This fact comes from history. There were mass famines at that population level around 1000 AD. The reason why vikings started to travel to other countries murdering and pillaging.
We do not know for the "mass famines", but this time was the Medieval Warm Period (800–1300). It is thought that between c. 950 and c. 1100 was the Northern Hemisphere's warmest period since the Roman Warm Period.
Of course, things will change once harvests will start failing, and if you guys had just a bad of a harvest as we had this year (Finland), then it doesn't matter if 50% or 10% of the food comes from local sources; you're going to be reliant on imports anyway.