I don't think booing poorly-performed players makes any difference at all (through misapplied market analogies or otherwise) . If anything, if I could play a lick, I'd much rather play for a club supported by fans who had their players' backs in all circumstances. They are the supporters I'd want to give my all for, and who I would be gutted to let down.
So, if it makes no difference, I guess as a fan you just have to ask yourself a question: am I the type of fan who wants to have a tanty and boo my own players to make myself feel better, but justify it on the grounds that it somehow improves the team, or do I not want to be a complete tool / Eagles supporter-type?
Some might say that's a leading question, but I would just boo them until they came over to my way of thinking. Because of economics etc.