The paper investigates prices and deadweight loss in multiproduct monopoly with linear interrelated demand and constant marginal costs. We show that, with commonly used models for linear demand such as the Bowley demand and vertically or horizontally differentiated demand, the price for each good is independent of demand cross‐effects and of the characteristics and number of other goods. This contrasts with the oft‐expressed view that prices critically depend on demand cross‐effects. We also show that for these linear models, the deadweight loss due to monopoly amounts to half the total monopoly profit. Finally, we show how a production subsidy might restore social efficiency.