Input price discrimination and non-controlling vertical shareholding

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.