There's a report that compares current iPad 2 vs 3 build prices. For the lowest end WiFi model:
iPad 2 $245 to build, and iPad 3 $316 to build.
With Apple selling them at $399 and $499. So roughly 38% and 36% profit.
I've not found updated numbers, since it has to cost far less to make them as they go along. But the estimated costs to manufacture iPhones when they first went on sale.
iPhone 3GS, $178 (here, from 2009)
iPhone 4, $188 (here)
iPhone 4S, $188 (here) to $203 (here)
And those prices have to be higher than they are now, as they're years old in some cases. To make a 3GS it seems it would be down to well under $100 by now (by Moore's Law, given the time it could be close to $50 for the 3GS). That's presumably the screen parts they would be using in the first generation iPad mini.
If a 7.85" iPad with a 1024x768 screen cost between the price of an iPad 2 and iPhone 4S to build: I'll use the high iPhone price estimate and average to call it $220 to build. A bit lower 26% profit on that would make it sell for $299.
And the build cost could be far less without a retina screen, it could be between the 3GS price and iPad 2, which could get under $150 to manufacture, and could retail for $199 or $249. If that one had just 8GB, and the upgraded one for $249/$299 had 16GB (and higher margins) they would do 25% or more profit on them too.
And it could also be between the iPhone 4S and the iPad 3 and cost around $250 to manufacture--WITH a retina display (using the same screen panels as the iPhone 4/4S.)
It could even be a combination of them, $199 for one with 8GB and a non-retina screen (perfect for schools to get for students, books take less space than apps, movies, etc.) $299 for 16GB plus a retina screen. There would be less profit margin on some, but then they'd cover all price ranges, and not leave any openings for competing tablets at all.