However, the real question is how the conversion rate for the same ad would change if it were displayed in a different position.

Varian has an answer for that question too. Another difficulty is that the average position number reported by Google is that it is an average over all auctions in which you participate, he adds. If you increase your bid, it is quite possible to see your average position move lower on the page! The reason is that when you increase your bid, your ad will appear in new auctions, and it will tend to come in at the bottom of those new auctions.