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What I I don't know about is if by trade tariffs it means profits from all goods, or just the tariffs section in the list of each export to your trade partners. If the latter, if it only affects that one item and not the 12+ trade goods, I don't think it beats out the flat 200 of the fairground, so hopefully that's not the case. (Edit: we confirmed it's the latter.)
See the below posts more research!
I recorded my trade account details and can confirm that it only affects the tariffs only. So i saw a reduction in tariffs from demolishing one embassy of about 60 gold, then when i destroyed a second embassy in that region i got a reduction of 45 but when i burnt down 17 (which i'll admit, i enjoyed) it was an average of about 80 so i don't know what's going on there, either the trade bonuses stacked or they didn't or the tariffs change a bit per turn. The value of goods produced (profit from all goods) and the long term partnerships remained relatively unchanged (apart from per-turn fluctuations).
I also checked out whether the effects stacked on ports and happy days, they do.
As far a figuring out which is better, if you're exporting 100% of your Elven Trinkets then i would probably build more Fairgrounds, 12 trinkets at about 20g each will fetch you about 240g on top of the 200g base income but you can only sell as many as your marketing team can peddle.
If you have an excess supply of trinkets then i would still consider the fairgrounds just for the 200g base income.
It is unlikely that the effect on trade tariffs will make up for the income even towards the end game (i am currently trading with Hexoatl, Dwarves, Border Kingdoms, Brettonia, Empire, Tlaxtlclanlll and i still only get about 80g at most from each embassy). And the effect from ports will only match the 200g if you have one big port and three little ones.
Of course embassies are worth considering if you have a healthy trade account, excessive trinket production, and a good couple of ports (i would say 3 little ones or 1 big one + one little one = 120g income from ports bonus), but even in this case you would be unlikely to even match the base 200g income from Fairgrounds.
Now i know if you're anything like me you'll also be thinking 'Ok this settlement has a fairground but whats better, embassy or promenade?' i would *consider* embassy if you have at least 2 little ports or one big port in the region (the 80g bonus plus the (40g to 80g endgame) tariff bonus will probably (just) outweigh the 120g income from the Promenade, but then there is the public order bonus to consider, probably really handy if you are colonising some unpleasant or inhospitable climates or have those pesky corruption and rebel uprising problems.
Personally, i am going to go and burn all of my embassies to the ground and build Fairgrounds on the rubble.
Hope this helped anyone pondering the same thing. If i am wrong in anything feel free to correct me, we're all only human. If i don't reply to anything that's because i don't forum much and i am pretty useless at it.
Cheers.
Case-in-point -- there's a High Elf event that lets you chose something like -50% tariffs. If you choose that, you won't lose that much per turn (certainly not thousands like you'd expect).
Embassy: 5% of tariffs (not total trade, just tariffs). You can check the tariff numbers for your own empire, but for a large trade empire of 10,000 per turn trade you will usually make about 1,000 tariffs, 5% of which is 50 per turn. In addition you make 10% from local ports. So for a zero port province it's 50 per turn total, for a province with one minor settlement port it's 90 per turn, for a province with two minor settlement ports or one capital port it's 130 per turn, and so on.
Entertainment: 60 at level 1, and much cheaper than an embassy.
As you can see, in economic terms (so forgetting about agent effects, public order, etc), there is a clear hierarchy:
Fairground>embassy in province with port(s)>entertainment building>embassy in province without port
nice summary :D thanks!