It increases
food production, which is different from the population cap. The cap is determined by the size of the planet. The amount of food produced depends on the planet's colony type, farm level, and food distribution centers. A guide to the planetary cap can be found
here in the GalCiv2 wiki. Be careful with the wiki information, though, it hasn't been updated since the game came out.
I have no problems with building up to advanced farms. A planet with one advanced farm (13 bil. population max) and one virtual reality center should have no problems even with high taxes. Just remember to build only
one farm,
don't use the farm tiles, and
don't build farms on home planets that already have a 12 bil. limit and you'll do just fine.

Spore. When you absolutely, positively got to kill every motherfrakker in the galaxy. Accept no substitutes.