The tax slider is with the domestic adviser. There are two of them: science and happiness. The science slider boosts you science output in cities, and the happiness one boosts happiness in the cities. Anything left over goes to treasury.
What I mean is the sliders simply divide up where the taxes from cities goes.
Depends. Usually I slide it to the point I'm researching techs the fastest while still making gold. If I really need the tech, I'll settle for losing gold per turn as long as it's not a lot.
Example, say I'm researching synthetic fibers; at 50% I'll research the tech in 10 turns and make +200 gold, at 40% 8 turns and +50 gold, and at 30% 7 turns and -6 gold. If I see I have 3000 gold in the bank. I'll choose 7 turns and lose 6 gold a turn.
In early game I usually rush towards new techs, having the lowest possible taxrate. When theres only 2 or 3 turns left before discovery, I'll start to rise the tax level. Usually you can get it higher without the research getting stalled. In the last turn, you can get even hundreds of gold "free" when doing this! You should also check your tax/science specialists within this fine tuning process...
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