Cooperative choice of corporate social responsibility in a bilateral monopoly model

ABSTRACT

This article presents an examination of a linear bilateral monopoly model with endogenous and cooperative choice of corporate social responsibility (CSR) level. This article also describes an investigation of the effects of cooperative choice of CSR on the market and welfare. New findings are explicit derivation of the necessary and sufficient condition for solving a double marginalization problem in the bilateral monopoly model with CSR. In addition, this report is the first demonstrating that cooperative CSR with Nash bargaining improves consumer surplus, social welfare and each firm’s profit to a level higher than that achieved through noncooperative CSR. Furthermore, cooperative CSR with Nash bargaining is shown to be capable of completely solving the double marginalization problem generated by a bilateral monopoly, although the manufacturer and the retailer are not vertically integrated.

KEYWORDS:

• Bilateral monopoly
• cooperative CSR
• double marginalization problem
• socially concerned firm

JEL CLASSIFICATION:

• D21
• L12
• L22
• M14

Acknowledgement

The author would like to thank an anonymous reviewer, Daisaku Goto and Katsufumi Fukuda fortheir valuable comments. Any remaining errors are the author's responsibility.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ For excellent CSR literature, see Chen et al. (2016), Crifo and Forget (2015), Fanti and Buccella (2017), Heal (2005), Kitzmueller and Shimshack (2012), Liu, Wang and Chen (2018), Matsumura and Ogawa (2014), Schmitz and Schrader (2015), Withisuphakorn and Jiraporn (2016) and Xu and Liu (2017). Furthermore, for recent studies of environmental CSR and environmental innovation, see Lambertini, Palestini and Tampieri (2016), Lambertini and Tampieri (2015), Liu, Wang and Lee (2015), Ouchida and Goto (2016a, 2016b), Yanase (2012) and others.

² Double marginalization is a phenomenon of pricing inefficiency arising from vertical relations. In a vertical supply chain composed of an upstream manufacturer and a downstream retailer, the feature is explained as follows. The retail price is higher than that in a vertically integrated case. The reason is that a downstream retailer applies a margin to the wholesale price that includes the margin of an upstream manufacturer. In addition, the retailer does not consider the externality exerted on the manufacture by changing the retail price. For this reason, the inefficiency occurs. As a result, total surplus is worse than under a monopoly (vertically integrated case). For details, see Belleflamme and Peitz (2015, Section 17.1) and Tirole (1988, Section 4.2).

³ Brand and Grothe (2013) completed Goering’s (2012) investigation.

⁴ Subscripts $m$ and $r$, respectively, denote the manufacturer and the retailer.

⁵ For details of the model and the solution procedures, see Brand and Grothe (2015, 271–280). The expressions presented here do not include a typographical error in the original: the equilibrium value of $P{S}^{\ast }$.

⁶ Brand and Grothe (2015, Appendix) provide a proof of these results.

⁷ The retailer’s reaction function is obtained from the first-order condition of the retailer’s profit maximization: $\mathrm{\partial }{\pi }_r^{\ast }/\mathrm{\partial }{\theta }_r=((a-c{)}^2({\theta }_m-2{\theta }_r))/b(4-{\theta }_m-2{\theta }_r{)}^3=0$. Therefore, the retailer’s reaction function is ${\theta }_r({\theta }_m)={\theta }_m/2$.

⁸ The manufacturer’s reaction function is obtained from the first-order condition of the manufacturer’s profit maximization: $\mathrm{\partial }{\pi }_m^{\ast }/\mathrm{\partial }{\theta }_m=-((a-c{)}^2{\theta }_m)/b(4-{\theta }_m-2{\theta }_r{)}^3=0$. Therefore, the manufacturer’s reaction function is ${\theta }_m({\theta }_r)=0$.

⁹ When the monopolist determines its output level $q$ to maximize its own profit: $\pi =(a-bq)q-cq$, the corresponding first-order condition is $d\pi /dq=a-2bq-c=0$. Consequently, the output level, consumer surplus, profit (i.e. producer surplus) and total welfare are obtained respectively as $q=(a-c)/2b$, $PS=(a-c{)}^2/8b$, $\pi =(a-c{)}^2/4b$ and $WF=3(a-c{)}^2/8$.

¹⁰ The optimal solution is not determined uniquely.

¹¹ Superscript $\mathrm{C}$ stands for the case of cooperative choice.

¹² See footnote 9.

¹³ See Brand and Grothe (2015, 277).

¹⁴ Producer surplus is $(a-c{)}^2/4b$.

¹⁵ For example, see Amaeshi, Osuji and Nnodim (2008), Ashby, Leat and Hudson-Smith (2012) and PricewaterhouseCoopers (PwC) (2010, 5). Particularly Amaeshi, Osuji and Nnodim (2008) introduced famous examples: Nike, GAP, Adidas and McDonalds. As other examples, ASICS, SONY, Nestlé and others also have established CSR supply chains.

¹⁶ For a relevant study of the food industry, see Maloni and Brown (2006).

¹⁷ While the difference in retailer profits is ${\pi }_r^{\mathrm{C}}-{\pi }_r^{\ast }{|}_{{\theta }_m=0={\theta }_r}=5(a-c{)}^2/128b$, the difference in manufacturer profits is ${\pi }_m^{\mathrm{C}}-{\pi }_m^{\ast }{|}_{{\theta }_m=0={\theta }_r}=3(a-c{)}^2/128b$. The former is greater than the latter.

¹⁸ For details, see Brand and Grothe (2015, 283).

¹⁹ See Auger et al. (2003), Mohr and Webb (2005) and Trudel and Cotte (2009).

²⁰ See Berman et al. (1999), Hillman and Keim (2001) and Sisodia, Wolfe, and Sheth (2007).

Additional information

Funding

This research is supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS KAKENHI), No. 16K03627.