Volume 37, Issue 1
Environmental corporate social responsibility : A note on the ​first-moveradvantage under price competition
Kosuke Hirose
Graduate School of Economics, The University of Tokyo
Sang-ho Lee
College of Business Administration, Chonnam National
University

Toshihiro Matsumura
Institute of Social Science, The University of Tokyo

Abstract
We consider a model in which two ​firms choose whether to adopt environmental corporate social responsibility
policies and then face Stackelberg competition under price competition. We show that the ​first-mover has theadvantage, which is in contrast to the second-mover advantage typically seen in standard price competition models.

We thank the seminar participants at Osaka University, the University of Tokyo, and National University of Kaohsiung for their helpfulcomments. We are responsible for any remaining errors. This work was supported by the National Research Foundation of Korea Grant(NRF-2014S1A2A2028188), the Murata Science Foundation, and JSPS KAKENHI (15k03347, 16J04589).
Citation: Kosuke Hirose and Sang-ho Lee and Toshihiro Matsumura, (2017) ''Environmental corporate social responsibility : A note on the​first-mover advantage under price competition'', Economics Bulletin, Volume 37, Issue 1, pages 214-221
Contact: Kosuke Hirose - h-kosuke@g.ecc.u-tokyo.ac.jp, Sang-ho Lee - sangho@chonnam.ac.kr, Toshihiro Matsumura - matsumur@iss.utokyo.ac.jp.
Submitted: November 09, 2016. Published: January 26, 2017.

1

Introduction

The industrial organization literature has extensively debated whether the first or second
mover earns larger profits. As Gal-Or (1985) and Dowrick (1986) showed in symmetricduopolies, for strategic substitutes (complements), the first mover (second mover) has theadvantage under the stability condition. Under standard condition, the strategies are strategic complements under price competition (Vives, 1999). Thus, under price competition, thesecond mover naturally enjoys an advantage. In this study, we incorporate environmental
corporate social responsibility (ECSR) into the standard price competition model and showthat this property does not holds.
ECSR has received increasing attention from broad research in social sciences. In particular, economic researchers have discussed this issue intensively (Liu et al., 2015) because
many listed firms are highly concerned about ECSR (KPMG, 2013). CDP (2013), for example, reported that some major companies such as ExxonMobil, Walt Disney, Walmart,and Microsoft use an internal (implicit) carbon price as an incentive and strategic planning
tool, although their internal carbon prices differ significantly, ranging from 6 to 60 dollars
per ton.1
In this study, we investigate Stackelberg competition after firms choose whether to adopt
ESCR. We show that only the follower adopts ECSR. This follower’s behavior increases thefirms’ profits, and further increases the leaders’ profits. As a result, this price competition
model shows a first-mover advantage. This result is in sharp contrast to the standard result
showing a second-mover advantage under price competition.
This study contains another implication. It explains why profit-maximizing firms adopt
ECSR and may explain why the degree of ECSR is different among firms. There are two wellknown reasons why profit-maximizing firms adopt ECSR. One is that ECSR is connectedwith the advertisement or reputation of firms; thus, it eventually increases the demand,
thereby earning the firms more profits (see Liu et al. (2015) and the works cited therein).
The other is that voluntary agreement may serve as a countermeasure for the regulatory
threat by the government, which allows firms to avoid more severe regulation (Maxwell etal., 2000; Antweiler, 2003). Without those assumptions, we show that firms strategicallychoose ECSR because it serves as a commitment device.
This study is closely related to the literature using a delegation game with strategic
reward contracts, which are a popular topic in the management science and industrial organization literature. Fershtman (1985), Vickers (1985), Fershtman and Judd (1987), andSklivas (1987) made groundbreaking theoretical contributions in this regard. They considered the separation of owners and managers and examined the following two-stage game. In
the first stage, the owners write managers’ reward contracts and announce them publicly.
In the second stage, having read the contracts, the managers maximize payoffs. In thesestudies, the managers’ rewards are proportional either to a linear combination of profits andoutputs or to profits and firm revenues. Later, researchers investigated different types ofstrategic contracts based on relative performance or market share. In fact, management
rewards often positively relate to firm revenues, market share, and/or relative performance,
1

We should say from 0 to 60 dollars because some firms not reported in CDP do not introduce explicit
internal carbon prices.

