I claim that iTunes could earn 40% more revenue than it currently does just by slashing its price from $1.00 to $.50 . Why? Let me explain.

Digital music is a virtual good. As v1.0 approximation, I assume:

- Marginal costs are essentially zero (e.g., hosting, processsing and bandwidth)
- Customers have limits on the quantities that they’d consume even if the good were costless
- Prices are somewhat inelastic because customers are price sensitive
- Each customer’s demand curve can be modeled with the classic Cobb-Douglas demand curve

The cost side of the equation is simple: zero marginal cost. These things are just digits, so hosting, processing and bandwidth costs are negligible. Sure, apple has to pay licensing fees for the music. But for the sake of argument, let say that these fees are revenue sharing agreements so apple’s profits are still proportional to total revenue.

The action is on the revenue-side. We can take a classic demand function, d=u^1(1/a)xp^(1-1/a), where d is demand, u is utility, p is price and a is a measure of price elasticity. The suppliers problem is to maximize profit, d*p.

It turns out for products with relatively elastic price sensitivity, you want to set p as low as possible. So, the itunes store should pick a low price for music because the lost revenue per track is more than made up by demand for more tracks. (Teenagers are extremely price sensitive!)

Conversely, for products with relatively inelastic prices, you want to set p as high as possible. I am not aware of any virtual products with this characteristic, but the math works out that you more than make up for the lost demand in the price increase. Perhaps some unique goods in Second Life fit this category, although there is a cost at least for players in terms of time to create some of the valuable objects.

How low should itunes set its price? In the ideal case, the price tends towards zero. But in practice, consumers have limits. How many songs would you download per week if itunes were free? 7? 14? 100? It wouldn’t really go towards infinity!

You must have a good estimate of the price elasticity, the utility and the maximum quantity demanded to solve the pricing problem. In particular, you pick the maximum price such that the consumer still demands his maximum amount.

For example, let us assume that digital music has an inelasticity coefficient a=0.4 and that a teenager would download a maximum of 20 tracks a week and has a u=2.2 (which implies that she currently downloads 7 tracks a week at $1 each on itunes). Note: all of these numbers are just my best guesses. The ideal price would then be $0.51, which would generate $10.10 in profits per week per customer rather than $7. That’s a 44% increase, and the kids would get nearly triple the tracks per week!

Of course, itunes has other considerations. They do have to share the profits per track, and I think that ituntes may have negotiated a flat rate rather than a percent of revenue. (A flat fee deal structure leads to deadweight loss, where the labels, Apple and consumers all lose.) In addition, they claim to have other considerations like “simplicity” in pricing and the labels are certainly wary of undermining their CD sales.

Finally, there are other constraints that I haven’t considered in this simple analysis. Teenagers have budgets, so perhaps $7 a week is the maximum that they can spend. (I doubt this.) Also, I totally guessed at 0.4 for the price elasticity. But actual itunes data bounds the possibilities. We know that itunes actually makes $7 in revenue, so values greater than .45 are implausible. We also know that consumers only buy 7 songs a week at $1, so values under .3 are also implausible.

This range, 0.3 to 0.45, is great to know if you are launching your own virtual good. Without additional data, you should use something in that range as your initial value. Similarly, you can also use u=2.2 as a starting point for knowing your utility. How attractive does your virtual good seem in comparison to digital music? Ratchet that number up or down a little. And as data comes in, you can tweak the parameters and figure out the best price.

This is a simple but useful model. Some possibly important complications: How much should you raise prices to signal higher quality? What if you have a means of discriminating per customer, e.g., should you charge different prices for heavy and light users? What you can discriminate by product, e.g., should you charge different prices for popular and unpopular products? I will examine some of these more advanced questions in the future because I suspect that iTunes (and other providers of virtual goods) could have an even greater increase in its profits by intelligently using dynamic pricing.

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