In the presence of a peer-to-peer economy, the option of sharing an item is valuable for consumers. By retaining control over the shareability of its products a monopolist can set a sharing tariff in conjunction with the purchase price of the product, in order to extract state-contingent surplus from consumers: the shareability rent. Using an overlapping-generations model with heterogeneous consumers, we determine the jointly optimal retail price and sharing tariff for durable products, and quantify the value for the control of shareability, thus defining the firm's financial boundary conditions for an investment in sharing-control technologies.