Corporate social responsibility and endogenous competition structure in an industry composed of asymmetric firms with managerial delegation

ABSTRACT

This study focuses on the endogenous choice between price and quantity contracts in a duopoly composed of asymmetric firms that care about corporate social responsibility (CSR) with managerial delegation. We find that the optimal strategy of a firm that cares about social welfare does not depend on both the degree of homogeneity of goods and the degrees of importance of CSR, while the that of one that cares about consumer surplus strictly depends on the degree on importance of CSR within its rival firm.

KEYWORDS:

• Corporate social responsibility
• cournot competition
• Bertrand competition
• managerial delegation
• competition structure

Acknowlegnment

We are grateful to the anonymous referee and associate editor for their comments and suggestions. We are grateful for the financial support of KAKENHI (21K01491). This research was also supported by a grant-in-aid from the Zengin Foundation for Studies on Economics and Finance. Any remaining errors are our own.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Note that Goering (2008) referred to a CSR firm here as a ‘NPO’ firm.

2. Nakamura (2021c) considered the endogenous selection problem of the strategies in an asymmetric duopoly composed of one firm whose objective is a weighted sum of its profit and social welfare and another whose objective is a weighted sum of its profit and consumer surplus without any managerial delegation. This study can be regarded as an extension of the analysis given in Nakamura (2021c) by introducing the FJSV delegation within each CSR firm.

3. This assumption is standard when assuming a mixed oligopoly with FJSV delegation in which the owners of firms delegate decisions to managers. See Barros (1995), White (2001), Bárcena-Ruiz (2009), and Bárcena-Ruiz (2013) for detailed discussions on this assumption.

4. Hence, the second-order condition for the manager of Firm 1 is satisfied.

5. The second-order conditions for the owners of Firms 1 and 2 are satisfied.

6. The second-order conditions for the managers of Firms 1 and 2 are satisfied.

7. The second-order conditions for the owners of Firms 1 and 2 are satisfied.

8. The second-order conditions for the managers of Firms 1 and 2 are satisfied.

9. The second-order conditions for the owners of Firms 1 and 2 are satisfied.

10. The second-order condition for the manager of Firm 1 is satisfied.

11. The second-order conditions for the owners of Firms 1 and 2 are satisfied.

12. Denoting with $z_1^{\ast }$ and $z_2^{\ast }$ the probability of choosing price for Firms 1 and 2, the mixed strategy equilibrium is given by

$z_1^{\ast }=\frac{V_2^{qq}-V_2^{qp}}{(V_2^{pp}-V_2^{pq})+(V_2^{qq}-V_2^{qp})},$

$z_2^{\ast }=\frac{V_1^{qq}-V_1^{pq}}{(V_1^{pp}-V_1^{qp})+(V_1^{qq}-V_1^{pq})}.$

Denoting with $z_1^{\ast }$ and $z_2^{\ast }$ the probability of choosing price for Firms 1 and 2, the mixed strategy equilibrium is given by

$z_1^{\ast }=\frac{V_2^{qq}-V_2^{qp}}{(V_2^{pp}-V_2^{pq})+(V_2^{qq}-V_2^{qp})},$

$z_2^{\ast }=\frac{V_1^{qq}-V_1^{pq}}{(V_1^{pp}-V_1^{qp})+(V_1^{qq}-V_1^{pq})}.$

13. Nakamura (2021c) considered the endogenous selection problem of the strategies in a duopoly composed of asymmetric CSR firms in the entrepreneurial situation without their managers.

Additional information

Funding

This work was supported by the JSPS [21K01491]; Zengin Foundation For Studies On Economics And Finance [2014].