as well as their own profits. Because the model formulation in these studies provides anapproximation of reality and explains much of the actual firm behaviors, it has become oneof the most popular models in industrial organization and management science.
The incentive of such delegation has been analyzed in oligopoly theory, which is mainly
focused on models of quantity competition (strategic substitute cases). Clearly, if we consider
a model of price competition in this framework, the owners must attribute a negative weight
to outputs, revenues, market share, or relative profits. It is, however, much less sustained
from the empirical perspectives.2 In our study, we discuss the commitment through adopting
an ECSR policy. We believe that our formulation is more natural to address such firm’s
commitment for many industries than the standard delegation setting.3
2

The Model

We assume a standard differentiated duopoly with linear demand (Dixit, 1979). The quasilinear utility function of the representative consumer is U (q1 , q2 ) = α(q1 +q2 )−β(q12 +2δq1 q2 +q22 )/2 + y, where y is the consumption of an outside good provided competitively with a unit
price. Parameters α and β are positive constants, and δ ∈ (0, 1) represents the degree of
product differentiation, where a smaller 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 − βδqj (i = 1, 2, i ̸= j), where pi and qi are firm i’s price andquantity, respectively. The common marginal production cost is constant and normalized tozero. Firm i’s emission level producing a negative externality is ηqi .4
The owners of firm i’s payoff is πi , and management’s payoff is Vi = πi −θi ηqi , where θi (≥0) is an internal (implicit) emission price, representing the degree of ECSR and determinedby the profit-maximizing owner of firm i.5
The game runs as follows. In the first stage, the owner of firm i independently chooses
θi . In the second stage, firms choose their prices sequentially (Stackelberg competition).

2

For empirical evidence, see Murphy (1985) and Coughlan and Schmidt (1985). These empirical studies
suggest that negative weight on these variables is not realistic. Matsumura and Matsushima (2012) showedthat firms put positive weight on a location-then-price model because it has a positive effect on location
choice, and this effect dominates the negative effect on price choice.
3
For example, most listed firms in Japan, as well as many Japanese economic associations, such as
the Japan Association of Corporate Executives, the Japan Business Federation, the Japan Iron and SteelFederation, and the Federation of Electric Power Companies of Japan emphasize ECSR in their reports andwebsites.
4
If we introduce an emission abatement activity that is independent of its production level, we obtain thesame qualitative results.
5
Our analysis is equivalent to the following scenario discussed in Graff Zivin and Small (2005) and Baron(2007). Firm i commits to donating a monetary amount to θi ηyi for environmental improvements, themanagement of firm i maximizes its net profit (the profit after subtracting the cost of donation), and theowner considers the corporate donation and private giving as perfect substitutes.

3

Results

First, we discuss the second-stage price competition. Firm 1 chooses its price and then firm
2 chooses its price. The first-order condition for firm 2 is∂V2α(1 − δ) + ηθ2 − 2p2 + δp1
=
= 0.
∂p2
β(1 − δ 2 )The reaction function for firm 2 isR2 (p1 ) =α(1 − δ) + ηθ2 + δp1.
2

Firm 1 maximizes π1 (p1 , R2 (p1 )) − θ1 ηq1 (p1 , R2 (p1 )) with respect to p1 . The first-order condition isα(−2 + δ + δ 2 ) + η((δ 2 − 2)θ1 − δθ2 ) + (4 − 2δ 2 )p1= 0.
2β(−1 + δ 2 )The Stackelberg equilibrium isα(−2 + δ + δ 2 ) + η((−2 + δ 2 )θ1 − δθ2 )2(−2 + δ 2 )α(4 − 2δ − 3δ 2 + δ 3 ) − η(δ(−2 + δ 2 )θ1 + (−4 + δ 2 )θ2 )=4(2 − δ 2 )(α(−2 + δ + δ 2 ) + η((−2 + δ 2 )θ1 − δθ2 ))(α(−2 + δ + δ 2 ) − η((−2 + δ 2 )θ1 + δθ2 ))),=8β(−2 + δ 2 )(−1 + δ 2 )H,=
16β(−2 + δ 2 )2 (1 − δ 2 )

p1 =
p2
π1
π2

where H := (α(4 − 2δ − 3δ 2 + δ 3 ) + η(δ(2 − δ 2 )θ1 + (3δ 2 − 4)θ2 ))(α(4 − 2δ − 3δ 2 + δ 3 ) −η(δ(−2 + δ 2 )θ1 + (δ 2 − 4)θ2 ).
We now discuss the first-stage actions.6 The owner of firm i chooses θi . The first-orderconditions are∂π1η 2 (2 − δ 2 )θ1
=
= 0,
∂θ1
4β(−1 + δ 2 )η(δ 2 (α(4 − 2δ − 3δ 2 + δ 3 ) − ηδ(−2 + δ 2 )θ1 ) − η(16 − 16δ 2 + 3δ 4 )θ2 )
∂π2
= 0.
=
∂θ2
8β(−2 + δ 2 )2 (1 − δ 2 )The equilibrium θi isθ1 = 0, θ2 =6α(−1 + δ)δ 2 (δ 2 − 2δ − 4):= θF > 0.
2
4
η(16 − 16δ + 3δ )(1)

In this study, we assume that firms choose θ simultaneously. Our results hold true if firms choose θsequentially.

