[WalterBright]

If it adjusted the prices as someone approaches, I suspect customers would soon notice it.

I'm not going to order food at a restaurant if the menu has no prices on it, even if I'm a zillionaire.

[pdonis]

Actually, restaurants that cater to the very rich often don't have any prices on the menu, on the theory that if you have to ask what it costs, you can't afford it.

[WalterBright]

I've been to the most expensive restaurant in Seattle, and there were prices on the menu. (It was for a special date, and worth every penny.)

I'm sure there are some, though, but I disagree with your theory. My theory is the patrons do it to show off their wealth by disregarding the prices.