We examine the impact of the licensing policies of one or more upstream owners of essential intellectual property (IP hereafter) on the variety offered by a downstream industry, as well as on consumers and social welfare. When an upstream monopoly owner of essential IP increases the number of licenses, it enhances product variety, adding to consumer value, but it also intensifies downstream competition, and thus dissipates profits. As a result, the upstream IP monopoly may want to provide too many or too few licenses, relatively to what maximizes consumer surplus or social welfare. With multiple owners of essential IP, royalty stacking increases aggregate licensing fees and thus tends to limit the number of licensees, which can also reduce downstream prices for consumers. We characterize the conditions under which these reductions in downstream prices and variety is beneficial to consumers or society.