 + 8δ2 θ2 + 2δ3 θ1 + 4δ3 θ2 + 2δ4 θ1 − θ1 θ22+8θ12 θ2 − 2θ13 θ2 + 3δθ1 θ22 + 12δθ12 θ2 − 12δ2 θ1 θ2 − 4δθ13 θ2 − 2δ3 θ1 θ2+δ2 θ13 − 2δ2 θ22 − 2δ3 θ12 + δ3 θ13 − 2δ3 θ22 − 6δθ12 θ22 + 5δ2 θ1 θ22 + 8δ2 θ12 θ2+2δθ13 θ22 − 2δ2 θ13 θ2 + δ3 θ1 θ22 − 2δ2 θ12 θ22 + 8,
B4 = 8θ2 − 8θ1 − 4δθ1 + 8δθ2 − 4θ1 θ2 − 6δθ1 θ2 − 6δ2 − 2δ3 + 2θ12 − 12θ22+3θ23 + 2δθ12 + 8δ2 θ1 − 10δθ22 − 2δ2 θ2 + 4δ3 θ1 + 3δθ23 + 2δ3 θ2 + 2δ4 θ2+8θ1 θ22 − θ12 θ2 − 2θ1 θ23 + 12δθ1 θ22 + 3δθ12 θ2 − 12δ2 θ1 θ2 − 4δθ1 θ23 − 2δ3 θ1 θ2−2δ2 θ12 − 2δ3 θ12 + δ2 θ23 − 2δ3 θ22 + δ3 θ23 − 6δθ12 θ22 + 8δ2 θ1 θ22 + 5δ2 θ12 θ2+2δθ12 θ23 − 2δ2 θ1 θ23 + δ3 θ12 θ2 − 2δ2 θ12 θ22 + 8.
B5 = 8θ1 − 8δ − 8θ2 + 4δθ2 − 4θ1 θ2 − 2δθ1 θ2 − 6δ2 + 4δ3 + 2δ4 − 12θ12 + 3θ13 + 2θ22
+2δθ12 − 10δ2 θ1 + 12δ2 θ2 + 4δ3 θ1 − 4δ3 θ2 − δ4 θ1 − 4δ4 θ2 − θ1 θ22 + 8θ12 θ2−2θ13 θ2 + 4δθ1 θ22 + 4δθ12 θ2 − 4δ2 θ1 θ2 − 2δθ13 θ2 + 6δ3 θ1 θ2 + 2δ4 θ1 θ2 + 10δ2 θ12−2δ2 θ13 − 4δ2 θ22 − 2δ3 θ12 + 2δ4 θ22 − 6δθ12 θ22 + δ2 θ1 θ22 + 2δθ13 θ22 − 2δ3 θ1 θ22−8δ3 θ12 θ2 + 2δ3 θ13 θ2 − δ4 θ1 θ22 + 2δ2 θ12 θ22 − δ2 θ13 θ22 + 2δ3 θ12 θ22 + 8,

B6 = 8θ2 − 8θ1 − 8δ + 4δθ1 − 4θ1 θ2 + 2δθ1 θ2 − 6δ2 + 8δ3 − 2δ4 + 2θ12 − 12θ22 + 3θ23
+8δ2 θ1 + 2δθ22 − 14δ2 θ2 − 4δ3 θ1 + 2δ3 θ2 + 5δ4 θ2 + 8θ1 θ22 − θ12 θ2 − 2θ1 θ23−2δθ1 θ22 + 6δ2 θ1 θ2 − 6δ3 θ1 θ2 − 2δ2 θ12 + 14δ2 θ22 − 3δ2 θ23 − 2δ3 θ22 − 4δ4 θ22+δ4 θ23 − 4δ2 θ1 θ22 + 2δ3 θ1 θ22 + 2δ3 θ12 θ2 − 2δ2 θ12 θ22 + δ2 θ12 θ23 + 8.
B7 = 8θ1 − 8θ2 − 8δ + 4δθ2 − 4θ2 θ1 + 2δθ2 θ1 − 6δ2 + 8δ3 − 2δ4 + 2θ22 − 12θ12 + 3θ13
+8δ2 θ2 + 2δθ12 − 14δ2 θ1 − 4δ3 θ2 + 2δ3 θ1 + 5δ4 θ1 + 8θ2 θ12 − θ22 θ1 − 2θ2 θ13−2δθ2 θ12 + 6δ2 θ2 θ1 − 6δ3 θ2 θ1 − 2δ2 θ22 + 14δ2 θ12 − 3δ2 θ13 − 2δ3 θ12 − 4δ4 θ12+δ4 θ13 − 4δ2 θ2 θ12 + 2δ3 θ2 θ12 + 2δ3 θ22 θ1 − 2δ2 θ22 θ12 + δ2 θ22 θ13 + 8,
B8 = 8θ2 − 8δ − 8θ1 + 4δθ1 − 4θ2 θ1 − 2δθ2 θ1 − 6δ2 + 4δ3 + 2δ4 − 12θ22 + 3θ23 + 2θ12
+2δθ22 − 10δ2 θ2 + 12δ2 θ1 + 4δ3 θ2 − 4δ3 θ1 − δ4 θ2 − 4δ4 θ1 − θ2 θ12 + 8θ22 θ1−2θ23 θ1 + 4δθ2 θ12 + 4δθ22 θ1 − 4δ2 θ2 θ1 − 2δθ23 θ1 + 6δ3 θ2 θ1 + 2δ4 θ2 θ1 + 10δ2 θ22−2δ2 θ23 − 4δ2 θ12 − 2δ3 θ22 + 2δ4 θ12 − 6δθ22 θ12 + δ2 θ2 θ12 + 2δθ23 θ12 − 2δ3 θ2 θ12−8δ3 θ22 θ1 + 2δ3 θ23 θ1 − δ4 θ2 θ12 + 2δ2 θ22 θ12 − δ2 θ23 θ12 + 2δ3 θ22 θ12 + 8.

(1)

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Figure 1: Equilibrium under asymmetric thetasdelta=0.2

delta=0.4
1.000

1.000

Bertrand
0.800

0.800

Cournot
0.600

asymmetry

0.600

theta2
asymmetry

theta2

0.400

0.400

0.200

0.200

Cournot

Bertrand
0.000

0.200

0.400

0.600

0.800

0.000
1.000 theta1

0.000

0.200

delta=0.6

0.400

0.600

0.800

0.000
1.000 theta1

delta=0.8
1.000

1.000

BertrandBertrand

0.800

0.800

asymmetryasymmetry
0.600

0.600

theta2

theta2

0.400

0.200

Cournot

0.000

0.200

0.400

0.400

0.600

0.800

0.000
1.000 theta1

0.200

Cournot

0.000

0.200

0.400

0.600

0.800

0.000
1.000 theta1(note) "asymmetry" means the equilibrium in which one firm chooses the price and the other firm chooses the quantity.