Since I am willing to pay $X that means my opportunity cost of not buying is -$X, thus my willingness to pay is indeed $X.   That appears to be what Google CEO Eric Schmidt is saying in the following deposition transcript talking about Google paying X=$1.65 billion for YouTube, a $1billion premium over what he estimated YouTube to be worth.  From an article at cnet.

Baskin: So you orally communicated to your board during the course of the board meeting that you thought a more correct valuation for YouTube was $600 million to $700 million; is that what you said, sir?

Mancini objects to characterization of the testimony.

Schmidt: Again, to help you along, I believe that they were worth $600 million to $700 million.

Baskin: And am I correct that you were asking your board to approve an acquisition price of $1.65 billion; correct?

Schmidt: I did.

Mancini objects.

Baskin: I’m not very good at math, but I think that would be $1 billion or so more than you thought the company was, in fact, worth.

Mancini objects.

Schmidt: That is correct.


Baskin: Can you tell us what reasoning you explained?

Schmidt: Sure, this is a company with very little revenue, growing quickly with user adoption, growing much faster than Google Video, which was the product that Google had. And they had indicated to us that they would be sold, and we believed that there would be a competing offer–because of who Google was–paying much more than they were worth. In the deal dynamics, the price, remember, is not set by my judgment or by financial model or discounted cash flow. It’s set by what people are willing to pay. And we ultimately concluded that $1.65 billion included a premium for moving quickly and making sure that we could participate in the user success in YouTube.