A model of music piracy with popularity-dependent copying costs

Anecdotal evidence and recent empirical work suggest that music piracy has differential effects on artists depending on their popularity. Existing theoretical literature cannot explain such differential effects since it is exclusively concerned with single-firm models. We present a model with two types of artists who differ in their popularity. We assume that the costs of illegal downloads increase with the scarcity of a recording, and that scarcity is negatively related to the artist’s popularity. Moreover, we allow for a second source of revenues for artists apart from CD sales. These alternative revenues depend on an artist's recognition as measured by the number of consumers who obtain his recording either by purchasing the original or downloading a copy. Our findings for the more popular artist generalize a result found by Gayer and Shy (2006) who show that piracy is beneficial to the artist when alternative revenues are important. In our model, however, this does not carry over to the less popular artist, who is often harmed by piracy even when alternative revenues are important. We conclude that piracy tends to reduce musical variety.