I see I must make explicit what I left as an exercise.

It is well known that

U_{b} = F_{i}*(A_{r} + V_{s})^{2}
Where

U_{b} = urgency to buy,

F_{i} = impulsivity factor,

A_{r} = anticipated rarity,

And

V_{s} = verified scarcity

Since A_{r} and V_{s} are both >0, and impulsivity (among Americans) approaches infinity as long as the mortgage isn't due, we have U_{b} approaching infinity as well.

Since it has been widely reported in the Silly Mathematics literature that P_{eBay} is directly proportional to U_{b}, we have P_{eBay} > what you really ought to pay. Q.E.D.

Any logical inconsistencies or antifactual facts noted by the reader are irrelevant because I say so.