Eduardo:
Tho my memory is a bit rusty and I haven't my book here, I am pretty sure that the book was clear-enough that
1 Laborer = 1 Person
and that the extraneous explanation that it takes 4 Laborers (capital L) to make 1 laborer (small L). That's 1 actual person doing work, with the other 3 being his/her family.
I took it to mean:
1 worker
His wife who takes care of the kids
Their two kids
A stable population is made this way; a couple has to have 2 kids, so that they have been replaced when they die. (This is not from the book, this is from real life.)
So your fudge-factor of 4 shouldn't be used, and indeed, you seem aware of this by calling it a cheat in an earlier post.
Now it is certainly possible that I managed to get my hexes mixed up. As I recall, tho, the book was quite clear that they were talking about 20-km hexes, and I'm pretty sure that's what I assumed. Fertility rates for crops were calculated on planetary hexes, of which there were 490 (iirc), but they certainly allowed you to apply them differently at the 20-km scale if you wanted to burden yourself that much.
Nonetheless, the largest fertility mod was 6x, and I can't see an entire world being so high above the "average" of 1x, and even if it was, we still need another 5 planets.
The sign in Kansas that was mentioned: I've seen it a few months back, and it did get me thinking about this thread again (but I've been busy lately). Assuming it is true, it doesn't tell us how much land is being used, or how many people are working a particular acre. Sure, we could stop by at a farm and ask the guy how much land he's got and how many people he has working it and get numbers that way, but I think that will get complicated with seasonal hiring variances and such.
It seems as if a couple of guys could use modern equipment to plant, maintain, and harvest several thousand acres of corn with little difficulty, however, I recall when I was younger getting a job as a detassler for a week. Me and about 20 other kids were sent out to pull tassles off cornstalks, and we did this by hand, and it took a few minutes to do an acre (maybe 20-30). (Don't ask why, I have no idea; I've been given conflicting explanations.)
The point of that little diversion was to illustrate that it might not be a simple matter to get a hard number of "how many people are needed to work an acre for a month to raise a month's food, and how many people will that feed?"
But if you know any farmers, and you've got some idle time on your hands, then by all means, go ahead and figure this out, and everyone here will thank you for all eternity! (Hush, Loren, don't tell them what'll really happen!)