This paper considers the market for digital music. We claim that the combination of the MP3 format and peer-to-peer networks has made music non-excludable and this feature is essential for the understanding of the economics of the music market. We study optimal business models for selling non-excludable goods and show that despite promising theoretical results, adding just a slight uncertainty about the number of customers has significant negative implications for profitability. Indeed, as the average number of customers tends to infinity the average payment per customer converges to zero. Therefore, the music industry should concentrate on alternative ways of creating profit such as selling access to listeners, concerts, merchandise, ringtones etc.