Optimal non-linear pricing with data-sensitive consumers

We introduce consumers with intrinsic privacy preferences into the monopolistic non-linear pricing model. Next to classical consumers, there is a share of data-sensitive consumers who incur a privacy cost if their purchase reveals information to the monopolist. The monopolist discriminates between privacy types using privacy mechanisms which consist of a direct mechanism and a privacy option, targeting, respectively, classical and data-sensitive consumers. We show that a privacy mechanism is optimal if privacy costs are large and that it yields classical consumers a higher utility than data-sensitive consumers with the same valuation. If, by contrast, privacy preferences are public information, data-sensitive consumers with a low valuation obtain a strictly higher utility than classical consumers. With public privacy preferences, data-sensitive consumers and the monopolist are better off, whereas classical consumers are worse off. Our results are relevant for policy measures that target the data-awareness of consumers, such as the European GDPR.