Abstract
In this paper, we consider that the public firm competes with a private firm caring about consumer surplus in vertically differentiated market. We explore the privatization policy, and the relationship between the optimal degree of privatization and the CSR degree of private firm. We find that if the public firm produces low-quality products, the government should adopt a policy of privatization, and the optimal degree of privatization is decreasing (increasing) in the CSR degree of private firm, if the cost difference of quality is sufficiently small (large). However, if the public firm produces high-quality products and the cost difference of quality is sufficiently large (small), the government should (not) adopt a policy of privatization. The government's privatization policy is related to the difference in quality and cost of the products produced by firms. We further analyze the endogenous selection of product quality between public firm and private firm and find that if the quality gap between high-quality products and low-quality products is sufficiently large, both firms will choose to produce high-quality products. If the product quality gap is of medium-intensity, the public firm chooses to produce low-quality products, and the private firm chooses to produce high-quality products. However, if the product quality gap is sufficiently small, there is no Nash equilibrium.
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Notes
Reviewing the history of CSR development, however, CSR efforts emerged not because of their completely voluntary, but rather out of a variety of social, environmental, and economic pressures (European Commission 2001).
See Li et al. (2019), in particular, in an import-competing duopoly model with vertical product differentiation, the tariff will decrease if the foreign firm switches from a purely profit-driven firm to a CSR firm. A consumer-oriented CSR strategy will always hurt the domestic firm’s profit, whereas the relationship between the foreign firm’s profit and CSR sensitivity (the degree to which a firm care about consumer welfare) is inversely U-shaped.
Our research provides a rich framework. If the CSR behavior of private firm is not considered, our model can be degenerated to examine the impact of vertical product differentiation on privatization policy.
Thanks to the reviewers and the editor for their comments and suggestions of doing this extension, which have substantially improved the analysis of this paper.
The forms of \(\Phi^{HH} (\alpha ,\delta )\) and \(\Psi^{HH} (\alpha ,\delta )\) are complicated, which we show in the Appendix.
The forms of \(\Phi^{HL} (\alpha ,\delta )\) and \(\Psi^{HL} (\alpha ,\delta )\) are complicated, which we show in the Appendix.
The forms of \(\Phi^{LH} (\alpha ,\delta )\) and \(\Psi^{LH} (\alpha ,\delta )\) are complicated, which we show in the Appendix.
Thanks to the comments of a reviewer, it deserves for further analysis in future studies.
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Acknowledgements
Financial support from Guangdong Basic and Applied Basic Research Foundation (2019A1515110690), is greatly appreciated. We are grateful to the Editor and two anonymous referees for comments that helped us to improve the paper.
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Appendix
Appendix
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①
\(\Phi^{{{\text{HH}}}} (\alpha ,\delta )\) and \(\Psi^{{{\text{HH}}}} (\alpha ,\delta )\):
$$\Phi^{HH} (\alpha ,\delta ) = \frac{{(1 + \delta )\left( \begin{gathered} 60536 + 144\alpha^{8} \delta (1 + \delta )^{8} + H_{1} (\alpha ,\delta ) + H_{2} (\alpha ,\delta ) - H_{3} (\alpha ,\delta ) + \hfill \\ H_{4} (\alpha ,\delta ) - 2\alpha^{2} (1 + \delta )^{2} H_{5} (\alpha ,\delta ) - \alpha (1 + \delta )H_{6} (\alpha ,\delta ) + H_{7} (\alpha ,\delta ) \hfill \\ \end{gathered} \right)}}{{\left( \begin{gathered} (36(3 - \alpha + (2 - \alpha )\delta )^{3} (5 - \alpha (1 + \delta )(3 + \delta ) + \delta (5 + \delta )) \hfill \\ (14 + 2\alpha^{2} (1 + \delta )^{2} - 2\alpha (1 + \delta )(4 + 3\delta ) + \delta (22 + \delta (10 + \delta )))^{2} ) \hfill \\ \end{gathered} \right)}}$$
where
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②
\(\Phi^{{{\text{HL}}}} (\alpha ,\delta )\) and \(\Psi^{HL} (\alpha ,\delta )\):
$$\Phi^{{{\text{HL}}}} (\alpha ,\delta ) = \frac{{\left( \begin{gathered} (1 + \delta )24\alpha G_{1} (\alpha ,\delta )\delta^{2} + G_{2} (\alpha ,\delta )\delta^{3} + G_{3} (\alpha ,\delta )\delta^{4} - 4G_{4} (\alpha ,\delta ) + 2G_{5} (\alpha ,\delta )\delta^{6} + \hfill \\ 2G_{6} (\alpha ,\delta )\delta^{7} + 2G_{7} (\alpha ,\delta )\delta^{8} - (3 - \alpha )G_{8} (\alpha ,\delta )\delta^{9} - G_{9} (\alpha ,\delta )\delta^{10} - G_{10} (\alpha ,\delta )\delta^{11} - \hfill \\ 2(3 - \alpha )^{7} (518 - \alpha (293 - 44\alpha ))\delta^{12} - 12(3 - \alpha )^{9} \delta^{13} ) \hfill \\ \end{gathered} \right)}}{{\left( \begin{gathered} (17 - (8 - \alpha )\alpha )\delta^{2} - 36(3 - \alpha )^{3} \delta (1 + \delta )^{2} (2\alpha + (7 + (2 - \alpha )\alpha )\delta + \hfill \\ (3 - \alpha )^{2} \delta^{3} )(6 + \delta (22 - 6\alpha + 2(13 - (7 - \alpha )\alpha )\delta + (3 - \alpha )^{2} \delta^{2} ))^{2} \hfill \\ \end{gathered} \right)}},$$
where
where
-
③
\(\Phi^{LH} (\alpha ,\delta )\) and \(\Psi^{LH} (\alpha ,\delta )\):
$$\Phi^{LH} (\alpha ,\delta ) = \frac{{\left( \begin{gathered} N_{1} (\alpha ,\delta ) - N_{2} (\alpha ,\delta ) + N_{3} (\alpha ,\delta ) + N_{4} (\alpha ,\delta ) - 4\alpha^{5} \delta^{2} N_{5} (\alpha ,\delta ) - \hfill \\ 9\alpha (1 + \delta )N_{6} (\alpha ,\delta ) + 2\alpha^{4} \delta N_{7} (\alpha ,\delta ) + 6\alpha^{2} (1 + \delta )N_{8} (\alpha ,\delta ) - \alpha^{3} N_{9} (\alpha ,\delta ) \hfill \\ \end{gathered} \right)}}{{\left( \begin{gathered} 36\delta (3 - \alpha + (2 - \alpha )\delta )^{3} (2\alpha - (3 - (5 - \alpha )\alpha )\delta - \hfill \\ (3 - \alpha )(1 - \alpha )\delta^{2} )(6 + \delta (13 - 6\alpha - 2(2 - \alpha )^{2} \delta ))^{2} \hfill \\ \end{gathered} \right)}},$$
where
where
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Wang, X., Wang, L.F.S. Corporate social responsibility, vertical product differentiation, and privatization policy. JER 73, 403–425 (2022). https://doi.org/10.1007/s42973-020-00053-9
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DOI: https://doi.org/10.1007/s42973-020-00053-9
Keywords
- Vertical product differentiation
- Mixed oligopoly
- Corporate social responsibility
- Privatization policy
- Cost-difference quality