Taxing and Patrolling... is it worth it?

[TheDemon]

In slightly more intuitive terms:

Both the 100% and the 150% sides of the equation had their income grown by Growth. I am ignoring the 6% income bonus, I am talking about only population growth. BUT, despite Growth the 150% side of the equation is losing population overall. Growth is a percentage; since the 150% loses population every turn, the gains from Growth are less every turn in absolute terms. By contrast, the 100% side gains population every turn, so it grows faster every turn in absolute terms.

Growth causes both incomes to grow, but the 100% side grows faster than the 150% side. Every turn the 150% slows as it bleeds population and the 100% speeds up as it gains population. That gap means the 100% side catches up to the 150% side earlier.

Just to put forth an example, with no Growth, the 100% side and the 150% side both hit 300 gpt at turn 20. With Growth 3, the 100% side and the 150% side both hit 355 gpt at turn 19. It's earlier, but both sides of the equation are making more gold in absolute terms.