What you've described is nothing like a real market. Where are the people in your model who are happy to pay $110? $120? If there are 10 who'd buy it at $200, and 100 who'd buy it at $100, surely there'd be 50 who'd buy it at $130 or so.
That ignores the social aspect entirely, too. How many who were originally willing to pay $100 will later pay $200 when they see others pay that amount for the item and it becomes scarce?
What you've described is nothing like a real market. Where are the people in your model who are happy to pay $110? $120? If there are 10 who'd buy it at $200, and 100 who'd buy it at $100, surely there'd be 50 who'd buy it at $130 or so.
That ignores the social aspect entirely, too. How many who were originally willing to pay $100 will later pay $200 when they see others pay that amount for the item and it becomes scarce?