You can get +2 experience levels for metsuke from philosophical tradition by building a law court, which itself increases your tax rate. It becomes a question of whether you want to sacrifice 23% bonus to research for increased income. Building top level market to a philosophical tradition province would therefore give at least +3 experience levels, which gives you total of +5 cunning when overseeing towns just from skill tree, add that to the stars you already have and that's an immense increase to your taxes.
Having metsuke in a town has no effect whatsoever to the town wealth growth. The negative effect of "tax level" depends on your global tax rate, but it gets higher as town wealth growth grows. For example 5 town wealth growth would cause -1 due to "tax level" while 10 would cause -2 (completely arbitrary numbers, actual amount seems to be higher and more complicated than that).
There is no negative effect whatsoever in hiring and having metsuke oversee your towns. This is only purpose I use them for as I too do my "apprehending" with ninjas :D
A metsuke can give you hundreds more tax income per turn even with few stars and mediocre town wealth.
Administrative cost works the same way it does in every total war, the more provinces, the higher your administrative cost.
I believe in economy panel it tells you your total administrative cost. It basically means that the shown percentage is taken from your total tax rate per province. 50% administrative cost would take 15% away from a province that has total 30% tax rate, but 25% away from a province with 50% tax rate.
So if you invest in chi research, it would definitely be worth it to build a top level market in a province with philosophical tradition.
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