Socially excessive dissemination of patent licences

Compared with the social optimum, a monopolist usually sells too little. This result seemingly includes the case of a lab that licences its patented cost innovation: Katz and Shapiro (1986) find 'conditions under which [the lab] will issue fewer than the socially optimal number of licences.' However, I find instead that its incentives can be socially too high; the monopoly seller may sell too much. For example, it can be profit maximizing to sell several licences, while it is socially optimal that none is sold.