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Generally speaking you won't be rich by supplying farmer needs, it's not their purpose. It does provide workforce, but then again you can just build more farmer houses and their basic needs are ultra easy, so yeah... I wouldn't bother
https://steamcommunity.com/app/916440/discussions/0/592887423803926952/#c592887534192754320
That video also ignores production and maintainance costs for ships, as well as all infrastructure such as piers and such that is needed to deliver the goods.
I want this compared to simply allowing farmers to use soap (no maintainance from ships and piers), including an analysis of the impact of providing additional lifestyle needs. Does it get more profitable to provide lifestyle needs the more different lifestyle needs you provide? Stuff like that.
Also, how is income calculated? That is also a question left unanswered.
The soap chain is 210 coins per minute and gives +1.875 coin per farmer residence per minute (on high income settings), so 210/1,875 = it takes 112 farmer residences to break even
According to https://anno1800.fandom.com/wiki/Needs, you would need 286 residences to consume 1 soap/minute, and the consumption will be the same regardless of how full those residences are. But if the residences are more full then they make more money from the need. So it shouldn't matter how many residences you have in terms of profitability, but instead, how full they are.
Multiply by 1.6875 for normal difficulty and that's 1.6875*286=482.625/minute in income if lifestyling 1 soap per minute, but that assumes your residences are full. If they're only 1/2 full then it's only 241/minute.
Buy price at the prison is 381 per 1 soap.
So the cutoff point for lifestyle soap making as much $ as prison soap is when the residences are about 381/482=79% full (in normal difficulty), or about 12.6 out of 16 farmers.
But it gets more complicated, because if you use lifestyle soap to raise the residence pop from 10 to 11 then you start making 10% more of other non-soap goods, and it doesn't increase your consumption of those goods. So in fact it should be cost effective to hand out lifestyle soap at a lower point than 12.6 per residence since you'll also be getting a 10% boost to schnapps/fish/clothes/pub/flour revenue.
If you assume all goods bring in the same revenue per residence per minute (and actually soap brings in less than average), then if you have 5 other needs fulfilled besides soap it'd bring in 50% more revenue and lifestyle soap would be worth it on normal difficulty for pop densities of ~8.4.
My analysis says that it's worth it in most cases, and it's more worth it the more other goods you can supply.