A model of music piracy with popularity-dependent copying costs

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