The RPi Foundation has said they didn't do this initially because they don't need the money. I doubt they're in worse financial shape now, so it seems unlikely.
Yes. But instead of letting people buy them for the asking price, and pocketing the difference on ebay, RPi Foundation should pocket the difference themselves.
Of course, they don't do this because they want to keep everything simple, and might even get reputational damage out of an auction. Also last time I talked to the guys (HN London), they were constrained by the founders time more than anything else. So they wanted to keep running the foundation as simple as possible.
As for the money: They could always donate to Doctors Without Borders or something like that.
No. They don't do this because that would actually increase the price of the RPi to its (commercial) market value, which they do not want.
Think about it this way: If they auctioned, and people value the Pi to $45, it would be impossible to get it for $35 because the price would never go that low.
However, the way they did it, some people get a bargain (they were willing to pay $45 but only had to pay $35), but some people get it at the intended price (which is still a bargain).
And the probability of winning the lottery of who actually gets one, becomes one that depends on persistence and not on direct monetary expense.
Nice in theory, but doesn't really work on practice, as markets are too efficient for transferrable goods.
Also, it is poor theory for a good with unlimited eventual production capacity.
They could put a serial number / batch number on each one, and sell the first many at a huge premium, and then then pour all those profits into selling later units at a huge discount.
Apparently, it did work in practice for them, starting from the 3rd week or so - most people who wanted one, got it at the official price. The people who wanted one right now paid whatever the scalpers were asking for.
They are optimizing for price=const, which they believe they could support ad-infinitum. Doing what you suggested would cause price fluctuations, if the premium dries up and they can't offer the discount any more.
Sure, there was a short transient period where it didn't work perfectly. But it was short. And now everyone can get one at $35, and would be able to do so in the future as well.
