Suppose somehow we got an amendment into the Constitution that replaced elections with the following system:

First, the U.S. government auctions off a seat, and the highest individual bidder gets it.

Next, a new seat is added, and a new auction is held. (The final price, presumably, will be lower this time.)

And then another... and another... until literally every single citizen of America who wants to be in a Senate can afford to pay what they think is a fair price for it.

Here's the question: given that everyone would know from the very beginning that later seats will be cheaper, and that everyone who wants one will be able to afford one, what would the price distribution look like in the end and how much revenue would be earned?

I don't really have any reason or point for asking this other than it quirks my interest. But if I must supply a purpose: could perhaps the answer give the true value of political representation in the Senate?