They might need to have seats on that flight offered to meet a contract with the airport, or they might be using personalized pricing to only offer the 50 dollar price to certain customers (if you keep searching often the price goes up for instance) or any number of other stuff. Airline pricing is like car pricing.

I don't see why they would _ever_ prefer an unsold seat unless:

* they are trying to artificially inflate the price

* they could send cargo that is, per pound, more lucrative than the cost of a ticket

It's not like the weight of a person is going to cost an extra $50 in jet fuel