Income and population mechanics

[shatner]

Omikron Warrior breaks down the income gain from population growth here. Granted it's from back when Growth got you +.2% pop-growth/scale instead of the .3% you get now. But if you pretend he says Growth-2 whenever he says Growth-3 then the math works out the same.

The reason I bring that up is that it allows you to do cost-benefit comparisons on the actual income brought in by the various scales. For example:

Order-2 gives you +12% income on turn 1, 2, 3, and so on. You will be averaging +12% income over all those turns. Growth-2 gives +4% income from turn 1 and an average of +12% income by turn 6 (+4% from scale, +8% from pop-growth). By turn 12 you have averaged +14% income, thus earning more money from an 80-point investment in Growth-2 over an 80-point investment in Order-2.

Of course, this all assumes you are allowing your population to grow. With overtaxing and Growth-2 you're are getting +24% income on turns 1, 2, 3, etc, for an average of +24% income each turn. That's as much as you would have gotten from roughly 42 turns of Growth-2 without overtaxing... and double what you would have gotten from just Order-2.

Since having a bigger income on turns 1 through 41 is usually more important than having a bigger income on turns 42+, there is definite merit in long-term overtaxing.

All that said, I'm not actually sure how all the money bonuses combine when determining your income. If I had those numbers I could math-hammer this problem and figure out the sweet spots. Does anyone know how Order-3's +18% + Production-3's +12% + Growth-3's +6% + Castle Administration + Overtaxation actually combine?