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I investigate the welfare effects of input price discrimination when an upstream supplier bargains over secret two‐part tariffs with two cost‐asymmetric downstream firms. I find that these welfare effects depend on the identity of the supplier's partner in negotiations after the ban. When the supplier bargains the common contract with the more cost‐efficient firm, then a ban on discrimination may increase welfare. In that case, there is below‐cost pricing in the upstream market despite strategic complementarity in the downstream market. When the supplier bargains the common contract with the less cost‐efficient downstream firm, banning discrimination always decreases welfare.