Input price discrimination under passive partial cross ownership

ABSTRACT

Hu, Mizuno, and Song (Applied Economics Letters, 2021) compare the welfare effects of input price discrimination (IPD) and uniform input pricing (UIP) under passive partial ownership (PPO) where one downstream firm holds equity shares of its rival. This paper extends their setup to accommodate passive partial cross ownership (PCO) where each downstream firm holds equity shares of its rival. A common conclusion is that IPD improves welfare if the cost asymmetry is sufficiently low. Interestingly, this finding holds regardless of whether the more efficient firm is also the dominant partial shareholder. Indeed, it is found that the likelihood that IPD is welfare enhancing increases as firms become more asymmetric in terms of equity shares. However, the critical level of cost asymmetry differs under PPO and PCO, meaning that there are cases where IPD performs better in terms of social welfare under PCO but not under PPO, and vice versa. The main conclusion of this paper is that, compared to the PPO structure, PCO reduces the likelihood that IPD results in better welfare outcomes than UIP.

KEYWORDS:

• Input price discrimination
• passive partial cross ownership
• vertical relationships
• competition policy

JEL CLASSIFICATION:

• D43
• L40
• L10
• G34

Disclosure statement

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

Notes

¹ Such objective functions can also capture the case of common ownership where both firms are fully owned by the same set of two shareholders, with the majority owner of each firm holding a minority stake in its rival (de Haas and Paha 2021). For an excellent discussion about more general forms of common ownership where agency frictions may be present, see Schmalz (2018).

² Since the former effect dominates, total output decreases in input price(s), with this reduction being mitigated by PCO.

³ The intuition behind Proposition 1 has well been discussed in HMS just after presenting their Lemma 2.

⁴ Due to space limitations, $\mathrm{\Delta }CS\equiv C{S}^D-C{S}^U,\mathrm{\Delta }TS\equiv T{S}^D-T{S}^U$ and $c_2^{TS}\left({\theta }_1,{\theta }_2\right)$ are only presented graphically. The full expressions are available upon request.

⁵ Working in terms of $c_2$ than $z\equiv c_2/\left(a-c\right)$ is more intuitive, hence all figures assume that $a-c=1$. This does not change the results qualitatively. Indeed, given $\overline{{\theta }_2}$, $c_2^{\ast }\left({\theta }_1,\overline{{\theta }_2}\right)$ and $c_2^{TS}\left({\theta }_1,\overline{{\theta }_2}\right)$ become steeper (respectively, flatter) as parameter $a$ (respectively, $c$) increases.