It would be nice to know the exact formula, but atm I am grabbing at any bit of info on the relation between colony cost->population->manufacturing->economy and everything in between.
I understand the basics, colony cost determine your max population, which determine your manufacturing capabilities and wealth production through trade. But all the intricacies allude me
Your workforce is divided into Agriculture/Environmental + Service Sector + Manufacturing = 100%. Manufacturing are the people you get to use for stuff like factories or research labs or mines.
As mentioned, Agriculture/Environmental scales with Colony Cost - it bottoms out at 5%, and goes up by 2.5% or something per 1 Colony Cost.
Service sector percentage scales with population. I think it's at about 400-500 million where it caps out at 75% of your population. I'm not sure the exact formula is known, since the last posts were a long time ago and it may have changed.
It's because of the way that service sector scaling works that moving people off of Earth is so useful - if you have 1 million spare workers on Earth, you can pick up 4 million people and drop them on colony and have 3 million available workers. It's worth it to move people off of Earth to a developing colony on an Ideal Habitable World until you hit 250M people or so. At that point you're not gaining much in terms of lower service sector needs.
EDIT: For Trade, supply and demand scale with population. Each world produces surpluses in different things. There are breakpoints at which colonies begin to demand specific goods, and I think it's 10M and 25M. A colony of size 1M only wants a fraction of the trade goods, a colony of size 11 million has demand for most of the trade goods, and a colony of size 26 million wants some of every type of trade good. So for ideal trade, you want multiple 25M+ worlds that specialize in different things so they can trade between them.