...So I am trying to determine the profitability of a corporation that produces Ag rations. Using the numbers and charts in the World Tamer's Handbook as a basis I was attempting to determine how much an Ag world could produce for exportation.
I seem to be running into a road block. The basis for an Ag trade classification is that it has a population of 5-7. This seems fine until you bring the "labor" value into question which is always a tenth of the population. Which reduces the effective labor force that can be put into use to harvest and maintain an Ag world.
For instance - a world of size 8 has a planetary hex area of roughly 1,165,324 sq km. Say the planet has 70% water and only can use 65% of the available area (these are nice numbers for an Ag world)...
That is - ambitious. There's a whole heap of unknown variables that are going to affect your corporation's profitability. In your case, your company is a prime source of "rations", which presumably means the world is a good source of dense-calorie nutrition-rich foodstuffs - but that could be anything from mangoes to a genegineered variety of soybeans. It's likely to be many different things given the different climates available on an earthlike world.
You know the surface area, but that's only going to give you a vague idea of the agricultural output since that output will depend on the specific plants and climates. A tropical climate will tend to grow more than a temperate climate, but how much depends on what specific foods you grow, how quickly they achieve maturity, and this, and that, and the other. A world with significant axial tilt will have pronounced growing seasons, while a world with little tilt will have fairly uniform year-round temperatures but may have a much larger percentage of regions where agriculture is restricted by cold weather and poor conditions. And, you don't have any information about the climates and growing seasons of your world.
Similarly, you know the population, but you don't know what fraction of the population is engaged in agriculture, only that agriculture is the world's dominant sector. As others have pointed out, it might be a world of farmers - or it might be a world where a few very industrialized farmers use technology to produce a large quantity of foods while the rest of the population pursues other careers. If agriculture is a profitable enterprise then there are likely to be a lot of people in it, but there still need to be people building the machines the farmers use, and people building the homes those people live in, and doctors, and lawyers, and - you get the point. If agriculture is a more marginal enterprise, requiring a big investment and a lot of land to make the kind of farm that can support its owners, there may be proportionally few farmers, but their total output may still be high enough that agriculture is the world's dominant export.
"Agricultural" means an earthlike world with a good balance of oceans and land, a good atmosphere to support an agriculture-friendly ecology and a population small enough that the agricultural sector outproduces the industrial sector. Doesn't mean they don't have industry - though the ones with pop codes of 5 or 6 will on balance be importing to meet their industrial needs. Pop 8, 9 and A worlds with appropriate ecologies will also have agricultural sectors and may in fact produce more total tonnage than an agricultural world just by virtue of having more people doing it, even with their own people eating a larger percentage of their own production - but their ag output will be dwarfed by their industrial output.
My suggestion would be do not try to calculate whether your corporation is profitable. Run the numbers for the world, figure in a variation of about an order of magnitude with your numbers at the middle, then decide how profitable you want the corporation to be and choose the numbers that make it so. Then the invisible variables in your world can flow toward making whatever number you choose a reality.
...Don't fall into the It was raining on Mongo fallacy. ...
That's not one I've heard before. Ming the Merciless thing, or is it about a Trav world? What does it mean?
Those trade classifications do mean something, they just don't mean as much as you'd like them do to. Remember, trade designations are used to strictly control which trade goods player characters may find available and not to strictly control what trade goods major corporations may be producing/purchasing on the same world. ...
They tend to mean a good deal more than that.
Striker uses them to modify the GNP of a world, implying that how rich or poor the locals are, on average, depends a lot on the trade classification. GURPS
Far Trader does the same - the modifiers are a direct lift from
Striker. They tend to paint a broad picture of the planetary economy.
Of course, planets are very big, complex things, as are economies generally, and a "broad picture" is by nature fuzzy and lacking in detail. Megacorps are famous for their resources and ingenuity. If one wants to have a megacorp getting rich growing tailored edible mushrooms in a specially constructed cavern biofacility on an otherwise nonagricultural world, then by jove there's a megacorp getting rich growing tailored mushrooms in a specially constructed cavern biofacility on an otherwise nonagricultural world. As you say, trade designations are a good general guide but should not handcuff your imagination.