Perhaps do a bit of Google searching around the psychology of "price anchoring". There's a lot of material out there that suggests that people are subconsciously affected by the first price they see in that it frames their expectations going forward. So if you quote a price, even if it's more than what they are willing to pay, it may help reset their expectations within a range that's still going to be higher than if they throw out a price "blind" because you've given them nothing at all to go on.