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We analyze the short‐ and long‐run implications of third‐degree price discrimination in input markets. In contrast to the extant literature, which typically assumes that the supplier is an unconstrained monopolist, in our model input prices are constrained by the threat of demand‐side substitution. In our model, the more efficient buyer receives a discount. A ban on price discrimination thus benefits smaller but hurts more efficient, larger firms. It also stifles incentives to invest and innovate. With linear demand, a ban on price discrimination benefits consumers in the short run but reduces consumer surplus in the long run, which is once again the opposite of what is found without the threat of demand‐side substitution.