Here I go, up to my usual pedantry.

Quote Originally Posted by Batcathat View Post
The tech level is approximately early medieval, with some magic (but mainly for the upper class so it probably won't affect the population numbers very much)
Your first problem. It's not that cities didn't exist in early medieval period, it's that they were extremely rare, with very few exceptions that were mostly in Romen empire remnants of some sort (parts of Outremer, Byzantium, Greek cities, Rome itself). Early medieval Florence has 1 000 people in it, while Constantinople has 150 000, Rome 80 000, Thessaloniki 40 000, Poitiers has 8 000 (this being one of the largest cities in one of the most arable areas of Europe). Sure, Luozang has half a million at this time, but that isn't early medieval, the term applies to Europe and Europe only.

Also note that Poitiers and Florence are busy trade hubs as well, and Constantinople, Rome and Thessaloniki will decline to as little as 30 000-50 000 so...

Another issue, very much related to this, is how densely populated the countryside is. A town needs to import almost all of its food, and pre-modern, that means you have less that 5% of population living in the city. Or rather, 5% is the high medieval estimate, eraly medieval is likely much lower. Which means that our busy trade hub of Florence has 1 000 people in the town and another 19 000 people in the villages around it - assuming a reasonable 500-1000 people per village, you get a total of 19-38 villages necessary for this city.

Poitiers with 9 000 people has rural population of 180 000, with 180-360 villages. Constantinople with 150 000 pop has a monstrous rural population of 3 million, needing 300 000 - 600 000 villages, or to put it in different terms, damn near entire Greece, to sustain it.

Also note that the absolute highest number of people that can farm land from a single town/village/point of origin is about 5000, provided they are surrounded by arable land. More people than that and you need to farm lands that is so far away from town you are better off founding a village there by virtue of travel time alone. That means that a city that has its farmers within its walls can have, at the absolute best, 250 city-dwellers and 5 000 farmers. That's... not really a city, maybe a market town? Or just a really big village.

The only way to fix these bottlenecks is to magic your agriculture into being way, way more productive - maybe that's what the sacrifices are for?

Provided you go that route, 1 farmer produces enough for 1+1/20 of a person. To figure out how many times you need to boost the yield to get to your city pop, take 5 000 as max farmers, 5 250 as max supported pop and multiply that 5 250. That means that should your magic just double the yields, your city can suddenly support 10 500 people on 5 000 farmers. Which is pretty neat, because you don't need crazy agrimagic, just making that corn twice the size will do.

Quote Originally Posted by Batcathat View Post
and the city is very isolated so the effect of immigration/migration on the population numbers should be pretty negligible.
Your immediate problem is, why is it a city then? The most plausible reason is probably a ramnent of a bygone empire, but it could be the one and only city-state left from the late stone age that actually figured out how to run a city state - that is no small task, a few would-be city-states probably floundered there.

Quote Originally Posted by Batcathat View Post
Anyway, I have an idea involving a city that regularly executes/sacrifices people for important and magical reasons. What I'm wondering is how big of a city it has to be for the sacrifices (I'm thinking maybe a few every month or so) not to have too much of an impact on the population. Basically I'm wondering what the smallest sustainable population would be for this to work long term.
It really depends, but here's the thing: even historical Florence has a total population of 20 000 people in total. With the mortality rate of this period being at 10% or worse, we have 2 000 natural deaths per year. Even our "5 000 farmers with magical double yield"-topia has a total population of 10 500, meaning 1 050 deaths per year. Even that borderline market town village of 5 000 will see 500 dead a year.

Granted, most of those deaths are infants - compare average life expectancy at birth versus at 20, being 25 and 40 respectively - but still.

tl;dr If it is large enough to qualify as a city and has the corrseponding historical population, the 12 sacrifices per year are a drop in the bucket.