I didn’t pay anything to download Radiohead’s “In Rainbows” last Wednesday. When the checkout page on the band’s Web site allowed me to type in whatever price I wanted, I put 0.00, the lowest I could go. My economist friends say this makes me a rational being.

Apparently not everybody is this lucid, at least not in matters related to their favorite British rock band. After Radiohead announced it would allow fans to download its album for whatever price they chose, about a third of the first million or so downloads paid nothing, according to a British survey. But many paid more than $20. The average price was about $8. That is, people paid for something they could get for free.

This phenomenon is not new. It’s called tipping. We do it when we go to the restaurant or the barber, or when we ride in a taxi. Though one could argue there are real tangible reasons for this payment — like not losing an ear the next time we get a haircut — the practice of paying more money than we are legally bound to do is still mystifying in an economic sense. For instance, why tip a cabdriver you will probably never see again?

“Since we economists don’t understand tipping, we can’t really say whether this new scheme will work,” Greg Mankiw, a Harvard professor of economics, said in an entry on his blog. He is not the only economist who is fascinated by the phenomenon. His Harvard colleague, Dani Rodrik, asked his blog readers, “Has Radiohead gone bonkers?” He concluded, “Not at all.” Radiohead will make money. But those who are paying for the download may truly be nuts.