The forces that shift: the cost of publishing and the predictability of success

The setup. Fifty candidate songs have revenues that follow a long tail: the best sells a lot, most sell little. Each song costs T to publish, and its producer publishes it when the revenue it expects covers T. Producers forecast with error, and σ sets how large that error is. Digitization lowers the cost from T to T′, so more songs are published. Aguiar and Waldfogel ask how much that adds to consumer surplus and welfare, and the answer depends on σ: with perfect foresight the added songs are the ones everyone knew were weak, and with unpredictable quality some of them turn out to be hits. Click a bar to see that song's demand curve, with its consumer surplus, its profit, and the cost it has to cover.

What to notice. The cost line T cuts the ranked list of songs: everything whose forecast lies above it is published. Lowering the cost to T′ adds the songs between the two lines. With σ = 0 the forecast is exact, the bars fall in order, and the added songs are the weakest ones, so consumer surplus grows by little: this is the usual long tail, the one Brynjolfsson, Hu and Smith measured for books. Raise σ and the bars scatter around the forecast line. The songs added when the cost falls now include some whose realized revenue beats the old cost T, marked with a dot, and the gain in consumer surplus is larger than the traditional calculation, which keeps the best sellers, would give. Tick complete unpredictability and entry becomes a lottery: the same number of songs clears each cost, but which ones is random, so hits stay unpublished, published songs fail to cover even T′, and welfare can fall while consumer surplus still rises.

How this maps to the paper. Aguiar and Waldfogel (2018) estimate that digitization tripled the number of new songs, and compare the 2011 catalog with a counterfactual holding one third of that year's releases. Which third is kept depends on what producers could predict. Removing the songs with the lowest realized appeal gives the perfect-foresight benefit, $0.51 million of consumer surplus in Table 6. Removing the songs with the lowest forecast appeal, with a forecast fitted on the previous year's releases, gives $10.09 million, 19.82 times larger; the welfare ratio is 11.57. The paper's third regime, no predictability, keeps a random third: its consumer-surplus ratio is 299 and its welfare change is negative, because the entry costs of the songs that never pay off are counted. The simulation reproduces the mechanism with a stylized demand: price is fixed at 1, each song's demand is linear, so its consumer surplus is half its revenue. The ratio here stays well below the paper's, because the paper's catalog holds over two million substitutable songs and its tail sells almost nothing, so the traditional calculation finds almost no gain to begin with. The ratio also depends on the draw of forecast errors, which is why the button redraws them.