Income and population mechanics

[shatner]

From the wiki we know

Every 3% tax above 100% kills 0.1% of the population.

In CBM 1.92, each level of growth increases population by .3%. So growth-3 gives +.9% growth which is enough to negate 27% taxation. Since we can only tax in increments of 10%, if you run tax at 130% you'll lose .1% of your pop each turn.


However, this does nothing to mitigate the unrest which will build up over time. Specifically the 6 unrest/turn from 130% taxation:

Every 5% tax above 100% increases unrest by 1.

I can't find the source but I seem to recall you lose 10 population for every point of unrest you reduce via patrol. That means that every 10% taxation above 100 is going to generate 20 deaths/turn from patrolling, in addition to the roughly .3% pop-death from over-taxation. Since we're now dealing in absolute numbers and not percentages, the larger the province's population, the less the unrest/patrolling deaths are going to matter. In a capital with a population of 30,000, with a tax rate of 130%, you are killing 1% of the population from over-taxation plus .2% of the population (60 people) from patrolling to reduce the unrest. That's 1.2% lost and .9% gained at growth-3 in your capital, resulting in a net loss of .3% each turn. For every province smaller than that (i.e. all of them), the patrolling deaths will count for a larger percentage of the population killed, further reducing the efficacy of using growth+overtaxing for profit.

As such, you have two options:
1) Take Growth-3 and overtax at 120% each turn (for -.8333% death rate mitigated by your .9% growth rate for .07% overall growth... assuming capital-size populations)

or

2) Take Growth-3 and repeat the following pattern: run 130% tax for 3 turns (while patrolling) and then set the tax to 100% for one turn. That will keep your population roughly stable and give you an average tax rate of 122.5% which is > option-1's 120% tax rate. Of course, this will be a micro-management nightmare so I'd recommend against this option.


TLDR: with full patrolling, you can overtax at 120% with growth-3 and have a stable population. Anything more and you're population will be in decline. If this is ever "worth it" it would only work in provinces with lots of money multipliers (high-admin castle, high order scales, no money loss from temperature).