According to Wikipedia, http://en.wikipedia.org/wiki/Land_use_statistics_by_country As of 2005, the world is cultivating well over half the arable land total. and the previous poster was right, there is still almost 10 times as much arable land remaining in the world as what the US is currently cultivating. I think it is safe to say that much of that remaining 15.75 million square kilometers is not comparable to the cornbelt, and there is a reason why it is not cultivated, some political, some more fundamental, but with enough motivation it will be cultivated.  Imagine, someday you may be growing crops in a  national park(included in the arable statistics), imagine the the hue and cry from the greenies if it ever comes to that!

I'm still trying to figure out which peaks first, population, or food production. I suspect population, just based on the current trends, and rates of change in them.