The resulting profits are
α2 (−1 + δ)(−2 + δ 2 )(−8 − 4δ + 4δ 2 + δ 3 )2:= π L22
2β(1 + δ)(4 − 3δ )(−4 + 3δ )2α (−1 + δ)(−4 − 2δ + δ 2 )2=:= π F .
4β(1 + δ)(4 − δ 2 )(−4 + 3δ 3 )

π1 =
π2

We obtain the following result.
Proposition 1 Only the follower adopts ECSR, and this increases both firms’ profits. The
leader earns the larger profit (i.e., first-mover advantage appears).
Proof First, we show that π L > π F .
πL − πF =α2 (δ − 1)δ 5 (5δ 3 + 4δ 2 − 16δ − 16)> 0.
4β(δ + 1) (4 − 3δ 2 )2 (δ 2 − 4)2

Let us now check that ECSR increases both firms’ profits. Firm 2 chooses θ2 = θF inequilibrium, and thus, firm 2’s profit must be larger than that when θ1 = θ2 = 0. Firm 1’s
profit is less than firms 2’s if θ1 = θ2 = 0 (i.e., the second mover has the advantage understandard price competition setting). Because π L > π F and ECSR increases firm 2’s profit,
it increases firm 1’s profit as well. ■Each firm has an incentive to commit to a higher price in order to induce the rival’s higher
price. The price leader chooses its price, and then the follower chooses its price. Thus, theleader can directly commit to a higher price without using ECSR. Therefore, choosing a
positive θ has no strategic value for the leader. In contrast, for the follower, ECSR has
strategic value because the follower can commit to setting a higher price by choosing a
positive θ as it increases the marginal cost. Observing a positive θ, the leader expects thehigher price of the follower and also sets a price higher than that without the follower’s
ECSR, because the leader’s pricing strategy is strategic complement. Firm 2’s strategic
behavior (less aggressive pricing rather than profit-maximizing pricing) benefits firm 1 andyields the first-mover advantage.
This result is in sharp contrast to the standard result under price competition. Gal-Or(1985) showed that when two symmetric firms move sequentially under price competition,
the follower enjoys the second-mover advantage. Although we assume that the firms are
identical, there is a difference between the leader and the follower in terms of adopting
ECSR. This generates heterogeneity between the two firms and changes the profit ranking
between the first and second movers.
Gal-Or (1987) and Shinkai (2000) also suggested that the standard result shown in GalOr (1985) may not hold under an incomplete information game. They assumed that the firstmover has informational advantage, and the action of the first mover reveals its information.
They showed that this signaling effect may change the profit ranking among the first andsecond movers. The mechanism of our study is completely different from theirs because we
discuss the complete information game.
Ono (1978) considered a duopoly in a homogeneous product market with cost asymmetry.
He showed that the firm with lower (higher) cost prefers the role of the leader (follower) if thecost difference is sufficiently large. Van Damme and Hurkens (2004) and Amir and Stepanova(2006) showed that this holds true in a differentiated product market. In contrast, Hirata
and Matsumura (2011) presented another duopoly model in a homogeneous product market
in which the firm with higher (lower) cost prefers the role of the leader (follower) if thecost difference is sufficiently large. In other words, they have already shown that in someprice competition models, there is no clear profit ranking (neither unanimous first-mover
nor second-mover advantage exits) under large cost difference. There are two importantdifferences between our model and theirs. One is that we do not assume exogenous costdifference between the two firms. The other is that in our model, both firms prefer the roleof the leader.
We now discuss the welfare implications of ECSR. The total social surplus (firm profits
plus consumer surplus minus the loss from the externality) is given by[]β(q12 + 2δq1 q2 + q22 )SW = p1 q1 + p2 q2 + α(q1 + q2 ) −− (p1 q1 + p2 q2 ) − η(q1 + q2 ).
2
Without ECSR, the total social surplus is
SW N =α (α (5δ 5 + 23δ 4 − 28δ 3 − 96δ 2 + 32δ + 96) − 8η (δ 5 + 3δ 4 − 6δ 3 − 14δ 2 + 8δ + 16))32β(δ + 1) (δ 2 − 2)2

