What is a taxi medallion worth?

New York City just auctioned off some more medallions. What did they go for? About $300,000. What should one cost? Ask Andrew Chamberlain:

...let’s do the math. Given a medallion cost of $300,000, how much does a cabbie have to make to justify buying one? Assuming he’ll use it for 20 years, and assuming a 5 percent discount rate—the forgone return he could’ve earned on a similar investment—he’d need to earn about … $28,300 a year.

That’s not much. So how much do taxi drivers actually earn? According to the New York Times here and here, most drivers pull in about … $30,000 a year.

Chamberlain also questions whether the medallion system makes sense in the first place. My knee-jerk free market reaction is to say no. That being said, it is easy to imagine that a congestion tax on Manhattan taxis is optimal. How close do current quantity restrictions come to such a tax? Hard to say, but at the very least non-Manhattan driving probably does not require medallions. Should we also allow taxis to raise their prices when it is raining? I have heard that Tokyo residents hailing a taxi will hold up two fingers to pay twice the state fare, three fingers to triple it, and so on.

Addendum: Daniel Akst notes that this calculation assumes a very low shadow price for labor. I'll predict that the immigrant drivers have discount rates higher than five percent a year, as well. That only intensifies the puzzle. On the other side of the equation, you can sell the medallion after twenty years.