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But what is the optimal level of software piracy?
The naive answer is zero. But consider that there are only two foolproof ways to prevent software piracy. The first is to never release the software at all—silly but effective—in which case revenue is $0. The second is to permit the work to be freely copied and redistributed—say, under an open-source license, which condones the otherwise piratical behavior—in which case revenue is also $0. But at both ends of this continuum, revenue is $0. So the maximum revenue happens in the middle, where some amount of piracy occurs. Therefore, the optimal level of piracy is greater than zero.