Recently, a co-worker had a short notice business trip. He hunted around the web and bought the cheapest ticket he could find. He only noticed that one of the segments was first class when he checked in at the airport.

Why would an airline offer first class for the cheapest ticket available? If the last seat on the flight is a first class seat, and the airline were willing to offer a seat on the flight at an economy price, wouldn't it be better for the airline to overbook economy (leaving the first class seat unbooked), then either offer a first class buy-up at checkin, or give the first class seat to an economy passenger using status or mileage or some such criteria?