Administrative Efficiency curve

I didn't find the final AE formula, so can anyone tell me at which point an increase in population stops lowering your AE by a similar percentage?

OK, translating your question into mathematics, let me know if I understood correctly.

It is a logarithmic scale, to drop your AE by the same value, you have to increase your army size by progressively larger numbers. The limit of this curve is 20%

So lets say if you're right at 100%
You buy/grow by 10k units and your AE will drop to 98%
However you'd now need to get another 15k units now to drop to 96%
And another 25k units to drop to 94%

Note: This example is inadequate to explain how AE drops right down to 20% for certain mathematical reasons. Such as the fact that to reach 20% you would need an army size of infinity. However I hope the point got across about you needing ever larger increases in AS to drop by the same % each time

I meant that it seemed that increasing my AS by 2% made the AE decrease by ~2%. Leaving me with no increase in income. If this gets better the larger I get, than I've already had the unpleasant. bit. Thanks for the answer.

Jiro wrote:If this gets better the larger I get, than I've already had the unpleasant. bit. Thanks for the answer.

purely technically it wont get better
Imagine you have 100k farmers. you get 10k farmers (increase your income by 10%) but your AE drops by 7%
Later you have 1 mil farmers, you get another 10k farmers (increase your income by 1%), but your AE drops by 0.7%

However from a practical viewpoint.
Someone who has more farmers will ALWAYS have a larger income than someone with less farmers.

If you worry about if you should get bigger population or not, then let me tell you that you should.

The more you raise your population, the more income you will earn than if you had spent the kuwal elsewhere (assuming you reached certain unit production).

I changed my mind, This is the most informative post I've read all morning, hope to find more...