We study how input price discrimination and non-controlling, vertical shareholding interact. We first discuss the implications of the invariance principle (Greenlee and Raskovich in Eur Econ Rev 50:1017–1041, 2006) for input price discrimination across independent downstream markets. We show that, in the short term, price discrimination based on non-controlling, backward shareholding is more likely to improve welfare than other forms of input price discrimination, because it results in a positive consumption reallocation effect. However, if the derived demand for the input is convex, and less so as output increases, input price discrimination is irrelevant in the long term, because the ownership structures that prevail under discriminatory and uniform input pricing yield the same market outcome. The main contribution of the paper is to show that input price discrimination matters, in the short and the long term, if downstream firms compete in prices. In particular, we find that input price discrimination improves welfare in the short term, for any given ownership structure, and in the long term, through its impact on shareholding.

我们研究投入价格歧视和非控制性垂直持股如何相互作用。我们首先讨论不变性原理（Greenlee 和 Raskovich，Eur Econ Rev 50：1017-1041，2006）对独立下游市场投入价格歧视的影响。我们发现，在短期内，基于非控股、落后持股的价格歧视比其他形式的投入价格歧视更有可能改善福利，因为它会产生积极的消费再分配效应。然而，如果对投入的衍生需求是凸的，并且随着产量的增加而凸出，那么从长远来看，投入价格歧视就无关紧要，因为在歧视性和统一投入定价下普遍存在的所有权结构会产生相同的市场结果。本文的主要贡献是表明，如果下游企业进行价格竞争，投入价格歧视在短期和长期都会产生影响。特别是，我们发现，对于任何给定的所有权结构，投入价格歧视可以在短期内改善福利，从长远来看，可以通过其对股权的影响来改善福利。