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keep that in mind if you want every rat even the unemployed one rich (become middle - high tier) you need to give them more gold when they're doing chore like mining and gathering. but anyway if you just want to torture your colony its up to your play style.
https://steamcommunity.com/id/doomZeion/screenshot/2219773166245355532/
this is my hard mode city with only middle-high tier in the town (just wanna try to make 100 rat go high tier) but it took sometime because you need at least 300k economy for circulate through them. and I love the bug that show you the lowest happiness is 0 because I didn't have any poor tier in my city lol
Unless you mean take 100% wealth and give back ~4000 coins (because there are not enough slots to allow ALL noble buildings and consumables be used by ALL classes).
But I think it would be easier to just tax a small amount from rich rats and float at about ~10k of reserve.
How this works:
At first you keep everyone poor but equal with 300 pia wealth. As your economy grows, once you reach about 10k savings despite population of 30, you can transfer everyone to middle class (total amount of money in circulation should be over 15 k for 30 rats to be middle class). You'll need around 450k pia in circulation to transfer 50 rats to nobles, but to keep with their demands you'll need to import a lot of luxury items and export a lot of things too. You can get the nobles but it is hard to keep the nobles, in my opinion. Middle class I was able to keep indefinitely. For a rat to be middle class, they need to have 500 wealth and have their middle class needs met. For them to be noble, they need 3000 pia wealth. So the calculation is easy. You need to have 500* number of rats + some buffer for trading and rebellion prevention for everyone to be middle class. Same thing only 3000* number of rats for golden leaves.
In real world, there is no way to determine someone's actual wealth, so governments implement progressive income taxes instead. You could accomplish the same thing with 50% income tax for income over 100, 75% for income over 150 and 90% income tax for income over 180 I guess, but that is making things needlessly difficult.
Just like real life.
and i still see some with as little as 15coins
so they spend multiple times a day when they have high desire
Taxing income is a waste of time, rats don't care about progressive marginal tax rates. All that matters is how much you need to keep government running and how much per rat in circulation. The actual price of an amenity doesn't matter as long as it can be purchased, theoretically, you could set them all to zero removing the user pays system, simplifying finances, so communism?!. If you are running low on money, just lower the wealth cap and mint/trade more money, you have too many rats in too small economy or maybe you have high wealth rats dying.
You don't need to directly subsidise toilets etc, just give them pia. However setting base amenities price to zero is a reversible quasi quantitative easing. So if you are running out of pia, make them free and lower the wealth cap.
I have no idea what "System" it is as they encompass not just economic, but social expectations. It's not socialist, communistic, capitalistic, the purge nor apocalypses bunker economics.
The rats have no ideology nor concept of "money", unless rioting, "suicide" or crying below certain happiness is "Ideology". Maybe the closest thing to what rats system would be the company town, but that doesn't work as you can trade outside with Pia, which can't be done with company script. Pia is ration card without actual rationing as a high income rat can still "buy more" that poor rats can't. High income is a spend it or lose it system, above the wealth cap given is it a "Closed" system with a single shop purchases is a not-tax.
Simply put, this economic system is impossible in the real world with current constraints. Once enough wealth is in the rats economic system, it is post scarcity, you work because you like it, but Rats work because that's their job you gave them.
Once you understand the rats system, Pia is a trivial consideration outside of trading, solved by building more (pia) pylons as you will as the code stone prevents you from making everything "free".
tl:dr The real currency is rat hours, not Pia.