Radiohead’s name-your-own-price sale of its new In Rainbows album has generated lots of commentary, especially since comscore released data claiming that 62% of customers set their price at zero, with the remaining 38% setting an average price of $6, which comes to an average price of $2.28 per customer. (There are reasons to question these numbers, but let’s take them as roughly accurate for the sake of argument.)

Bill Rosenblatt bemoaned the low price, calling it a race to the bottom. Tim Lee responded by pointing out that Rosenblatt’s “race to the bottom” is just another name for price competition, which is hardly a sign of an unhealthy market. The music market is more competitive than before, and production costs are lower, so naturally prices will go down.

But there’s another basic economic point missing in this debate: Lower average price does not imply lower profit. Radiohead may well be making more money because the price is lower.

To see why this might be true, imagine that there are 10 customers willing to pay $10 for your album, 100 customers willing to pay only $2, and 1000 customers who will only listen if the price is zero. (For simplicity assume the cost of producing an extra copy is zero.) If you price the album at $10, you get ten buyers and make $100. If you price it at $2, you get 110 buyers and make $220. Lowering the price makes you more money.

Or you can ask each customer to name their own price, with a minimum of $2. If all customers pay their own valuation, then you get $10 from 10 customers and $2 from 100 customers, for a total of $300. You get perfect price discrimination – each customer pays his own valuation – which extracts the maximum possible revenue from these 110 customers.

Of course, in real life some customers who value the album at $10 will name a price of $2, so your revenue won’t reach the full $300. But if even one customer pays more than $2, you’re still better off than you’d be with any fixed price. Your price discrimination is imperfect, but it’s still better than not discriminating at all.

Now imagine that you can extract some nonzero amount of revenue from the customers who aren’t willing to pay at all, perhaps because because listening will make them more likely to buy your next album or recommend it to their friends. If you keep the name-your-own-price deal, and remove the $2 minimum, then you’ll capture this value because customers can name a price of zero. Some of the $10-value or $2-value people might also name a price of zero, but if not too many do so you might be better off removing the minimum and capturing some value from every customer.

If customers are honest about their valuation, this last scenario is the most profitable – you make $300 immediately plus the indirect benefit from the zero-price listeners. Some pundits will be shocked and saddened that your revenue is only 27 cents per customer, and 90% of your customers paid nothing at all. But you won’t care – you’ll be too busy counting your money.

Finally, note that none of this analysis depends on any assumptions about customers’ infringement options. Even if it were physically impossible to make infringing copies of the album, the analysis would still hold because it depends only on how badly customers want to hear your music and how likely they are to name a price close to their true valuation. Indeed, factoring in the possibility of infringement only strengthens the argument for lowering the average price.

By all accounts, Radiohead’s album is a musical and financial success. Sure, it’s a gimmick, but it could very well be a smart pricing strategy.