When the follower adopts ECSR, the total social surplus is
SW E =α2 (5δ 9 + 71δ 8 − 92δ 7 − 696δ 6 + 496δ 5 + 2336δ 4 − 896δ 3 − 3200δ 2 + 512δ + 1536)
8β(δ + 1) (4 − 3δ 2 )2 (δ 2 − 4)2αη (δ 5 + 7δ 4 − 12δ 3 − 32δ 2 + 16δ + 32).
−
2β(δ + 1) (δ 2 − 4) (3δ 2 − 4)

We obtain
SW E − SW N =αδ 2 (δ 3 − 3δ 2 − 2δ + 4) G,
32β(δ + 1) (4 − 3δ 2 )2 (δ 2 − 4)2 (δ 2 − 2)2

where G := 8η(3δ 8 − 6δ 7 − 34δ 6 + 44δ 5 + 136δ 4 − 96δ 3 − 224δ 2 + 64δ + 128) − α(25δ 8 − 2δ 7 −240δ 6 + 24δ 5 + 800δ 4 − 32δ 3 − 1088δ 2 + 512). This is positive if and only if
η > η :=α (25δ 8 − 2δ 7 − 240δ 6 + 24δ 5 + 800δ 4 − 32δ 3 − 1088δ 2 + 512)> 0.
8 (3δ 8 − 6δ 7 − 34δ 6 + 44δ 5 + 136δ 4 − 96δ 3 − 224δ 2 + 64δ + 128)

These lead to the following proposition.
Proposition 2 ECSR improves welfare if and only if η > η.
There is a tradeoff between the environment and the anti-competitive effect. On one
hand, ECSR reduces emissions that yield negative externalities. On the other hand, it
raises the prices and reduces consumer surplus. Thus, it does not always have a beneficial
effect on welfare. Because the equilibrium level of θF η, the additional marginal cost due

to ECSR, is independent of η, the equilibrium prices (and outputs) are independent of η.
From the viewpoint of social welfare, the optimal outputs are decreasing in η. Therefore,
the equilibrium outcome is more likely excessive when η is larger. If the degree of negative
externalities is significant, the emission-reducing effect dominates the price-raising effect,
and thus ECSR benefits welfare.
In energy-intensive industries, such as electricity, steel, cement, and some other heavy
industries, the negative externality is significant, and thus the welfare improving effect of
ECSR may be prominent. However, in industries with less significant negative externality(industries with low emission per output), it is possible that the price-raising effect dominates
the emission-reducing effect. In this context, estimating the degree of negative externalities
in industries (e.g., emission per unit of outputs) is important.7
Finally, we discuss outcomes for endogenous timing in the second-stage competition (i.e.,
when the first mover identity is endogenous). Consider the following model. The first stage
remains the same as in the basic model; however, in the second stage, firms experience
Hamilton and Slutsky’s (1990) observable delay game.8 As Hamilton and Slutsky (1990)
showed, if two firms have the same costs, two Stackelberg equilibria (either firm 1 or firms
2 is the leader) exist. As Amir and Stepanova (2006) demonstrated, if the two firms havedifferent costs (in our model if θ1 ̸= θ2 ), the firm with the lower cost becomes the leader.9
Thus, given θ1 = 0, firm 2 becomes the follower unless it chooses θ2 = 0. If it chooses θ2 = 0
and may become the leader, the leader’s profit when θ1 = θ2 = 0 is less than π F (because of
the second-mover advantage under the standard price competition). If firm 2 becomes thefollower, choosing θ2 = θF is optimal. Therefore, firm 2’s best reply is choosing θ2 = θF ,thus becoming the follower in the subsequent game. Under these conditions, Stackelberg
competition appears in equilibrium if the firms’ roles are endogenous. Therefore, Stackelberg
competition is natural in this context.

7

For the empirical works on this problem, see Holland et al. (2016).
The observable delay game is the most popular model among endogenous timing games and has been
adopted extensively in various contexts. See Pal (1998), Bárcena-Ruiz (2007), and Matsumura and Ogawa(2014).
9
Strictly speaking, two Stackelberg equilibria can exist, but the equilibrium with the lower-cost firm’s
leadership is risk dominant. In the context of price leadership, Ono (1978) first pointed out that the firmwith lower costs becomes the price leader.
8

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