You presume that 7" iPad Mini sales would come at the expense of 10" iPad sales. It's doubtful that will be the case. Most people who have parted with $500+ for an iPad have already done so. The "New" iPad (i.e. iPad 3) wasn't a big enough shaker to everyone dump their iPad 2's, but even still, people that want a 10" iPad will continue to buy the latest 10" version as it gets even better.
Try this with your numbers: Apple makes $10M still selling 20M 10" iPad's AND it makes another $3M selling 60M 7" iPads, AND Apple now has 60M additional people (well, probably some already had a 10" iPad) in the Apple ecosystem that it didn't have before, spending cash like there's no tomorrow.
Can't race at Indy if you don't have an Indy race car; Can't compete for the 7" tablet market if you don't make a 7" tablet device...
Apple has to choose: either it wants to capture the 7" market, or it wants Google & Amazon to enjoy every dollar of 7" tablet profit to be made.
I'm betting that Apple wants to be in that race, because ultimately, it means more money in the coffers, and not less...And in this race, any money NOT going into your coffers is going to your business enemies, and funding their overall efforts against you. Fight or die.
Can't believe Apple wants to die....too many funerals coming up in the near future (Blackberry, M$ Surface, etc.)...
Apple wants to maximize profit. If selling both an iPad mini and full size iPad results in maximum profit then they'll do it. Competition will play no part in such a decision because it makes sense all by itself.
Currently there is no profit in making 7" tablets so that suggests Apple would be foolish to enter the ring.
But there's a different kind of elephant in the room now. Today selling mobile devices is all about getting customers into your ecosystem and keeping them there for as long as possible. Amazon and Google have both shown they're willing to lose money on hardware to tie customers to their gardens and keep them out of Apple's.
If Apple believes they may lose a significant number of potential customers for life, they may be willing to act in a way not typical for Apple. They might be willing to accept total profits for iPad + iPad mini that are no higher than just selling the iPad.
I think there is a good reason to believe that Apple will not do that: there's no upgrade pricing for apps. It's incredibly important.
On the desktop you buy applications and learn to use them and when it's time for the next generation you get a big discount to stay on the platform.
In mobile there's a minimal learning curve for most apps and there's no upgrade pricing. When the next generation of app comes out everyone pays full price so there's no incentive to stick with your current platform. Re-buy the apps you actually use, copy over your DRM-free music and move on.
The only thing tying customers to a platform is media that still has copy protection like movies and TV shows and I don't think that's enough to keep people from switching to what they perceive to be a superior mobile platform.
Apple believes they only get and retain customers by continuing to produce the best possible products in each market segment they choose to compete in. If there's an iPad mini coming out it's because the leadership at Apple thinks it's the right thing to do.