After a bit of tinkering a few weeks back, I finally worked out that tax income is given by

sqrt(pop)*(sum of buildings on planet)*(racial ability bonus)*(government form bonus)*(tax rate)

Here, population is measured in millions, so 5 billion means sqrt(5000)

Sum of buildings on the planet can be seen in the colony details screen. 4 stock exchanges (120%) gives a multiplier of 2.2.

Racial ability bonus is visible in the civilization stats screen. eg Racial ability bonus of 65% gives a multiplier of 1.65.

Government form bonus goes 10%/20%/30% (multiplier 1.1/1.2/1.3), not the values reported.

Now this formula works perfectly quite a way into the game, but it seems that eventually it starts to dramatically overestimate. That is, in the late game, you'll get substantially less income from 5B people on a planet (all other things being equal) than you did at the start. This seems very odd. Is it intentional or a bug?

If it's intentional, has anybody been able to work out the triggers? Unlike the economy penalty you get for passing 20000BC in the treasury, you won't see a sharp drop in income, just a reduced rate of increase over what you should expect. This suggests there's no *hard* boundaries involved. The most likely candidate is that it's based on total tax income. Anybody been able to figure it out?