Hypothetically speaking, of course.

Let's say you know this wonderful couple, Mik and Tam Snirp. Mik and Tam are sort of, maybe, perhaps considering purchasing a new vehicle and therefore getting rid of one of their current ones, a 2001 Accord. Mik and Tam took the Accord over to a dealer that will buy your car even if you don't buy theirs, XamRac, and they got an offer right at Blue Book trade-in price. They expect a similar offer from whatever dealer they decide to purchase their new vehicle from (assuming they decide to buy a new car, that is). (In the state Mik and Tam live in, they have to pay sales tax on the price of the new car -- in some states, it's new car minus trade-in -- so there's no really good reason to choose one over the other.)

However. There is a another option for the Snirps. Kelly Blue Book also says that, in a private sale, they could expect to get $1700 more than XamRac is offering them. Tam is thinking, "Hmm, we sold our last house by ourselves -- and quickly -- by pricing it smartly (about half way between its true price and its true price minus a 6% percent dealer commission), so perhaps we should try to sell it ourselves for $500 or so below Blue Book, accept any offer that's about $800 or so below, and voila! We're up about $1000!" (Needless to say, if the dealer they would buy their new vehicle from would offer them something close to that, they'd take it without worrying about having to sell it.)

So. Assuming they buy a new vehicle and thus sell their old one -- not a foregone conclusion -- should they try to sell it themselves for the extra $1000?