The Rise of Streaming Music and Implications for Music Production

Appendix 1: Derivations

Appendix 2: Album Option

Our paper assumes a user’s decision is between MP3 purchases and streaming music. In this appendix, we explore the additional value that can come from albums. We first consider the consumer’s decision to purchase a bundle or individual MP3s in an unbundled form, without a streaming service option. We begin by examining the relevance of extras in the bundled form, which implies that L > 0. Assume that the number of songs to be sold as singles (with utility greater than zero) is D. In order for digital singles to strictly dominate bundled sales it must be that:

Or that Σi=1I(F(Aij))−PW>Σi=1D(F(Aij))−DPMP3, which implies that if D = I and PW<IPMP3 then the bundle will be preferred. Intuitively, if every song is good enough to be sold as a single, then the relative price of a bundle versus MP3s will determine the format. However, if any song has low or no utility, then purchasing a bundle requires that PW<DPMP3, which becomes less likely as the number of high quality songs diminishes in a bundle. Since the strategy employed by the artist has implications even in the absence of a streaming option, we examine the effects of extras on album sales using differing strategies. We start by employing the medium strategy in a fully-served market. A consumer that prefers the bundled option relative to purchasing MP3s is represented by:

Solving for the level of appreciation of extras included in a bundle, we see that the bundle must satisfy Ly>(PW−IPMP3), or the consumer’s level of appreciation for the added value of the bundle must exceed the price difference to sell albums. Similarly, considering an album with one high value song and the remainder low, a consumer prefers the bundled option if:

Implying that the bundle must satisfy y>1L(PW+xτ(I−1)−PMP3). Since PMP3>xτ for all x, it is clear that PW−IPMP3<PW+xτ(I−1)−PMP3. As this property will always hold, we can conclude that the threshold is higher for a user to prefer purchasing an album from an artist that used the “hits” strategy relative to the “medium” strategy. For that reason, we state the following:

Our approach provides a theoretical reason for the empirical findings of Elberse (2010) that demand for bundles of songs with similar appeal is less impacted by alternative formats. Albums composed of similar songs (medium strategy) fare better than albums with songs of differing appeal (hits strategy), due to the value of the songs included. The advantage of purchasing an MP3 single is that it allows users to avoid the tying of bad songs to good ones, an effect magnified as artists incorporate additional lower appeal songs in an album. The removal of this effect makes users indifferent to bundled albums and buying every song individually. This indifference and the inclusion of extras that have utility within the bundle will therefore tip the users preference to purchasing the bundle.

Our result indicates that the dedication of fans may lead to different strategies. An artist with a dedicated fan base may find bundles more profitable, whereas a new or struggling artist may aim for a hit to derive profit. Moreover, in the absence of extras a bundle’s price under the hits strategy will certainly exceed the price of an individual MP3. Owning the remaining low value songs adds some utility, but the bundled premium will surpass any additional benefit.

As shown by Boluk (2015), the only music formats to increase in spending in the last 15 years are digital download and digital streaming, therefore we assume that when an artist identifies an optimal strategy they concern themselves less with the implications for bundled sales with extras.^[43] Obviously, the dedication of fans plays an important role in the demand for music. Since our focus is the digital market, we proceed with the assumption that L = 0, to illustrate the potential for streaming to affect the digital market for music. We have shown that for the medium strategy, purchasing all singles is strictly preferred if PW>IPMP3 in the absence of extras, which we assume in our analysis. This allows us to focus on the comparison between (durable) digital songs and (non-durable) streaming.^[44]